CARNEGIE MELLON UNIVERSITY
INDENTATION METHODS
FOR ADHESION MEASUREMENT IN THERMAL
BARRIER COATING SYSTEMS
A DISSERTATION
SUBMITTED TO THE CARNEGIE INSTITUTE OF TECHNOLOGY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
for the degree of
DOCTOR OF PHILOSOPHY
in
MECHANICAL ENGINEERING
by
QIN MA
Pittsburgh, Pennsylvania
M ay 24, 2004
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UMI Number: 3126927
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Carnegie Mellon University
C a r n e g i e In s t i t u t e
of
T echnology
THESIS
Submitted in Partial Fulfillment o f the Requirements
For the Degree o f Doctor o f Philosophy
TITLE
INDENTATION METHODS
FOR ADHESION MEASUREMENT IN
THERMAL BARRIER COATING SYSTEMS
P r esen ted B y
QIN MA
VA c c e p t e d
b y the
D epartm ent
of
M e c h a n ic a l E n g in e e r in g
^/■2.C / z o o ^
'
M a
A jTo
Or
R 1P r o f e s s o r
M
D ate
D epartm ent H ea d
D ate
A ppro ved
D ean
b y the
C o l l e g e C o u n c il
D ate
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ABSTRACT
This thesis investigates the fundamentals of indentation-induced delamination of
electron beam physical vapor deposition thermal barrier coatings (EB-PVD TBCs).
Thermal barrier coatings are thin ceramic coatings used to insulate gas turbine
components. In the as-proeessed state, TBCs are well-bonded to the metallic substrate
they are deposited upon. However, as these coatings are exposed to high temperatures
during turbine operation, they lose their adhesion. The goal of this thesis is to determine
how to use indentation testing techniques, coupled with fracture mechanics principles, to
track this loss of adhesion and to identify mechanisms causing it.
This thesis addresses four primary topics. First, a detailed fracture mechanics
analysis of indentation-induced delamination is made, including the quantification of
energy release rates, interfacial toughnesses and mode mix. The second topic addressed
is application of the indentation test to track toughness losses in TBC systems subjected
to a variety of thermal exposures. Three subtopics are included: 1) mechanism-based tests
for the isothermal dry air exposures; 2) mechanism-based tests for exposures with water
vapor and 3) meehanism-based tests for cyclic thermal exposures. In the first subtopic,
TGO thickening and TBC sintering are modeled. Various mechanisms that lead to
toughness degradation are discussed and analyzed quantitatively. An Arrhenius analysis
has been performed to understand accelerated testing methods. The second subtopic
presents the results of toughness degradation and the evolution of microstructures due to
isothermal exposure with water vapor. The third subtopic investigates the toughness
degradation for cyclic thermal exposures in dry air. Piezospectroscopy method has been
applied to track the evolution of residual stresses in the TGO layer with thermal cycles.
Quantitative analysis has been provided to give insights into the effects of oxide damage
during thermal cycling. The final two topics of this thesis relate to extensions of the
indentation test to make it applicable to a wider variety of TBC systems. These include
the use of different indenter shapes and the indentation of TBCs deposited onto curved
substrates.
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ACKNOWLEDGMENTS
This thesis could not have been completed without a great deal of assistance from
others. First and foremost, I would like to take this opportunity to thank my advisor, Prof.
Jack L. Beuth, for his invaluable input, guidance and support during my graduate study at
CMU and in the course of the eompletion of this thesis. I have benefited from many
discussions with him, from his strict academic attitude and his attempts to approach a
problem in more than one way, from his encouragement and academic direction, from his
expertise and mentoring, which have allowed me to reach this point in my academic
career.
I would also like to take this opportunity to thank the members of my thesis
committee. Prof. Paul S Steif, Prof. Philip R. LeDuc, Prof. Frederick S. Pettit, and Prof.
Gerald H. Meier for their invaluable input and mentoring, and for their comments and
criticism of this thesis.
I would also like to give my special appreciation to Matt Stiger (University of
Pittsburgh) for his help on starting the experimental work (including the SEM work), and
for his valuable suggestions during this research program.
My appreciation goes out to many of the staff in the Mechanical Engineering
Department for their assistance beyond the scope of their respective job duties. I would
like to give my thanks especially to Jim Dillinger and John Fulmer for their help in the
Mechanical Engineering Machine Shop, and for their consistently excellent and
expeditious work in machining my test samples; I thank Gary Novay and Rich Tourville
for their help on computing setups and networking problems. Michael Scampone, I thank
you for your help on purchasing and other matters relating to this research. Kate
McClintock, I thank you for proof reading a part of this thesis. I wish to thank Chris Zeise
for her advice and help with all the paper work.
I have also benefited from the friendship and resources of my colleagues. I would
like to thank Aditad (Tom) Vasinonta, Roy Flandoko and Raymond Ong for their warm
welcome to join their research group when I first arrived here, and for their help early on
in this research topic. I would like to thank Huang Tang, Pruk Aggarangsi, Andrew
Bimbaum, Steve Bianculli, and Nandhini Dhanaraj for their friendly support and for
111
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making my graduate experience more enjoyable. Thanks also go to N. Meltem Yanar,
Monica Maris-Sida and Kivilcim Onal (University of Pittsburgh) for their kind
collaboration during this research project, and their help on the oxidation and material
processing matters in the Department of Materials Science, University of Pittsburgh.
My appreciation also goes to Albert Stewart (Materials Science Department,
University of Pittsburgh) for his expert advice and assistance related to my work in the
SEM laboratory. And I would like to thank Tom Nuhfer for his training course and help
in the SEM laboratory, in the Material Science Department of Carnegie Mellon
University.
I would like also to take this opportunity to express my deep appreciation for all
the collaborators from the industrial institutes, national laboratories and universities
during this research project. I am grateful to GE Aircraft Engines and the Howmet
Corporation for providing the TBC specimens. I would like to thank Dr. Ken Wright and
Dr. Ram Darolia of the GE Aircraft Engines for their interactions in this research. Thank
you. Dr. Michael Lance of ORNL for performing the piezospectroscopic stress
measurements. My thanks to you Dr. William Ellingson of ANL for performing optical
backscatter experiments on the destructive vs. non-destructive TBC testing specimens.
My appreciation goes to Dr. Marion Bartsch and her co-workers, in the Institut fiir
Werkstoffforschung (Institute for Materials Research) of Deutsches Zentrum fiir Luftund Raumfahrt (German Aerospace Center), Linder Hohe, for their helpful information
regarding the thermal gradient mechanical fatigue (TGMF) tests and the indentation
images on their cylindrical EB-PVD TBC specimen. I wish to thank Dr. Christopher
Mercer, University of California at Santa Barbara, for providing the NiCoCrAlY burner
rig specimen to realize our delamination analysis on a curved substrate from the
experimental point of view.
I could have not reached this point in my academic career without the assistance
and support from my dear friends. Especially, I would like to express my deep
appreciation to Mrs. Eileen Lapree for providing us a home when we first arrived here,
for all her hospitality and family-like love, and for her unwavering support during all
these years of my studies in the United States of America. I would like to express my
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deep appreciation to Dr. Chengxian Lin and Jing Wu for their steadfast friendship, for
their recommendation and for supporting me in my plans to come to the US. I would like
to express my many thanks to Leora DeWitt, Pastor Wayne and Jean Johnson, Jean and
Albert Durica, Dr. Dominic Alfonso, Sinai Jun and Eric Flottman, Harold Pangbum,
Lauren and Robert Painter, Margaret and Max Davidson, and Ruby and Henry Davidson.
I wish to express all my heart felt appreciation and gratitude for their friendship and
support.
Last but not least I want to thank my family. I thank my parents, Zhengyang Ma
and Xiuhua Liu, and my parents-in-law, Yongqin Wu and Xuefen Yang, for their untiring
support in all o f my professional aspirations. I would like to thank my wife, Zheng Wu,
and my son, Matthew JunXiang M a for their loving support and sacrifice.
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CONTENTS
ABSTRACT.................................................................................................................................. ii
ACKNOW LEDGEM ENTS.....................................................................................................iii
C O N T EN T S................................................................................................................................ vi
NOM ENC LA TUR E................................................................................................................... x
LIST OF FIG U R ES..................................................................................................................xii
LIST OF TA BLES................................................................................................................... xxi
1. INTRODUCTION
1
1.1 Background........................................................................................................................ 1
1.2 Existing W ork................................................................................................................... 4
1.3 Motivation ........................................................................................................................9
1.4 Organization ..................................................................................................................10
2. FRACTURE ANALYSIS OF INDENTATION TESTS IN EB-PVD TBC
SYSTEMS
14
2.1 Chapter Overview ..........................................................................................................14
2.2 Energy Release Rate for Delamination o f an Annular Plate Subject to Equi-biaxial
Residual Stresses............................................................................................................. 16
2.3 Energy Release Rate for Delamination due to Indentation.......................................21
2.3.1 Delamination o f a Single L ayer..........................................................................22
2.3.2 Delamination o f a Composite P la te ................................................................... 23
2.4 Mechanics o f Interfacial Cracks....................................................................................32
2.5 Finite Element Modeling ............................................................................................. 35
2.5.1 Model Description and V alidation.................................................................... 35
2.5.2 Stress Intensity Factor K vs. R/a .......................................................................41
2.5.3 Mode Mixity v|/ vs. R/a .......................................................................................43
2.6 Chapter Summary ......................................................................................................... 46
3. APPLICATIONS OF CONICAL INDENTATION TESTS
47
3.1 Chapter Overview ........................................................................................................ 47
3.2 Effects o f Unloading on Indentation-Induced Stress Intensity F a c to rs.................. 49
vi
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3.2.1
Unloading on a Homogeneous S u b strate...................................................... 50
3.2.2
Unloading Effects for a PtAl/N5 TBC Specim en......................................... 53
3.3 Mechanism-Based Tests for Isothermal Dry Air E xposures....................................55
3.3.1 Introduction...........................................................................................................55
3.3.2 Toughness Loss vs. Isothermal Exposure Timein Dry A ir............................. 56
3.3.3 Measurements and Model o f Oxide Thickening..............................................58
3.3.4 Measurements and Model o f TBC Stiffness Modulus Due to Sintering .....64
3.3.5 Toughness Measurements from Indentation Including Changes in Oxide
Thickness and TBC Sintering ........................................................................... 69
3.3.6 Model o f TBC Duration and Arrhenius Plotfor Accelerated Tests................ 80
3.3.7 Concluding Remarks............................................................................................ 83
3.4 Mechanism-Based Tests for Exposures with Water Vapor .....................................84
3.4.1 Introduction...........................................................................................................84
3.4.2 Experimental Procedure...................................................................................... 85
3.4.3 Results and Discussion ....................................................................................... 89
3.4.3.1 Initial Tests on Steam-Exposed Specim ens......................................... 89
3.4.3.2 An In-Depth Study o f Toughness Degradation Including AsProcessed Toughness Values ................................................................ 92
3.4.3.3 Fracture Surfaces and Structure o f the Alumina S cale.....................102
3.4.4 Concluding R em ark s..........................................................................................106
3.5 Mechanism-Based Tests for Cyclic Thermal Exposures ....................................... 107
3.5.1 Introduction.........................................................................................................107
3.5.2 A Preliminary Investigation............................................................................... 108
3.5.2.1 Indentation Tests and Toughness M easurements.............................. 108
3.5.2.2 Toughness Degradation Compared to the Isothermal Dry Air
112
3.5.2.3 Fracture Surfaces and Structure o f the Alumina S cale.....................114
3.5.3 An In-depth Study by Integrating Improved Non-destructive M ethods...... 119
3.5.3.1 Toughness Measurements from Indentation Assuming No Changes
in the TBC S y ste m ................................................................................119
3.5.3.2 Optical Backscattering R esults............................................................ 123
Vll
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3.5.3.3 Toughness Measurements from Indentation Including Changes in
Oxide Thickness and Stress................................................................ 127
3.5.4 Concluding Remarks........................................................................................ 132
3.6 Chapter Sum m ary...................................................................................................... 133
4. INDENTER SHAPE EFFECTS ON THE DELAMINATION MECHANICS OF
INTERFACIAL FRACTURE
135
4.1 Chapter Overview ........................................................................................................135
4.2 Limitations o f the Existing Conical Indentation T est..............................................136
4.3 Constitutive Behavior and Finite Element M o d el................................................... 139
4.3.1 Constitutive B ehav io r........................................................................................ 139
4.3.2 Finite Element M o d e l........................................................................................ 146
4.4 Mechanics o f Conical Indentation............................................................................. 151
4.4.1 Loading Curves vs. Contact S iz e s ................................................................... 151
4.4.2 Surface Displacement P ro file s......................................................................... 161
4.4.3 Surface Strain Profiles ...................................................................................... 163
4.5 Mechanics o f Spherical Indentation.......................................................................... 168
4.5.1 Loading Curves vs. Contact Sizes.....................................................................168
4.5.2 Surface Displacement P ro file s......................................................................... 175
4.6 Interfacial Stress Intensity Factor Distribution due to Various Shapes o f Indenters
........................................................................................................................................ 179
4.6.1 K vs. R/a due to Conical Indentation............................................................... 179
4.6.2 K vs. R/a due to Spherical Im pression............................................................ 183
4.7 Effects o f Unloading for Various Indenter Shapes ................................................. 187
4.7.1 Effects o f Unloading for Various Conical Indentations.................................187
4.7.2 Effects o f Unloading for Spherical Indentations.............................................189
4.8 Quantification o f Interfacial T oughness....................................................................191
4.8.1 Results due to the Conical Indentation T e s ts ................................................. 191
4.8.2 Results due to the Spherical Indentation T e sts...............................................195
4.9 Chapter Summary ........................................................................................................197
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5. CONTACT AND FRACTURE ANALYSIS OF DELAMINATION ON
CURVED SUBSTRATES
198
5.1 Chapter O v erv iew ........................................................................................................198
5.2 Indentation Mechanics on a Curved Substrate......................................................... 201
5.2.1 Geometrical Consideration............................................................................... 201
5.2.2 Dimensional Analysis for Surface Strains ..................................................... 207
5.2.3 Energy Release Rate ......................................................................................... 208
5.3 Finite Element Modeling .......................................................................................... 209
5.3.1 Model Description for Contact on 3-D Curved S u b strates..........................209
5.3.2 Model Verification for Contact on a 3-D Flat Substrate .............................214
5.3.3 Model Verification for Contact on 3-D Hollow Cylinders...........................217
5.4 Numerical Results and Discussion ........................................................................... 221
5.4.1 Indentation Results on Hollow Cylinders without Roller Constraints
221
5.4.2 Indentation Results on Hollow Cylinders with Roller Constraints............. 230
5.4.3 Indentation Results on a Solid C ylinder......................................................... 243
5.5 Guidelines for Indentation Tests on Curved Substrates ........................................ 249
5.5.1 Onset Buckling and Valid Indentation Load Range.......................................249
5.5.2 Effects o f Unloading on the Toughness M easurem ent................................. 256
5.6 Toughness o f a Typical EB-PVD TBC Fabricated on a Curved Substrate ........ 258
5.6.1 Specimen A n aly sis............................................................................................ 258
5.6.2 Indentation Tests ...............................................................................................262
5.6.3 Critical Energy Release Rate and Interfacial Fracture T o u g h n ess............. 266
5.7 Chapter Summery ....................................................................................................... 268
6. CONCLUSIONS
270
6.1 Contributions o f This T h e sis......................................................................................270
6.2 Recommendations for Future W o rk ..........................................................................273
REFERENCES
275
APPENDIX
285
IX
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NOMENCLATURE
a, ac
Ideal and actual contact radius in the 2-D analysis
az, ae
Ideal contact radius in the axial and circumferential directions
A
Area
b, bo
Half width, critical half width
E
Young’s modulus
Ea, Q
Activation Energy
Eeff
Effective Young’s modulus
H, H bc, H s
Hardness
K, K u/l
Stress intensity factor
Kc, Gc
Interfacial fracture toughness; critical energy release rate
kp , Ks
Parabolic rate constant
G
Energy release rate
Ic
Transformed moment of inertia per unit width
r
Conical indenter tip round radius
R, Reff
Debond radius, effective debond radius
Re, Rz
Debond radius in the circumferential and axial directions
Rb
Ball radius
M
Net moment per unit width
N
Hardening exponent
Pm
Mean pressure
P
Load
t
Thickness
T , Tq
Temperature
Ur, ue.
Displacement
U
Elastic strain energy; radial surface displacement
U’^
Elastic unloading displacement
Vf
Columnar volume density
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a
Hardening parameter; Dundurs’ parameter
P
Inclination of the cone surface; Dundurs’ parameter
5
Penetration depth; relative crack face displacements
8
Strain; bi-material mismatch parameter
£' 8*
Indentation induced strain
Effective residual strain
£rr, £ee
Strain
V
Poisson Ratio
p
Shear modulus; friction coefficient
Gyy, Qxy
Stress components
( 7 o , <7 t b c , ( 7 t g o
Residual stress
o
Effective residual stress
Oy, CTys, CTybc
Yield stress
P i, p o
Inner radius and outer radius of the cylindrical specimen
T
Time
\(/
Phase angle
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LIST OF FIGURES
Figure 1.1: A Standard TBC Button Specimen and Cross Section Schematic
of the
Individual L ayers................................................................................................... 2
Figure 1.2: Schematic Diagram of the Indentation Test for TBC S y stem s..........................5
Figure 2.1: Delamination of an Annular Plate Driven by Equi-biaxial Residual Stresses
................................................................................................................................... 17
Figure 2.2: Energy Release Rate Formulation due to the Combination of Residual Stress
and Indentation Induced S tress.............................................................................26
Figure 2.3: U/a vs. R/a due to a Standard Conical Indentation with Major Load Levels
................................................................................................................................ 30
Figure 2.4: Energy Release Rate vs. TGO Thickness for Bending Contribution due to
Different Form ulations....................................................................................... 31
Figure 2.5: Interface Crack between Two Isotropic M e d ia .......................................... 32
Figure 2.6: Finite Element Model Used for the Combined Indentation and Fracture
A nalysis................................................................................................................ 40
Figure 2.7: Result Comparison for K vs. R/a due to the Formulation with Contact
Analysis and the Fracture and Contact Model with Rj/R=0.9 under Asprocessed Properties in the EB-PVD TBC system s..........................................42
Figure 2.8: Phase A n g l e , v s . R/a Using As-processed Properties with Two Oxide
Thickness Obtained From Numerical Solutions...............................................45
Figure 3.1: A Sectioned SEM Micrograph of an As-Processed EB-PVD TBC System...49
Figure 3.2.1: K l/u vs. R/a due to a Standard Conical Indentation on a Homogeneous
Substrate Including Unloading Effects............................................................... 52
Figure 3.2.2: K l/u vs. R/a due to a Standard Conical Indentation with Major Load Levels
Including Unloading Effects.................................................................. ............54
Figure 3.3.1: Apparent Toughness as a Function of Exposure Time for TBC Systems at
Various Temperatures..............................................................................
57
Figure 3.3.2: Least Square Correlation of TGO Thickness (pm) vs. Square Root of
Exposure Time (s)......................................................................................
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...60
Figure 3.3.3 Oxide Thickness vs. Exposure Time between the Measurement and Model
Prediction.................................................................................................................63
Figure 3.3.4: Young’s Modulus of EBPVD TBC vs. Thermal Exposure Time (hr) based
on Thermally Activated Mechanisms Considering As-Processed E to be
44GPa and 175GPa in Fully Densed C ondition................................................ 66
Figure 3.3.5: Toughness Loss vs. Isothermal Exposure Time at 1100 °C Assuming No
Changes Both in the Alumina Layer and in the TBC Layer (same results as in
Figure 3.3.1) and Taking Into Account Measured Alumina Layer Thickening
.................................................................................................................................. 71
Figure 3.3.6: Toughness Loss vs. Isothermal Exposure Time at 1100 °C Assuming No
Changes Both in the Alumina Layer and in the TBC Layer (same results as in
Figure 3.3.1) and Taking Into Account the TBC Sintering Properties
72
Figure 3.3.7: Toughness Loss vs. Isothermal Exposure Time at 1100 °C Assuming No
Changes Both in the Alumina Layer and in the TBC Layer (same results as in
Figure 3.3.1) and Taking Into Account the Changes Both in Oxide
Thickening and TBC Sintering............................................................................73
Figure 3.3.8: Toughness Loss vs. Isothermal Exposure Time at 1200 °C Assuming No
Changes Both in the Alumina Layer and in the TBC Layer (same results as in
Figure 3.3.1) and Taking Into Account Measured Alumina Layer Thickening
.................................................................................................................................. 77
Figure 3.3.9: Toughness Loss vs. Isothermal Exposure Time at 1200 °C Assuming No
Changes Both in the Alumina Layer and in the TBC Layer (same results as in
Figure 3.3.1) and Taking Into Account the TBC Sintering Properties
78
Figure 3.3.10: Toughness Loss vs. Isothermal Exposure Time at 1200 °C Assuming No
Changes Both in the Alumina Layer and in the TBC Layer (same results as in
Figure 3.3.1) and Taking Into Account the Changes Both in Oxide
Thickening and TBC S intering............................................................................79
Figure 3.3.11: Arhennius Plot of Toughness D egradation.................................................. 82
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Figure 3.4.1; A Typical SEM Charging Image of the Debonded TBC After Indentation
using a Major Load of 100 kg (Steam Pressure O.IO atm with 120 hrs
Isothermal Exposure)..............................................................................................86
Figure 3.4.2: UHDR Method for Determination of Debonding Radii; Unaxisymmetric
with Undebonded Gaps Observed in 5D Specimen (a) and 4B Specimen (b)
at I50Kg Indentation Load Under As-Processed Conditions........................... 88
Figure 3.4.3: Apparent Toughness vs. Exposure Time for TBC Systems in Dry Air and
the First Specimen at IIOO°C with O.IO atm. Vapor Pressure of Steam
(Dashed L in e ).........................................................................................................91
Figure 3.4.4: Indentation Test Locations on Specimen 5D: O.IO atm Vapor Isotherm ....97
Figure 3.4.5: 4B Specimen Surface at Different Exposure History Before and at its Final
Failure due to Indentation and Thermal Exposure Events................................ 98
Figure 3.4.6:
Toughness Loss vs. Exposure Time for Specimens with Measured As-
Processed Toughnesses....................................................................................... lOI
Figure 3.4.7:
SEM Photographs for Fracture Surfaces of Specimen 7C, Exposed
Isothermally at I IOO°C with 0.30atm W ater Vapor.........................................102
Figure 3.4.8: SEM Images of Fracture Surfaces for Two Different Exposure Conditions
After 120 hrs at I I 0 0 ° C ......................................................................................103
Figure 3.4.9:
Sectioned Views of TBC and Oxide Scale Morphology under Different
Exposure C onditions........................................................................................... 104
Figure 3.4.10: Oxide Thickness vs. Time IIOO°C under Different Isothermal Exposures
.......................................................................................................................
105
Figure 3.5.1: 4A Specimen Surface at Different Exposure History Before and at its Final
Failure due to Indentation and Thermal Exposure Events.....................
Figure 3.5.2:
112
Toughness Loss vs. Exposure Time for Specimens with Measured As
Processed Toughnesses for Cyclic and Isothermal Dry A ir ........................... 113
Figure 3.5.3: SEM Photographs for Fracture Surfaces of Specimen 4A and 7C under
Different Exposure Conditions after Experiencing the Same Equivalent
Isothermal Exposure Time of I20hrs....................................................
XIV
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114
Figure 3.5.4: SEM Photographs for Fracture Surface of Specimen 4A and 4B at 350hrs
................................................................................................................................ 115
Figure 3.5.5: Fracture Surface Analysis as a Function of Exposure Time for Different
S pecim ens............................................................................................................. 116
Figure 3.5.6: Sectioned Views of TBC and Oxide Scale Morphology in Failed Specimens
118
Figure 3.5.7: Plot of TBC Interfacial Toughness vs. Exposure Time for Specimens #2
and # 3 ...................................................................................................................... 122
Figure 3.5.8: Composite Figure Showing Micrograph, Backscatter and SEM Charging
Images after 170 Cycles. Center Indent was Performed before any Thermal
Exposure, Left Indent was after 50 Cycles and the Right Indent was after 170
Cycles..................................................................................................................... 123
Figure 3.5.9: Backscatter (a and b) and SEM Charging (e) Images of TBC Indent after
270 Cycles. Backscatter (a) is Constructed by Establishing the Ratio of the
Signals from the Two Detectors and (b) by Summing the Output of Both
Detector S ig n als...................................................................................................124
Figure 3.5.10: Toughness Loss vs. Number of Cycles Assuming No Changes in the
Alumina Layer (Same Results as in Figure 3.5.7) and Taking Into Account
Measured
Alumina
Layer
Thickening
and
Reductions
in
............................................................................................................................
Stress
130
Figure 3.5.11: Toughness Loss vs. Number of Cycles Assuming Debonding of the
Alumina and TBC (Same Results as in Figure 3.5.7) and Debonding of the
TBC o n ly ...............................................................................................................131
Figure 4.1:
Illustration of Problems Observed in Previous Indentation Tests of the
EBPVD T B C s ...........................................................................................
138
Figure 4.2: Tensile Stress vs. Strain Behavior for Mar-M200 in the [100] Direction Used
in Vasinonta and Beuth (2001) and the Modified Ramberg-Osgood Relation
by Setting N=2 and 0^=14.................................................................................... 144
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Figure 4.3: Tensile Stress vs. Strain Behavior for Polycrystalline NiAl Used in Vasinonta
and Beuth (2001) and the Modified Ramberg-Osgood Relation by Setting
N=2.87 and a=1.7
145
Figure 4.4: Schematic of the Indentation Models (a) by a Rigid Conical Indenter; (b) by a
Rigid Spherical Indenter..................................................................................... 150
Figure 4.5: Indent Load vs. Contact Radius Compared with the Analytical Predictions
due to a Standard Conical Indentation, Illustrating the Role of Hardening
Behavior on the Effects of load vs. contact radius a ..................................... 154
Figure 4.6: Indent Load vs. Contact Radius Compared with the Analytical Predictions
due to a 90° Conical Indentation, Illustrating the Role of Hardening Behavior
on the Effects of load vs. contact radius a ........................................................ 155
Figure 4.7: P vs. a due to Various Conical Indentation Geometries Considering Typical
EB-PVD TBC Properties....................................................................................159
Figure 4.8: P vs. 5 due to Various Conical Indentation Geometries Considering Typical
EB-PVD TBC Properties...............................................................
160
Figure 4.9: U/a vs. R/a due to Various Conical Indentation Geometries Considering
Typical EB-PVD TBC Properties.......................................................................162
Figure 4.10: Axial Compressive Strain vs. R/a as a Function of Conical Indenter
Geometry Compared with the Analytical Solution for a Single Material
(Substrate Properties o n ly )................................................................................. 166
Figure 4.11: Circumferential Strain vs. R/a as a Function of Conical Indenter Geometry
Compared with the Analytical Solution for a Single Material (Substrate
Properties o n ly ).................................................................................................... 167
Figure 4.12: H vs. a/Rb due to the Spherical Indentation of Various Diameters on a
Typical EB-PVD TBC System without TBC on T o p ..................................... 173
Figure 4.13: P/trdRb vs. 5/Rb due to the Spherical Indentation of Various Diameters on a
Typical EB-PVD TBC System without TBC on t o p .............................
174
Figure 4.14: U/a vs. R/a as a Function of a/Rb for the Spherical Indentation on a Large
Single Material (nickel based superalloy properties) to Illustrate its Size or
Load Dependence (3 sizes of ball used: 0.79mm, 1.59mm and 3.18mmin
XV I
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diameter and U/a vs. R/a overlaps at the same a/Rb of different size ball)
................................................................................................................................. 177
Figure 4.15: U/a vs. R/a as a Function of a/Rb for the Spherical Indentation on a Standard
EB-PVD TBC System without Bondcoat on Top (3 sizes of ball used:
0.79mm, 1.59mm and 3.18mm in diameter at the same load level of 150Kg)
.................................................................................................................
178
Figure 4.16: K vs. R/a for Different Shapes of Conical Indenters Based on the Indentation
Simulation on a Standard EB-PVD TBC system ............................................ 181
Figure 4.17: K vs. R/5 for Different Shapes of Conical Indenters Based on the Indentation
Simulation on a Standard EB-PVD TBC system ............................................ 182
Figure 4.18: K vs. R/a for a Spherical Indentation on a Standard EB-PVD TBC System(3
sizes of ball used: 0.79mm, 1.59mm and 3.18mm in diameter at the same
load level of 150K g)............................................................................................185
Figure 4.19: K vs. R/6 for a Spherical Indentation on a Standard EB-PVD TBC System (3
sizes of ball used: 0.79mm, 1.59mm and 3.18mm in diameter at the same
load level of 150K g)............................................................................................186
Figure 4.20: K vs. R/a for Different Shapes of Conieal Indenters Ineluding Unloading
E ffe ets...................................................................................................................188
Figure 4.21: K vs. R/a for Spherical Indentations Including Unloading Effects at the Same
Load Level of 150 k g ..........................................................................................190
Figure 4.22: Debonding Behavior Upon the Same Indentation Depth of 0.1mm Caused
by Different Shapes of Indenters. Debonding Size and Pattern Are Seen
Differently for Different Cones at the Same Penetration D e p th ....................192
Figure 4.23: Debonding Behavior Upon the Same Indentation Load of 150KgDebonding
Size and Pattern Are Seen Differently for Different Cones at the Same Indent
Load L e v e l..................................................................................................
194
Figure 4.24: Backseattered SEM Photographs to Illustrate the Debonding Behavior for
Different Spherieal Indenters at the Load Level of 150K g............................ 196
Figure 4.25: Debonding Behavior Upon upon a 1.588mm Diameter Spherical Rigid
Indenter at the Load Level of 150Kg............................................................ ....196
X V ll
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Figure 5.1: Delamination Pattern of TBC Coating on a Cylindrical Specimen with Outer
Diameter = 14.7mm, Inner Diameter = 6mm, NiCoCrAlY Bond Coat
Thickness = llO pm , and EB-PVD TBC Thickness = 220pm.
Indentation
Performed with a Rockwell Hardness Tester by a Standard Brale C Diamond
Conical Indenter (Bartsch, et.al, 2 0 0 2 )............................................................ 199
Figure 5.2: Schematic of Indentation on a 3-D Curved Substrate...................................... 203
Figure 5.3: Schematics of Indentation Geometry on Determination of Contact Radius
in the Axial Direction
and Circumferential Direction a e ...........................204
Figure 5.4: Curvature Effect of Contact Radii ae Compared with
at the Same
Penetration D e p th ................................................................................................ 206
Figure 5.5: A Simplified 3-D FEA Contact Model of a Hollow Cylindrical Specimen .212
Figure 5.6: FEA Contact Analysis of a Sharp 90° Conical Indentation on the UCSB
Specimen with Bondcoat/Substrate S y stem .....................................................213
Figure 5.7: Contact on a 3-D Flat Substrate with Results Compared to the 2-D Standard
Analysis to Show the Validation of 3-D Mesh R esolution....................
215
Figure 5.8: Compressive Strain vs. RJa^ for a Standard Conical Indentation on a Flat
Substrate with Comparison to Standard 2-D Results..............................
216
Figure 5.9: Compressive Strain vs. R/a for a Standard Conical Indenter Contact on
Hollow Cylindrical Substrates with Roller Constraints at Inner Surfaces and
at the Same ae/po in the Circumferential Direction and the Same az/po in the
Axial D irection............................................................................................
219
Figure 5.10: Tensile Strain vs. R/a for a Standard Conical Indenter Contact on Hollow
Cylindrical Substrates with Roller Constraints at Inner Surfaces and at the
Same ae/po in the Circumferential Direction and the Same az/po in the Axial
Direction.......................................................................................................................220
Figure 5.11: Compressive Strain vs. R/a for a Standard Conical Indenter Contact on a
Hollow
Cylinder
(po=5.11mm,
Pi=3.00mm)
Traction-free
at
Inner
Surface................................................................................................................ 223
xvm
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Figure 5.12: K vs. R/a for a Standard Conical Indenter Contact on a Hollow Cylinder
(po=5.11mm, pi=3.00mm) in the As-processed Condition and Traction- free
at the Inner Surface..........................................................................................
224
Figure 5.13: Compressive Strain vs. R/a for a Standard Conical Indenter Contact on a
Hollow Cylinder (po=3.08mm, Pi=0.97mm), Traction-free at the Inner
S urface................................................................................................................ 226
Figure 5.14: K vs. R/a for Contact on the Small Cylinder at the As-processed Condition
for a Standard Conical Indenter Contact on a Hollow Cylinder (po=3.08mm,
Pi=0.97mm), Traction-free at the Inner Surface..........................................
227
Figure 5.15: Indentation Load as a Function of Contact Size for a Standard Conical
Indenter Contact on a Hollow Cylinder (po=5.IImm, Pi=3.00mm), with
Roller Constraints at the Inner S u rface............................................................ 233
Figure 5.16: Compressive Strain vs. R/a for a Standard Conical Indenter Contact on a
Hollow Cylinder (po=5.IImm, Pi=3.00mm), with Roller Constraints at the
Inner Surface......................................................................................................... 234
Figure 5.17: Tensile Strain vs. R/a for a Standard Conical Indenter Contact on a Hollow
Cylinder (po=5.IImm, Pi=3.00mm), with Roller Constraints at the Inner
S urface.................................................................................................................. 235
Figure 5.18: K vs. R/a for a Standard Conical Indenter Contact on a Hollow Cylinder
(po=5.IImm, Pi=3.00mm) At the As-processed Condition with Roller
Constraints at the Inner Surface........................................................................ 236
Figure 5.19: Indentation Load as a Function of Contact Size for a Standard Conical
Indenter Contact on a Hollow Cylinder (po=3.08mm, pi=0.97mm), with
Roller Constraints at the Inner Surface..............................................................239
Figure 5.20: Compressive Strain vs. R/a for a Standard Conical Indenter Contact on a
Hollow Cylinder (po=3.08mm, Pi=0.97mm), with Roller Constraints at the
Inner Surface.................................................................................................
240
Figure 5.21: Tensile Strain vs. R/a for a Standard Conical Indenter Contact on a Hollow
Cylinder (po=3.08mm, pi=0.97mm), with Roller Constraints at the Inner
Surface................................................................................................................ 241
XIX
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Figure 5.22: K vs. R/a for a Standard Conical Indenter Contact on a Hollow Cylinder
(po=3.08mm, Pi=0.97mm), with Roller Constraints at the Inner Surface
.............................................................................................................................. 242
Figure 5.23: Indentation Load as a Function of Contact Size for a 90° Conical Indenter
Contact on a Solid Cylinder (po=5.50mm) (UCSB Specim en)..................... 245
Figure 5.24: Compressive Strain vs. R/a for UCSB Specimen for a 90° Conical Indenter
Contact on a Solid Cylinder (po=5.50mm)...................................................... 246
Figure 5.25; Tensile Strain vs. R/a for UCSB Specimen for a 90° Conical Indenter
Contact on a Solid Cylinder (po=5.50mm)...................................................... 247
Figure 5.26: K vs. R/a for UCSB Specimen at the As-processed Condition for a 90,o
Conical Indenter Contact on a Solid Cylinder (po=5.50mm)........................ 248
Figure 5.27: Convention for Delamination in the Circumferential Direetion...................251
Figure 5.28: Critical Half-width for Buckle-driven as a Function of TGO thickness
................................................................................................................................ 252
Figure 5.29: K vs. R/a for the 90° and 120° Conical Indentation on a Flat EB-PVD TBC
System with 110pm Bondcoat Thickness Including Unloading Effects
257
Figure 5.30: TBC Specimen from UCSB, for Interfacial Toughness Measurement
260
Figure 5.31: Typical TGO Morphology and TBC Thickness M easurem ent....................260
Figure 5.32: Typical TGO Morphology and Bondcoat Thickness M easurem ent............261
Figure 5.33: Typical TGO Thickness M easurem ent........................................................... 261
Figure 5.34: Typical SEM Images for Delamination Patterns and Contact Regions due to
the Indentation at Three Standard Load Levels, Available from a Rockwell
Hardness Tester.................................................................................................... 263
Figure 5.35: SEM Images Reveal Cracking Interface is at or Near to the Interface of TBC
and TGO................................................................................................................ 265
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LIST OF TABLES
Table 3.3.1: TBC Sintering and TGO Thickening as a Function of Exposure Time and
Tem perature............................................................................................................68
Table 3.3.2: Properties of Each Layer in an EB-PVD TBC System Under As-processed
C onditions...............................................................................................................68
Table 3.4.1:
Summary of Measured Data and Kc Values from Indentation Tests
Performed on a TBC Specimen Exposed at 1100°C, with Vapor Pressure =
O .la tm ..........................
90
Table 3.4.2: Specimen Exposure Conditions and T im e s.................................................... 92
Table 3.4.3: Results for the As-Processed Interfacial Toughnesses................................... 94
Table3.4.4:
Summary of Measured Data and Kc Values from Indentation Tests
Performed on 5D TBC Specimen Exposed at 1100°C, with Vapor Pressure =
O.latm and 1C TBC Specimen Exposed at 1100°C, with Vapor Pressure =
0 .3 a tm ......................................................................................................................96
Table 3.4.5: Summary of Measured Data and Kc Values from Indentation Test Performed
on 4B TBC Specimen Exposed at 1100°C under Dry Air Isothermal
conditions...............................................................................................................99
Table 3.5.1: Summary of Measured Data and Kc Values from Indentation Tests
Performed on 4A TBC Specimen Exposed at I100°C under I hr Cyclic Dry
A ir .......................................................................................................................... I l l
Table 3.5.2: First Round Tests of TBC Specim ens..............................................................120
Table 3.5.3: SEM Charging vs. Optical Backscattering Measurements of Debond Size
after 170 Cycles (Specimen # 3 ) ....................................................................... 126
Table 3.5.4: SEM Charging vs. Optical Backscattering Measurements of Debond Size
after 270 Cycles (Specimen # 3 ) ....................................................................... 126
Table 4.1: Conelated Coefficients for Eqn. (4.7) due to Different Conical Indenters ....162
Table 4.2: Measurements of Interfacial Toughness due to the 90 Degree Conical
Indentation and Comparison with the Results of the Standard Conical
Indentation......................................................................................................... 192
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Table 4.3: Measurements of Interfacial Toughness due to the 150 Degree Conical
Indentation and Comparison with the Result of the Standard Conical
Indentation.......................................................................................................... 194
Table 4.4: Summary of the Measurements of Interfacial Toughness due to Various Shapes
of Indenters at the Indent Load Level of ISOKg..............................................196
Table 5. T. Cases Considered in the FEA Sim ulations..................................................... 211
Table 5.2: Indentation Depth as a Function of Cone Type and Bondcoat Thickness at the
Loads of 60Kg, lOOKg and I5 0 K g ................................................................... 255
Table 5.3: Half-width Determination at a Certain Toughness Level with bo=2.58mm by a
Standard Conical Indentation...............................................................................255
Table 5.4: Characterization of the UCSB Solid Cylindrical Specim en............................ 259
Table 5.5: Contact Radius due to 90 Degree Cone at Various Load L e v e ls.................... 265
Table 5.6; Effective Delamination Sizes from the Tests on the UCSB Specimen
267
Table 5.7: Kc and Go at the Final Unloading State for the UCSB Specimen................... 267
xxn
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Chapter 1. Introduction
CHAPTER 1.
NTRODUCTION
1.1 Background
Ceramic thermal barrier coatings (TBCs) have been used to increase the creep
resistance of gas turbine components for more than two decades. Although their first uses
were primarily for thermal protection of combustor and after burner components in
aircraft engine applications, TBCs are now used to insulate rotating components such as
blades and vanes.
They are also being used in land-based turbines used for power
generation. As compared to new alloy development, the use of TBCs can be a low-cost
approach for allowing increases in turbine operating temperatures and turbine efficiency.
As the applications of TBCs increase, designers want to fully exploit them in
turbine designs. However, because of problems with the durability of TBCs, they cannot
be relied upon to provide thermal protection for the life of a turbine or until scheduled
turbine rebuilds.
Initially, in the as-deposited state, TBCs are well-bonded to the
superalloy component upon which they are deposited. As the coating system is exposed
to operating temperatures, however, its adherence degrades. Poor adhesion can lead to
the spontaneous debonding or spallation of the coating, which is driven by compressive
residual stresses. In addition, in actual gas turbine environments, small-scale impacts of
moving components by particles ingested into the gas turbine (termed foreign object
damage) can help initiate and drive coating debonds.
Improving the life of thermal barrier coatings is a key goal of gas turbine design
and it requires an in-depth understanding of the mechanisms leading to loss of TBC
adhesion leading to spallation failures. The ultimate goal of this research is to help to
quantify the contribution of various mechanisms leading to TBC adhesion loss under
simulative environmental exposures. That goal will be achieved through the analysis and
implementation of indentation tests for tracking fracture toughness losses in exposed
TBC systems.
Figure I.l shows a TBC "button" specimen, which is the standard specimen
geometry used in the gas turbine industry. The button specimen is 25.4 mm in diameter,
with a thickness of 3.18 mm. The two principal methods of depositing thermal barrier
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Chapter 1. Introduction
coatings are plasma spray and electron beam physical vapor deposition (EBPVD).
Though the work of this thesis may be applicable to plasma sprayed TBC systems, this
thesis will focus on EBPVD TBC systems. Furthermore, two types of bond coats are
commonly used in TBC systems: platinum aluminide (PtAl) alloys and nickel-cobaltchromium-aluminum-yttrium (NiCoCrAlY) alloys. This thesis will address PtAl bond
coat systems directly. The EBPVD specimens considered in this study were provided by
the General Electric (GE) and Howmet Corporations, and were fabricated using identical
processing standards.
25.4 mm3.18 mm
100 |j.m
0.25-5 jL im
50 ) L im
TBC
i'CK.)
_
Figure l.I: A Standard TBC Button Specimen and Cross Section Schematic
of the Individual Layers.
Figure 1.1 also gives a schematic of the cross section of this type of multi-layered
EBPVD TBC system.
It consists of an N5 single crystal nickel-based superalloy
substrate, a platinum-aluminide bond coat which is applied by chemical vapor deposition
(CVD) with a thickness of approximately 50 |im, a thermally grown oxide (TGO), and
the TBC itself. The TGO is an alumina layer, which is grown on the bond coat before
TBC deposition, to a thickness of approximately 0.25 |im. During exposure the TGO
continues to grow and can become as thick as 4 - 5
|U.m
or more before spallation occurs.
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Chapter 1. Introduction
The TBC itself is yttria stabilized zirconia (YSZ) with a thickness of approximately 100
|im.
The TBC has a columnar microstructure aligned in the vertical direction.
This
structure is not fully dense, which results in a net in-plane stiffness that is a fraction of
that for fully dense zirconia.
During TBC spallation, fracture typically occurs at or near the interface between
the oxide and bond coat layers, although in some cases the fracture path can include the
TBC/oxide interface or even be entirely within the TBC, near the TBC/oxide interface.
From a mechanics standpoint, a number of factors can lead to decreases in the spallation
resistance of a TBC system. First, as the TBC system is exposed at a high temperature
(1000°C is a typical operating temperature), the thickening of the alumina scale increases
the strain energy stored in the system.
Because the oxide scale is highly stressed
(compressive stresses of 3-4 GPa are typical) this can significantly increase the energy
available to drive a debond of the alumina scale and the TBC above it. The ceramic TBC
is also in a state of compression at room temperature (compressive stresses of 10-50 MPa
are typical). Also, as the TBC is exposed to high temperatures it can sinter and densify.
The result is an increase in the effective elastic modulus of the TBC and an increase in the
magnitude of the TBC compressive stress at room temperature. As is true for oxide scale
growth, TBC sintering can significantly increase the energy available to drive a debond
crack.
The two mechanisms for toughness degradation described above can occur
independent of a “true” loss of adhesion or interfacial toughness in the TBC system. A
true reduction in interfacial toughness can be caused by chemical or mechanical damage
near the interface and these are the two final mechanisms which can lead to reductions in
TBC spallation resistance.
Chemical damage can occur due to segregation to the
interface region of elements that weaken or embrittle the interface. For example, if the
sulfur content is not controlled in the bond coat or superalloy, sulfur can segregate to the
interface and weaken it. The same phenomenon can occur if anything other than low
sulfur fuel is used in the gas turbine. Although it can occur during a single thermal cycle,
mechanical damage at the interface is typically seen for cyclic thermal exposures. As a
result of multiple thermal cycles, micro-scale cracking damage can occur in the region
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Chapter 1. Introduction
near the thermally grown oxide, weakening that part of the TBC system.
The
development of this type of damage can be made more prominent by a “ratcheting”
phenomenon (Evans et. al, 2001) where compressive stresses in the oxide scale at high
temperatures cause it to buckle even while it remains bonded to the bond coat alloy
(which has very low creep resistance at high temperatures).
This change in oxide
geometry can lead to substantial crack formation in and near the oxide scale.
Which mechanism dominates the TBC system failure is strongly dependent on the
type of TBC system (e.g. EBPVD vs. plasma spray), the materials used in the system (e.g.
the bond coat alloy used) as well as environmental factors, such as combustion gas
temperature, water vapor content and the presence of small, hard particle impacts. The
goal of this thesis is to use fracture mechanics tests and analyses coupled with insights
from materials science collaborators to help identify dominant mechanisms leading to
failure for an industry-standard TBC system and common exposure conditions. In this
way, we hope to guide TBC system developers, suggesting on what aspects of the TBC
system design they should focus their efforts.
By developing a testing method and
applying it to a key TBC system used in industry, it is also hoped to motivate the
development of similar testing methods for other TBC systems in use and under
development, and in other brittle coating/ductile substrate coating systems.
1.2 Existing Work
1.2.1
Existing Work Involving Indentation to Measure Interfacial Toughness
The mechanics framework for the quantification of the interfacial fracture
toughness for brittle coatings on relatively ductile substrates due to indentation by a
diamond brale “C” conical indenter was established by Drory and Hutchinson (1995).
Their work includes an extensive review of indentation-based interfacial adhesion
measurement techniques and concludes with application of their indentation test to a
diamond-coated titanium alloy.
Their work assumes: (I) the thickness of the film
deposited on the substrate is very small compared to the characteristic size of the
indentation field such that it deforms with the substrate and does not influence the
substrate deformation induced by the indentation, (2) the film is in a state of bi-axial
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Chapter 1. Introduction
compressive stress and (3) linear elastie fracture occurs under mode II conditions. Based
on these assumptions, two formulas for the energy release rate of the debonding coating
are derived, applicable to two types of coating behavior behind the crack front.
Debonding TBC
and TGO Layers
Indenter
Bond Coat
Compressive
Stress a
'Superalloy Substrate
Plastic Zone
3.2 mm
R
a=Contact Radius
R=Debond Radius
Figure 1.2: Schematic Diagram of the Indentation Test for TBC Systems.
Building on the work of Drory and Hutchinson (1995), Vasinonta and Beuth
(2001) developed procedures for using a Rockwell-type indentation test to quantify the
toughness of (TBC) systems (see Fig. 1.2). They used finite element models to quantify
displacement fields caused by a rigid conical indenter on a bond coat/superalloy substrate
system. Indentation displacement fields were then used to determine energy release rates
of debonding oxide scale and thermal barrier coating layers as a function of normalized
distance from the center of the indent. Analysis results were applied to a small number of
indentation tests, yielding some of the first data for interfacial fracture toughness in asprocessed and exposed EBPVD TBC systems. A key aspect of the TBC systems studied
in this work that made use of the indentation test possible is that the TBC and bond coat
layers are relatively thin compared to the depth of the indentation. The comparatively
thin TBC layer is fully penetrated by the indenter and its existence does not alter the
deformation of the substrate (analogous to the assumptions made in the work by Drory
and Hutchinson). The thin bond coat layer also has a limited effect on the indentation
strain field (despite its being part of the indented substrate). This means that accurate
modeling of the elastic-plastic properties of the bond coat (which are not well-known) is
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Chapter 1. Introduction
not critical to the analysis.
The test developed by Vasinonta and Beuth (2001) was
applied to track toughness loss in isothermally exposed TBC systems at three
temperatures by Handoko et al. (2001). In their work, fracture calculations are used to
quantify the relative contribution of oxide thickening, TBC sintering and interfacial
damage to apparent losses of toughness seen in the indentation tests. Analysis of their
tests required the derivation of new energy release rate formulas that take into account the
contribution of a relatively thick oxide scale to the energy release rate of the oxide and
TBC.
Interfacial adhesion of brittle films on ductile substrates has also been quantified
by the use of wedge-shaped indenters.
Indentation by a wedge indenter was first
introduced by Vlassak, Drory and Nix (1997) for measuring the adhesion of diamondcoated titanium. Analogous to a conical indentation test, the plastic deformation of the
Interfacial adhesion of brittle films on ductile substrates has also been quantified by the
use of wedge-shaped indenters. Indentation by a wedge indenter was first introduced by
Vlassak, Drory and Nix (1997) for measuring the adhesion of diamond-coated titanium.
Analogous to a conical indentation test, the plastic deformation of the substrate caused by
the wedge indentation drives the film to delaminate from the substrate and the size of the
delaminated area can be related to the interface toughness.
Notable studies on the
application of wedge indentation methods to thermal barrier coating systems were
performed by (Begley et a l, 2000; Mumm and Evans, 2000). Mode mixity for TBC
system debonding was considered in the study of wedge indentation using an approximate
formulation (Hutchinson and Suo, 1991), with the debonding bi-layer of TBC and TGO
converted to an effective single layer. It is important to consider the mode mix in TBC
system fracture testing, because the TGO layer grows with the specimen’s exposure.
With the increase of the TGO thickness, bending deformation may act to open the crack,
making a crack extension under mixed mode instead of under purely mode II. In such
cases, measured changes in toughness may be due to changes in mode mix, so that mode
mix must be accounted for.
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Chapter 1. Introduction
1.2.2
Existing Work on Water Vapor and Cyclic Loading Effects on TBC System
Adherence
The injection o f steam into the combustion stream o f land-based gas turbines can
increase turbine efficiency and reduce emissions; however, there is concern that water
vapor can have a negative effect on the oxidation resistance o f gas turbine alloys and
there is a concern that it could have a similar effect on TBC systems with a growing
alumina scale. Although significant research exists on the effect o f water vapor in the
high temperature corrosion o f metallic alloys (Walter et a l, 1991; Hayashi et a l, 2001;
Fukunoto et a l, 2001; Yu et a l, 2001) as well as ceramics (Geng et a l, 2001; Gogotsi et
a l, 1994; Foerthmann et a l, 1994), work on the influence o f water vapor on the
oxidation o f alumina-forming alloys is not extensive. Moreover, there is little literature
available on the effect o f steam-air mixtures on EB-PVD TBC systems (Tamai et a l,
2000; Janakiraman et a l, 1999).
In tests on superalloys with a-A l 203 scales by
Janakiraman et al. (1999), water vapor was found to increase the spallation o f a-A l 203
scales significantly compared to scales grown on specimens exposed in dry air if the
alumina scales are marginally adherent. However, for alloys with extremely adherent aAI2O 3, water vapor did not manifest significant effect on the spallation and cracking
behavior compared to the scales exposed in dry air even though it was observed that
water vapor had access to the a-A l 203 - alloy interface during cyclic oxidation.
A more recent study by Maris-Sida et al. (2003) shows that the water vapor
affects the oxidation o f alloys in three different ways: (1) The water molecules decrease
the true fracture toughness o f the alumina/alloy interface. (2) Water vapor accelerates the
formation o f transient oxidation to cause thicker oxides to be formed during oxidation in
wet air than dry air. (3) Substantially more spinel phase is formed at the a-A l 203/gas
interface resulting from the outward diffusion o f nickel under water vapor conditions due
to cracking in the oxide scale.
It is well known that the failure o f PtAl EB-PVD TBC systems is strongly
influeneed by the growth o f the TGO layer. Tests described above on alumina scales
without a TBC deposited on top have indicated an effect o f water vapor on scale
adherence. Water vapor may increase the rate o f growth o f an alumina scale. It has been
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Chapter 1. Introduction
found, however, that the presence of water vapor does not significantly affect the residual
stresses in the TGO layer (Janakiraman et al., 1999).
For TBC systems, it remains
unknown if water vapor alters the residual stresses in the TBC layer or stiffness of the
TBC or any other properties of TBC and TGO layers. At this time it is not known if there
are effects of water vapor on adhesion in Pt-Al, EB-PVD TBC systems under various
loading conditions. Part of the research of this thesis will apply indentation tests to study
the degradation of EBPVD TBCs in the presence of water vapor.
1.2.3
Existing Work on the Role o f Indenter Shape
The mechanics of conical and spherical indentation of an elastic-plastic substrate
has been considered by multiple researchers. Early research in this area mainly focused
on determining the mean contact pressure beneath the indenter to obtain insight into
materials hardness testing with various indenter geometries (Tabor, 1951; Johnson, 1970,
1985; Hill, 1950; Bhattacharya and Nix, 1988, 1991). Begley et al. (1999) present a
detailed study of surface strain distributions beneath or near a spherical indenter on an
elastic-plastic substrate with an elastic film on top. Results are given detailing the strain
distributions in the contact region, where non- proportional loading occurs, and insight is
given into the interpretation of elastic thin film cracking patterns beneath the indenter.
However, there are no details given for the field solutions away from the indentation. In
particular, there appears to be no existing literature on the use of spherical indentation to
quantify interfacial toughness in TBC systems. Indenter shape has been considered in the
case of wedge indentation of TBC systems (Begley, et al., 2000; Mumm and Evans,
2000). Their work considers wedges having angles of 90° and 120°, with some model
results compared with those from models of conical indentation.
Despite some existing work looking at the role of indenter shape in the adhesion
testing of coatings, there is a lack of a complete study on the effects of indenter shapes,
especially for substrates that undergo significant work hardening during indentation. In
adherent coating systems such as as-processed TBCs and oxide scale systems (with no
TBC on top) indentation by some indenter shapes is not sufficient to induce interfacial
debonding. Depending on the application, some indenter shapes may be more efficient at
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Chapter 1. Introduction
inducing debonding than others.
These issues serve as the primary motivation for a
detailed study in this thesis on the role of indenter shape in coating toughness testing.
1.2.4
Existing Work on Indentation and Delamination o f Coatings on Curved
Substrates
The subject of delamination of films or coatings on a flat substrate due to a
combination of residual and applied stresses has been richly studied. However, there are
few available studies on the delamination of coatings on a curved substrate. One notable
exception is a recently published article by Hutchinson (2001) regarding thin film
debonding on a curved substrate due to equal biaxial compressive residual stresses in the
film. This paper presents a detailed study of delamination phenomena for thin elastic
films debonding in both axial and circumferential directions of a hollow cylinder using
simple analytical solutions. However, there is no current work considering indentation
toughness testing of films and coatings deposited on a cylindrical surface.
Very recent research involving thermal gradient mechanical fatigue (TGMF) tests
on TBC systems (Bartsch et al., 1999, 2002) has made the consideration of indentation
testing on curved substrates highly relevant. The goal of these tests is to realistically
simulate fatigue loads and thermal gradients imposed on a turbine blade during a service
cycle.
In order to impose specified thermal gradients, hollow cylindrical specimens
coated with EB-PVD TBC are used in performing these tests, with heating applied
externally and cooling air circulated internally, through the hollow cylinder.
In this
research, there is a need to study the degradation of toughness in the TBC system as a
function of exposure. A natural test to achieve this goal is indentation of the cylindrical
substrate. A goal of this thesis is to use analysis results to explain coating cracking paths
and cracking pattems induced by indentation of a curved substrate, to relate delamination
size to fracture toughness, and to assist in the use o f such tests for TBC and other brittle
coating systems.
1.3 Motivation
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Chapter 1. Introduction
This thesis is primarily motivated by existing work by Vasinonta and Beuth
(2001) and Handoko, et al. (2001) developing an indentation test to measure interfacial
toughnesses in thermal barrier coating systems. The test for TBC systems (see Fig. 2)
involves indenting a standard TBC button specimen using a Rockwell hardness tester and
a conically-shaped brale indenter.
The TBC and oxide layers are penetrated by the
indenter and the metallic bond coat and superalloy substrate are plastically deformed.
This plastic deformation induces compressive radial strains in the substrate, which are
transferred to the TBC and oxide layers. This causes an axisymmetric debond, with the
debond crack running at or near the interface between the alumina scale and the metallic
bond coat. The radial extent of the debond is directly related to the fracture toughness of
the interface.
By indenting multiple locations and single locations multiple times, a
single button-shaped TBC specimen can yield many toughness values for different
exposure times.
At the time research for this thesis was initiated, this test had been analyzed and
used in a small number of tests to characterize the loss of interfacial toughness in EBPVD
TBC systems with a PtAl bond coat as a function of the duration of isothermal exposures
at 1100°C, 1135°C and 1200°C in dry air.
Attempts were made to relate apparent
changes in toughness to changes in the TBC system, including oxide scale growth and
TBC sintering, in an attempt to rank the importance of various mechanisms in the
degradation of TBC adherence. The primary goal of this thesis is to more fully develop,
analyze and apply this testing method and to propose other fracture mechanics-based
indentation test methods applicable to other TBC systems and other brittle coating
systems.
In the process, it is hoped to gain a more thorough understanding of TBC
system degradation under simulative environmental conditions. It is also hoped to obtain
a more in-depth understanding of the mechanics of indentation tests with regard to their
use for measuring interfacial toughnesses.
This includes insights into indentation by
spherically-shaped indenters, which can give insight into spallations induced by high­
speed ball impacts.
1.4 Organization
10
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Chapter 1. Introduction
In the next chapter, interfacial fracture mechanics issues for the delamination of
TBCs or oxides due to the combination of biaxial residual stresses and the indentation
events are addressed. First, the chapter begins with a rigorous derivation of the energy
release rate for the delamination of an annular plate subject to equi-biaxial stresses. Then
a brief review and diseussion are presented on the issue of delamination of a thin annular
plate on a substrate due to conical indentation. Next the issues of delamination of a
composite plate due to indentation with an emphasis on the application of EB-PVD TBC
systems are presented. Energy release rates are formulated with a full consideration of the
bending contribution from the oxide scale. Then the mechanics of interfacial cracks are
presented to review the fundamental issues for cracking at bi-material interfaces with a
specific application in a TBC system emphasized. In the subsequent section, the finite
element modeling of a full elastic plastic contact fracture analysis is described on
extracting the energy release rate and mode mix on the cracking along the interface of
oxide and bondcoat due to indentation in an EB-PVD TBC system. Next, the results of
the stress intensity factor vs. R/a directly from the numerical models are presented and
compared to those from the formulation and the contact finite element model only.
Finally, this chapter ends with the presentation of the numerical results of the mode mix
\|/ vs. R/a and chapter summary and conclusion.
Chapter 3 addresses the applications of conical indentation techniques developed
in the previous chapter and previous work by Vasinonta and Beuth (2001). Three
subtopics are addressed: mechanism-based tests for isothermal dry air exposures;
mechanism-based tests for exposures with water vapor, and mechanism-based tests for
cyclic thermal exposures. In the first subtopic, toughness degradation as a function of
exposure time and temperature is evaluated for isothermal dry air exposures considering
the properties in the TBC to be the same as in its as-processed state. The research results
obtained herein are the first of this type available in the literature. Next, the results of
toughness degradation from indentation considering the changes in oxide thickness and
the TBC modulus along with its residual stresses caused by sintering effects are
presented. Those results are found to be valuable in identifying and ranking the
importance of each mechanism causing apparent and true interfacial toughness loss.
11
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Chapter 1. Introduction
Lastly, results are presented in the form of an Arrhenius plot as a means for understanding
the validity of accelerated tests.
The second subtopic in Chapter 3 addresses the investigation of the toughness loss
in a simulative environment. This subtopic begins with some details of experimental
procedures and debonding pattems observed throughout the tests. Then, the results are
presented for tests on steam-exposed specimens. The in-depth study of the effects of
water vapor includes a full set of specimens to compare the toughness degradation at the
same exposure time under various exposure conditions including exposure with the
presence of water vapor at different vapor pressures. Next, the fracture surfaces and
structural evolution of the oxide scales are compared for various cases with the same
thermal history. The results of the oxide thickness of the specimens exposed at various
conditions are presented and compared with those in the literature by Chang et al (2002).
The third subtopic in Chapter 3 addresses the integration between the destructive
and nondestmctive methods on the evaluation of the TBC toughness degradation under
cyclic exposure conditions. The toughness measurements from indentation are first
presented by assuming no changes in the TBC system. Next, the results of debonding
images from the destructive evaluations are mapped again through optical backscattering
techniques. The stresses in the oxide are tracked continually with each exposure using
piezospectroscopy (a non-destmctive method). Then, the toughness measurements from
indentation including the changes in oxide thickness and stresses are presented along with
a more detailed discussion of the role of oxide damage along the interface during the
cyclic exposure.
Chapter 4 first addresses the limitations of interfacial toughness measurements
due to the standard conical indentation techniques. Then the constitutive behaviors used
to describe the TBC substrate systems and the finite element methods considered herein
are revisited and extended from the previous studies by Vasinonta and Beuth (2001). In
the subsequent sections, the mechanics of contact due to the conical and spherical
indentations are presented separately. This includes the discussion of indentation load vs.
contact size and the surface displacement and strain distributions in comparison to
available analytical solutions. Next, the results of the numerical models are extended to
12
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Chapter 1. Introduction
the evaluation of stress intensity factors along the top surface of the bondcoat in its asprocessed state. Again results are presented separately for conical and spherical
indentations. Lastly, experimental results are presented to demonstrate application of
results from the numerical simulations and how special indenters can be utilized for the
benefit of the multiple indentation test techniques.
Chapter 5 presents delamination mechanics on a curved substrate due to
indentation. The indentation geometries and dimensional analysis of the surface strain
solutions are presented first. Next, the accuracy of the finite element modeling of contact
on a cylinder are evaluated through a model of 3D contact on a flat substrate with surface
strain results compared with those of the 2D model. This simple method allows the
determination of how many elements in contact are necessary for the convergence of the
3D contact results to the 2D standard results. Then the 3D curved model is validated
through a numerical analysis at the same ae/po for the contact of two different sizes of
hollow cylinders. With the confidence of the convergence of the 3D contact analysis, the
numerical results of the contact on cylinders are presented. The cases studied in the
numerical 3D contact analysis include two hollow cylinders considered in experiments by
Bartsch et al. (1999 and 2002) and one solid TBC-coated cylinder from the University of
California at Santa Babara (UCSB). Two types of conical indenters are simulated
separately on the hollow cylinders and the solid cylinder. One is the standard conical
indenter with 120° tip angle and the other is the special sharp indenter with 90° tip angle.
The results of the 3D numerical modeling are presented in the order of contact load vs.
contact size and surface strains vs. R/a in the axial as well as in the circumferential
directions. Stress intensity factors in the axial and in the circumferential directions are
then evaluated as a function of R/a with the axial results compared with the relevant 2D
results. A road map on how to perform a valid test is then presented. Next, results from
testing of the UCSB specimen are presented and toughness results were evaluated based
on the experimental data and the numerical simulations.
Finally, in chapter 6 , contributions of this thesis research are reiterated, after
which recommendations are provided for future work. The references are included
thereafter.
13
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
CHAPTER 2. FRACTURE ANALYSIS OF
INDENTATION TESTS IN
EB-PVD TBC SYSTEMS
2.1 Chapter Overview
This chapter addresses the prohlems o f interfacial fracture mechanics due to
indentation on a standard EB-PVD TBC specimen considered in a previous study by
Vasinonta and Beuth (2001). As an extension o f the previous investigation o f indentation
induced delamination mechanies on an EB-PVD TBC system, the primary goal o f this
chapter is to resolve two major concems. One is the validation and extension o f the
energy release rate formulation used previously, and the other is the issue o f fracture
mode mixity involved in the currently studied EB-PVD TBC systems. The energy release
rate formulation in EB-PVD TBC systems based on as-processed conditions will be
shown to overestimate the energy release rate. A modified formulation will be necessary
to extract the correct results, and those results will be validated through a new finite
element contact and fracture model. The same contact and fracture model is then used for
a detailed study on the concems o f mode mixity involved in this multilayered system.
The approach taken herein starts with the investigation o f some fundamental and
yet critical issues involved in the delamination mechanics o f multiple-layered thin films
or coatings deposited on metal substrates. Among these issues, the energy release rate of
the delamination o f an annular plate due to the presence o f bi-axial residual stresses are
going to be the first to be investigated. This investigation employs fundamental linear
elastic solutions for an annular plate subjected to a free traction along its inner surface,
and a prescribed condition along its outer edge, to resolve the stress distributions in the
debonded annular coating plate. The classical theory o f linear elastic fracture mechanics
(LEFM) is then employed for a strict derivation o f the energy release rate for
delamination o f the kind driven by the residual stresses only.
To proceed from here, the energy release rate o f delamination o f an annular plate
debonding on a substrate with the consideration o f the indentation event is then
14
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
postulated from the literature by Drory and Hutchinson (1995). Both the derived
formulation and the postulated solutions will be shown to be in perfect agreement for the
case without the presence o f the indentation event. They both reduce to the steady state
solution o f a straight interface debonding on an infinite substrate driven by a uniform
residual stress providing a sufficiently narrow strip is left behind the crack front. Thus,
the results from the analytical derivation support the reasoning behind the postulated
solutions by Drory and Hutchinson (1995).
Following this, the delamination o f a composite annular plate with direct
application in EB-PVD TBC systems is reviewed and extended from the previous study
by Vasinonta and Beuth (2001). As the composite annular plate becomes very narrow, the
solution approaches the steady-state advance o f straight interface cracking, however, now
with a bi-layer above the cracking interface in consideration. Due to the great difference
in magnitude o f the residual stresses presented in each layer, a more complete formulation
o f the energy release rate is derived to overcome the error introduced by the simple
formula used in the previous study under as-processed conditions in EB-PVD TBC
systems.
Numerous studies have been performed in the literature related to the bimaterial
layers rnider different expansions since the 1980s. The most fundamental and conceptual
development in this area are the studies o f Rice (1988) and Shih (1991). Great enrichment
has been achieved by more detailed studies in different directions and applications o f
interfacial cracking issues. Among those detailed developments: crack paralleling an
interface between dissimilar materials first studied by Hutchinson et al. (1987); a
methodology o f extracting stress intensity factors o f interfacial cracks by Matos et al.
(1989); fracture resistance o f bimaterial interfaces under four-point bending by
Charalambides et al. (1989); interfacial fracture testing o f deposited metal layers (tri-layer
materials) under four-point bending by Klingbeil and Beuth (1997); interfacial cracks in
dissimilar anisotropic media by Suo (1990); and separation o f crack extension modes in
orthotropic delamination by Beuth (1996).
Interfacial fracture issues on the delamination o f a thin film or coating deposited
on a substrate that were also extensively studied and the timing is almost parallel to the
15
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
other studies mentioned previously include: cracking and decohesion o f residually
stressed thin films first studied numerically by Drory et al. (1988), and Evans et al.
(1988); a more detailed study on the cracking o f thin bonded films in residual tension by
Beuth (1991); delamination in deposited multi-layers by Beuth and Narayan for straight
interfacial cracking (1996) and with axisymmetry (1996); and continuous delamination o f
sprayed deposits via applied curvature by Klingbeil and Beuth (1998).
An extensive summary o f the issues o f mixed mode cracking in layered materials
up to the early 1990s was performed by J. W. Hutchinson and Z. Suo (1992). The focus
o f this study was a direct application o f interfacial fracture mechanics on the delamination
in EB-PVD TBC systems. Its purpose was to scrutinize the interfacial fracture issues such
as mode mixity possibly existing in such systems and at the same time to get a closer look
at the validations o f the derived formulations based on certain critical assumptions. The
methods applied in this chapter will be extended for the applications, in subsequent
chapters, on the issues o f interfacial fracture mechanics.
2.2 Energy Release Rate for Delamination of an Annular Plate Subject
to Equi-blaxlal Residual Stresses
In this section, we will present a rigorous derivation o f the energy release rate for
delamination o f an annular plate (or film) subject to equi-biaxial stresses (Figure 2.1).
The main assumptions made here are as follows: (1) the annular plate remains unbuckled
for the detached portion and remains intact behind the advancing interface crack front; (2 )
the film plate thickness is very small compared to the substrate dimension. The
significance o f this derivation is seen in its final results, which shed much light on a more
complicated problem and makes the subsequent arguments more explicit.
16
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
Inner free edge
crack front
(a) Top View
detached annular plate
Substrate
Centerline
(b) Side View at the Cross-section Through the Center
Figure 2.1: Delamination o f an Annular Plate Driven by Equi-biaxial Residual Stresses.
17
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
Let us designate the equi-biaxial stress in the undebonded portion as a ^ with
delamination left out o f an annular plate with a traction free inner surface o f radius Ri and
crack front o f radius R. The stress and displacement solutions for an annular static elastic
plate without body force are given as follows (Timoshenko and Goodier, 1951):
1
E
B
- ( l + v ) + 2 C ( l- v ) r
( 2 . 1)
Un = 0
( 2 .2 )
a , = ^ + 2C
(2.3)
B
(2.4)
■2C
Next let’s consider the detached annular thin plate (or film)subject to traction
free at its
inner edge and with prescribed boundary conditions atthe outer. Thus we have:
u,|,^R = R 8 q(R)
(2.5)
o I
(2 .6 )
=0
where, Sn = Sn =
(2.7)
^ a.
Substitute these mixed boundary conditions o f (2.5) and (2.6) into (2.1) (2.3), we have:
B=-
E 8 e(R)
( 2 . 8)
(l + v ) ^ + (l + v ) ^
2C =
ESe(R)
(2.9)
( l - v ) + (l + v)
vRy
Therefore the stress distributions in the detached armular plate are:
2
E 8 e(R)
1-
( l - v ) + (l + v)
"
UJ
vRy
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( 2 . 10)
Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
Oq =
E 6 e(R)
1+
( l - v ) + (l + v) Ri
vRy
fRiY
—
i r
(2 .11)
J J
Since only in-plane stresses are present, elastic strain energy for an annular plate can be
written as:
dV
(2 .12)
By substituting (2.10) and (2.11) into (2.12), the initial elastic strain energy for the
annular plate before delamination occurs can be obtained:
R^( r ^ - R f )
U:„M ate=^E 8 e^(R)( l - v ) R ' + ( l + v)Rf
(2.13)
After the crack extends to R+A a, the strain energy in the annular plate becomes:
^ 2 .x, * X (R + Aa)"((R + A a ) " - R f )
UpinalPlate ^ ^ESg (R + Aa)--------------r-----------®
(1 - v)(R + Aa)' + (1 + v)Rf
(2.14)
At the same time, strain energy change due to the release o f equi-biaxial stresses upon the
crack extension can be derived as:
,2
^ M 2 R + Aa]Aa
E
(2.15)
Therefore, the total change o f the elastic strain energy upon crack extension yields:
AU = (U pinaipiate “ U jnjpiate ) +
(2.16)
After substitution and rearrangement, we have:
AU = TrtESg (R + Aa)
Aa{2R[2R' - R f ] [ ( l - v ) R ' +(1 + v)Rf ] - 2 R '( r ' - R f ) ( l - v ) }
[(1 - v)(R + A a)' + (1 + v)R,' ][(1 - v )R ' + (1 + v)Rf ]
- ■ r t d - v K [2 R .,A a]A a
(2.17a)
There is no external work for this process, therefore: AW = 0
(2.17b)
The energy release rate o f the annular plate upon debonding can be obtained through the
following classical formulation under the framework o f linear elastic fracture mechanics:
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
1 lim
1 r
^
G=— AW-AU
BAa^OAa^
^
(2.18)
Where B=27tR
By substituting (2.17a and b) into (2.18) and simplifying, the following simple solution
can be obtained;
,2 ^
^
t(l-V ) 2
G = F a c ------------On
2E
(2.19)
vR y
Where, Fac =
2“
( l - v ) + (l + v) f R . ^
Note that two extreme cases are:
G=0
t(l-v^)
2E
when R;
when R; -> R
(2 .20)
(2 .20 ) is the well-known solution for delamination o f a film o f thickness t on an infinite
substrate subject to a uniform stress oo due to a steady-state advance o f a straight
interface crack. We also note that the energy release rate (2.19) is independent o f the
substrate properties.
Two important arguments may be drawn from this straight derivation based on the
fundamental theory o f classical LEFM. First, from (2.20), we see that the energy release
rate is independent o f the component o f residual stress in the film parallel to the crack
front as the strip becomes very narrow. Under this circumstance, the energy release rate
becomes the same as the difference between the elastic energies per unit area o f the plate
when it is attached to the substrate and when it is released, subject to the condition of
zero strain change parallel to the crack front. We may further contemplate that the energy
release rate can be expressed the same as (2 .20 ), but with ao replaced by ar when the
stress field is altered by other events such as indentation providing assumption #2 now is
extended so that the film thickness is very small compared to the characteristic size o f the
indentation field.
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
Second, by taking (2.20) as the upper boundary o f the energy release rate, the
detached annular plate supplies a constraint which always reduces the overall energy
release rate. This can be seen from the expression, Fac, in (2.19), which shows that Fac is
always less than 1 and equal to 1 atRj = R . However, the formulation o f (2.19) can be
easily deduced from the previous argument in a much simpler manner. Let’s take the
change o f radial stress across the crack front to be the only contribution to the energy
release rate. And then substitute the stress jum p in the radial direction across the crack
front into (2 .20 ), then it becomes:
G=
(« -))“
(2 .21 )
Where a^{R) is the stress at r=R and cr^(R“) is the radial stress component at the outer
edge o f the armular plate, which is given by (2.10). In the case o f residual stress only,
(2.21) can be simplified and found the same as (2.19). However, we notice that the stress
jump
across
i.e.. A c t ,. =
the
crack
front
does
not
only
exist
in
the
radial
direction,
(R) - <r^ (R~), but also in the circumferential direction, which is the direction
parallel to the crack front, i.e.,Aag =o-^(R)-cr^(R“). This shows that the change of
stress in the circumferential direction across the crack front does not contribute to the
energy release rate, but to the change o f radial stress only. Thus, we may conclude that the
energy release rate for the delamination o f the annular plate is independent o f the stress
parallel to the craek front, regardless o f whether the strip is narrow or not.
2.3 Energy Release Rate for Delamination due to Indentation
In this section, the important formulations o f energy release rates for cracking in
EBPVD TBC systems caused by indentation are to be presented. Cracking along different
interfaces in EBPVD TBC systems are observed through this research. More details will
be addressed in chapter 3 on the topics o f conical indentation applications. Thus,
formulations due to delamination o f a single layer, i.e., only TBC coating cracking along
the interface o f TBC and TGO, or an oxide layer for an oxide system without TBC
coating on top, will be presented first. Then formulations due to the delamination o f a bi-
21
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
layer composite will be analyzed for cracking along the interface o f TGO and bondcoat in
EBPVD TBC systems.
2.3.1 Delamination of a Single Layer
Based on the previously derived results and deduced conclusions in section 2.2,
two important formulations on the energy release rate o f a single layer debonding on a
substrate are to be presented. These two formulations were first postulated by Drory and
Hutchinson (1995) based on similar arguments discussed in our previous section, but now
with the confidence o f conceptual clearness and proven arguments from the analytical
analysis o f a simpler case.
The first formulation is the energy release rate o f delamination o f a very narrow
strip left behind the crack front due to the combination o f residual stress and the
indentation induced stress field, which can be expressed as:
2G(l-v^)
/
x2
---- ^ = ( s , +VEe )
t, t
(2 .22 )
8^ = £ ( , + 8[
(2.23)
where:
“ ^0
(2.24)
e; = ^
dr
(2.25)
£e=r
(2.26)
and
We notice that this formulation can be obtained by simply replacing stress ctq by
ar(R) in (2 .20 ) and then replacing ar(R) by the in-plane axisymmetric strains, where
(T^ (R) = cj-(, + cxl (R) is the combination o f the residual stress and the radial component of
stress due to indentation in the attached film at r=R. The validity o f using Or(R) has been
concluded from the previous analytical analysis, which states that the energy release rate
does not depend on the stresses parallel to the crack front.
In the case o f an annular plate, the radial stress ar that drives the delamination is
reduced due to the presence o f the stress behind the crack front.
Thus, Or must be
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
replaced by Aar, which is the radial stress jump across the crack front as indicated in
(2.21). Then replacing A<t^ =a-^(i?)-<T,(i?“)b y the in-plane axisymmetric strains
foro-^ {R) and the expression o f (2-10), the second formulation may be drawn as:
2
(l-v^)Se
2G(l-v^)
Et
e, +vsr
1-
\2
'
UJ
( l - v ) + (l + v)
(2.27)
R
Special attention shall be paid to (2.27); it reduces to (2.19) in the absence o f indentation.
We also notice that the material properties o f E and v in (2.22) and (2.27) are the
properties o f the oxide film or TBC coating with thickness t. In an EB-PVD TBC system,
the energy release rate for a very narrow TBC coating strip left behind the crack front is
2.7 J/m^, by taking the as-processed parameters frequently considered in this study, which
can also be found elsewhere. In an oxide system, i.e., w/o TBC coating on top, G is found
to be 3.7 j W . We see that the energy release rate is much larger for the delamination o f a
single oxide layer than that o f a single TBC coating layer, although the oxide layer is
much thinner, where t is taken to be 0.25 pm as oxide thickness under the as-processed
condition, while the TBC coating is taken to be 100 pm. This simply contributes to the
fact that the residual stress in the oxide is much larger than that in TBC coatings. For
completeness, if consideration is given to the case o f debonding along the interface o f the
oxide (TGO) and the bondcoat layers, under as-processed conditions, the energy release
rate is found to be 3.8 j W
and the toughness Kc is about I.O MPaVm. The related
formulations o f delamination o f a composite layer are going to be detailed in the
subsequent section.
2.3.2 Delamination of a Composite Plate
In EB-PVD TBC systems, delamination often occurs at or near the interface o f the
TGO and bondcoat layers. This is especially true when a specimen experiences a certain
period o f isothermal exposure as detailed in chapter 3. Since the debonded materials
include the top TBC coating and the TGO oxide layer, the delamination is analogous to
23
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
that o f an annular composite plate debonding on a ductile substrate. The total energy
release rate can be expressed as:
G = Gi +G 2
(2.28)
Where, Gi is the energy release rate upon the crack propagation due to the combination of
the effective residual stress and the radial component o f stress caused by the indentation.
G 2 is the energy release rate due to the release o f the elastic energy caused by the resultant
bending moment within the TBC and TGO layers due to the difference in magnitude of
residual stresses in each layer and their thicknesses.
Figure 2.2 illustrates the process o f the total energy release rate formulation. The
original problem is defined as in Figure 2.2(a). Upon indentation, the TBC and TGO
layers buckled up and broken with only a small portion o f a narrow strip left behind the
crack front as is typical. To simplify this problem, the following assumptions still hold:
(1) The overall composite plate thickness constituted by TBC and TGO layers is very
small compared to the indent depth and the other characteristic size o f the indentation
field, so that a ‘local’ condition o f steady-state at the current crack front holds as an
approximation; (2) R/a is large compared to tec/a such that the bondcoat properties are
insignificant; and (3) Indentation induces axisymmetric debonding and buckling with a
very narrow strip left behind the crack front.
Special attention shall be paid to the first assumption, which is essential for the
problem simplification. The essence o f the first assumption is that the debonded top
layers are so thin that they will not deform independently, but follow the deformation of
the substrate. Thus the problem can be finally simplified in such a way that the only
unknown would be the surface field solutions on top o f the bondcoat due to indentation.
A contact FE model constituted only by bondcoat and superalloy substrate layers is then
the only necessity to be solved for the entire problem. How thin would be thin enough for
this assumption to be valid depends on the problem itself. For the currently studied TBC
system, the TBC coating has essentially the same magnitude in thickness as the
indentation depth, however, it will be clear that this problem is essentially dominated by
the TGO thickness as well as its properties, and the TGO layer is in fact much thinner
than the indentation characteristic sizes. Nevertheless, the formulations based on these
24
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
assumptions will be validated through a complete contact fracture finite element model as
will be detailed in subsequent sections.
Indenter
o TBC
Bond Coat
Compressive Stress
Center Line
lastic Zone
Superalloy Substrate
(a) Problem Definition for the Energy Release Rate due to Indentation
in the EB-PVD TBC systems
Indenter
a
eflf
effective
'single la y e r
Compressive Stress
Center Line
Bond Coat
lastic Zone
Superalloy Substrate
(b) Gi Formulation: Energy Release Rate due to the Combination o f the Effective
Residual Stress and Radial Component o f Stress due to Indentation
25
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
Neutral Axis
Center Line
Bond Coat
Superalloy Substrate
(c) G2 Formulation: Energy Release Rate due to Bending Effect
Figure 2.2: Energy Release Rate Formulation due to the Combination o f Residual Stress
and Indentation Induced Stress
The original problem stated in Figure 2.2(a) can be regarded as a combination o f
two problems as shown in Figure 2.2(b) and 2.2(c). The problem stated in Figure 2.2(b) is
equivalent to a single annular plate debonding on a substrate due to the combination of
residual stress and the stress due to indentation. However, the residual stress along with
the associated material properties are now taken as the effective stress and effective
properties defined by Vasinonta and Beuth (2000).
The effective residual stress is defined as:
„ e ff
where,
^
TBC ^ TBC
^
TGO ^ TGO
(2.29)
= ---------------------------C bc L go
and o ^qq are the residual stresses in TBC and TGO layer, respectively
And the effective Young’s modulus is defined as:
_
-^eff ~
E-pbcL bC +ETG0LG0
C bc
(2 .3 0 )
A go
The effective residual strain becomes:
26
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
_ e ff
e ff
_
0 ~
^ 0
(2.31)
^eff
where, E^fj. is defined analogous to (2.30 ), but with E replaced by E :
E=
(2.32)
1- v
The energy release rate for delamination with an unbuckled composite annular
plate left behind the crack tip can be expressed similarly to (2.27), but with thickness
replaced by the total thickness o f the composite plate, and E by the effective Young’s
modulus (Vasinonta and Beuth, 2001).
2‘
2s
( 1 - V )£^ 1 -
R /
2G.(l-v^)
^ eff
TOO
1-TBC )
(2.33)
( l - v ) + (l + v) h
vRy
where R is the radial distance to the crack front (the delamination radius) and R is the
radial extent o f any broken up portions o f the debonded coating.
In eq. (2.33) it is
assumed that there is no Poisson ratio mismatch between the TGO and TBC layers.
Strain values £r and Se are the sum o f the applied strains caused by indentation (which can
be calculated from the plot o f Fig. 2.3 for EB-PVD TBC with as-processed properties)
and the effective residual strains as expressed in (2.31).
For indentation o f the EBPVD TBC systems considered herein, using major loads
in the range o f 60 - 150 kg, debonding without buckling is rare.
In most cases,
delamination is accompanied by axisymmetric buckling o f the debonded TBC and TGO
layers. In fact, for all o f the tests presented in this paper, indented specimens experienced
some amount o f buckling, though in some cases the amount o f lateral displacement o f the
debonded coating was small. In such cases, the energy release rate, Gi, by assuming that
no stress is held in the buckled coating behind the crack front, can be expressed as
follows:
27
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
2G ,(l-v^)
E' e f f V(t'’ T B C “1'" t'- TnG O .
(2.34)
= ( e ^ + v 8 e }2
The other part o f the overall energy release rate is the release o f elastic energy due
to bending effects, as stated in Figure (2.2c). We notice that the contribution to the overall
energy release rate due to bending is independent o f the indentation event. Again, this
contributes to the assumption made above, that the composite plate does not deform
separately.
As for the case o f a very thin TGO layer such as EB-PVD TBC under the asprocessed conditions, the bending contribution, G 2, can be estimated by assuming the
neutral axis to be in the center o f the TBC layer. Under this simplification, G 2 is given by
Vasinonta and Beuth (2001).
3(l-v^)(a
G2 =
)"t"
‘• T G O
TGO
2 (txBC
■ ^TB C /
(2.35)
GgO,)Ei
.'^TBC
However, as the TGO grows thicker, discrepancy is found between the computed
G based on the contact model, and that obtained from the contact fracture model. It was
found that the previous formula overestimates the total energy release rate, G, by an
added extra bending contribution in G 2. To modify G 2 into a correct formulation, the
relocation o f the neutral axis o f the composite plate must be considered. The correct G 2
expression can be derived from formulas presented by Klingbeil and Beuth (1997) with
the following result:
G, =
2F
(2.36)
I
where M is the net moment per unit width from the residual stresses, Ic is the transformed
moment o f inertia per unit width o f the composite plate and the bar designation over E
designates the plane strain modulus E/(l-v^). The moment per unit width is given by
M —OrpQQtjQQ y _ .
■^ tbcG bc
■+ t T G O
(2.37)
and Ic is given by
I
|3
12
E
. -‘•^TGO x3
^TBC
V
^
TBC
‘'T G O
^TBC
‘'T B C
+ t TGO
/
T7
+ ^750 t T G O
^TBC
\2
- _
2
28
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tg o
(2 .3 8 )
Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
where, in both expressions y is the location o f the neutral axis as measured from the base
o f the composite plate, which is given by
-
_
2 E jg p tj0 c l-T G O
tM
ExbC^TBC
t
^ V ^ T B C '-T B C ^
E T G O tT O O
~t
^ T G O ''T G G
,r y
oqn
/)
Figure 2.4 illustrates the effects on the total energy release rate due to the
simplified G 2 by (2.35) and the exact G 2 by (2.36). Note that the total energy release rate
in Figure 2.4 is calculated under as-processed parameters far away from the indentation
region due to (2.28), and is plotted as a function o f TGO thickness. It is further assumed
that the TBC/TGO layers buckled and broke such that the R; effect is negligible, and Gi
can be approximated by (2.34). Since the bending effect on the total energy release rate is
a constant for a certain TGO thickness, and irrelevant to the indentation, this figure gives
us an overall picture o f the bending effects due to the growth o f the TGO layer as well as
the difference caused by using different G 2 formulas. It is clear that the simplified
formulation is only accurate under an as-processed TGO thickness. Significant error may
be introduced after the TGO thickness becomes 0.75pm. At this level o f TGO thickness,
the relative error o f the total energy due to this calculation is ~I2% . However, the neutral
axis relocation is only ~5%, which indicates that a slight relocation o f the neutral axis
may alter the total energy release rate significantly. This is again simply due to the fact
that the residual stress in the TGO layer is much higher than that o f the TBC layer, which
is about 70 times larger in magnitude.
29
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
0.015
d
O
B
D
0
’E
•01
^
Q
60 Kg
100 Kg
150 Kg
0.012
0.009
0.006
'T3
(U
N
0.003
O
0
2
4
6
8
10
12
14
16
Normalized Radial Distance, R/a
Figvire 2.3: U/a vs. R/a due to a Standard Conical Indentation with M ajor Load Levels.
30
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
250
G - G 1+ G
CN
2
Approx-
G “ G i + G 2 Exact
200
h—5
O
clT
150
<L>
VI
cd
100
W)
i-t
<D
50
w
0
0
1
2
4
3
5
TGO Thickness, tioo (iiim)
6
Figure 2.4: Energy Release Rate vs. TGO Thickness for Bending Contribution due to
Different Formulations
31
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7
Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
2.4 Mechanics of Interfacial Cracks
Material //I
Material #2
Figure 2.5 Interface Crack Between Two Isotropic Media
For an interfacial crack between two dissimilar media, shown in Figure 2.5, it
becomes standard practice to use the complex stress intensity factor K to characterize the
severity o f loading near the crack tip. Unlike the case in homogeneous materials, the
stress and strain fields for a plane traction boundary value problem are independent of
elastic constants. For a bi-material interface problem, the stress and strain fields depend
on two dimensionless combinations o f the four material parameters pi, vi and \i2 , V2.
These two dimensionless parameters are known as Dundurs’ parameters, a and p defined
by Dundurs (1969).
a =
Fi(K 2 - 1) - F 2(K, - 1)
(2.40)
P i (k 2 +1) + P2(K i +1)
Where E; = Ei for plane stress and Ej = Ei /(l-v^) for plane strain.
The parameter a is a measure o f the relative stiffness o f the two materials and it
can take values in the range o f -l< a < l, with a = I signifying that material 1 is rigid, and
vice versa. The P parameter does not have a clear physical interpretation, but for
32
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
Poisson’s ratio in the range o f 0<v<l/2, we have -I<a-4P<1, therefore P can be
interpreted as a measure o f the relative compressibility o f the two materials. For the
currently considered TBC system, as the crack along the interface o f the TGO and the
bondcoat layer, under given as-processed parameters, a and P are found to be 0.326 and
0.0596, respectively.
The singular stresses directly ahead o f the crack tip (along 0 = 0) are given by:
K
v
(2.41)
27IX
where K is the complex stress intensity factor and it takes the dimensional form:
K = Ki+ i Ka = f X (stress) x Vh h “”^
(2.42)
Where, f is non-dimensional and, in general, a complex function o f the material
properties and the specimen geometry. The parameter h is the characteristic length o f the
problem. And s is the bi-material mismatch parameter that depends on elastic constants of
the two materials, and can be related to the Dundurs’ parameter p as:
s = -^ In
^ 1 -P ^
(2.43)
+
The near tip relative crack face displacements are related to the interface stress intensity
2ti
factor through the expression (Klingbeil and Beuth 1997):
r\ X
|x|
(1 + 2is) eosh( 7ie)EjE
where 5y =
U y(r,0 = %)- U y(r,0
= -7t) and 5x =
U x (r,0 = ti) - U x (r,0
(2.44)
= -n)
Instead o f using Ki and K 2, linear elastic interfacial fracture mechanics (LEIFM)
characterizes the crack tip loading by two parameters, energy release rate G and phase
angle vj/. Kj and K 2 can be expressed by the opening displacements explicitly from (2.44)
(a -i-2 sb )5 y + (b -2 sa)5 j^
^
C[(a + 28b)" + (b - 2ea)"] '
(a + 2 sb) 6 ^ - ( b - 2 s a ) 5 y
'
C[(a + 2sb)" + (b - 2sa)" ]
(2.45)
where a = cos(sln(r)) and b = sin(8ln(r))
33
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
1/2
4 ( E ,+ E ,)
(2.46)
(l + 4s )cosh(7is)EiE2
We notice that when s=0, a=l and h=0; Ki and K 2 become the classical
expressions, Kj and Kn, in terms o f crack tip opening displacements in homogeneous
materials.
Furthermore, the mode mix can be described by the phase angle o f the quantity Kh'*^ and
defined as:
^ =
(2,47)
[Re(Kh“ )J
where v(/ is defined to be independent o f h, the characteristic length, and can be
considered as a consistent measure o f the ratio o f the shear traction to normal stress
ahead o f the crack tip. Consideration o f equations (2.41) and (2.47) shows that \\j is the
phase angle o f the complex quantity
+ ia,^y minus the phase angle o f the quantity
(x/h)■^
An explicit expression for the mode mix phase angle \\i can be derived as follows:
f(5j + 2 s 52 )cos( 8 ln(h/|x|) + (52 -2 s 5 ,)s in (8 ln (h /|x |)l
VI/ = tan <------------------------------ rn--------------------------------- ^ >
|(5 2 -2 s 5 j)c o s (s ln (h /|x |) - (5i + 2 s 52 )sin( 8 ln(h/|x|)J
(2.48)
The energy release rate can be expressed in terms o f the interface stress intensity factor
(Malyshev and Salganik 1965) as:
G = ---------------------- Ik I'
2 cosh (ti 8)E jE 2
(2.49)
The total energy release rates can be converted to stress intensity factors using the
interfacial fracture toughness relation:
For the TBC systems considered herein, this formula results in the following conversion
between K (in MPaVm) and G (in J/m^):
34
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
K=J—
V3.58
(4.51)
2.5 Finite Element Modeling
2.5.1 Model Description and Validation
The new finite element model for the contact and fracture analysis was established
based on the argument o f the superposition principle. Thus, biaxial residual stresses can
be applied at the two edges o f the model - the inner and outer edge o f the debonded and
buckled annular composite plate. The composite plate includes the composition o f the
TBC and the TGO layers. Residual stresses are present in both layers, but with a much
larger value in the TGO layer such that the resultant bending effect tends to open the
crack. Fig. 2.6 shows the equivalent loading condition o f the distributed load at the edges
o f the composite plate and other boundary eonditions, together with the overall mesh and
model dimensions. The detailed mesh resolutions for the region near to the indenter and
around the erack front are presented in Fig. 2.6 (b) and Fig. 2.6 (c), respectively. The
model is axisymmetric, modeling half o f the TBC specimen coupon, with total elements
o f 23,321, nodes o f 117,384 and the total number o f DOFs, along with the Lagrange
multiplier variables, is 211041. The element chosen is an eight-noded biquadratic reduced
integration, hybrid with linear pressure, i.e., CAX8RH. Considering the incompressibility
in the plastic region, especially just below the contact enshrouding the indenter’s outer
hoimdary, the hybrid element type is used. This type o f element adds the hydrostatic
component o f stress as an additional degree o f freedom to avoid stress generated by the
nearly incompressible plastic deformation around the indenter. Hybrid elements with the
reduced integration are expected to reduce running time and provide more accurate
results.
Attention shall be paid that a contact model is setup prior to this contact fracture
model. This eontact model has the same resolution distribution as the contact fracture
model, except that there are no TGO and TBC layers on top and no focused mesh
throughout. We refer to this contact model as the current contact mode to distinguish it
from the previous one by Vasinonta and Beuth (2001), which we refer to as the standard
35
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
model. Compared to the standard model, the current contact model utilizes the same
element size, thus the same mesh density, at the contact region as the standard one (see
Fig. 2.6 (b); but now the element is biquadratic rather than bilinear. The mesh density
right away from the indentation region is reduced to half the density o f the contact region,
and this mesh resolution is then kept until it passes the crack tip region, where Rj is
labeled the dimension o f the crack tip in Fig. 2.6(a). As the mesh away from the crack tip
region, the mesh resolution is again back to that o f the standard one. The current contact
model was tested and the results o f U/a vs. R/a and K vs. R/a were compared against the
standard model. The results o f R/a vs. R/a and K vs. R/a, from both contact models yield
perfect agreement with each other, though both models are constructed with different
element types and essentially different mesh density distributions.
Based on the validation o f the current contact model, the model for the contact
and fracture analysis was built. The contact and fracture model was built with two
additional layers added onto the top o f the current contact model. The first additional
layer is the TGO layer and the second additional layer is the TBC layer, which is right on
top o f the TGO layer. At the same time, a special spider-web-like focused mesh was
created around the crack tip region. Special attention shall be given to the focused mesh
at the crack tip region. The regular mesh o f the current contact model at the very near
crack tip region is changed to be a focused mesh and the full focused mesh is extended to
half o f the TGO layer, see Fig. 2.6 (c). The width o f the narrow annulus plate left behind
the crack front is taken to be O.IR or, Ri/R=0.9.
Furthermore, the rigid conical indenter is modeled as a constraint on the surface
displacement and enforced with a penalty method. The ABAQUS code uses internally
generated gap elements to determine which nodes are in contaet with the indenter at every
load increment. Friction between the indenter and the substrate, the surface o f the
bondcoat, was modeled with a Coulomb friction law, ort - p an, where p is the friction
coefficient, and at and a„ are the tangential and normal tractions at the contact interface,
respectively. For slipping nodes, this relation is enforced using Lagrange multipliers. The
friction coefficient was taken to be p=0.7, unless otherwise specified. The contact status
is identified as the sticking status. A small sliding formulation is utilized, which gives
36
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
sufficiently accurate contact results under current loading conditions. The contact load is
obtained from the reaction force at the reference point o f the rigid indenter.
The properties used in the contact fi*acture model are the same as in previous
studies by Vasinonta and Beuth (2001) unless otherwise specified. The following gives a
list o f the as-processed EBPVD TBC properties used for those studies:
E tbc“ 44 GPa, txBc~ 100
cttbc”
"50 MPa, Vtbc~ 0.22.
Eoxide= 393 GPa, toxide= 0.25 pm, aoxide= -3.5 GPa, Voxide= 0.22.
We note that the TGO layer thickness considered herein for the contact fracture
model will be investigated within a wide range to reflect the oxide growth effect from the
increase o f exposures, especially in the study o f fracture mode mixity. The plastic
properties o f the PtAl bondcoat and the nickel-based superalloy substrates are the same as
in the previous studies, but the bondcoat with an extreme yield stress, 900MPA, is used.
It is worthwhile to mention that prior to the current contact model, as well as in
the contact and fracture model, there existed another similar contact model, as well as a
contact fracture model, constructed o f 4-noded bilinear elements and with much coarser
resolutions than these formally used 8-noded biquadratic element models. Though that
previous contact model as well as the previous contact and fracture model had a sparser
resolution near the indenter as well in the crack tip region , the difference in U/a and K
vs. R/a between these models was found to be insignifieant. This again verifies that the
mesh resolution is not a critical issue for this contact fracture analysis.
37
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CD
■D
O
Q.
C
oCD
Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
Q.
■CDD
C/)
C/)
oo
■D
cq'
CD
■D
O
Q.
C
a
o
■o
o
Rigid Indenter
3.28 m m
CD
Q.
■CDD
C/)
C/)
u„ = 0
12.7 mm
Figure 2.6 (a): Schematics o f the FEA Model Showing the Global Mesh and the Boundary Conditions
Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
Rigid Indenter
Bondcoat
Layer.
100pm
I N
I I !■ i
Figure 2.6(b): Mesh Near to the Rigid Indenter
39
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
TBC Layer
TGO
Layer
Crack
Boadcoat
Layer
Figure 2.6(c): Focused Mesh at the Crack Tip
Figure 2.6: Finite Element Model Used for the Combined
Indentation and Fracture Analysis
40
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
2.5.2 Stress Intensity Factor K vs. R/a
For the extraction o f the energy release rates from the contact fracture models, the
J integral method was used. Under the framework o f small scale yielding fracture
mechanics, J and G are the same. The values o f the stress intensity factor, K, were
obtained by using (2-50). To ensure that the small scale yielding is still applicable for the
current analysis, two sets o f J values were obtained. One set contains the full elastic
plastic analysis and the other comes from the analysis o f partially elastic and partially
plastic properties applied onto the bondcoat and substrate layers. The partially elastic
plastic model is modeled in such a way that the plastic zone induced by the contact events
are always kept unaltered, while the erack tip region is kept under fully elastic behavior.
The results from these two different models are exactly the same as for the valid region o f
K extraction, which is found to be the region for R/a>~2.5, about the size o f the plastic
zone region induced by the indentation.
Fig. 2.7 provides some representative results o f K vs. R/a. In all cases, Rj/R is
taken to be 0.9, which indicates that a narrow strip left behind the crack front is 10% o f
the initial crack length. The energy release rates were calculated for cases where the TGO
thickness is 4.5 and 7.5 pm, respectively. The computed results shown as smooth curves
were obtained by the formulas (2.28), (2.33) and (2.36), based on the current contact
model. The results o f two thick TGO layers, 4.5 and 7.5 pm, respectively, were compared
with those from the contact fracture model, shown with solid diamonds and solid circles,
respectively. It can be seen that the results due to the complex FEA contact fracture
model are in agreement with the computations from the standard contact model and
formulations.
41
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems
12
Via. Formulas
# 4 Via. Cont.Frac. FEA
10
in'
o
8
O
d
tin
m
(D
-k
C/D
AA
t^QG = 7.50
|Lim
Itg o ^
4.50
|LLm
Itg o =
2.50 |am
t/D
(U
C/3
A—
t r a n = 1 . 0 0 |Um
i-TGo ““ 0.25 jam
0
4
6
8
10
12
14
Normalized Radial Distance, R/a
Figure 2.1 \ Result Comparison for K vs. R/a due to the Formulation with Contact
Analysis and the Fracture and Contact Model with Ri/R=0.9 under As-processed
Properties in the EB-PVD TBC systems.
42
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16
Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
2.5.3 Mode Mixity v|/ vs. R/a
As the TGO thickness increases, fracture mode mix may come into play. When
the TGO layer is very thin, such as in the as-processed cases, at about 0.1~l|j.m, the
debonding is under pure mode II (Begley and et. al. 2000, Vasinonta and Beuth 2001).
However, as the specimen comes under certain thermal exposure, and the TGO thickness
grows, the mode mix should be more carefully considered. In EB-PVD TBC systems
under isothermal exposure, the mode mixity mainly depends on how thick the TGO layer
can grow under the fixed thickness o f the TBC layer. However, the TGO thickness at its
failure was reported quite differently according to different investigators. According to
the most recent results as reported by Chang (2001), TGO thickness can be grown to
~15|j.m before it fails under isothermal exposure conditions, while it may fail before 5pm
under cyclic exposure. In recent studies, it was found the failure o f the TGO thickness
was barely over 7 pm (Pettit and Meier, private communication).
To accurately capture \)/, the elastic behavior around the crack tip region, the
partially elastic plastic model was used to ensure that the SSY assumptions were valid.
Nevertheless, the difference in the \\i values between the results o f the fully elastic plastic
model and the partially elastic plastic models were found to be insignificant. Furthermore,
penetration was allowed for pure mode II evaluations such that the phase angle was
allowed to be less than -90°.
The procedures for obtaining the phase angle \|/ can be described as follows. At
each node point located at a distance |x| behind the crack tip, the relative crack face
displacements are extracted from the finite element solution, and the interface stress
intensity factor is computed using equation (2.45). The energy release rate is then
calculated using eq. (2.49) and compared to independent J-integral estimates for G. The
phase angle,!]/, is then evaluated using eq. (2.48) at the distance |x| where the values o f G
obtained from the crack face displacements most closely match the J-integral estimates.
The differences between these two Gs are usually within less than 1%. In some cases it
may be even more than 10%. Nevertheless, it was found that the phase angle values were
43
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
very insensitive to the different values o f G calculated, compared to that obtained through
the J integral.
Some representative results o f \\i vs. R/a solved for TGO thickness 4.5 pm and
7.5pm, respectively, are presented in Figure 2.8. Due to the coordinate setup o f the FEA
modeling, Vu is a negative value. If Vv is also negative, which indicates pure mode II,
then the phase angle will be in the third quadrant in the KII vs. KI coordinate, having a vj;
larger than 90 degrees in absolute value. From the Figure presented here, there is indeed
pure mode II only for the TGO thickness less than or equal to 4.5 pm. This can also be
seen by taking a look at the differences in the output displacements in the y direction, Vv,
which are all negative values behind the crack front.
For the case o f the TGO layer thickness o f 7.5 pm, it was found that the phase
angle was about -90“ for R/a>10, indicating also mode II. However, after a more careful
check, one may find that there is a slight opening behind the crack front, which is
indicated by the difference in the output displacements in the y direction, Vv, which are
now all positive values behind the crack front. How can this be? The problem is that the
formulation for the \|/ calculation at the interface o f two different materials involves a
characteristic length, h, and the bi-material mismatch parameter, s. This characteristic
length, h, sometimes, may complieate the interpretations o f
In faet, if we take a
sufficiently small value o f h, for example, let h =0.25 pm instead o f 7.5pm, \\j would be 89“. Another extreme to be considered is that when the bi-material mismatch parameter,
E,
is disregarded, then the mixity becomes that for an interface o f a single material. The
above equation, (2-48), becomes:
i(/ = t a n - ' | | k |
(2.52)
Then, the largest phase angle,v(/, is about -87“. This indicates that at the most, the
possibility o f having mode mix is negligibly small.
These results agree with the widely held opinion that there is only pure mode II
crack propagation in TBC systems, Hutchinson [1996], Mumm and Evans [2000], based
on the fact o f a thin TGO layer and rough calculations. This fact indicates that the
44
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Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
residual stress mismatch between TGO and TBC layers are not big enough to open the
crack and promote mixed mode crack propagation although the induced bending is not a
negligible effect on the calculations o f the energy release rate.
10
8
12
14
0
tiGo = 4.50 |rm
-20
^
Itg o ~
7 . 5 0 )L ir r i
-40
"S)
c
C
<u
CO
cd
Valid ^
-60
-80
Ph
-100
-120
-140
Normalized Radial Distance, R/a
Figure 2.8: Phase Angle,i|;, vs. R/a Using As-processed Properties with
Two Oxide Thickness Obtained From Numerical Solutions.
45
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16
Chapter 2. Fracture Analysis o f Indentation Tests in EB-PVD TBC Systems ________________
2.6 Chapter Summary
A more thorough fracture analysis o f the indentation test considered by Vasinonta
and Beuth (2001) was performed in this study. The energy release rate o f an aimular plate
delamination on a substrate was derived analytically due to the presence o f equi-biaxial
stresses. The derived results confirm that the energy release rate o f an annular plate
debonding on a substrate is independent o f the stress parallel to the erack front, regardless
o f whether the strip is narrow or not. Under the condition o f buckled TBC due to
indentation, complete formulation o f the energy release rate with grown TGO thickness
was presented, and it was found that the simplified energy release rate formula presented
in the previous study due to the bending effect can give enough accuracy as long as the
TGO layer grows less than 0.75 mm. However, significant errors may be introduced with
a TGO layer thickness larger than the as-processed thicknesses. A eomplete formulation
on the energy release rate considering the bending effects was then given to correct the
previous formulation without consideration o f the neutral axis relocation due to the
variation o f the TGO thickness.
A contact and fracture FE model was setup for the full consideration o f materials
and characteristic dimensions in the EB-PVD TBC systems. It was found that the energy
release rate agrees well with that due to the contact modeling, with the calculations o f the
energy release rate formulations considering the exact bending energy release rate
contribution formulation for the case o f a sufficiently narrow strip left behind the crack
front. At the same time, the formulation with simplified bending eontributing to the total
energy release rate, overestimates the overall energy release rate signifieantly as the TGO
layer grows. This validates the essential assumption made that the formulation o f the total
energy release rate still holds such that the characteristic indentation size can be regarded
to be much larger than the coating thicknesses in the application o f conical indentation
tests on the quantification o f interfacial fracture toughness in the EB-PVD TBC systems.
Furthermore, the mode mixity investigation reveals that mode II craeking dominates for
practical oxide thicknesses in EB-PVD TBC systems.
46
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Chapter 3. Application o f Conical Indentation Tests
CHAPTER 3. APPLICATION OF
CONICAL INDENTATION
TESTS
3.1 Chapter Overview
This chapter addresses the topics of the application of the conical indentation
method presented in the previous chapter. Before presenting the details of the application
topics, the effect of indentation unloading has been first addressed. The consideration of
indentation unloading makes the evaluation of the interfacial toughness more complete
since the whole process of the indentation tests, i.e., loading and unloading, is now
included. Following this, three topics have been studied with an introduction at the
beginning of each topic to detail its background and address its research scope. The first
topic of this chapter is on the tracking of apparent interfacial toughness loss with thermal
exposure times under different isothermal exposure temperatures. Models based on
thermally activated mechanisms for predicting the oxide thickness, sintering rate in the
TBC coating layer will be presented to serve the lifetime prediction model of the TBC
systems. The Arrhenius relation will be provided for the benefit of the accelerated testing
methodology. Mechanisms that contribute to the interfacial toughness degradation will be
addressed and analyzed quantitatively on their importance to the toughness degradation.
The second topic addresses the effect of water vapor on the toughness
degradation. Initially, it is not known if the presence of water vapor may affect the
toughness significantly in the presently involved TBC systems, though the literature is
rich regarding how the presence of water vapor may significantly affect the lifetime of
many kinds of alloys and ceramics. Recent studies on bare alumina on top of nickel
superalloys also show that water vapor may significantly reduce the lifetime for some
kinds while it has no effect on others (Janakiraman et al., 1999). However, it remains an
unknown if water vapor affects the durability of the EB-PVD TBC systems. Based on this
need, two sets of specimens were exposed and studied with the second set of specimens
designed to have exposures under different conditions for comparison while their initial
47
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Chapter 3. Application o f Conical Indentation Tests
conditions are comparable. Furthermore, details o f the micro structures o f each specimen
in a different exposure environment will be scrutinized to further the details on the effect
o f the presence o f water vapor.
The third topic addresses the toughness degradation under cyclic thermal
exposures. In this part, the non-destructive methods are used to improve the indentation
toughness measurement techniques. Among these non-destructive methods, the optical
backscatter imaging technique served as an accurate means for the quantification o f the
oxide debonds. The piezospectroscopy method has been used to track the stresses in the
oxide layer with the increase o f the exposure times. The stresses measured at each
exposure time can thus be integrated with the toughness mathematical models for a better
understanding o f the toughness degradation. And furthermore, by integrating the in-situ
measured values at each exposure, true interfacial toughness may be provided more
accurately, and micro-failure at the interface may be quantitatively given before the
spontaneous spallation occurs.
Throughout this research, multiple indentations at the same location and multiple
indentations within a single specimen at different locations are utilized by acknowledging
that the debond size is small and the indent induced strain field is confined within a small
region such that the edge effects can be ignored. This technique is very important for this
study so that many toughness values may be generated after each exposure within a single
specimen and the analysis may thus be based on as many research values as possible.
Moreover, all the specimens for the mechanism-based studies are EB-PVD
TBC/PtAl types with heavy grit blast at the bond coat surface before prior to the TBC
application. Figure 3.1 provides a sectioned micrograph o f an as-processed EB-PVD/PtAl
TBC system. Although the current work is applicable to other TBC systems, all o f the
experimental results presented in the subsequent sections relate to this type o f TBC
system.
48
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Chapter 3. Application o f Conical Indentation Tests
I
m
Figure 3.1: A Sectioned SEM Micrograph of an As-Processed EB-PVD TBC System
3.2 Effects of Unloading on Indentation-Induced Stress Intensity
Factors
This section addresses the effects of unloading on stress intensity factor values for
the conical indentation test considered in Chapter 2.
As discussed previously, the
mechanism leading to indentation-induced debonding is plastic deformation caused by
indenter penetration. Indentation of an elastic-plastic substrate leads to large-scale plastic
deformation beneath and around the indenter. This plastic deformation induces
compressive radial strains away from the indentation region on the substrate surface.
However, the process of the indentation includes loading and unloading, and the
unloading step acts to increase (slightly) the compressive radial strains on the substrate
surface. The result is an increase in the stress intensity factor at a given location on the
specimen surface.
Although indentation on a metal or metal alloy substrate causes much more plastic
deformation than elastic deformation, the amount of the elastic recovery upon unloading
may not be negligible. For a specified applied load, the significance of unloading depends
on the substrate material properties, especially the elastic modulus yield stress and initial
yield strain (Begley et al., 1999). In existing work quantifying the interfacial toughness in
thermal barrier coating systems (Vasinonta and Beuth, 2001; Handoko et a l, 2001;
Begley et a l, 2000; Mumm and Evans, 2000) unloading effects are not considered. In this
49
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Chapter 3. Application o f Conical Indentation Tests
section, it will be shown that unloading effects for the currently considered EB-PVD TBC
system are not substantial, but they are significant enough to justify their inclusion in K
vs. R/a curves used to extract interfacial toughness values from tests.
3.2.1 Unloading on a Homogeneous Substrate
The surface displacements outside the eontact region (r>a) due to an elastic
conical indentation or an elastic spherical indentation of a single-material substrate can be
approximated using the solution for a concentrated force on a homogeneous half-space
(Boussinesq, 1885). Conversely, the elastic unloading displacements after elastic-plastic
indentation can be described by the same solution with the sign of the load reversed:
u U ^ (l-2v)(l + v)P
2tiE
r
In eq. (3.1), a is the elastic-plastic contact radius, P is the maximum applied indentation
load and r is the distance away from the indentation center on the surface. E and v are the
elastic modulus and Poisson’s ratio of the homogeneous substrate. For indentation tests
on TBC systems with an indentation depth large enough to make results insensitive to
bond coat properties, it is reasonable to use E and v of the N5 substrate. Later in this
section it will be shown that this approach yields acceptable results.
It has been demonstrated that for conical indentation of TBC systems with
indentation depths large enough to make results insensitive to bond coat properties, plots
of K (or Kc) vs. R/a are essentially load-independent. A natural question is whether or
not this property will be preserved when unloading effects are added. The properties of
the Boussinesq solution suggest that it will. Plots of K vs. R/a for elastic-plastic loading
and elastic unloading are superimposed using the eontact radius, a, from the elasticplastic indentation simulation to generate both plots. It will be shown in Chapter 4 that
during the elastic-plastic loading step, the applied load, P, is approximately proportional
to a^. As a result, if the load is increased by a factor of 2, the contact radius, a, is
increased by a factor o i ^ f l . The Boussinesq solution has the property that stresses and
strains are proportional to P/r^. Thus doubling the load will double the strains, but when
they are evaluated at the same value of r/a (where a is from the elastic-plastic solution), r
50
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Chapter 3. Application o f Conical Indentation Tests
is increased by a factor Q^^[2. As a result, the strain value is unchanged. Thus, the
important features of self-similarity and load-independence for conical indentation are
expected to hold even when unloading effects are included.
Figure 3.1 provides a plot of K vs. R/a for a homogeneous substrate including
unloading effects, with different approaches used to model the unloading step. In the
plot, the thick solid curve labeled “LU Simulation” represents the stress intensity factor
vs. the normalized distance directly extracted from a finite element model of the complete
elastic-plastic loading and unloading (LU) process. The computational method used is the
built-in algorithm of the contact unloading analysis available in the finite element
package ABAQUS. The thin solid curve is for results obtained by superimposing K
values from the elastic-plastic indentation (at a load level of 150 kg) and the K values
from an elastic finite element contact analysis with the same load level. The thin, dashed
line represents the results obtained by superimposing K values from the finite element
elastic-plastic indentation model and those from the Boussinesq solution. The dotted
curve shows the results of K vs. R/a, which are the results due to loading only. The
properties used for the simulations are the same as for the N5 substrate of a standard EB­
PVD TBC specimen as listed in Appendix I. The model size considered herein is also the
standard TBC specimen size.
As the plot in Fig. 3.1 indicates, the three methods for including unloading effects
yield approximately the same results for R/a > 2.5, and they are larger in magnitude than
the results due to loading only. This plot suggests that the standard-sized TBC specimen
is sufficiently large to be considered as a half space for the evaluation of stress intensity
factors due to unloading. As will be seen in the next subsection, the difference between
the results of the loading-unloading and the loading only cases are not substantially
different when the bondcoat layer is included in the analysis.
51
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Chapter 3. Application o f Conical Indentation Tests
150Kg LU FEA
150Kg superposition
150Kg superBoussi
150Kg loading Only
5
Vh
o>
o
c:i
c/3
C
(D
c /3
C /3
(D
!-h
■I— >
00
4
6
8
10
12
14
16
Normalized Radial Distance, R/a
Figure 3.2.1: Kivu vs. R/a due to a Standard Conical Indentation on a Homogeneous
Substrate Including Unloading Effects
52
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Chapter 3. Application o f Conical Indentation Tests
3.2.2 Unloading Effects for a PtAl/N5 TBC Specimen
To capture the effects of unloading for the indentation of a standard
bondcoat/substrate system, a series of simulations have been carried out analogous to
those performed for a homogeneous substrate.
For the case of superposition of the
Boussinesq solution to model the strains from unloading, a choice must be made of what
elastic material properties to use (those of the substrate or those of the bondcoat).
Because the indentation test is designed to be used in cases where the indentation depth is
large enough that the substrate properties dominate the mechanical behavior, substrate
properties will be used to simulate the unloading step.
Figure 3.2 presents the results of K vs. R/a for conical indentation on a standard
PtAl bondcoat/N5 substrate system with properties used listed in Appendix I. In this plot,
each line type is used two times representing the loading results at levels of 60 kg and 150
kg. Analogous to the previous plot for the indentation on a homogenous substrate, the
thick solid curve labeled “LU Simulation” represents the results directly extracted from a
finite element model of the complete elastic-plastic loading and unloading (LU) process.
The thin solid curve is for results obtained by superposing K values from the elasticplastic indentation and the K values from an elastic finite element contact analysis. The
thin, dashed line represents the results obtained by superposing K values from the finite
element elastic-plastic indentation model and those from the Boussinesq solution. The
dotted curves show the results of K vs. R/a, which are the results due to loading only. The
“Loading Only” curves are the same as those presented for an oxide thickness of 0.25
microns in chapter 2, Fig. 2.7 and are due to indentation loading only.
This plot
demonstrates several important points. First, it is clear that the feature of self-similarity
apparent in the “Loading Only” curves is maintained when the unloading strains are
included (as expected based on arguments for a homogeneous substrate). Second, it is
clear that results from superposition of either elastic finite element results or the
Boussinesq solution agree well with those results from the full loading/unloading finite
element simulations. The relatively small difference between the curves is primarily due
to differences in the near-indent geometry between the elastic-plastic indentation problem
and the elastic solutions used for the superposition results. Overall, the results with the
53
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Chapter 3. Application o f Conical Indentation Tests
bond coat included agree well with the results obtained for a homogeneous N5 substrate
for values of R/a>3.
7
~ LU Simulation
- Superposition
■Superposition by (3.1)
Loading Only
6
Ph
J
O
o
Ph
(/]
C
CO
CO
00
5
4
3
2
1
0
4
6
8
10
12
14
16
Normalized Radial Distance, R/a
Figure 3.2.2: K ivu v s . R/a due to a Standard Conical Indentation with Major Load Levels
Including Unloading Effects
54
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Chapter 3. Application o f Conical Indentation Tests
3.3 Mechanism-Based Tests for Isothermal Dry Air Exposures
3.3.1 Introduction
The rate of alumina scale growth depends on the supply of A1 and O 2 atoms at the
alumina/metal interface. For the case of the partially stabilized zirconia (PSZ) EB-PVD
TBC deposited onto a PtAl bond coat, the outward diffusion of A1 from the bond coat and
the inward diffusion of oxygen through the PSZ result in the formation and growth of the
TGO layer (Chang et a l, 2001). Under ideal conditions, the growth of a pure a-alumina
scale with increasing exposure time obeys a parabolic kinetic law, meaning the scale
thickness is a linear function of the square root of the exposure time. The growth of the
TGO layer has been identified as an important mechanism for high-temperature EB-PVD
TBC exposures (Begley et al, 2000; Vasinonta and Beuth, 2001; Handoko et al, 2001;
Mumm and Evans, 2000; Evans et al, 2000). Other mechanisms potentially contributing
to TBC and alumina spallation include TBC sintering, which causes the TBC layer to
become stiffer and more highly stressed; segregation of elements to the TGO/bond coat
interface, and the development of mechanical damage at the TGO/bond coat interface.
These two final mechanisms lead to a true loss of toughness at the interface. The
mechanisms of oxide growth and TBC sintering do not affect the interface, but instead
provide more elastic energy to drive debonding of the TBC and TGO, leading to an
“apparent” loss of interfacial toughness.
For increasing exposure times, actual or apparent reductions in the TGO/bond
coat interfacial toughness are manifested through increases in the debond radii caused by
indentation. Through the use of an accurate model of the indentation problem and
LEIFM, debond radii can be used to determine the interfacial toughness. In other words,
regardless of the mechanism leading to apparent toughness loss, the fracture mechanics
analysis of the indentation test developed previously (Vasinonta and Beuth 2001) allows
the determination of an interfacial toughness for the interface between the TGO and bond
coat layers based on a measured debonded radius. In research described herein, constant,
as-processed properties of the TBC system are used in the fracture mechanics
calculations, not accounting for the effects of TGO growth or potential TBC stiffness and
stress increases due to sintering. Because non-interfacial changes in the EB-PVD TBC
55
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Chapter 3. Application o f Conical Indentation Tests
system can result in a measured reduction in toughness, measured toughness losses are
referred to as “apparent” losses of toughness.
3.3.2 Toughness Loss vs. Isothermal Exposure Time in Dry Air
Figure 3.3.1 provides a plot of measured apparent toughness values vs. exposure
time under dry air conditions at isothermal exposure temperatures of 1200”C, 1135‘’C and
1100“C. The curves shown in the figure are drawn by hand to show trends for apparent
toughness degradation with time at a certain exposure temperature. Apparent toughness
values were determined from room temperature indent tests. The as-processed toughness
value, taken to be 4.3 MPaVm in the plot, was determined by averaging values obtained
from two GE specimens designated by the two upper hollow rectangles. In Fig. 3.3.1, the
times of 60, 500 and 1000 hours are approximate times for spontaneous spallation at
temperatures of 1200°C, 1135“C and 1100“C, respectively. At such times, the apparent
interfacial fracture toughness matches the applied stress intensity factor due to thermal
strains alone, which is approximately equal to 1.0 MPaVm. This experimental data, which
was developed by Roy Handoko as part of his Masters thesis at Carnegie Mellon, is the
first data of this type available for EB-PVD TBC systems. It indicates that substantial
toughness loss occurs at a fraction of the time needed for spontaneous failure to occur at a
certain exposure temperature. One consequence of this finding is that it may be possible
to use measurements of toughness losses for short exposure times to infer the TBC
system’s life. In other words, it may be possible to use toughness losses measured at early
times as an accelerated test method for evaluating TBC system endurance because early
toughness losses are now correlated with the EB-PVD TBC system’s life.
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Chapter 3. Application o f Conical Indentation Tests
1200 C
^1135C
1100 C
□ As-Processed
■- TBC Fails
A
o - £ . _ ....
60 hrs
(1200‘’C)
500 hrs
(1135"C)
1000 hrs
(1100°C)
0
0
100
200
300
400
500
Exposure Time (hrs)
600
700
Figure 3.3.1: Apparent Toughness as a Function of Exposure Time for TBC Systems at
Various Temperatures
57
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Chapter 3. Application o f Conical Indentation Tests
3.3.3 Measurements and Model of Oxide Thickening
If the oxide growth is controlled by diffusion in the oxide, and the thickness of the
oxide layer is sufficiently large, then the growth of the aluminum scale obeys the
parabolic kinetic law with the increase of exposure time; which provides a linear
relationship between the alumina scale thickness and the square root of exposure time
such that the oxide thickness can be expressed as follows:
t=. ^
+b
(3.3.1)
where, t is the oxide thickness in m, kp is the parabolic rate constant in m^/s, and b is the
initial oxide thickness. However, it is observed that the growth of the early stage is not
stabilized and the parabolic kinetic growth rule may NOT be applied to the early oxide
growth, therefore b can be taken as an arbitrary value regardless of the true as-processed
oxide thicknesses for this study. By virtue of other trusted experimental data taken from
the early exposure history, the oxide known as TGO thickness, b is thus determined from
the linear correlation by the least squares method and then b is obtained by extrapolating
the correlation. Care shall be taken that we are pursuing the proposed formulation through
(3.3.1) for capturing the growth kinetics of alumina oxidation on the PtAl bondcoat with
a TBC on top at certain exposure from its as-processed state. Therefore, the oxide growth
during the EB-PVD fabrication is not a concern therein. This is reflected through the term
b in the (3.3.1) formula. Therefore the time t in (3.3.1) refers to the thermal exposure time
excluding the as-processed thermal history.
On another aspect, the oxide thickening and its growth rate are greatly affected by
temperature. The relationship between the parabolic rate constant, kp, and the temperature
can be expressed in such a way that the parabolic rate constant can be related to
temperature by an Arrhenius equation:
k p = c e “’^“*'^
(3.3.2)
Where c is a proportionality constant to be determined. R is the gas constant: R=
8.315J/mol.K, Ea is an apparent activation energy: J/mol, which plays the reaction energy
barrier of the formation of oxide. The activation energy Ea is regarded independent of
temperature, which can be determined through experimental data. We observe that the
58
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Chapter 3. Application o f Conical Indentation Tests
activation energy remains as a constant indicating that the material activation energy is
relatively stable even though the oxide may grow and properties o f the TBC and TGO
layers may have some changes during thermal oxidation. In fact, the oxide thickness does
not affect the activation energy, which is the product o f the negative o f the slope o f the
Arrhenius plot and the real gas constant.
From the experimental results o f currently studied cases and those o f Walter et al
(2001) and Chang et al. (2001), due to the observation o f the unstable oxide growth at the
early stage o f the exposure time, it is found reasonable to have the first data, which was
obtained at its as-processed state, excluded for the 1100°C and 1200°C. Also for 1100°C,
the oxide thickness at 500 hours is due to currently tested experimental results and all
other data are taken from other sources (Walter et al, 2001; Chang et a l, 2001).
Furthermore, it is observed that there is an intermixed zone region, taking about 1pm in
thickness o f oxide for all 1200°C data with close properties (including density) to the
TGO layer. Although an intermixed zone is also sometimes observed at lower
temperature oxidation (including 1100°C exposure cases), it is much less in the currently
tested specimens at 1100°C. Therefore, the intermixed zone is considered only for the
oxidation at 1200°C with the properties taken to be the same as the TGO layer.
Figure 3.3.2 plots the experimental measured values o f TGO thicknesses and the
correlated results due to the least squares rule. We notice that the extrapolated initial
value o f the oxide thickness for both 1100°C and 1200°C is taken as b = 9.95E-7 m. The
parabolic rate constants, kpi and kp2, are 4.84E-18 m^/s and 6.68E-17 m^/s. For 1100°C,
the rate constant is very close to 2.1E-9 m/Vs (Chang et a l, 2001) (corresponding to
4.31E-18 m^/s) and less than 1.4E-17 mVs (Walter et a l, 2000) for the growth o f pure
alumina from the oxygen-controlled reactions with aluminum. The higher temperature
makes the rate constant much higher, as we see that there is about a factor o f 14 for the
ratio o f the parabolic rate constant for 1200°C and for 1100°C. This indicates that
temperature is the main control factor. As the temperature increases, the reaction and
transportation o f atoms are all going to be faster which results in the parabolic rate
constant being much higher than the lower temperature may activate.
59
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Chapter 3. Application o f Conical Indentation Tests
14
A 1100°C
• 1200°C
12
- - 1200°C, Least Square, R=0.98
rGO 10
1100°C, Least Square, R -0.99
(D
!=l
8
S
O
H
0
0
0
200
400
600
800
1000
1200
1400
Vsecond
Figure 3.3.2: Least Square Correlation of TGO Thickness (|am) vs. Square Root of
Exposure Time (s)
60
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Chapter 3. Application o f Conical Indentation Tests
The Arrhenius activation energy, Ea, and the preexponential constant, c, can be
determined from (3.3.2) by considering two known rate constants of kp from above at two
different temperatures, 1100°C and 1200°C, respectively. Here we give the results as:
c s 0.306 m/Vs and Ea = 442 KJ/mol.
This activation energy is found in excellent agreement compared to the value of
452KJ/mol, which is the activation energy for grain boundary diffusion of oxygen in an
aluminum oxide (Mistier and Coble, 1974). Care must be taken on the method of
obtaining these two constants, Ea and c. They are only based on the two sets of
experimental results at two different temperatures, 1100°C and 1200°C, respectively.
This limitation keeps us from being able to do a better job of obtaining the activation
energy by fitting more values into the least squares rule. Nevertheless, the author has also
attempted to add other results of the oxide thickness as a function of exposure time at
1150°C from Walter et al. (2000). Those results at 1150°C are not from the experimental
tests, but predicted values based on the oxide thickening model by W alter et al. (2000)
based on the experimental results at 1100°C. By adding these results, three parabolic rate
constants, kpi, kp2, and kps, are obtained at three different temperatures of 1100°C,
1150°C and 1200°C, respectively. Then the activation energy obtained is 444KJ/mol,
which is very close to 442KJ/mol without considering the values at 1150°C. Therefore,
we see the activation energy determined from the two sets of experimental results at
1100°C and 1200°C can be considered valid results.
Figure 3.3.3 provides a plot of the oxide growth (pm) vs. exposure time (hours)
under a constant isothermal temperature predicted by (3.3.1) and (3.3.2). Agreement of
the predictions with the experimental results is obvious for the cases under the exposure
condition of 1100°C and 1200°C. It would be better and provide more confirmations if
we have more experimental results for the exposure time between 10 to 500 hours at the
exposure temperature of 1100°C. The 1200°C predicted results are essentially sufficiently
accurate since the specimen will fail under a short exposure time. The relationship
modeled by (3.3.1) and (3.3.2) can be used to predict isothermal oxide TGO layer growth
thickness as a function of the thermal exposure temperature and duration length. These
61
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Chapter 3. Application o f Conical Indentation Tests
predicted results may then be integrated in other models to determine the TBC lifetime or
toughness predictions.
However, care shall be taken on the application o f the simple parabolic oxide
growth model. The growth o f an oxide scale is a rather complicated process, which means
that it is not always easy to describe by a parabolic growth relation. Additionally, the
definition o f a single oxide thickness is a gross simplification since the thickness varies a
lot on a single specimen for a single exposure time. The complexity o f the oxide growth
and other factors will ultimately dictate the accuracy o f the model. Nevertheless, our goal
is to obtain some estimates o f oxide growth rates in order to quantify the relative role of
oxide growth on TBC apparent toughness loss. From this aspect, the parabolic model,
which is based on the experimental measurements o f the oxide thickness at each exposure
time and temperature, is significant.
62
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Chapter 3. Application o f Conical Indentation Tests
6
(/3
Exp.llOO°C
1000°C
1100°C
1200°C
5
<U
c
•1o—<
4
H
O
O
H
3
• E xp.l200°C
- - 1050°C
— 1135°C
2
1
0
100
200
300
400
500
Exposure time (hrs)
600
Figure 3.3.3; Oxide Thickness vs. Exposure Time between the Measurement and
Model Prediction
63
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700
Chapter 3. Application of Conical Indentation Tests
3.3.4 Measurements and Model of TBC Stiffness Modulus Due to Sintering
The sintering effects on the TBC modulus can be modeled by considering the
TBC columns as fibers and the porous space as the matrix. To simplify the analysis, the
rule of mixtures (ROM) formula (Barbero,1999) can be applied to obtain an effective
modulus of the TBC columnar structure in the longitudinal direction. Since the stiffness
of the porous space is zero, the effective stiffness in the columnar direction is linearly
related to the volume fraction and the fully densified TBC stiffness as
Ei=Vf*Ef
(3.3.3)
Where, Vf is the columnar volume density, Ei is the effective stiffness and Ef is the
stiffness of the TBC when it is fully densified. In this study, the fully densified TBC
modulus is taken to be 175GPa, which is slightly lower than the bulk modulus of Zr 02
(-200GPA) and consistent with the value of the plasma sprayed thermal barrier coating
after lOOhrs exposure in an air atmosphere at 1100°C reported by Siebert et a/.(1999).
In fact, the effective modulus along the longitudinal direction of the fiber based on
the assumptions of the ROM provides the upper bound for modulus vs. volume fraction
for a “composite” of two constituents (Siebert et al., 1999). Nevertheless, we are making
these assumptions only to approximate the stiffness changes with time and temperature.
Therefore, once the initial modulus and the fully densified modulus are properly
determined, as an approximation, the modulus from this model is acceptable for the study
of identifying the main mechanisms of the TBC life degradation.
To predict the TBC modulus with sintering temperature and time, the relationship
between the TBC columnar volume density and the sintering parameters remains to be
discovered. Although the voids in the columns of an EB-PVD TBC may actually grow in
size with exposure, the spaces between the columns do “heal” or fuse together. For the
simplicity of analysis, we assume that the void type porosity is not significant. In the
studies of sintering behavior of Atmospheric Plasma Spraying (APS) zirconia thermal
coating by Itoh et al. (1998,1999), it was found that the TBC shrinkage obeys an
Arrhenius relation. In another more recent study, it is accepted that the change of porosity
in Zr0 2 -Smol% Y 2O 3 powder compact with sintering temperature obeys an Arrhenius
relation (Sen et al., 2003). We hereby assume that, in this study for the EB-PVD TBC, the
64
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Chapter 3. Application o f Conical Indentation Tests
change o f the coating columnar density with the sintering temperature also follows an
Arrhenius relation. Therefore, the change o f the TBC effective modulus with the sintering
temperature must also follow an Arrhenius relation.
Furthermore, the studies by Itoh et al. (1998, 1999) show that the linear shrinkage
in the APS TBC followed a 2/5 power time law. However, to the best knowledge o f the
author, there is no experimental data regarding the relationship between the stiffness
modulus and sintering time in EB-PVD TBC systems. Therefore, to be simple and
consistent with the modeling o f oxide thickening, the stiffness modulus is assumed to
follow a P2 power time law as an approximation.
From the arguments we just made, similar to the previous section, now we may
propose a linear relationship between the stiffness modulus and the square root o f
exposure time with the sintering rate, Ks being expressed through an Arrhenius relation
following the thermally activated mechanism. Thus the TBC modulus as a function of
exposure time and temperature can be modeled as:
E = Vk ^ + E o
(3.3.4)
and
(3.3.5)
= Co
From the experimental observation, we assume that the TBC will be fully densified at
1100°C after about lOOOhours, and 1200°C after about 56 hours. The TBC stiffness
modulus in the as-processed state is taken to be 44GPa as always in this study and
175GPa at its full densification as mentioned previously.
By recognizing the rate
constants, Ks, at each temperature o f 1100°C, and 1200°C, can be determined in the same
marmer as developed in the previous section. Then it follows that the full relationship o f
E as a function o f T and t can be thus determined. Here we provide the final results for
the constants in (3.3.4) and (3.3.5).
co= 1.32E+16 GPa^/s, Q=485 KJ/mol and Eo=44GPa.
Again only two sets o f modulus values at each temperature o f 1100°C, and 1200°C are
used for the determination o f the constants. However if we include the assumed values at
1135°C, i.e., the TBC is considered to be fully densified at 500hrs, by providing a plot of
Ln(Ks) vs. the reciprocal o f temperature 1/T(K) at the three temperatures, the Q value was
65
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Chapter 3. Application o f Conical Indentation Tests
found to be 482KJ/mol, which is about the same compared to the results due to the two
data points only.
Figure 3.3.4 provides a plot for the predicted modulus results from (3.3.4-5) due
to sintering effects as a function of exposure time at a specified temperature. From this
plot, we see that the exposure temperature is the most important factor on the control of
TBC densification from the indication of the stiffness modulus with the increase of
exposure history.
200
c3
CL.
160
W
t/T
3
'T3
O
120
c/5
‘'CJD
C
o
80
40
1050°C
1200°C
0
0
200
400
600
800
Exposure Time (hrs)
1000
Figure 3.3.4: Young’s Modulus of EBPVD TBC vs. Thermal Exposure Time (hr) based
on Thermally Activated Mechanisms Considering As-Processed E to be
44GPa and 175GPa in Fully Densed Condition
66
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Chapter 3. Application o f Conical Indentation Tests
As is well known, the stresses in the oxidation layer (TGO), and the TBC layer are
developed due to the mismatch of the thermal expansion coefficient (TEC) upon thermal
cooling. Although some growth stress in TGO can also be expected, its role is
insignificant. Therefore, the equi-biaxial compressive stresses developed in the TBC and
the TGO layer can generally be evaluated by a simple formula (Vasinonta and Beuth,
2001; Sarioglu et a l, 2000) and the calculated results are found to be in good agreement
with the experimental tests (Johnson et al., 1998; Sarioglu et a l, 1997; Lipkin et a l, 1996
and 1997) under isothermal exposure conditions. The simplified formula is given as
follows:
Of = - { a , - a J ( T - T j
(3.3.6)
where ttf and as are the linear thermal expansion coefficients of the film (either TBC or
TGO for this study) and substrate, respectively, Ef and v are the film modulus and
Poisson’s ratio, respectively, T is the current temperature, and To is the initial temperature
at which the film and substrate were in a stress-free state.
To accomplish the evaluation of the contribution of each mechanism to the
toughness degradation, which will be detailed in the next section, the TGO thickness, the
sintered TBC stiffness modulus and stresses must be first modeled and evaluated. Table
3.3.1 provides the values from the previously developed models based on the asprocessed properties listed in Table 3.3.2. More specifically, the formulations of (3.3.1)
and (3.3.2) are used for the prediction of oxide thickness at 1135°C as listed in Table
(3.3.1) and the oxide thicknesses at 1100°C and 1200°C are simply taken from the
measured values; (3.3.4) and (3.3.5) are used for the evaluation of stiffness modulus at
various exposure times and temperatures.
Based on the evaluated modulus, Poission’s
ratio listed in Table 3.3.2 and the oxide thickness, the stresses in the TBC layer are then
evaluated at each exposure time and temperature. Special attention will be paid to the
values of the thermal expansion coefficient (TEC), which are taken as references (Wright
and Evans, 1999; Mumm and Evans, 2000; Begley et al., 2000) and a specific value has
been taken by satisfying the residual stresses in the TBC layer in the as-processed state.
Thus the stresses in the TBC layer with the increase of exposure are essentially due to the
67
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Chapter 3. Application o f Conical Indentation Tests
evaluated modulus from the model by (3.3.4) and (3.3.5) regarding a constant TEC
mismatch. That is, the predicted stresses in the TBC layer upon each temperature at a
specific exposure time is calculated based on the stiffness modulus after considering the
sintering effect from the same as-processed state.
Table 3.3.1: TBC Sintering and TGO Thickening as a Function of
Temperature
(°C )
Exposure
Time
(Hrs)
1200
1200
1200
1200
1135
1135
1135
1135
1100
0
10
20
56
0
50
120
200
0
1100
1100
1100
1100
120
200
350
500
tTGO
0.25
2.5
3.5
4.5
0.25
2.5
3.3
4.0
0.25
2.4
2.9
3.5
3.9
CtTBC
(MPa)
E tbc
(GPa)
44
99
122
175
44
94
50
112
121
139
198
50
106
137
143
44
163
50
89
103
121
137
101
116
137
155
Table 3.3.2: Properties of Each Layer in an EB-PVD TBC System
Under As-processed Conditions
Layer
In-plane
Thermal Expansion
Layer
Thickness
Modulus
Coefficient
(pm)
(GPa)
(p.p.m.)
Poission
Ratio
TBC (ZrOz)
100
44
11-13.2
0.22
TGO (a-AEOs)
Bondcoat (PtAl)
Substrate (Nickel
based superalloy)
0.25
50
393
189
8-9
0.22
13-16
0.313
3125
318
15-18
0.38
68
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Chapter 3. Application o f Conical Indentation Tests
3.3.5
Toughness Measurements from Indentation Including Changes in
Oxide Thickness and TBC Sintering
The oxide growth, TBC sintering, and actual loss in toughness at the interface due
to chemical or mechanical damage are the principal mechanisms that can contribute to an
apparent toughness loss as a function of thermal exposure. The TGO layer will grow
thicker during exposure of the TBC as a result of the oxidation process of the bond coat
layer. An increase in oxide thickness increases the elastic energy acting to drive debond at
the interface. Furthermore, during the exposure at a high temperature, the TBC sintering
causes the coating layer to beeome denser that leads to the increasing of TBC’s effective
modulus. An increase in effective modulus increases the residual stress magnitude of the
TBC at room temperature and also the elastic energy available to drive delamination. The
change in net stiffness also has an effect on the delamination energy release rate. The
toughness changes that remain, brought about by the chemical or mechanical damage at
the interface, are identified as ‘true’ changes in toughness.
Figure 3.3.5 provides a plot of TBC interfacial toughness as a function of
isothermal exposure hours at 1100°C, demonstrating the effect of the increase of alumina
thickness with the increase of exposure hours. The curves shown in the figure are drawn
by hand to show trends for toughness degradation with time.
In the plot, the data with
solid circles and solid lines is the same data presented in Figure 3.3.1. The data presented
as open rectangles with dashed lines is the same experimental data, but with the
toughnesses calculated using measured alumina layer thicknesses in Table 3.3.1. As the
plot in Figure 3.3.5 shows, if the alumina layer thickness is accounted for, a toughness
loss may still be seen at the interface (open symbols), though it is much smaller in
magnitude for the entire exposure range than the loss suggested if the change of oxide
thickening is not included (solid symbols). Also the curve designating the stress intensity
factor due to residual stresses only is no longer a horizontal line. It increases with
exposure (open symbols). It is still true for the open symbol data, that when the upper
curve (designating interfacial toughness, or resistance to debonding) reaches the lower
curve (designating the stress intensity factor due to residual stresses aeting to drive
debonding), spontaneous spallation can occur. However, now the stress intensity factor.
69
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Chapter 3. Application o f Conical Indentation Tests
converted from the stored elastic energy due to residual stresses is shown to be increasing
with the thermal exposures.
As a result, most, if not all of the observed “apparent”
toughness losses in Fig. 3.2.1 at 1100°C are due to an increase in stored elastic energy in
the alumina because of oxide thickening.
Similarly, Figure 3.3.6 provides a plot of TBC interfacial toughness as a function
of isothermal exposure hours at I100°C, demonstrating the effect of the change of
stiffness modulus and residual stresses with exposure in the TBC layer due to sintering.
Again the curves shown in the figure are drawn by hand to show trends for toughness
degradation with time.
Now the data presented as open rectangles with dashed lines is
the same experimental data, but with the toughnesses calculated using modeled modulus
and stresses in the TBC layer at each exposure hour listed in Table 3.3.1. As the plot in
Figure 3.3.6 shows, if the sintering effects are accounted for, a toughness at the interface
(open symbols) still degrades, but at a smaller rate than the degradation suggested if the
change of sintering effects are neglected (solid symbols). This indicates that the sintering
effects are responsible for some of the toughness degradations, but in a much smaller
magnitude than that of the oxide thickening accounted for.
Figure 3.3.7 provides a plot of TBC interfacial toughness as a function of
isothermal exposure hours at 1100°C when both oxide thickening and sintering effects in
the TBC layer are accounted for (curves are drawn by hand to show trends). Since now
the factors affecting the apparent toughness loss are all included except those caused by
chemical and mechanical damage at the interface, therefore, the toughness presented in
the upper open circles can be regarded as “true” interfacial toughnesses. In the asprocessed state, the toughness for this case is taken as 4.3MPa m'^^, which is the averaged
value for the as-processed toughness shown in Figure 3.3.1. As the plot in Figure 3.3.7
shows that the “true” toughness values at each exposure decrease away from the asprocessed state, which indicates some degradation has occurred at the interface due to
chemical segregation or mechanical damage. However, the losses of toughness are
apparently not significant since all the “true” toughness values at each increase are lower
in a very small magnitude, than that in the as-processed state.
Again the curve
designating the stress intensity factor due to residual stresses, only considering both oxide
70
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Chapter 3. Application o f Conical Indentation Tests
thickening and TBC sintering, are no longer a horizontal line. However, again it is still
true for the open symbol data, that when the upper curve reaches the lower curve,
spontaneous spallation can occur.
6
• No Change
□ Oxide Included
5
4
CLh
3
U
t/j
C
W)
O
H
2
1
0
0
100
200
300
400
500
Exposure Time (hrs)
600
700
Figure 3.3.5: Toughness Loss vs. Isothermal Exposure Time at 1100 °C Assuming No
Changes Both in the Alumina Layer and in the TBC Layer (same results as in
Figure 3.3.1) and Taking Into Account Measured Alumina Layer Thickening.
71
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Chapter 3. Application o f Conical Indentation Tests
6
• No Change
□ Sinter Included
5
C3
pL,
U
(/T
CO
CD
c
tpi
US
4
3
2
o
H
1
0
0
100
200
300
400
500
Exposure Time (hrs)
600
700
Figure 3.3.6: Toughness Loss vs. Isothermal Exposure Time at 1100 °C Assuming No
Changes Both in the Alumina Layer and in the TBC Layer (same results as in
Figure 3.3.1) and Taking Into Account the TBC Sintering Properties.
72
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Chapter 3. Application o f Conical Indentation Tests
6
• No Change
□ Both Included
a
c3
Cl,
4
U
t/T
C/D
(D
C
x;
bO
X
O
H
3
2
1
0
100
200
300
400
500
Exposure Time (hrs)
600
700
Figure 3.3.7: Toughness Loss vs. Isothermal Exposure Time at 1100 °C Assuming No
Changes Both in the Alumina Layer and in the TBC Layer (same results as in
Figure 3.3.1) and Taking Into Account the Changes Both in Oxide
Thickening and TBC Sintering.
73
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Chapter 3. Application o f Conical Indentation Tests
Figures 3.3.8 to 3.3.10 provide the plots o f toughness values for TBC systems
exposed at 1200°C at different isothermal exposure times, assuming as-processed
properties and accounting for the effects o f oxide thickening and TBC sintering. Again
the curves shown in the figures are drawn hy hand to show trends for toughness
degradation with time.
Very similar analysis may be performed with the previous one at 1100°C
exposures. But now, we see that the exposure time lasts a much shorter time
(approximately 10 times less) before the specimen experiences spontaneous failure.
Moreover, the as-processed toughness for this specimen is unknown, but this does not
hinder the analysis from the perspective o f toughness degradation with exposure. As the
results in the "Sintering Included" plot in Figure 3.3.9 indicate, the amount o f sintering
included in the toughness calculations could account for some o f the apparent toughness
loss. The fall-off in apparent toughness values from an as-processed value o f 4.3 MPaVm
or higher is reduced somewhat by approximating sintering effects. In contrast, the "Oxide
Included" plot in Figure 3.3.8 demonstrates that oxide thickening could account for most
o f the apparent toughness losses seen in this specimen.
The same conclusion can be made in looking at the final plot for each
temperature, where both sintering and oxide thickening effects are included. There is no
evidence o f a significant “true” loss in interfacial toughness with exposure. An interesting
aspect o f the results in this plot is that some values in the “Both Included” cases at 56 hrs
are less than those in the "Oxide Included" cases. This is due to the fact that including
sintering effects reduces the contribution o f oxide thickening to the Kc values. This is
primarily due to the increase in the TBC modulus, which decreases the energy release rate
due to bending. Care shall be taken for the results in Figure 3.3.8 that there exists a dip in
the curve cormecting the upper open symbols o f Kc vs. time when the oxide thickening is
included.
Similarly, the dip is also seen in Figure 3.3.10 for the results when “Both
Included” and in Figure 3.3.9 for the results when “Sinter Included”. This phenomenon is
essentially caused by the insufficiently accurate estimation o f the oxide thickening and
sintering at the early or late exposure times at 1200°C. When those mechanisms are
74
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Chapter 3. Application o f Conical Indentation Tests
included quantitatively in the analysis o f fracture mechanics, this type o f nonphysical
phenomenon may occur. Therefore, care must be taken on making too broad conclusions
based on those results.
The toughness values were also evaluated as a function o f exposure time for the
TBC systems exposed at 1135°C. The evaluations were made in the same way as those
considered previously for the exposures at 1100°C and 1200°C. However, all the
parameters o f the oxide thicknesses, the stiffness modulus and stresses necessary for the
evaluation o f toughnesses at this temperature are based on the model predictions. Again
the toughnesses at this temperature at different isothermal exposure hours, assuming asprocessed properties and accounting for the effects o f oxide thickening and TBC sintering
were considered separately. Those results confirm all the main observations shown
previously at the exposures o f 1100°C and 1200°C. That is to say, the toughness values
with “Oxide Included” or “Both Included” shows insignificant decrease or even no
decrease at all with the increase o f the exposure time, which indicates the oxide
thickening accounts for most o f the toughness loss. At the same time, the toughness
values with “Sinter Included” shows a trend to decrease but with a much less magnitude
than those with only as-processed state considered, which indicates some o f the toughness
losses are due to the TBC sintering effects. Therefore, the figures at this temperature are
not included.
Care will be taken that oxide thicknesses are as measured from SEM images, but
they are not always well defined due to the occasional existence o f an intermixed zone o f
alumina and TBC where those two layers meet. Thickness values cited in Table 3.3.1
include the intermixed zone, which equaled approximately 1 pm in the 1200°C
specimens. As mentioned earlier, no sizeable intermixed zones were seen in the 1100°C
specimen. The effects o f sintering are modeled by allowing the TBC modulus to vary
from 44 GPa in the as-processed case to 175 GPa at spontaneous failure (approaching the
modulus o f fully dense zirconia, which is 200 GPa) as stated in the previous section. The
magnitude o f the compressive residual stress in the TBC is specified as increasing
proportionally with the effective TBC modulus based on the model in the previous
section. This four-fold increase in modulus and stress represents close to an upper bound
75
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Chapter 3. Application o f Conical Indentation Tests
for changes that could occur due to sintering.
For exposures less than that causing
spontaneous spallation, modulus in the TBC layer is assumed to obey the thermally
activated relation as expressed in (3.3.4) and (3.3.5). The stress changes are assumed to
be proportional to changes in modulus.
Because o f the assumptions used in obtaining the numbers presented in Figures
3.3.5-10, caution should be exercised before making broad conclusions based on them.
Also, even the oxide thicknesses cited in Table 3.3.1, though measured, have some
uncertainty associated with them, including the existence o f intermixed TBC/oxide zones.
However, the numbers suggest that oxide thickening is an important mechanism in the
degradation o f this particular TBC system due to isothermal exposures. Sintering has an
effect, but its role appears less important. For this industrial-grade TBC system, chemical
or mechanical damage (including damage caused by ratcheting, which is tied to the initial
roughness o f the bond coat surface from the grit blast treatment) as a result o f isothermal
exposures appears least important and may not be significant. Thus the "true" toughness
o f the TGO/bond coat interface may be changing very little. This result is consistent with
the notion that cyclic thermal loading, which can cause increasing amounts o f non-planar
deformation o f the TGO, is needed for substantial mechanical damage to be induced at
the TGO/bond coat interface. It is also plausible that substantial chemical degradation of
the interface (such as could be caused by segregation o f sulfur) is not typically seen in the
industry-grade TBC system tested herein.
This system and its bond coat have been
developed over a number o f years with the goal o f limiting such effects.
76
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Chapter 3. Application o f Conical Indentation Tests
6
• No Change
O Oxide Included
5
Oh
4
u
c/T
00
(D
C
X
tJ)
O
H
3
2
1
0
0
20
40
60
80
Exposure Time (hrs)
Figure 3.3.8: Toughness Loss vs. Isothermal Exposure Time at 1200 °C Assuming No
Changes Both in the Alumina Layer and in the TEC Layer (same results as in
Figure 3.3.1) and Taking Into Account Measured Alumina Layer Thickening
77
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Chapter 3. Application o f Conical Indentation Tests
6
• No Change
O Sinter Included
5
a
Oh
4
u
vT
CO
(D
!=1
bi)
P
O
H
3
2
1
0
0
20
40
60
80
Exposure Time (hrs)
Figure 3.3.9; Toughness Loss vs. Isothermal Exposure Time at 1200 °C Assuming No
Changes Both in the Alumina Layer and in the TEC Layer (same results as in
Figure 3.3.1) and Taking Into Account the TEC Sintering Properties.
78
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Chapter 3. Application o f Conical Indentation Tests
6
• N o C hange
O B oth Included
5
PLh
4
o
-
t/T
C/)
<u
a
W)
o
H
0“
3
2
1
0
0
20
40
60
E xposure T im e (hrs)
80
Figure 3.3.10: Toughness Loss vs. Isothermal Exposure Time at 1200 °C Assuming No
Changes Both in the Alumina Layer and in the TEC Layer (same results as in
Figure 3.3.1) and Taking Into Account the Changes Both in Oxide
Thickening and TBC Sintering.
79
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Chapter 3. Application o f Conical Indentation Tests
3.3.6 Model of TBC Duration and Arrhenius Plot for Accelerated Tests
So far, we may have already recognized that the currently investigated TBC
duration under isothermal exposures can be predicted from the models developed in the
previous sections. Although the evaluated TBC duration before spontaneous spallation
may highly depend on the experimental data tested in the previous specimens, for the
purpose of accelerated tests, these models developed herein may provide significant help
for the testing decisions. For example, the trend lines shown in Figure 3.3.1 based on the
measured toughness values can be evaluated from the previously developed models by
just knowing the as-processed toughness of a relevant TBC system. This is due to the fact
that the debonding ratio R/a can be determined from the Kc vs. R/a curve at each specific
exposure time and temperature. Attention shall be taken such that those curves of Kc vs.
R/a are obtained by considering a specific change happened in the TGO layer or the TBC
layer or both. Then using these predicted values of R/a, the apparent toughness values can
be determined from the Kc vs. R/a curve without considering the changes of oxide
thickening and sintering.
To gain further insight into the mechanisms leading to the TBC system
oxide/bond coat interfacial adhesion loss, the results presented in Fig. 3.3.1 have been re­
cast in the form of an Arrhenius plot.
Figure 3.3.11 gives a plot of ln(l/tim e) vs.
1/Temperature, where the "time" variable is the time to reach a specified value of
apparent interfacial toughness. In other words, a single line in Fig. 3.3.11 is determined
by drawing a horizontal line across the plot of Fig. 3.3.1, at values of Kc = 2.5, 2.0, 1.5 or
1.0 MPam*^^, and determining intersection points with test data at 1200°C, 1135°C and
1100°C. Data plotted for a Kc value of 1.0 MPam*'^^ denote times required to experience
spontaneous spallation. It is clear from Fig. 3.3.11 that the slopes of the plotted lines for
each Kc value are approximately the same. Thus, the thermally activated mechanism(s)
that lead to apparent toughness loss appear to be unchanging and appear to be the same as
those leading to spontaneous spallation (final failure). As a result, as just suggested, use
of an indentation test to obtain measured toughness losses at early exposure times appears
to be a valid approach for gaining information on the TBC system’s durability without
having to perform long-term tests until failure.
80
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Chapter 3. Application o f Conical Indentation Tests
Moreover, the magnitudes of the slopes in Figure 3.3.11 with respect to each
apparent toughness level are the ratios of the activation energy over the universal gas
constant, i.e., Ea/R. Therefore, the activation energy for the degradation to each apparent
toughness level can be determined from the slopes in Figure 3.3.11. It follows that the
values of the activation energy are 540, 563, 553, and 483 KJ/mole at Kc =2.5, 2, 1.5, 1.0
MPaVm, respectively.
At the same time, the activation energy can be determined from the models
developed previously by taking an initial apparent toughness. Then an Arrhenius
relationship can be presented similar as those in Fig. 3.3.11. But the predicted slopes
remain the same at each apparent toughness level since the mechanism used for the
prediction is the same.
It was found Ea=442KJ/mol by “Oxide Included”, Ea =
485KJ/mol by “Sinter Included” and Ea = 449KJ/mol if “Both Included”. Those values of
activation energy are found consistent with those reported in the literature. According to
Yanar et al. (2001), the activation energy from the a-A l 203 growth on PtAl bondcoat
with top coat is 520KJ/mole. In a recent study considering two types of bondcoat NiCoCrAlY and PtAl, the activation energy reported is 85.1kcal/mole (corresponding to
356KJ/mol). (Yanar et a i, 2003). Meanwhile the activation energy for grain boundary
diffusion of oxygen in an aluminum oxide was found to be I08kcal/mole (corresponding
to 452KJ/mol) by Mistier and Coble (1974).
81
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Chapter 3. Application o f Conical Indentation Tests
0
1
2
3
C
H-l
4
5
6
7
8
6.7
6.8
6.9
7.0
7.1
7.2
7.3
1/Temperature (1/K) (xlO'"^)
Figure 3.3.11: Arhennius Plot of Toughness Degradation.
82
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7.4
Chapter 3. Application o f Conical Indentation Tests
33.1 Concluding Remarks
Toughness degradation has been studied as a function of isothermal exposure time
and temperatures. These values are some of the first of their type and are the first used to
consider mechanisms controlling spallation-induced failure in TBC systems. The results
presented in the beginning of this chapter show that for isothermal high temperature
exposures, there is a substantial apparent toughness loss at a fraction of the time needed to
cause spontaneous failure upon cooling. This has been seen in TBC systems exposed to a
wide range of temperatures.
Models have been developed based on the thermally activated mechanism for the
degradation of toughness in EB-PVD/PtAl TBC systems under the dry air isothermal
exposure conditions for including the in-situ oxide thickening, sintering properties in TBC
coatings at each exposure time. Calculations approximating the effects of TBC sintering
and oxide thickening suggest they can account for most or all of the observed apparent
losses of toughness in the tests. This indicates that oxide thickening is the most important
mechanism leading to spallation of isothermally exposed TBC systems. Sintering appears
to be less important. Chemical or mechanical damage at the interface appears to be least
important and could be insignificant for this isothermally exposed industry-grade TBC
system.
The assumptions used to extract interfacial toughness values from the tests
suggest some caution should be exercised in making broad conclusions from the available
results. Also, the oxide thicknesses used to perform the calculations, though measured,
have some uncertainty associated with them.
Arrhenius analysis has not only given insight into mechanisms behind toughness
loss, but has also allowed the generation of predicted toughness loss curves (and life) for
these systems under isothermal conditions.
83
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Chapter 3. Application o f Conical Indentation Tests
3.4 Mechanism-Based Tests for Exposures with Water Vapor
3.4.1 Introduction
Mechanisms that control the durability of thermal barrier coating systems under
elevated temperatures (1000°C-1200°C) and dry air conditions have been well addressed
by multiple researchers (Vasinonta and Beuth, 2001; Handoko et al., 2001; Mumm et a i,
2000, 2001; Begley et a l, 2000, 2001; Evans et a i, 2001; Yanar et al, 2001; Stiger et a i,
1999; Kim et a l, 2001). However, the studies on the influence of water vapor on the
oxidation of alumina-forming alloys are not extensive, and there is little literature
available about the effect of steam-air gas mixtures on EB-PVD TBC systems
(Janakiraman et a l, 1999; semi-annual report, July 2001). Although there are numerous
studies on the effect of water vapor on high temperature corrosion of metallic alloys
(Hayashi and Narita, 2001; Walter et al. 1991; Fukumoto et al., 2001; Henry et al., 2001;
Asteman et al., 2001; Y\x et al., 2001) as well as ceramics (Geng et al. ,2001; Gogotsi et
a l, 1994; Foerthmann et a l, 1989; Tamai et a l, 2000). In a recent study of superalloys
with a-A l 203 scales, water vapor effects were found to be a factor 2 to 4 times more on
the spallation of a-AlaOs scales as compared to dry air (Janakiraman et a l, 1999) under
the condition that spallation occurs for both in a dry air and in a vapor environment. The
argument is that the water vapor may not show any effect if the alumina scales are
extremely adhesive. Whether the effects of water vapor on the oxide spallation are
present or not, water vapor does have access to the a-ABOs - alloy interfaces during
cyclic oxidation of low sulfur alloys (Janakiraman et a l, 1999).
It is well known that the failure of the PtAl EB-PVD TBC system is mainly
caused by the growth of a thermally grown oxide (TGO) scale layer (Evans et a l, 2001;
Mumm et a l, 2001), and it is believed that there exists a critical TGO thickness and
spallation may occur when the TGO grows beyond that value. It appears that water vapor
enhances the spallation when this critical value is reached and this is true for bare
alumina scales with low sulfur at the interface of OC-AI2O 3 and the bond coat (BC) under
cyclic loading conditions (Janakiraman et al, 1999). It was found that the presence of
water vapor does not significantly effect the residual stresses in the TGO layer, like in dry
84
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Chapter 3. Application o f Conical Indentation Tests
air. However, it is unknown if water vapor alters residual stresses in the TBC layer or the
stiffness of the TBC layer or any other properties of the TBC and TGO layers and further
affects the degradation of the EB-PVD TBC system. Therefore, it still remains unknown
if there are possibly effects of water vapor on the Pt-Al, EB-PVD TBC system under
various loading conditions. This study is an attempt to investigate such effects.
This test has been used to characterize the loss of interfacial toughness or
adhesion in EBPVD TBC systems with a PtAl bond coat as a function of the duration of
isothermal exposures at 1100, 1135 and 1200°C in dry air (Handoko et al,, 2001).
Apparent changes in toughness have also been related to changes in the TBC system,
including oxide scale growth and TBC sintering, in an attempt to rank the importance of
various mechanisms in the degradation of TBC adherence.
The goal of the current work is to apply this testing and analysis approach to
quantify and understand the effects of steam on the TBC system degradation, by
comparing toughness losses in steam-exposed specimens to existing data on the same
TBC system in dry air. All steam-exposed specimens and most of the dry air specimens
described in this paper were subjected to isothermal exposures; however, the results from
a single TBC specimen subjected to dry air cyclic thermal exposures are also presented to
demonstrate a range of failure behaviors possible for this TBC system.
3.4.2 Experimental Procedure
The standard TBC specimens were provided by General Electric Aircraft Engines.
The compositions as well as the properties of each layer of the TBC disc-shaped
specimen were described elsewhere (Vasinonta and Beuth, 2001; Handoko et a l, 2001).
Each specimen was exposed for a certain length of time under different environmental
conditions, then, indentation tests were performed at room temperature on a Rockwell
hardness tester with a standard Brale C diamond indenter. Each tested specimen was
loaded incrementally with major loads of 60, 100 and 150Kg at each location using the
multiple indentation technique. After each indentation, the specimen was observed using
optical microscopy and scanning electron microscopy (SEM).
An SEM charging
technique was used to quantify the extent of the debonded region, where the debonded
85
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Chapter 3. Application o f Conical Indentation Tests
portion of TBC becomes charged and appears as a bright image on an otherwise dark
(uncharged) background. A typical SEM charging image of the debonded portion of the
TBC is shown in Figure 3.4.1. The entire bright region is the debonded TBC (as viewed
from above). A circular cracked region of the TBC and some radial cracking are also
evident in the image.
The characteristic dimensions after each indentation that need to be obtained from
the SEM photographs include: (1) the indenter contact radius, a, and (2) the debonding
radius, R. Note that an assumption implicitly made here is that each indentation causes
the same buckling and broken scenarios so that no stresses remain to hold in the buckled
TBC portion, i.e., the unbuckled portion to form the inner radius, Rj, of an annular plate is
very narrow such that Ri ->R.
Figure 3.4.1: A Typical SEM Charging Image of the Debonded TBC After Indentation
using a Major Load of 100 kg (Steam Pressure 0.10 atm with 120 hrs Isothermal
Exposure)
The quantification of apparent toughness is based on the axisymmetric debond
phenomena as seen in Figure 3.4.1. However, a non-axisymmetric debonding pattern is
often observed for most of the indentation cases under as-processed conditions. For some
cases after a specimen experiences certain exposures, especially after a specimen
experiences some cyclic exposures. This makes the initial toughness measurement
86
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Chapter 3. Application o f Conical Indentation Tests
somewhat more difficult. To overcome this, an effective debond radius used previously is
such that the debonding area of the unaxisymmetric case is determined by averaging the
debonding area (Handoko et a l, 2001). To extend this idea, more details are to be given
for various debonding scenarios of un-axisymmetric cases caused by the indentation
events and how we shall deal with each classification.
The first class of non-axisymmetric debonding observed is that either the
debonding occurs much more on one side than the other, which is often seen for
indentation under as-processed conditions; or the debonding undergoes normally on one
side, but the other side buckles away, which is often seen for indentation on a wellexposed specimen. Typical SEM pictures for such kind of debonding patterns are
illustrated as in Figures 3.4.2 (a), (b). We refer to this method to determine this kind of
debonding area as the upper half debonding region (UHDR) so that the side with
undebonded gap, the side with much less debonding or the side with buckling driven will
not be included in the calculation, but the upper half region away from the abnormal side
only. Apparent toughness values evaluated based on the UHDR method would either
provide lower bound apparent toughness values for as-processed cases, or upper bound
values for well-exposed cases where buckling-driven occurred compared with the results
due to averaging the whole debond region only. Care should be taken for the
measurement of the total pixels in Matlab for the UHDR cases; the number of pixels, N,
is doubled in the effective debond area calculations, i.e., A = 2 N
kL j
effective debond radius is determined by Reff =
A
. And then the
; where N is the total pixels of the
V^
UHDR, S is the scale ((im), L is the total length of the scale pixels; and S/L represents
each pixel length.
87
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Chapter 3. Application o f Conical Indentation Tests
Figure 3.4.2: UHDR Method for Determination of Debonding Radii; Unaxisymmetric
with Undebonded Gaps Observed in 5D Specimen (a) and 4B Specimen (b)
at 150Kg Indentation Load Under As-Processed Conditions.
Another type of debonding exists. Although it is not axisymmetric in a strict
sense, there is no gap or buckling-driven delamination occurred around the indentation
region. For this type of non-axisymmetric debonding, an effective debonding radius can
be easily determined by taking the whole debonding region (WDR) area (Handoko et al. ,
2001).
In general, three types of debonding patterns exist observed from the indentation
tests studied currently. One is not only non-axisymmetric, but also with non-debonding
gaps present or buckling driven delamination occurring on one side. Another is still nonaxisymetric, but no non-debonding gaps or buckling driven delamination on one side and
usually with a symmetric line; and the third kind is axisymmetric, which is frequently
seen in isothermal cases. The last kind of debonding is observed for most of our cases of
exposed specimens, and is the standard case for the determination of toughnesses. For
the first kind, the debonding radii can be determined by UHDR. For the second kind, the
debonding radii can be determined by the WDR method. And the standard axisymmetric
debonding can be simply determined by direct measurement.
Finally, because of the expected thermal exposure history, the tested specimen
was then ready for making samples of further microstructure analysis at its cross sections.
The samples were carefully prepared using the material processing techniques including
mounting by using Epofix Resin and Epofix Hardener, sectioning by using a Struers auto
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Chapter 3. Application o f Conical Indentation Tests
materialographic cutting machine, grinding and polishing using Struers automatic
electrolytic polisher and each sample was then coated using a sputter coating system
before examination.
3.4.3 Results and Discussion
3.4.3.1 Initial Tests on Steam-Exposed Specimens
The initial investigation o f steam effects involved a single EBPVD TBC/PtAl
bondcoat specimen exposed three times at 1100°C with a steam vapor pressure o f 0.10
atm. Following each exposure, two or three indentation tests were performed.
The primary measurements made in the indent tests are the indenter contact radius (a) and
the debonding radius (R). Table 3.4.1 summarizes the measured data (shaded entries)
from SEM and optical micrographs o f the vapor-exposed specimens. Calculated values
for interfacial fracture toughness are also given. These values do not take into account
changes in the TBC system such as oxide thickening and TBC sintering that can degrade
TBC adhesion even in the absenee o f a true loss o f adhesion at the alumina/bond eoat
interface.
Thus these are referred to as "apparent" toughness values.
The locations
designated in Table 3.4.1 refer to different locations experienced after each exposure.
While location #1 is at the specimen center, the other two locations, #2 and #3, are at the
middles from the center to the edge to avoid the effects o f interaction with previous
debond spots and the free edge o f the specimen.
The results o f Table 3.4.1 were initially compared to existing results for the same
type o f TBC system exposed in dry air, which are given in reference (Handoko et a l,
2001). This comparison is summarized in Figure 3.4.3, which provides a plot of
toughness loss as a function o f isothermal exposure time for temperatures o f 1100, 1135
and 1200°C. The results from the steam exposure tests from Table 3.4.1 have been added
to the plot. The curves shown in the figure are drawn by hand to show trends for
toughness degradation with time under each exposure temperature and environmental
condition. For an exposure temperature o f 1100°C, the results suggest that the apparent
fraeture toughness loss is greater for the case o f exposure with steam vapor. The results
also indicate that the most significant loss is at early exposure times.
89
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Chapter 3. Application o f Conical Indentation Tests
Table 3.4.1: Summary of Measured Data and Kc Values from Indentation Tests
Performed on a TBC Specimen Exposed at 1100°C, with
Location
Exposure
Load
R
a
Time
(kg)
(mm)
(mm)
R/a
Kc
[MPa
(hrs)
1
120
100
1.47
0.25
5.88
1.6
1
120
150
1.50
0.33
4.55
2.3
2
200
60
1.05
0.21
5.00
1.9
2
200
150
1.61
0.33
4.88
2.0
3
350
60
1.20
0.21
5.71
1.7
3
350
100
1.S8
0.31
6.06
1.6
90
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Chapter 3. Application o f Conical Indentation Tests
1200 C
1135 C
1100 c
1100 C (steam)
c;
W
“O - As-Processed
c /3
cn
(U
C
W
P
TBC Fails
o
H
■i—>
i=i
<u
Q.
Q.
<
60 hrs
(1200°C)
500 hrs
(1135°C)
1000 hrs
(1100°C)
0
0
100
200
300
400
500
Exposure Time (hrs)
600
700
Figure 3.4.3; Apparent Toughness vs. Exposure Time for TBC Systems in Dry Air and
the First Specimen at 1100°C with 0.10 atm. Vapor Pressure of Steam (Dashed
Line)
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Chapter 3. Application o f Conical Indentation Tests
3 A .3 .2 An In-Depth Study o f Toughness Degradation Including As-Processed
Toughness Values
It is important to note that the plot o f Fig. 3.4.3 includes toughness data from
multiple TBC specimens. Although all specimens were provided by the same supplier
and were made to industry specifications, there is evidence o f toughness variations
between specimens. In particular, in the as-processed state, indentations on two different
specimens plotted in Fig. 3.4.3 yielded debonding in the first specimen and a Kc value of
3.4, and no debonding in the second specimen, resulting in a lower bound Kc value o f
5.2. In Fig. 3.4.3, all plotted lines (including that for the steam-exposed specimen which
was not tested in the as-processed state) are drawn through an as-processed toughness
value o f 4.3, which is the average o f these two numbers. This approach was acceptable in
studying general trends in toughness loss as a function o f exposure. However, a more
detailed accounting o f as-processed toughnesses is needed to quantify potentially subtle
effects o f steam exposure on toughness loss.
Table 3.4.2 outlines three additional specimens tested to provide additional asprocessed toughness values, and toughness values as a function o f time for various types
o f exposures at 1100°C. These specimens include another isothermal specimen exposed
with 0.10 atm o f water vapor, another isothermal dry air specimen, and an isothermally
exposed specimen with 0.30 atm o f water vapor.
Table 3.4.2: Specimen Exposure Conditions and Times
Specimen ID
Exposure Condition
Toughness Test Exposure Time
2Y5D
1100°C, isothermal, water
Ohrs, 50hrs, 120hrs
vapor 0.10 atm
2Y4B
Ohrs, 50hrs,120 hrs, 200hrs, 350hrs,
1100°C, dry air
SOOhrs
2Y7C
1100°C, isothermal, water
Ohrs, 50hrs, 120hrs
vapor 0.30 atm
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Chapter 3. Application o f Conical Indentation Tests
Note that the specimen IDs listed here are the original IDs inscribed on the back
of each specimen. For convenience, we also refer the 5D specimen to be the O.IOatm
vapor isotherm #2 to distinguish it from the initially tested specimen with the inscribed
ID of 2Y3B, which we also refer to be the O.IOatm vapor isotherm#!; similarly, we refer
the 4B specimen also to be the dry air isotherm #2; and the 7C specimen to be the 0.30
atm vapor isotherm specimen.
Table 3.4.3 lists the measured values of as-processed toughness for the three
specimens. The immediate conclusion to be drawn from the results given in Table 3.4.3
is that the as-processed toughnesses for this batch of specimens is significantly lower than
the Kc value of 4.3 M Pa (m )i /2 used in the plot of Fig. 3.4.4. In fact, if the as-proeessed
toughness of the first specimen exposed with 0.10 atm. vapor pressure of steam equaled
that of the specimens in Table 3.4.3, that alone might account for its lower toughnesses as
a function of the exposure time seen in Fig.3.4.4. To study this issue further, the three
specimens were subjected to the exposures described in Table 3.4.2. Because all the three
specimens had comparable as-processed toughnesses, a direct comparison of the effects
of each type of exposure was possible.
As mentioned previously, from Table 3.4.3, we see that most of the as-processed
indentation tests experienced non-axisymmetric debonding, thus either the UHDR or the
WDR method was used for determining the debonding radii (shaded entries). Next, more
detailed results on the measurement of apparent toughnesses of each of these three
specimens are to be given as a function of their thermal exposure history.
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Chapter 3. Application o f Conical Indentation Tests
Table 3.4.3; Results for the As-Processed Interfacial Toughnesses
Location
Exposure
Load
R
a
Time
(kg)
(mm)
(mm)
R/a
Kc
Kc
[MPa (m)'^^]
[MPa (m)'^^]
Average
(hrs)
Specimen ID: 2 Y 5 D
I
0
100
X
I*
0
150
1.29
0.35
3.68
2.9
2*
0
100
0 .9 7
0.29
3.35
3.3
2*
0
150
1.19
0.35
3.40
3.2
3 .1
Specimen ID: 2 Y 4 B
I*
0
100
1.00
0.29
3.45
3.1
0
150
1.24
0.35
3.54
3.0
2*
0
100
1.09
0.29
3.76
2.8
2*
0
150
1.28
0.35
3.66
2.9
3 .0
Specimen ED: 2 Y 7 C
I
0
100
0 .9 3
0.29
3.21
3.5
0
150
1.37
0.35
3.91
2.6
(*—obtained using UHDR method;
WDR method ; X—not available)
94
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3 .0
Chapter 3. Application o f Conical Indentation Tests
Tests on the Vapor Specimens o f 5D and 7C
Table 3.4.4 lists the measured values of debonding radii (shaded entries) and the
apparent toughness values after each exposure for specimen 5D and 7C. We notice that
both specimens were exposed with the presence of water vapor isothermally at 1100°C
like the previous O.IOatm vapor isotherm #1. But, these two new specimens experienced a
much shorter exposure time before we ended the exposure for other investigations. This is
due to the fact that the early exposure is the most important stage for the apparent
toughness degradation. Therefore, a closer look at the early exposed specimen with the
presence of water vapor under indentation events may reveal more possible differences
caused by the presence of water vapor. In other words, if the presence of water vapor does
not affect apparent toughness significantly at early exposures, it may not have much effect
thereafter for isothermal exposures from the previously observed indentation tests on
vapor specimens. Moreover, to study more carefully the effect of water vapor, the effect
of the presence of different vapor pressures with 0.10 atm for 5D and O.SOatm for 7C has
been investigated.
Figure 3.4.4 reveals the 5D specimen surface, similarly for the 7C specimen
surface, after the 120 hrs of isothermal exposure were completed with the indentation
spots labeled at each location. It is clear that even from this optical image, the indentation
events tend to generate axisymmetric debonds more easily after the specimen experienced
some exposures than that in an as-processed state. And the debond spots (buckled-up
region) after 50hrs at location #3 and 120hrs at location #4 are seen to be much larger
than those indented at the as-processed state as shown in location #1 and #2. This direct
experience reveals significant apparent toughness degradation after a short exposure from
the as-processed state.
From the toughness values listed in Table 3.4.4, we draw the conclusion
immediately that the apparent interfacial toughness is not degraded at all by tbe increase
of the presence of water vapor pressure under isothermal exposures since the values of Kc
due to 0.30 atm vapor pressure are even higher than those at 0.10 atm vapor pressure.
Moreover, all those toughness values are again found to be much lower that those for the
original dry air isothermal specimen. For example, at 120hrs, the original dry air
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Chapter 3. Application o f Conical Indentation Tests
specimen toughness value gives about 2.2 M Pa
which is about 29% higher than
the averaged value of the 5D specimen and 16% higher than the averaged value of the 7C
specimen. This again suggests that the as-processed toughness plays an essential role and
takes the most responsibility for the apparent subsequent toughness degradation. If the
toughness is higher in the as-processed condition, then it will most likely remain higher
after each subsequent exposure. Therefore, to improve the bond strength at the initial
stage is an effective way to control toughness degradations in the TBC systems.
Table 3.4.4: Summary of Measured Data and Kc Values from Indentation Tests
Performed on 5D TBC Specimen Exposed at I IOO°C, with Vapor Pressure =
O.Iatm and 7C TBC Specimen Exposed at IIOO°C, with Vapor Pressure =
0.3atm
R
a
R/a
Location Exposure Load
Kc
Kc
Time
(kg)
(mm)
(mm)
[MPa (m)^^^]
(hrs)
[MPa (m)'^^]
Average
Specimen ID: 2Y5D
3
3
3
4
4
4
50
50
50
120
120
120
60
100
150
60
100
150
X
X
X
1.52
0.29
5.24
1.55
0.35
4.43
1.18
0.21
5.62
1.67
0.29
5.76
1.72
0.35
4.91
Specimen ID: 2Y7C
X
1.8
2.2
1.7
1.6
2.0
2
2
2
3
50
50
50
120
120
120
60
100
150
60
100
150
X
1.20
l..'S6
X
1.27
1.83
X
2.4
2.2
X
2.3
1.8
3**
X
0.29
0.35
X
0.29
0.35
X
4.14
4.46
X
4.38
5.23
96
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2.0
1.8
2.3
2.0
Chapter 3. Application of Conical Indentation Tests
Figure 3.4.4: Indentation Test Locations on Specimen 5D: 0.10 atm Vapor Isotherm #2
Tests on the Dry A ir Isothermal Specimen 4B
The dry air isothermal specimen, 4B, was tested until it almost completely failed
at SOOhrs. The test data and the apparent toughness values are listed in Table 3.4.5. The
toughness can be well quantified before 350hrs. However, at 350hr exposure and
thereafter, indentation tests on this specimen began to experience some problems without
causing buckling driving delamination and without interacting with other previously
indented spots. Indentation loads of 60Kg and lOOKg were performed at location #6. It
was found that even at the smallest load level, 60Kg, at location #6, the delamination
tends to buckle away and coalesce with another previously indented spot at location #5.
At the lOOKg indent load level, the left part was completely spalled off and almost the
entire left half-side ligament has fallen off and then it coalesced with the previous spot
#5. And at the same time, the right side of the indentation spot tends to buckle away in a
very similar manner at the left side as seen after the 60Kg indentation was performed.
Therefore, the only toughness value approximated for this case is at 60Kg using the
UHDR method. Because of the coalescence and buckling-driven experience, the ISOKg
load test was not necessary to be performed for this case. Moreover, attention should be
paid to the scenario of a clear crack running through the TBC; this behavior suggests the
change of the crack mode mix and also further indicates that the buckling-driven criterion
97
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Chapter 3. Application o f Conical Indentation Tests
is now reached. Under this circumstance, the toughness value cannot be approximated
using current formulations, which do not include the contribution to an energy release rate
due to buckling and postbuckling behavior.
Upon further exposure to SOOhrs, the coating is almost completely spalled off
from the specimen surface as shown in Figure 3.4.5 (b). Therefore, it is not possible to
obtain a test value at this final exposure, but the value should be very close to IMPa
m^O.5, which is the apparent toughness at spontaneous spallation directly relevant to the
elastic energy stored in the TBC and TGO layers in the as-processed state. Furthermore, it
is interesting to note that the final failure almost always starts from its free edge with or
without previous mechanical damage.
The apparent toughness values listed in Table 3.4.5 are found to be very close to
those of the 5D specimen at its early exposure times. Flowever, all the toughness values
are found to be significantly lower than those obtained through the previous dry air
isotherm#!. For example, at 350hrs, the toughness value of the previous dry air specimen
is about 26% higher than that of 4B specimen at the same exposure time.
W
(a) at 350hrs
(b) at 500hrs
Figure 3.4.5: 4B Specimen Surface at Different Exposure Flistory Before and at its Final
Failure due to Indentation and Thermal Exposure Events
98
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Chapter 3. Application o f Conical Indentation Tests
Table 3.4.5: Summary of Measured Data and Kc Values from Indentation Tests
Performed on 4B TBC Specimen Exposed at 1100°C
Location
Exposure
Load
R
a
Time
(kg)
(mm)
(mm)
R/a
Kc
Kc
[MPa (m)'^^]
[MPa (m)*^^]
Average
(hrs)
Specimen ID: 2Y4B
3
3
3
4
4
4
5
5
6*
6
6
50
50
50
120
120
120
200
200
200
350
350
350
60
100
150
60
100
150
60
100
150
60
100
150
X
1.54
1.59
X
1.70
1.77
1.35
1.75
1.81
1.19
X
X
X
0.29
0.35
X
0.29
0.35
0.21
0.29
0.35
0.21
X
X
X
5.31
4.54
X
5.86
5.06
5.95
6.03
5.17
7.10
X
X
X
1.8
2.2
X
1.6
1.9
1.6
1.6
1.8
1.4
X
X
99
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2.0
1.8
1.7
1.4
Chapter 3. Application o f Conical Indentation Tests
Toughness Desradation due to Various Thermal Exposures
Figure 3.4.6 shows the apparent toughness vs. exposure time for the initial dry air
and 0.10 atm vapor exposed specimens, along with test results for the three specimens of
Tables 3.4.4 to 3.4.5. In this plot, the black dots represent toughness values of the original
dry air isothermal specimen. This specimen was considered to have an initial toughness
of approximately 4.3 MPa Vm (Handoko et a l, 2001). The specimen designated as
“O.Iatm Vapor Isotherm #1” was the first vapor-exposed specimen to be tested and its
toughness values do lie below the values measured in dry air. However, the as-processed
toughness of this specimen was not measured. As is apparent from the figure, all of the
test results now lie below the initial isothermal dry air toughness vs. time values. This
includes specimen 4B, which was also subjected to dry air isothermal exposures. The
most reasonable explanation for this observed difference is that it is due to lower asprocessed toughnesses in the latest group of samples.
The lower initial toughness
continues to affect toughness values after long exposure times.
Another important observation from Figure 3.4.8 is that all of the latest toughness
vs. time results are comparable, and those results include specimens exposed with 0.10
atm and 0.30 atm of water vapor. Thus it does not appear that water vapor content is
radically changing toughness loss over time. It is also presumably having little effect on
TBC life.
It is instead variability in as-proeessed toughnesses that is causing any
observed differences in toughness loss with time. This result is consistent with
observations of spallation for different alumina scales made by Janakiraman et al. (1999).
They found that steam exposure may cause the degradation rate of poorly bonded alumina
scales (with no TBC on top), where some cracking and spading of the alumina scales
occurs in dry air, to be increased by a factor of 2 to 4. However, water vapor appeared to
have little effect on well-bonded alumina scales, where there is no cracking or sampling
under dry air exposures. The PtAl bond coat used in the TBC system studied here does
form a highly adherent alumina scale.
100
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Chapter 3. Application o f Conical Indentation Tests
Original Dry Air Isotherm
O.Iatm Vapor Isotherm #1
O.Iatm Vapor Isotherm #2
n Dry A ir Isotherm #2
O O.Satm Vapor Isotherm
3.5
a
Dh
2.5
u
O
c/T
c/3
(U
c
bJO
13
O
H
+->
c
<D
Oh
O h
1.5
Simultaneous
debond line
0.5
0
0
50
100 150 200 250 300 350 400 450 500
Time (hrs)
Figure 3.4.6: Toughness Loss vs. Exposure Time for Specimens with Measured
As-Processed Toughnesses
101
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Chapter 3. Application o f Conical Indentation Tests
S.4.3.3 Fracture Surfaces and Structure of the Alumina Scale
Figure 3.4.7 shows fracture surfaces (viewed ffom above) o f the 7C specimen in
its as-processed state, and the states after 50 hrs o f isothermal exposures at 1100°C with
the presence o f 0.30atm vapor pressure. The fracture surface caused by indentation in an
as-processed state is shown in Fig. 3.4.7(a). It is clear that there is only a gray color on the
fracture surface, which indicates no TGO (AI2O 3, black) or bond coat (PtAl white), but
only TBC is present on the cracking interface. This kind o f as-processed fracture surface
indicates the indentation-induced failure occurs either within the TBC layer or near the
interface o f the TBC and the TGO layers. The as-processed failure pattern is apparently
due to the imperfections occurred in the TBC near the interface o f the TBC and TGO
during the coating processing; such imperfections may include detached TBC, grit blast
particles, and surface defects (Yanar et a i, 2002). However, the stored elastic energy in
the TGO layer accumulates with the increase o f its thickness with further thermal
exposures. The accumulated elastic energy in the TGO layer acts as the driving force to
cause the cracking along the interface o f TGO and bond coat. Therefore, a transition of
cracking interface is observed with the increase o f thermal exposures from the asprocessed state. As indicated in Figure 3.4.7(b), after 50hr isothermal exposure, a
significant portion o f the fracture surface appears white, indicative o f a direct exposure o f
the bond coat material. Similar phenomena apply to the cases in the dry air isothermal as
well as the one-hour cyclic conditions.
(a) 7C as-processed
(b) 7C SOhrs
Figure 3.4.7: SEM Photographs for Fracture Surfaces o f Specimen 7C, Exposed
Isothermally at 1100°C with 0.30atm Water Vapor.
102
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Chapter 3. Application o f Conical Indentation Tests
In Figure 3.4.8, indentation-induced fracture surfaces of TBC systems exposed at
1100°C for 120 hrs are presented.
Again the images were taken in an SEM and are
viewed from above. In each image, the white color indicates the bondeoat material, the
black color the TGO and the grey color the TBC.
It can be seen that the fracture
morphologies of the dry air and water vapor specimens are very similar. This consistency
in fracture surfaces further indicates that the effect of water vapor on interface
degradation is insignificant.
vvwr*
I
%JBr
* '#
f
(a) 4B Isothermal Dry Air 120 Hrs
(b) 5D Isothermal 0.1 atm Vapor 120 Hrs
Figure 3.4.8; SEM Images of Fracture Surfaces for Two Different Exposure Conditions
After 120 hrs at 1100°C.
So far, it can be seen that there is no obviously significant difference observed for
the vapor effect as compared to the dry air isothermal case. Figure 3.4.9 provides further
insight into fracture location and alumina scale morphology as a function of vapor
exposure and dry air exposure. These two micrographs give a direct comparison between
specimens exposed to isothermal dry air and isothermal exposure with water vapor. It is
clear that most of the debonding is occurring at the oxide/bond coat interface.
The
micrograph in Figure 3.4.9(b) is of specimen 3B, which was exposed isothermally with
0.10 atm of water vapor for 350 hours. The morphology of the near-oxide region in this
specimen is highly similar to that of specimen 4B, which was exposed isothermally in dry
air for 500 hours.
Debonding is almost exclusively at the oxide/bond coat interface.
Measurements of oxide scale thicknesses in the vapor-exposed specimens have not shown
103
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Chapter 3. Application o f Conical Indentation Tests
significant differences in their thicknesses vs. time compared to those of specimens
exposed to dry air.
Bond Coat
100 urn
(a) 4 B d ry a ir 1100°C 500hrs
Bond Coat
100 ^im
(b) 3B vapor O.lOatm 1100°C 350hrs
Figure 3.4.9: Sectioned Views of TBC and Oxide Scale Morphology under Different
Exposure Conditions
Figure 3.4.10 gives further insight and compaiison for the TGO growth under
different exposure conditions. The value points indicated by black diamonds were taken
from the literature (Chang et a l, 2001). We can see that the current TGO values are all
above those in dry air after the values were all converted to the cases with the initial TGO
thickness of 0.25pm. However, the current results are taken without the consideration of
104
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Chapter 3. Application o f Conical Indentation Tests
the as-processed TGO thickness. It is very possible that the TGO thicknesses for the asprocessed cases for our current specimens are over 0.25pm. With this in mind, our
current 4B dry air, sectioned at SOOhrs, 5D vapor O.lOatm, sectioned at 120hrs, and 3B
vapor O.lOatm, sectioned at 350hrs, do indeed follow the previous dry air TGO growth
trend and magnitude closely. From this figure, we may conclude that the dry air and 0.10
atm vapor, all with the isothermal exposure condition, appear to have very similar TGO
formation mechanisms and nearly the same growth rate.
O
oH
C/D
( /)
(D
C
2^
•^o
X!
H
O
3
♦ Chang et al (2001)
Dry air #2
0. lOatm vapor #1
0. lOatm vapor #2
-O- O.SOatm vapor
2
o
H
^-----------------------------
0
0
100
200
300
400
Exposure time (hrs)
500
600
Figure 3.4.10: Oxide Thickness vs. Time at 1100°C under Different Isothermal Exposures
105
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Chapter 3. Application o f Conical Indentation Tests
3.4.4 Concluding Remarks
The investigation into the effects of steam exposure on TBC systems has been
performed. Despite significant evidence that water vapor can affect the adherence of bare
alumina scales, it appears that vapor exposures are having little affect on the PtAl TBC
system tested. This is evidenced in similar measured toughness loss vs. time data and in
observed fracture surface morphology and fracture paths. The rate of oxide scale growth
also does not appear to be strongly affected by vapor exposure. Work remaining is that a
possible visible effect on the degradation of PtAl TBC systems under harsh cyclic
exposure with the presence of water vapor be examined and a careful study of potential
differences in oxide scale microstructure also shows that there is no significant difference
between isothermally exposed specimens with or without the presence of water vapor.
However, a significant difference does exist between cyclic microstructure and isothermal
structures as will be stated elsewhere in this thesis. This further indicates that the
presence of water vapor at cyclic exposures may be important for further studies and also
it is still unknown if there will be noticeable differences in microstructure resulting from
vapor exposures before it manifests any visible influence. Nevertheless, it appears that
macro-scale changes in scale adherence or scale growth rates are not seen for this TBC
system in the isothermal dry air case, even for the relatively high exposure level of 0.30
atm of vapor.
106
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Chapter 3. Application o f Conical Indentation Tests
3.5 Mechanism-Based Tests for Cyclic Thermal Exposures
3.5.1 Introduction
In this section, research work has been directed toward a better understanding of
the degradation mechanism in the EB-PVD/PtAl TBC systems under cyclic loading
conditions. The fundamental mechanisms of cyclic oxidations controlling the TBC
degradation are to be investigated systematically by integrating the traditionally used
destructive/nondestructive methods (indentation/SEM imaging) with other novel non­
destructive methods (optical backscattered imaging and piezospectroscopy).
In the following sub-sections, an attempt has been made to describe how
destructive and nondestructive test methods have been combined to study the TBC
degradation. In the first sub-section, a preliminary study on the toughness degradation
due to cyclic thermal loading has been performed. This sub-section details not only the
difference of the toughness degradation with thermal history due to the cyclic and due to
the isothermal exposure conditions, but also the difference of the microstructures at the
interface caused by the different thermal exposure conditions. From the microstructure
observation, oxide damage at the interface is observed for exposures under the cyclic
thermal exposure while there is no apparent damage in oxide due to isothermal exposure.
The oxide damage apparently causes the relaxation of the residual stresses in this layer.
However, in this sub-section, the evolution of the in-situ stresses in the oxide layer with
the thermal cyclic exposure is not tracked quantitatively and assumed to remain the same
as in its as-processed state.
In the next sub-section, an in-depth study has been performed to integrate more
non-destructive methods to improve the toughness measurement and to track the residual
stress evolution after certain thermal cycles. Destructive indentation tests results are still
presented first which track “apparent” losses of interfacial toughness assuming that
fracture occurs at the alumina/bond coat interface and that no structural changes occur in
the TBC system with exposure. These results are important in assuring that the specimens
tested are equivalent not only in the as-processed state, but also after thermal exposure.
These results are also useful in quantifying losses in adhesion as seen by an observer who
107
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Chapter 3. Application o f Conical Indentation Tests
is not aware of structural changes in the TBC system (such as changes in oxide thickness
or residual stress).
Following this, nondestructive optical backscattering (by Dr. William Ellingson
and Mr. Robert Visher at ANL) and SEM charging results are presented which allow
precise tracking of the size of indentation-induced debonds.
In this way, these
nondestructive techniques have given more insight into the destructive indent test.
Lastly, results from the indentation tests are presented again, this time taking into account
known measured increases in oxide thickness (from the literature and previous work) and
measured reductions in oxide stress (from piezospectroscopy by Dr. Michael Lance at
ORNL) with thermal cycling. The remaining decreases in toughness with exposure are
then used to estimate the percentage of debonded area caused by cycle-induced
mechanical damage. These estimates give feedback on a possible cause of measured
stress reductions or the degree of micro-scale debonding that might be detectable via
optical backscattering.
3.5.2 A Preliminary Investigation
3.5.2.1 Indentation Tests and Toughness Measurements
The initial investigation on the cyclic exposures was done on a specimen,
designated to be the 4A specimen. The thermal cycles for the specimen 4A consist of 10
minutes heating from room temperature to 1100°C, 45 minutes at 1100°C and 10 minutes
cooling to room temperature. For the cyclic tests, the equivalent isothermal exposure
time per cycle is 45 minutes, so that 50 cycles is equivalent to 38 hrs of isothermal
exposure, 170 cycles equals approximately 120 hrs, 270 cycles equals approximately
200hrs, 470 cycles equals approximately 350hrs, and 670 cycles equals approximately
500hrs.
Similar to the 4B specimen in the previous study of the isothermal dry air
exposures, the 4A specimen is also exposed until almost complete failure occurs at an
equivalent isothermal exposure of 500hrs (670cycles). Compared with other isothermal
specimens, this cyclic exposed specimen was observed to experience more non-circular
108
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Chapter 3. Application of Conical Indentation Tests
debonds upon indentation events, therefore either the UHDR or the WDR method stated
previously was used for the measurement of the characteristic debond dimension R.
Table 3.5.1 lists the tested values of apparent toughnesses on this specimen. The
indentation tests at Ohrs refer to the as-processed toughness tests. We see that the
specimen can be well tested up to 470 cycles (equivalent to 350hrs isothermal). The
tested locations with labels up to 470 cycles are shown in Figure 3.5.1(a), which also
serves as a comparison of the surface before and after its pending spontaneous spallation
that occurred at about at 670cylces (or equivalent isothermal 500hrs) shown in Figure
3.5.1(b). Before the last indentation at location #7 was performed, the coating was found
still intact for most of the specimen surface. The spallation scenario seen in Figure
3.5.1(b) did happen upon the last indentation events. As the first load level of 60Kg was
gradually applied, the delamination at the left side at location #7 coalesced immediately
with the previous spots at locations #1 and #2 and then the interface cracking continued
to propagate and coalesce with each other and with the debonding found propagating
from the lower edges as shown in Figure 3.5.1(b). Although it is very clear that the
specimen is reaching its final complete spallation, the remaining intact ligaments of the
upper part of the specimen and the right side of spot #7 still suggest the apparent
toughness value is still larger than l.OMPa m*^^. To approximate the measurement of
apparent toughness at this exposure, it is reasonable to consider only the upper part of the
debonding region by the UHDR method. Moreover, at larger load levels of lOOKg, it was
found there is no buckling-driven delamination experienced upon indentation to the right
side, similar to what happened at 60Kg. This was also true for 150Kg. This suggests that
the toughness values at these three load levels can still be roughly approximated by the
UHDR method with the results listed in Table 3.5.1. Thus, we may have a rough idea of
the magnitude of apparent toughnesses before the spontaneous spallation occurs.
Special attention should be paid to some cases due to indentation after a certain
exposure. It was observed that the delamination size would not grow as it should do upon
subsequent larger indent load levels. As seen in Table 3.5.1, for example, the debonding
radii, R, of the cases at location #6 and #7 show little difference between that caused by
60Kg and lOOKg , or by lOOKg and 150Kg. This observation is rarely observed for the
109
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Chapter 3. Application o f Conical Indentation Tests
as-processed indentation tests, but frequently observed for indentations on a well-exposed
specimen. This is due to the fact that indentation on a well-exposed specimen is easier to
experience and satisfy the buckling-driven delamination criterion upon the first indent
event since the detached TBC layer is not totally broken before the release of the
indentation load. Thus the mode II propagation assumed here may change to the
combination of mode I and II. A small portion of mode I will tend to open the crack and
make the propagation of debonding much easier. That is to say, at a lower indentation
level, the delamination may experience over-debond and have an apparent size much
larger than that normally propagated under solely mode II conditions. After the film or
coating was broken, the further indentation event may not cause further debond or a very
slight increase in debond, since the over-debonded region at the lower indentation load
level may be too large to cause further crack propagation, or reach its subsequent critical
stress intensity factor to continue its propagation from its currently over-debonded front
from the previous indentation at lower load levels. Thus the lower load level debond
region may tend to underestimate the toughness value, while the subsequent debond size
due to a larger load level may tend to overestimate the toughness since the actually
undebonded location is not known. Thus the averaged toughness value is still found to be
the best for the approximation to annul the opposite effects of small load level indent and
large load level indent on the toughness evaluations.
Although some different debonding behaviors were observed for this cyclic
specimen as compared to the isothermal specimens, there is little indication from the
apparent toughnesses in Table 3.5.1 that there is any significant difference on the issue of
toughness degradation at the same equivalent thermal history compared with those of the
4B dry air isothermal specimen and those of the vapor specimens of 5D and 1C at early
exposure times. Yet all those values listed in Table 3.5.1 are all lower than the previous
dry air specimen toughness values at the same equivalent thermal history. Nevertheless, it
will be clear that significant differences exist between the microstructures caused by a
cyclic exposure and by an isothermal exposure.
110
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Chapter 3. Application o f Conical Indentation Tests
Table 3.5.1:Summary of Measured Data and Kc Values from Indentation Tests Performed
on 4A TBC Specimen Exposed at 1100°C under 1 hr Cyclic Dry Air
Location
Exposure
Load
R
a
Time
(kg)
(mm)
(mm)
R/a
Kc
Kc
[MPa (m)'^^]
[MPa (m)*^^]
(hrs)
Average
Specimen ID: 2Y4A
I
0
100
0.88
0.29
3.03
3.7
I
0
150
1.33
0.35
3.80
2.8
2
0
100
1.12
0.29
.3.86
2.7
2
0
ISO
1.36
0.35
3.89
2.7
3
3
3
3
3
3
5
5
5
6
6
6
7
7
7
37.8
37.8
37.8
120
120
120
200
200
200
350
350
350
500
500
500
60
100
150
60
100
150
60
100
150
60
100
150
60
100
150
X
1.22
1.40
X
1.63
1.75
1.37
1.68
1.67
1.70
1.70
1.88
2.10
1.95
2.92
X
0.29
0.35
X
0.29
0.35
0.21
0.29
0.35
0.21
0.29
0.35
0.21
0.29
0.35
X
4.21
4.00
X
5.62
5.00
6.52
5.79
4.77
8.52
6.17
5.37
10.00
6.72
8.34
X
2.4
2.6
X
1.7
1.9
1.5
1.6
1.9
1.2
1.5
1.8
1.2
1.4
1.2
111
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2.9
2.5
1.8
1.6
1.5
1.3
Chapter 3. Application o f Conical Indentation Tests
K,
o>
(a) al 470 cycles (350hrs)
(b) at 670 cycles (SOOhrs)
Figure 3.5.1: 4A Specimen Surface at Different Exposure History Before and at its Final
Failure due to Indentation and Thermal Exposure Events
3.S.2.2 Toughness Degradation Compared to the Isothermal Dry Air
Figure 3.5.2 shows the apparent toughness vs. exposure time for the isothermal
dry air and the one hour cyclic specimens. We see that the dry air cyclic thermal specimen
exhibits toughness degradation rates that are similar to those seen in the isothermal dry air
exposures. This result was expected. Previous work comparing cyclic and isothermally
exposed PtAl bond coat specimens using a 10 min/45 min/10 min thermal cycle
suggested that coating life is not strongly affected by this type of cyclic exposure.
Interestingly, examination of the fracture surface and structure of the alumina scale
suggests that the fracture event occurring after this type of cyclic exposure is quite
different from that occurring after isothermal exposures as will be detailed in the next
section.
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Chapter 3. Application o f Conical Indentation Tests
X Dry A ir Cyclic
3.5
□ Dry A ir Isotherm #2
3
u
oc
C /5
<D
C
4:3
tol)
o
H
-(—>
Sh
<u
Oh
C
2.5
2
1.5
I:
1
0.5
0
0
100
200
300
400
Time (hrs)
500
600
Figure 3.5.2: Toughness Loss vs. Exposure Time for Specimens with Measured As
Processed Toughnesses for Cyclic and Isothermal Dry Air
113
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Chapter 3. Application o f Conical Indentation Tests
3.S.2.3 Fracture Surfaces and Structure of the Alumina Scale
In Figure 3.5.3 the fracture surface under the same equivalent thermal history for
cyclic specimen 4A is compared with that of the isothermally exposed specimen. We see
that the cyclic fracture surface indicates most of the failure interface is at the mixture of
the TGO and TBC, while the failure occurs predominantly at the interface of TBC and
bondeoat for the isothermal specimen after 120hrs exposure. With the increase of thermal
exposure, the fracture surface under isothermal exposures reveals more and more
bondeoat surface. And the embedded TBC and TGO islands become smaller and smaller
as manifested by small isolated pockets after a sufficiently long isothermal exposure such
as shown in Figure 3.5.4(b) after 350hrs. However, a significant mix of TBC and TGO
still remains at the cracking interface of the cyclic specimen 4A such as shown in Figure
3.5.4(a) due to the back-scatter contrast and EDS analysis. It is also worth noting that as
more bondeoat surface is exposed isothermally, the oxide imprints left on the fracture
surfaces become larger and clearer. And at the same time, the shrinking pockets with
more TGO embedment than TBC embedment can be easily seen from Figure 3.5.4(b).
This is consistent with the observations stated in the literature (Mumm and Evans 2000).
nug
(a) 4A Ihr Cycle I70cycles (I20hrs)
(b) 7C Isothermal 0.3atm Vapor I20hrs
Figure 3.5.3: SEM Photographs for Fracture Surfaces of Specimen 4A and 7C under
Different Exposure Conditions after Experiencing the Same Equivalent Isothermal
Exposure Time of I20hrs
114
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Chapter 3. Application o f Conical Indentation Tests
i 2
r¥
iT'-.iP
■F'-'
(a) 4A Ihr Cycle 470cycles (350hrs);
(b) 4B Dry Air 350hrs
Figure 3.5.4; SEM Photographs for Fracture Surface of Specimen 4A and 4B at 350hrs
Figure 3.5.5 plots the relation between the white colored portion expressed as a
percentage of the whole fracture surface as a function of the exposure time for the dry air
specimen and the cyclic specimen. It is clear that the white color, indicative of the
exposed bondeoat surface, always increases with the increase of exposure regardless of
different exposure conditions as shown by the trend curves drawn by hand. At the same
time, we see that even at the early exposure time, significant oxide damage may have
occurred by observing the differences between the curve due to isothermal exposure and
that due to cyclic exposure. And this is consistent with the stress measurement indicating
a significant stress fall-off at the early exposure time due to cyclic loading as will be
presented in the later sub-sections. Furthermore, the results also show that the growth rate
of the white color (bond coat exposure) portion is about the same for the cyclic and the
dry air specimen with the increase of thermal exposure. We also see that at the failure
time, ~500hrs, the white area portion for the cyclic is about 58% and about 85% for
isothermal dry air, which suggests that significant TBC and TGO still remain for the
cyclic interface even at its final spontaneous spallation stage. This observation will be
even clearer from the cross-section view of the specimens as stated subsequently in this
section. Furthermore, the vapor specimen’s fracture behavior was observed to be only a
little different from the dry air ones.
115
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Chapter 3. Application o f Conical Indentation Tests
100
a
<D
80
(D
JC3
60
O
<D
wa
c3
+-•
a
(D
O
Vh
<D
CLh
40
20
X D ry air cyclic
[— I
T A
•
/1
^ Dry air #2
0
0
100
200
300
400
500
E xposure tim e (hrs)
Figure 3.5.5: Fracture Surface Analysis as a Function of Exposure Time
for Different Specimens
116
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600
Chapter 3. Application o f Conical Indentation Tests
So far, it can be seen that the fracture path can be very different in a PtAl TBC
system under cyclic loading compared to that in isothermal loading. The significant
difference found in the cyclic fracture morphology may be due to the formation of the
transient oxide spinels(Yanar et a l, 2002) at the TBC-TGO interface, and these oxide
spinels together with that of interface imperfections assume the major responsibility for
the cracking in the TBC-TGO interface. Such combined cracking patterns, i.e., cracking
simultaneously along two interfaces of TBC-TGO and TGO-BC as well as cracking
through the TGO layer directly, are not observed in isothermal exposures with or without
water vapor present.
In summary, from the above fracture surface results, it is worth noting that the
TBC specimens subjected to cyclic thermal exposures do not undergo a transition in
fracture surface morphology or fracture location to the extent that isothermally exposed
specimens do.
As with isothermally exposed specimens, there is a transition from
debonding almost exclusively in the TBC to a mixed type of debonding and
predominantly at the interface of the TGO and bondeoat; however, for cyclically exposed
specimens the debonding remains mixed until failure.
This is presumably caused by
cycle-induced microcracking in the region near the TGO.
This difference in fracture
surface evolution is seen even for the thermal cycle used in specimen 4A, which shows
no significant difference in toughness degradation vs. time.
Figure 3.5.6 provides further insight into fracture location and alumina scale
morphology as a function of vapor exposure and thermal cycling. These micrographs
give a direct comparison between specimens exposed to isothermal and cyclic thermal
exposures after 500 hours. In the isothermal case, it is clear that most of the debonding is
occurring at the oxide/bond coat interface.
In the cyclic thermal case, the debonding
behavior is quite different. The TGO appears to be broken up and debonding clearly
involves a mix o f TBC, oxide and oxide/bond coat interface fracture. Again, it should be
noted that despite this very different fracture behavior, both the isothermal and cyclic
thermal specimens show similar toughness values.
117
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Chapter 3. Application o f Conical Indentation Tests
! 1
Bond Coat
100 ^m
(a) 4 B d ry a irll0 0 ° C 500hrs
Bond Coat
1 0 0 |im
(b) 4A Ihr cyclic 1100°C 670cycles (500hrs)
Figure 3.5.6: Sectioned Views of TBC and Oxide Scale Morphology in Failed Specimens
118
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Chapter 3. Application o f Conical Indentation Tests
3.5.3 An In-depth Study by Integrating Improved Non-destructive Methods
3.5.3.1
Toughness
Measurements
from
Indentation
Assuming
No
Changes in the TBC System
Based on the preliminary investigation on the cyclic exposed specimen, we have
noticed that significant differences exist between the microstructures of the isothermal
dry air exposed specimen and the cyclic exposed specimen, regardless of the apparent
toughness degradation, registering no significant change as compared to each other. This
is envisioned due to the fact of the dual effect of the oxide layer damage due to the cyclic
exposure. One is that the damage at the interface between the TBC layer and the bondeoat
layer causes the stress relaxation, which tends to lower the true interfacial toughness
values. At the same time, the damage caused stress relaxation also decreases debond
driving energy at the interface. These dual effects cause the apparent toughness values to
remain consistent with the dry air exposed specimens. These observations initially
provided an incentive for a detailed study of the investigation of the in-situ measurement
of the stresses caused by the cyclic damage in the TGO layer through nondestructive
testing congruent with destructive methods.
Three EBPVD/PtAl TBC specimens were initiated for the first round of
destructive/nondestructive tests. The original designation inscribed on the back of the
specimens are 7A, 8A and 6A respectively and thereafter we refer them as #1, #2 and #3,
respectively for the sake of convenience. Destructive measurement of specimen
interfacial toughness via indentation has been carried out in parallel with nondestructive
tests. Toughness measurements are used to not only track TBC system degradation, but
also as a quality control method for ensuring that individual specimens are equivalent.
Specimen exposures consisted of thermal cycles of 10 minutes heating, 45 minutes at
1100°C and 10 minutes cooling. The test plan for the 3 specimens is shown in Table
3.5.2.
119
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Chapter 3. Application o f Conical Indentation Tests
Table 3.5.2; First Round Tests of TBC Specimens
Specimen
Cycles
Time at
Tests Performed
Temperature (hrs)
1
0
0
Indent, Piezo, Opt Back
2
0
0
Indent
50
37.5
Indent
170
127
Indent, Piezo
270
202.5
Indent, Piezo
470
352.5
Indent
0
0
Indent
50
37.5
Indent
170
127
Indent, Opt Back
270
202.5
Indent, Opt Back
470
352.5
Indent
3
Figure 3.5.7 provides a plot of indentation test results for TBC specimens #2 and
#3. The times of exposure for identically exposed specimens are shifted slightly to allow
clear viewing of the plotted points. Values of Kc are calculated from measured debond
areas (converted to average debond radii by dividing the debond area by pi and taking the
square root) using fracture mechanics formulas that assume “as processed” oxide
thickness and stress values of 0.25 p m and 3.5 GPa for all exposure times. As a result,
the plot gives an “apparent” loss of toughness with exposure, ignoring changes in the
structure of the TBC system. Under these assumptions, the value of K solely due to
residual stress in the TBC and oxide is approximately 1 MPam'^^. As a result, when the
toughness falls to this value (designated by a horizontal dashed line in Figure 3.5.7),
spontaneous spallation of the TBC can occur.
As indicated in the plot, specimens #2 and #3 had highly similar toughnesses in
the as-processed state and after 50, 170, 270 and 470 thermal cycles. Furthermore, their
toughness values were similar to those measured in another specimen fabricated during
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Chapter 3. Application o f Conical Indentation Tests
the same processing run.
Although it is not plotted in Fig. 3.5.7, the as-processed
toughness for specimen #1 (which has not been thermally exposed) was comparable to
those of specimens #2 and #3 and the previously tested specimen. The consistency in
measured toughnesses for all three specimens tested confirmed that they were comparable
with respect to their resistance to spallation. This allowed specimens #2 and #3 to be sent
separately to ORNL and Argonne after 170 and 270 cycles of exposure, with confidence
that both techniques were being applied to comparable specimens. It also allowed results
from nondestructive evaluations of specimen #1 to be treated as indicative of the asprocessed state for all 3 specimens (see Table 3.5.2).
As has been noted in the previous sections of the same chapter and as seen in
Figure 3.5.7, a large amount of apparent toughness loss occurs at early exposure times.
This suggests the possibility that substantial mechanical damage at and near the
alumina/bond coat interface also occurs at early exposure times, and that this damage
might be detectable by non-destructive evaluation (NDE) methods. In the third section on
TBC systems, an attempt will be made to quantify the relationship between toughness
loss and interfacial damage by accounting for known changes in the TBC system with
exposure.
121
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Chapter 3. Application o f Conical Indentation Tests
4
O Specimen #3
□ Specimen #2
^ Previous Specimen
3.5
3
u
c/T
CO
<D
2.5
2
W)
3
o
■t—
>
c
D
a
a
<
1.5
1
K Due to Residual
Stresses Only
0.5
0
0
100
200
300
400
Exposure Time (hrs)
500
600
Figure 3.5.7: Plot of TBC Interfacial Toughness vs. Exposure Time for Specimens #2
and #3.
122
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Chapter 3. Application o f Conical Indentation Tests
3.5.3.2
Optical Backscattering Results
Accurate measurements of debond radii are required for interfacial toughness
measurements. The two techniques for debond radius measurements in development are
laser backscatter (developed at ANL) and SEM charging imaging (developed by Pis at the
University of Pittsburgh). TBC specimen 3 was imaged after 170 and 270 thermal cycles
at 1100°C and images of indents are presented in Figures 3.5.8 and 3.5.9 respectively.
These four indents were induced in the as-processed state, after 50 cycles, after 170 cycles
and after 270 cycles. The first three indents were imaged after 170 cycles.
Initially indented
after 50 cycles
Initially indented in
as-processed condition
Indented after
I70cycles
O ptical M acrograph
L aser Scatter Im age
debonds appear dark
SEM C harging Im age
debonds appear light
Figure 3.5.8: Composite Figure Showing Micrograph, Backscatter and SFM Charging
Images after 170 Cycles. Center Indent was Performed before any Thermal
Exposure, Left Indent was After 50 Cycles and the Right Indent was After 170
Cycles.
123
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Chapter 3. Application o f Conical Indentation Tests
Figure 3.5.9: Backscatter (a and b) and SEM Charging (c) Images of TBC Indent after
270 Cycles. Backscatter (a) is Constructed by Establishing the Ratio of the
Signals from the Two Detectors and (b) by Summing the Output of Both Detector
Signals.
The experience at ANL regarding the development of the elastic optical back
scatter method, is that the ratio “image” data is a measure to the extent of the de­
polarization of the light, and often produces a gray-scale inversion as compared to the
summation image. Determining how to properly interpret these two data sets is an area of
study at ANL. The first image type, ratio, is constructed from the ratio signals from the
two detectors and the other type, sum, is created by the summation of these signals. A
comparison of a ratio and sum image is shown in Fig. 3.5.9.
Debond imaging by the laser backscattering technique utilizes one of two laser
systems at ANL. One system uses a 633nm He-Ne laser and the other system uses a
tuneable solid state Ti; Saphhite laser with a tuneable wave length between 670
nanometers and 970 nanometers. Both setups use similar detectors for data collection.
Visualizing debonded regions in TBC systems by the SEM charging technique
requires use of the high voltage settings on a standard SEM. The high voltage induces a
negative charge in the debonded portions of the coating. Charged regions appear lighter
because of the high intensity of scattered secondary electrons. This effect is evident in
SEM images in Fig. 3.5.8 and 3.5.9, where the debonds are viewed from above. Imaging
by this technique has allowed rapid determination of debond radii.
Because of multiple indents, this specimen also allowed a direct comparison
between the SEM charging technique and the optical backscattering technique in
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Chapter 3. Application o f Conical Indentation Tests
quantifying the size of the debonded regions. As indicated in Tables 3.5.3 and 3.5.4, both
methods give similar values for R, the debond radius, with the charging technique
generally yielding slightly smaller values. These lower values from the SEM charging
images are a result of two phenomena. First, this is consistent with the expectation that
the charging technique may not be able to distinguish debonded TBC and oxide layers
that are still in contact with the substrate from fully bonded layers, thus this short circuit
can cause an underestimated debond size. Secondly, features not sensitive to charging
appear smaller in the SEM as compared to the backscatter image. An example is the
missing TBC near the indent in Fig. 3.5.9 where the longest dimension is 2.51 and
2.25mm from the backscatter and SEM image, respectively. The error in the SEM image
results from the negative charge that develops on the surface of the sample. In addition to
increasing the secondary electron intensity, this negative surface charge deflects the
electron beam that results in scanning a larger area. This produces an image of lower
magnification than reported. Errors in the debond measurements will be addressed in
future work and appropriate corrections will be developed.
Tables 3.5.3 and 3.5.4 give debond size results from four indent tests performed
on the TBC button specimen #3, using the SEM charging and Optical Backscattering
techniques. In each case, an effective debond radius is obtained by measuring a debond
area, then taking the square root of that quantity divided by Pi. Although indentations
were done in the as-processed, 50 cycle, 170 cycle and 270 cycle conditions, debond size
measurements of existing indents were taken after 170 cycles (see Table 3.5.3 and the
images in Fig 3.5.8) and after 270 cycles (see Table 3.5.4 and the image in Fig. 3.5.9).
The debond radius values given in Tables 3.5.3 and 3.5.4 indicate, that the
underestimation of the debond area or radius from the SEM charging technique is small.
The difference is also small if it is put in terms of a fracture toughness value, Kc,
calculated from the measured debond radii.
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Chapter 3. Application o f Conical Indentation Tests
Table 3.5.3; SEM Charging vs. Optical Backscattering Measurements of Debond Size
Cycles
R
R
SEM
Backscatter
(mm)
(mm)
0
1.39
1.40
0.7
2.63
2.60
-1.1
50
1.60
1.66
3.8
2.17
2.08
-4.1
170
1.74
1.82
4.6
1.95
1.86
-4.6
for
% Diff
Kc
Kc
SEM
Backscatter
Initial
(MPa
% Diff
(MPa m’^'")
Indent
Table 3.5.4: SEM Charging vs. Optical Backscattering Measurements of Debond Size
Cycles
R
R
SEM
Backscatter
(mm)
(mm)
0
1.49
1.46
50
1.67
170
270
Kc
Kc
SEM
Backscatter
(MPa m'-"^)
(MPa m^'"')
-2.0
2.39
2.45
2.5
1.80
7.8
2.06
1.89
-8.3
1.88
2.01
6.9
1.79
1.67
-6.7
1.99
2.15
8.0
1.68
1.56
-7.1
for
% Diff
Initial
% Diff
Indent
126
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Chapter 3. Application o f Conical Indentation Tests
3.5.33
Toughness Measurements from Indentation Including Changes in
Oxide Thickness and Stress
As noted previously, the plot of toughness loss vs. time provided in Figure 3.5.7
does not take into account changes in the TBC system that are known to take place with
cyclic thermal exposure.
For instance, for the case of a constant residual stress in a
growing alumina layer, the “apparent” toughness of the alumina/bond coat interface
would degrade even in the absence of a true loss of toughness at the interface. In other
words, the TBC would become less adherent due to increased energy stored in the
alumina acting to drive debonding, independent of true interfacial toughness loss
mechanisms such as mechanical damage or segregation of elements to the interface. In
order to link measured toughness losses to interfacial damage (which can potentially be
tracked by nondestructive methods), an accounting must be made of other changes in the
TBC system that can affect “apparent” toughness or adherence.
It is also important to note that the plot of Figure 3.5.7 assumes that debonding
occurs at the alumina/bond coat interface. However, under cyclic loading conditions, the
fracture path is observed to be mixed, with some cracking occurring at the base of the
TBC and in the alumina in addition to occurring at the interface with the bond coat.
Cracking above the alumina/bond coat interface is important to consider because it is not
driven by a release in energy from the debonding of the alumina. As a result, it is not
affected by thickening of the alumina or changes in its residual stress.
Figure 3.5.10 provides a plot of TBC interfacial toughness (for debonding at the
alumina/bond coat interface) as a function of thermal cycles with trend curves drawn by
hand, demonstrating the effect of alumina thickness increases and reductions in alumina
scale residual stress. For reasons that will become apparent, the toughness is presented in
terms of a critical energy release rate, Gc, in J/m^ instead of a critical stress intensity
factor, Kc in MPa
In the plot, the data with solid circles and solid lines is the same
data presented in Figure 3.5.7, converted to energy release rates. The data presented as
open boxes with dashed lines is the same experimental data, but with energy release rates
calculated using measured alumina layer thicknesses from previous work by Vasinonta
and Beuth (2001), Handoko et al. (2001), and from the literature (Chang et a l, 2001) and
127
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Chapter 3. Application o f Conical Indentation Tests
the values of -3.86GPa, -1.46GPa and -1.27GPa measured by piezospectroscopy at 0, 170
and 270 cycles, respectively. Although the measured stress value of -3.84 GPa is used to
obtain the open box data point for 0 cycles in Figure 3.5.1, the resulting Gc value is
essentially the same as that obtained using a stress value of -3.5GPa (solid circle). This is
due to the oxide thickness of 0.25 p m in the as-processed state. Because the alumina is
very thin, it does not contribute significantly to G regardless of the magnitude of its
residual stress. The oxide thickness values used at 170 and 270 cycles were 2.49 and 2.75
jum, respectively (Chang et al., 2001).
As the plot in Figure 3.5.10 shows, if alumina layer thickness and stress changes
are accounted for, a toughness loss is still seen at the interface (open symbols), though it
is smaller in magnitude than the loss suggested if such changes are not included (solid
symbols). Also, the curve designating the energy release rate due to residual stresses only
is no longer a horizontal line. It increases with exposure (open symbols). It is still true
for the open symbol data, that when the upper curve (designating interfacial toughness or
resistance to debonding) reaches the lower curve (designating the energy release rate due
to residual stresses acting to drive debonding), spontaneous spallation can occur.
However, now the stored energy is shown to be increasing with thermal cycling. What
these two curves collectively indicate is that the increase in stored elastic energy due to
the increase in alumina thickness (by a factor of approximately 11 compared to the asprocessed thickness of 0.25 pm ) more than makes up for the decrease in stored elastic
energy due to the decrease in alumina residual stress (a decrease in residual stress
measured in this program via piezospectroscopy). As a result, some, but not all of the
observed “apparent” toughness losses in Fig. 3.5.7 are due to a net increase in stored
elastic energy in the alumina.
Although all potential mechanisms that could lead to apparent toughness loss have
not been accounted for, if it is assumed that the toughness loss shown by the dashed curve
in Fig. 3.5.10 (including known changes in the alumina layer) is a true toughness loss due
to mechanical damage, the extent of that damage can be estimated. The energy release
rate driving debonding is defined as the stored elastic energy released by the debonding
event, divided by the crack surface area created during the debonding event. Because of
128
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Chapter 3. Application o f Conical Indentation Tests
this, if the bonded area is reduced by 50% before the debonding event occurs (due to
microcracks that have already debonded half of the interface) the amount of energy
needed to drive debonding will also be reduced by 50%. As a result, the measured value
of Gc, which is obtained by dividing the energy released by the total interfacial area will
be reduced by 50%.
Based on this argument, if it is assumed that the dashed curve
indicates a toughness loss due to mechanical damage at the interface, a percentage
toughness loss expressed in terms of Gc equals a percentage loss of bonded interface
before the delamination occurs. As a result, the data from Figure 3.5.10 suggests that
approximately 43% of the interface is debonded after 170 cycles and 57% is debonded
after 270 cycles.
Figure 3.5.11 gives a plot analogous to that of Figure 3.5.10, however, a
comparison is made between the results originally plotted in Figure 3.5.1 (debonding at
the alumina/bond coat interface and no changes in the alumina) and results from the same
experimental data, but with Gc values determined assuming debonding of the TBC only.
If only the TBC debonds, stress and thickness changes in the alumina do not contribute to
apparent toughness losses. Because the alumina remains bonded to the bond coat and
superalloy substrate, its elastic energy is not released.
As in Figure 3.5.10, the link
between percentage reductions in Go and percentage loss of bonded interface before
delamination still exists, however, now the interface is the interface between the TBC and
the alumina.
The data of Figure 3.5.4 then indicate that approximately 67% of the
TBC/alumina interface is already debonded after 170 cycles and 76% is debonded after
270 cycles.
If the debond occurs below the alumina, the elastic energy stored in the alumina
can be released. For debonding to occur at the TBC/alumina interface, the toughness at
that interface must be lower than that at the alumina/bond coat interface. However, even
if the two interfaces have roughly equal toughnesses in the as-processed state, a condition
of effectively lower toughness at the TBC/alumina interface can result if more
microcracking occurs there as a result of thermal cycling.
The results of Figures 3.5.10 and 3.5.11 suggest that the amount of debonded area
existing after 170 and 270 cycles is substantial - independent of whether the debond
129
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Chapter 3. Application o f Conical Indentation Tests
crack propagates below, above or within the alumina layer.
Because it suggests
accumulation of significant, potentially measurable damage for a small numbers of
cycles, this finding is consistent with the concept of using nondestructive evaluation
(NDE) methods to detect damage early in TBC life, and with the goal of predicting life by
using NDE to track damage accumulation at early stages.
50
No Changes
Thickness and
Stress Changes
40
u
o
(D
GO
cd
30
20
13
tUQ
CJ
c
W
10
0
0
100
200
300
400
Exposure Time (cycles)
500
Figure 3.5.10: Toughness Loss vs. Number of Cycles Assuming No Changes in the
Alumina Layer (Same Results as in Figure 3.5.7) and Taking Into Account
Measured Alumina Layer Thickening and Reductions in Stress.
130
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Chapter 3. Application of Conical Indentation Tests
50
Debonding of
TGO & TBC
T^D ebonding of
TBC Only
(N
40
u
a
(D
Id
<D
c/i
cd
(Oi
(D
I'll '
30
20
bJ)
<D
fi
10
-
t —
0
0
100
200
300
400
500
Exposure Time (cycles)
Figure 3.5.11: Toughness Loss vs. Number of Cycles Assuming Debonding of the
Alumina and TBC (Same Results as in Figure 3.5.7) and Debonding of the TBC
Only.
131
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Chapter 3. Application o f Conical Indentation Tests
3.5.4 Concluding Remarks
In this research, a conventional destructive indentation method has been integrated
with the non-destructive methods for an improved evaluation and better understanding of
toughness degradation at interface during thermal cycles. Optical backscatter imaging
technique (nondestructive) significantly improves the measurement of oxide debonds due
to indentation and it shows that the measurement by the SEM charging technique (also
nondestructive) underestimates the debond radius in general. However, the difference
between oxide debonds due to these two techniques are negligibly small. This proves that
the SEM charging technique serves an inexpensive way for the evaluation of oxide
debonds without losing significant accuracy. Piezospectroscopy measurement of oxide
stress (nondestructive) techniques has been used to track the stress evolution in the oxide
layer quantitatively. And those stresses are then integrated into the fracture model to have
a better understanding of the issue of interfacial toughness degradation.
132
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Chapter 3. Application o f Conical Indentation Tests
3.6 Chapter Summary
In this chapter, mechanics due to standard conical indentation presented previously
in Chapter 2 have been applied to various mechanism-based studies of toughness
degradations in EB-PVD/PtAt TBC systems. Knowledge of free-edge effects has allowed
multiple indents on a single specimen in eases where delamination radii are relatively
small. This and incremental indentation techniques explored in this study allow multiple
toughness values to be obtained from a specimen and from a single location within a
specimen. By greatly increasing the number of toughness values from a single specimen,
these methods have helped in understanding specimen-to-specimen variability in
toughness, which can be significant. Through these studies, it was found that the
indentation mechanics developed herein is not only a valid means to track apparent
interfaeial toughness loss with exposure hours, but also an efficient way to identify failure
mechanisms underlying various thermal exposure environments. Significant devopments
on those mechanism-based tests include ranking the failure mechanisms , promoting TBC
duration relevant models and aeeelerating testing methods by Arrhenius plot for dry air
isothermally exposed specimens; identifying the effects of water vapor in a simulative
environment with those in isothermal dry air and cyclic conditions; utilizing the
combination of destructive vs. non-destruetive techniques to provide a quantitative
evaluation of the portion of micro-failure, i.e, decohered area portion at interface before
macro-failure at spontaneous spallation.
For dry air isothermally exposed specimens, the ranking among the mechanisms that
cause the apparent toughness degradation from most important to least important are
found as: (1) oxide thickening, (2) sintering; and (3) chemical reaction or mechanical
damage at interface. Moreover, increasing exposure temperature significantly increases
the oxidation rate and sintering rate and thus temperature is identified as the main factor
in causing the TBC failure effectively. Quantitative analysis o f toughness degradation as a
function of exposure time including oxide thickening at a fixed temperature indicates that
the oxide thiekening is responsible for most of the apparent toughness degradation. The
quantitative analysis also indicates that the sintering effects may also contribute to the
apparent toughness loss. Chemieal reaction and mechanical damage may take the least
133
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Chapter 3. Application o f Conical Indentation Tests
responsibility for causing the as-processed toughness degradation. Thermally activated
mechanisms are used to model the oxide growth as well as the sintering effects on the
TBC stiffness modulus as a function of temperature and exposure time effectively. Those
simple models may be used efficiently for the prediction of toughness loss and TBC
duration before spontaneous failure. Furthermore, Arrhenius analysis may serve as an
efficient tool for the use of accelerating tests in TBC systems.
Although through this study, we found the presence of water vapor does not
significantly affect the apparent toughness degradation as compared to the isothermal and
cyclic conditions, still there exist significant differences on the microstructures of the
thermally cycled specimens with those of isothermally exposed specimens with or
without the presence of water vapor. Therefore, it is unknown if water vapor may effect
toughness degradations in cyclic exposed environments. As the studies proceed in the last
part of this chapter, it becomes very clear that the oxide damage at the interface due to
cyclic exposures relaxes the residual stresses significantly with the increase of exposure.
If the stresses are considered as in-situ exposures, the apparent toughness would be much
lower than those under isothermal exposures. Furthermore, nondestructive evaluation
methods assist in the evaluation of destructive methods on significantly improved
quantitative evaluations of interface degradations.
134
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
____________Fracture _______________________________________________________________________________
CHAPTER 4. INDENTER SHAPE
EFFECTS ON THE
DELAMINATION
MECHANICS OF
INTERFACIAL
FRACTURE
4.1 Chapter Overview
In this chapter, the limitations of the existing standard conical indentation tests
will be first addressed. This limitation discussion elicits an idea for obtaining optimal
debonding sizes to extend the capabilities of the quantifieation of interfaeial fracture
toughness due to the standard conical indentation method. Next, the eonstitutive
behaviors of the EB-PVD TBC substrate system considered in the previous study by
Vasinonta and Beuth (2001) will be reviewed and compared to a more generalized
description — the modified Ramberg-Osgood relation. Finite element methods including
the algorithm of spherical indentation will be introduced.
Following the general description of the hardening behaviors of the substrate
systems, the mechanics of conical indentation will be addressed first. The approaches
include the indent load distributions as a function of contact sizes for the various conical
indenters, the surface displacement distributions and the surface strain distributions as a
function of normalized distance away from the contact region. As a common procedure, a
general study on a large substrate with a single material will be performed before the
analysis on the standard EB-PVD TBC specimen. The purpose of this is to obtain
confidence on the numerical results by comparing them to those of the analytical results.
The mechanics of spherical indentation is addressed following the investigation of the
mechanics of conical indentation. Load distributions as well as the surface displacement
profiles are obtained from the numerical simulations on the standard EB-PVD TBC
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfaeial
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substrate systems. The behavior of the spherical indentation is very different in nature as
compared to that of the conical indentation as this will be detailed in the relevant section.
To proceed from here, the numerical results of the surface field solution profiles
are then integrated with the formulations developed in the second chapter. The interfaeial
stress intensity factor distributions are evaluated based on the indentation induced by
various shapes of indenters. These include the curves of the K vs. R/a of the conical
indentation with various tip angles and the curves of the K vs. R/a of the spherical
indentation as a function of a/Rb.
Finally, the experimental studies have been performed to illustrate and validate
the idea of using different shapes of indenters to obtain interfaeial toughness values on a
well-exposed EB-PVD TBC specimen. The study of this section includes the tests of a
sharper cone vs. the standard cone at the same indentation depth; the tests of the standard
cone vs. a blunter cone at the same indentation load level; the spherical indentation with
different sizes of diameters at the same indentation load level of 150Kg. This is
accompanied by a discussion on the insights gained from the numerical results as well as
the experimental studies, and the benefits of using different shapes of indenters are
summarized.
4.2 Limitations of the Existing Conical Indentation Test
The mechanics of conical and spherical indentation of an elastic-plastic substrate
has been considered by many researchers. Early research in this area mainly focused on
determining the mean contact pressure beneath the indenter to obtain insight into
materials hardness testing with various indenter geometries (Tabor, 1951; Johnson, 1970,
1985; Hill, 1950; Bhattacharya and Nix, 1988, 1991). Begley et al. (1999) presents a
detailed study of surface strain distributions beneath or near a spherical indenter on an
elastic-plastic substrate with an elastic film on top. Results are given detailing the strain
distributions in the contact region, where non- proportional loading occurs, and insight is
given into the interpretation of elastic thin film cracking pattems beneath the indenter.
However, there are no details given for the field solutions away from the indentation. In
particular, there appears to be no existing literature on the use of spherical indentation to
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfaeial
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quantify interfaeial toughness in TBC systems. Indenter shape has been considered in the
case of wedge indentation of TBC systems (Begley, et al., 2000; Mumm and Evans,
2000). Their work considers wedges having angles of 90° and 120°, with some model
results compared with those from models of conical indentation.
Despite some existing work looking at the role of indenter shape in the adhesion
testing of coatings, there is a lack of a complete study on the effects of indenter shapes,
especially for substrates that undergo significant work hardening during indentation. In
adherent coating systems such as as-processed TBCs and oxide scale systems (with no
TBC on top) indentation by some indenter shapes is not sufficient to induce interfaeial
debonding. Depending on the application, some indenter shapes may be more efficient at
inducing debonding than others.
These issues serve as the primary motivation for a
detailed study in this thesis on the role of the indenter shape in coating toughness testing.
Recent tests on the EBPVD TBC systems and tests directed at other applications
have highlighted limitations of the existing conical indenter test. These limitations may
be addressable by considering the use of a range of indenter shapes to determine
interfaeial toughness.
For example, one EBPVD TBC specimen tested in the as-
processed condition before isothermal exposure at I200°C in dry air did not undergo clear
debonding upon indentation using a standard 120° cone. As shown in Fig. 4.1(a), SEM
images of this specimen showed a clear indent spot but no delamination. For such cases
the interfaeial toughness cannot be determined.
The cause of this is most likely a
specimen with a large interfaeial toughness, coupled with an energy release rate from
indentation using a standard cone that is not sufficiently large to cause delamination.
Figure 4.1(b) illustrates how multiple indentations are made on a single specimen
to track toughness loss. This specimen was exposed isothermally at I IOO°C in dry air.
As shown in the figure, indentation can result in the coalescence of debonds and/or
buckle-driven delaminations. Neither of these conditions is accounted for in the analysis
of the indent test and toughness values cannot be extracted when they exist. It is clear
that the coalescence of debonds is due to the interaction with nearby debonds made after
earlier exposures. Buckle-driven debonds are caused by the indentation-induced debond
reaching the critical size for buckling of the coating. In both cases, reducing the size of
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfaeial
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the indentation-induced debond by using a different indenter shape could be the solution.
In this situation, the goal would be to pick an indenter shape that yields smaller energy
release rates at a given radial distance than are seen in the standard test.
I
iK:
»'
^
,
.
d - .1 "
’
*^1 . ,
.j
t'
.
\ i
I
,
-
.
a) Dry air specimen for 1200°C exposure;
No debonding in as-processed condition
b) Dry air specimen at 1100°C after 350 hrs
® Crack coalescence; @ Buckling driven
Figure 4.1: Illustration of Problems Observed in Previous Indentation Tests of the
EBPVD TBCs
In observing the above problems encountered in the standard indentation test, a
key question is how a change in indenter shape may benefit those tests. Using different
shaped indenters, the capability of measuring interfaeial toughness of various systems is
expected to be much broader. In analyzing new indenter shapes, special attention will be
paid to the peak values of K vs. R/a curves.
It is expected that peak values will be
sensitive to not only indenter shape but also substrate material properties and contact
conditions.
Attention will also be paid to the distribution of K va. R/a curves,
determining conditions where large K values are confined to small values of R/a versus
cases where large K values extend to large R/a values. It is expected that a change in
indenter shape (and substrate properties and contact conditions) will result in changes in
the distribution of K vs. R/a, with corresponding changes in indentation-induced debond
sizes.
138
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfaeial
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One feature of conical indentations is that results presented as a function of R/a
(i.e. normalized by the indent size) are load independent. In contrast, indentation by other
shapes, such as by a sphere, is load dependent.
The reason is that the geometry of
spherical indentation is not self-similar like a conical indentation. For small indentation
depths, spherical indentation involves indentation by a blunt object. For large indentation
depths, the indentation strain field is like that from a sharp object. Because it can induce
a range of indentation behaviors, and because it is a standard shape used in indentation
and impact testing, a study of spherical indentation tests for interfaeial toughness is
planned for this thesis.
In summary, observations from some existing indent tests indicate a need for the
investigation of different indenter shapes to optimize toughness testing. Therefore, it is
proposed to model and perform static indentations on EB-PVD systems by various
conical and spherical indenters. Specifically, indenter shape geometries of rigid cones
with various tip angles, namely, 60°, 90°, 120°, 150°, and solid spheres, with diameters of
1/8", I/I6", and 1/32", (corresponding to 3.18mm, 1.59mm, and 0.79mm, respectively)
will be investigated using finite elements.
4.3
Constitutive Behavior and Finite Element Model
4.3.1 Constitutive Behavior
Let us give a brief review of the constitutive behavior often used in recent
literature (Biwa et al., 1995; Drory and Hutchinson, 1996; Begley et a l, 2000; Vasinonta
and Beuth, 2001; Hill et ah, 2004) to describe the behavior due to work hardening. Three
hardening versions of isotropic J 2 flow theory are to be discussed herein; a piecewiselinear/power-law, the Ludwigson modified power-law and a modified Ramberg-Osgood
strain-hardening law. For all the descriptions, the yield strength is defined by ay, the yield
strain by 8y and the initial slope of the uniaxial stress versus strain curve defines the
Young’s modulus E =Oy/8y.
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfaeial
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•
Piecewise-linear/Power-law Hardening Law
In the simple piecewise-linear/power-law hardening under uniaxial tension, the
total strain is linear in strain for£T<aY , and is power-law in strain beyond the yield
strength, c r >a Y
£=—
E
K
fors<—
E
(4.1a)
fore>—
E
(4.1b)
where, N is the strain-hardening exponent, and K satisfies K = o,,
SO that the
V^Y
relationship at the transitory point may be consistent.
Although, this version of uniaxial stress vs. strain behavior is simple and easy to
use, this relation is hard to describe for many material behaviors since there is only one
hardening parameter, N, to justify. The experimental data is hard to capture by this
hardening relationship. Nevertheless, we include this version for utilizing and
commenting on some useful results of the spherical indentation by Biwa et al. (1995); and
Hill et al. (2004). Additionally, the relation that can be described by this linear power-law
relation can also be described by the modified Ramberg-Osgood relation as illustrated in
the next subsection; for the instance of the bondcoat properties used in the previous study
by Vasinonta and Beuth (2001) from Wasilewski, et al. (1967).
•
Ludwigson Modified Power Law Hardening
The hardening behavior following Ludwigson modified power law takes the form
(Ludwigson 1971) of;
o
= K ,8 " '+ e ‘^^e"^^
(4.2)
where a and e are the true stress and logarithmic strain, respectively and Ki, ni, K 2 and n 2
are the numerically fitting results from the experimental data.
This version of the hardening rule captures the experimental stress strain curve
very well as shown in the previous work by Vasinonta and Beuth (2001). However, the
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
____________ Fracture _______________________________________________________________________________
disadvantage is its lack of flexibility since there are several hardening parameters
involved, and this makes it difficult if a general study is necessary for the investigation of
the influence of hardening parameters.
•
Modified Ramberg-Osgood Hardening Law
The traditional Ramberg-Osgood relation as the hardening rule is frequently used
in the literature (Drory and Hutchinson, 1996; Begley et al., 2000). However, we find in
that the traditionally used Ramberg-Osgood relation it is also difficult to capture most of
the hardening behavior of metal alloys. The limitation extends to the parameter, a, which
bears the meaning of the control at the onset of nonlinearity. For a certain material that
can be described by the Ramberg-Osgood relation, the parameter a, is a constant, thus
only the hardening exponent N can be justified to fit the uniaxial stress-strain curve. In
fact, the material that can be descrbed by the Ramberg-Osgood rule behaves nonlinearly
throughout. However, in approximation, when this hardening rule is practically used in
the numerical simulation, a true strain offset, a£y, must be taken so that a linear behavior
before yielding is approximated (ABAQUS Mannuel, Hibbitt, Karlsson & Sorensen, Inc.
2002). This greatly limits the capability of the Ramberg-Osgood relation to describe a
vast number of material hardening behaviors. Especially, when the hardening exponent N
is small (with a large amount of hardening), there is a sharp transition in the stress vs.
strain curve at yielding such that the Ramberg-Osgood law does not capture the behavior
near the initial yielding very well. To extend its capability, we may relax the constraints
for the meaning of the onset parameter of nonlinearity, a , so that the full description of
the hardening behavior under uniaxial tension may be described as follows:
o
8
=
„
. o.
•
/
o
a
8 = — h U 8,
E
' v*^Y y
-I
for 8 >
E
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(4.3a)
(4.3b)
Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
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In this way, we have two parameters, a and the strain hardening exponent, N,
together to justify the hardening curve obtained from experiments. Thus we have retained
the 2-parameter fit character of the Ramberg-Osgood law, but we have made it into a twopart fit like the power law hardening relationship.
The post-yield behavior has clear
elastic and plastic contributions to the strain, with the plastic contribution equaling zero at
the yield stress.
Overall, we have taken the Ramberg-Osgood law and made it into an effective fit
for the elastic-plastic behavior by taking the parameter a as a fitting parameter. Thus, the
parameter a can have a wide range of values and is not tied to being interpreted as an
"offset". The advantage from this modification is very useful and it greatly extends the
capability to describe the hardening behavior, and yet it still remains valid for the
traditional meaning of each parameter if the material behaves exactly as the RambergOsgood relation describes.
For instance, the work hardening behavior of the nickel based superalloy in this
study can be described by the Ludwigson Modified Power Law Hardening and the fitting
parameters are Kj = 2.88X10^, ni = 0.44, K 2 = 19.9, and n 2 = 25. However, by choosing
proper hardening parameters of a and N in the modified Ramberg-Osgood hardening law,
the uniaxial stress-strain curve described by Ludwigson can also be captured adequately.
Figure 4.2 shows the comparison of the true stress vs. true strain behavior of Mar-M200
in the [100] direction at room temperature due to the Ludwigson and modified RambergOsgood law. One may have noted that the single crystalline nickel based superalloy has
approximately the same hardening behavior as that described in Mar-M200 along [100]
direction at room temperature (Kear et al., 1967; Vasinonta and Beuth, 2001). We see
that the two methods provide very close true stress-strain relationships by taking a=14
and N=2 in the modified Ramberg-Osgood relation.
The strain hardening behavior of the polycrystalline NiAl bondcoat at room
temperature in the previous study by Vasinonta and Beuth (2001) was taken to be the
power law hardening behavior, such that, a = c8", where n is about 3.4, and c is
4780MPA for a yield stress at 900MPA, (Vasinonta and Beuth, 2001; Wasilewski, et a l,
1967). Figure 4.3 provides a plot to demonstrate that the true stress vs. strain curve
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfaeial
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approaches the one used by Vasinonta and Beuth (2001); excellently taking a=1.7 and
N=2.87 in the modified Ramberg-Osgood relation.
Although
the
bondcoat
properties
and
strain
hardening
behavior
were
approximated from the literature of Wasilewski et al. (1967), it has been pointed out that
those bondcoat properties and hardening behavior are not known (Vasinonta and Beuth
2001) and therefore penetration to surpass the bondcoat is often recommended and even
compulsory in order to avoid the effect of the uncertainty of the bondcoat properties.
Therefore, more careful investigation on the influence of the bondcoat properties may be
essential to have more accurate evaluations of the relevant TBC systems. Recent studies
(Pan, 2003; Pan et al., 2003) reveal that the bondcoat properties are rather dynamic with
the increase of exposures, and the determination of its behavior can be crucial for
understanding the failure mechanisms seen EB-PVD TBC systems. This suggests a more
careful investigation is needed on the effects of bondcoat properties. The modified
Ramberg-Osgood relation is thus a useful tool to investigate the effects of the uncertainty
of the bondcoat in a vast range of hardening behaviors.
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
Fracture
3
Vasinonta and Beuth,
2001
N=2, a=14
2.5
2
00
.5
,5 -1
1
0.5
0
0
0.2
0.4
0.6
0.8
1
True Strain
Figure 4.2: Tensile Stress vs. Strain Behavior for Mar-M200 in the [100] Direction Used
in Vasinonta and Beuth (2001) and the Modified Ramberg-Osgood Relation by
Setting N=2 and a=14.
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
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5
4
1/3
to
<L>
1
Vasinonta and Beuth,
2001
- - N=2.87, a=1.7
0
0
0.2
0.4
0.6
True Strain
0.8
1
Figure 4.3: Tensile Stress vs. Strain Behavior for Polycrystalline NiAl Used in Vasinonta
and Beuth (2001) and the Modified Ramberg-Osgood Relation by Setting N=2.87
and ct=1.7
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
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4.3.2 Finite Element Model
A schematic of the indentation model is given in Fig. 4.4. The conical indenters
and the spherical indenters were assumed to be rigid. Upon a certain impression load, the
conical indenter or spherical indenter penetrates a certain depth, 6, into the substrate.
Every conical indenter has a round at its tip. The round radius may vary from indenter to
indenter. In the finite element models, the round tip of the conical indenters is simulated
as the same as the physical round tip provided by the manufacturer. The round tip radii
for the non-standard cones of 60°, 90°, and 150°, are -0.1m m respectively, and for the
standard cone, the round tip radius is ~0.2mm. Nevertheless, as the penetration increases,
the round tip effects become negligible. This is especially true for the conical indentation
using a Rockwell hardness testing machine with a minimum major load of 60 Kg.
In Figure 4.4a, the label 6j implies the imaginary indentation depth when there is
no round radius. It is essential to have a certain size of round at the indenter tip in order to
avoid brokenness upon indentation or avoid blunting of the indenter tip. Due to the effect
of the hardening behavior and the contact condition, namely the friction coefficient p
imposed between the contact surfaces, the deformed material surface around the indenter
may be either higher or lower than the original surface. The former phenomenon refers to
piling-up while the latter refers to sinking-in effects. Currently involved bondcoat and
superalloy substrate properties cause a slightly sinking-in effects upon indentation when
the non-slip condition is imposed between the contact surfaces. Therefore, the actual
contact radius, ac, directly from the FE modeling is smaller than the ideal contact radius,
a, as regards the deformed surface, keeping the same level as the original surface away
from the contact region. The concept of the ideal contact radius is adopted as the contact
radius in this entire thesis unless otherwise specified.
There are several reasons to use the ideal contact radius rather than the actual
contact radius ac. First, the ideal contact radius is a simple geometric parameter and can
be converted directly from the penetration depth. Therefore using the ideal contact radius
is straightforward and simple. Second, the magnitudes of the surface strain distributions
away from the indentation region are not sensitive to the contact radii reported from the
simulations at a certain impression depth. This fact corroborates that the stress intensity
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
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distribution or the energy release rate along the surface as a function of the distance from
the contact center is not sensitive to the contact radii reported from the simulation. That is
to say, the curves of the K vs. R/a or G vs. R/a at a certain penetration depth may shift to
the left or to the right if different contact radius is applied, but the magnitude of K or G
will not be changed. Third, to be consistent with the 3-D analysis presented in Chapter 5
also requires the usage of the ideal contact radius instead of the actual contact radius. In
the 3-D cases, the mesh resolution adopted in the FEA analysis is not able to capture the
actual contact radius accurately. However, the impression depth 6 can be accurately
captured.
In fact, the accuracy of the actual contact radius may be dictated by many factors.
In general, the amount of strain hardening and the yield strain of the substrate materials
dominate the behavior on how close it can be between the ideal contact radius and the
actual contact radius. For a small amount of strain hardening, or low yield strains, the
FEA results illustrate that piling up (a<ac) around the edge of the indenter is more
pronounced. Conversely, for large amounts of strain hardening or high yield strains,
plastic deformation is reduced and elastic contributions are more important and the FEA
results illustrate that the sinking-in around the edge of the indenter is more pronounced
(a>ac).
At the same time, the friction coefficient imposed between the contact surfaces
also affects the behavior of the piling-up or sinking-in around the edge of the indenter.
For the contact under frictionless (p=0) condition, the material directly beneath the
indenter flows out easier along and around the edge of the indenter such that the material
around the indenter edge is raised above the general level before the deformation takes
place, which pronounces the piling-up behavior. However, if the contact is under a non­
slip condition, the behavior is different. In this case, the adjacent metal which lies deeper
below the indentation flows out easier to eause the material around the indentation to be
at a lower level than the material farther away form the indenter, which pronounces the
sinking-in effect.
Nevertheless, if the actual contact radius is desired in an analysis, the results of
the currently involved simulations of the various shapes of indenters including the
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
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spherical ones show that a eonversion exists between a and ac: ac = 0.955a-0.009 (mm).
We see that the errors between the actual and the ideal contact radii are within a few
percentages.
Finite strain and large displacement analysis were used to model the substrate
including the bondcoat. The finite element modeling utilized the commercial code
ABAQUS. The contact algorithm utilizes the available one in the ABAQUS code. The
rigid conical or spherical indenter is modeled as a constraint on the surface displacement
and enforced with a penalty method. The ABAQUS code uses internally generated gap
elements to determine which nodes are in contact with the indenter at every load
increment. Friction between the indenter and the substrate, and the surface of the
bondcoat, was modeled with a Coulomb friction law, at = pan, where p is the friction
coefficient, and at, an are the tangential and normal tractions at the contact interface,
respectively. For slipping nodes, this relationship is enforced using Lagrange multipliers.
The friction coefficient was taken to be p = 0.7 herein, to reduce slipping events. The
contact status is identified by sticking contact status, except, sometimes by slipping,
which may occur at the very edge of the contact region. The contact load is calculated due
to the reaction force at the rigid indenter of the reference point. It can also be obtained
through the summation of the reactions at each nodal point along the bottom line. The
latter method becomes the most efficient way for evaluating the contact loads during the
unloading process.
Convergence studies show that the mesh resolution developed by Vasinonta and
Beuth (2001) is adequate enough for capturing the strain, or displacement profiles near
the surface of the substrate for most of the cases involved herein. Moreover, the mesh
dependence was extremely localized near the edge of contact and did not affect the strain
distributions in the areas of interest. Therefore, the previously developed mesh resolution
was referred to and utilized as the standard one. Unless otherwise specified, the standard
mesh methodology was adopted to obtain analysis results in this study. The standard
finite element model includes 4 regions dominated by different mesh resolutions. The
first region consists of 64 by 64 elements covering a region of 4mmX4mm, the second
region is away from the first enclosed by a Im m X lm m boundary with 36 element along
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
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the top line, and then the third and fourth with 40 and 20 elements used along the top
surface of the bondcoat. The smallest element used is roughly 6 pm. Depending on the
substrate properties and the combination of the bondcoat and nickel superalloy substrate,
for the standard TBC specimen, currently used plastic properties of the bondcoat and
nickel superalloy substrate with the J 2 flow theory, the contact region encloses about 34
elements at ~60Kg, with a penetration depth of about 100 pm, which is twice that of the
bondcoat thickness; and the contact reaches about 55 elements at ~150Kg with a
penetration depth of about 170 pm, more than three times the bondcoat thickness, under a
standard conical indentation.
The model is axisymmetric, modeling half of the TBC specimen coupon, with
total elements of 12812 and nodes of 26,096.
The TBC coupon size is 3.18 mm in
thickness and 25.5mm in diameter. The element chosen is a four-noded bilinear element
with reduced integration. Considering incompressibility in the plastic region, especially
where just below the contact enshrouding the indenter’s outer boundary, a hybrid element
type is used. This type of element adds the hydrostatic component of stress as an
additional degree of freedom to avoid the large hydrostatic stress generated by the nearly
incompressible plastic deformation around the indenter. Hybrid elements with the
reduced integration are expected to reduce running time and provide more accurate
results. Special attention will be paid to the surface displacement solution away from the
indentation region, since it is extremely important in this study. Fortunately, the surface
displacement solution away from the indentation is much less sensitive to the mesh
resolution, and the choice of element type in the indented region, rather than those
extracted from beneath the indenter or near the indenter, such as when R/a<2, which is
not of interest for this study.
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
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cone
original surface
deformed surface
substrate
(a) Schematic View of Conical Indentation
rigid ball
original surface
deform ed surface
substrate
(b) Schematic View of Spherical Indentation
Figure 4.4: Schematic of the Indentation Models
(a) by a Rigid Conical Indenter; (b) by a Rigid Spherical Indenter
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfaeial
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4.4 Mechanics of Conical Indentation
4.4.1 Loading Curves vs. Contact Sizes
It is necessary to have some investigation of the hardness on a bi-layer substrate.
This is especially useful for the analytical evaluation of the surface displacements and
strains by blunt indenters. The hardness refers to the ratio of indent load over the
projected area of the contact region, i.e., H = P/A, where P is the load perpendicular to the
contact slave surface and A is the area of the projected indentation region.
For a single material under a conical indentation, if the cone is blunt and the
material does not experience work hardening, then the hardness can be derived based on a
spherical cavity model (Hill 1950, Johnson 1970 and 1987). The cavity model is idealized
without considering the material sinking-in or piling-up effects. A hemispherical plastic
core is assumed to be attached to the indenter. Outside the core, it is assumed that the
stresses and displacements have radial symmetry and are the same as in an infinite elastic
perfectly-plastic body which contains a spherical cavity under pressure. These stresses
and displacements are given by Hill (1950). And the mean pressure beneath the indenter
or the hardness is given by Johnson (1970) as.
V m = ^ Y ~ 1 + ln
3a,
(4.4)
■tan|3
and thus the load can be written as:
T
^ 1 + ln
P3 = Tia2Ov —
3a,
-tanP
(4.5)
This analytical solution of hardness works fairly well for blunt indenters and it
correlates the experimental results reasonably well up to values of 3=30° (i.e. 120° tip
angle) (Johnson, 1970). However, Johnson’s hardness solution does not work well for the
cases of sharp indentation and fails to work if the material undergoes significant work
hardening upon indentation. Nevertheless, Johnson’s model does provide a good formula
and clearer insights on the conical indentations than just pure numerical simulations do.
Figure 4.5 and Figure 4.6 provide plots of hardness (H=P/7ia^) vs. contact radius,
a, for the standard conical indentation on a single substrate. The substrate yield stress is
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taken as 776MPa and the Young’s modulus is taken as 138GPa, which are the properties
of the nickel based superalloy used in the EB-PVD TBC system as listed in Appendix I.
Several hardening behaviors of the substrate material are chosen for this investigation.
These two plots attempt to illustrate several points. One is to compare the hardness results
due to Johnson’s model and those due to the FEA for currently involved material
properties and contact algorithm. The second point is to see how the curves of H vs. a
deviate from the analytical solutions for various hardening behaviors. And the third is to
verify that the hardening behavior described by the modified Ramherg-Osgood relation
for the nickel based superalloy yields approximately the same results as the one by
Ludwigson’s model.
Figure 4.5 presents the results of the standard conical indentation. In this plot, the
H vs. a due to the analytical solution is described by the dashed line. The H vs. a curve
due to the EE simulation based on the perfect elastic-plastic material behavior with no
hardening involved is presented by the curve with solid triangles. From the analytical
model, we see that the value of H /ay has a dependence on the single parameter of
(E/aY)tanp. Therefore it predicts a straight line under fixed indenter geometry as well as
constant substrate material properties. The FEA simulation results also predict a constant
value of hardness providing sufficient penetration depth (>~50pm). We see that the
analytical prediction underestimates the hardness value compared to that due to the FEA
simulation as shown by the solid triangles. If frictionless is considered in the FEA
simulation, the hardness predicted is slightly closer to the analytical results. However, the
Johnson’s model still underestimates the hardness values as compared to the FEA results.
This observation essentially agrees with the results presented by Johnson (1970).
Nevertheless, care shall be taken not to make too broad a conclusion regarding the
comparison between the analytical prediction and the FEA results without strain
hardening. More careful study on this matter is beyond the scope of this thesis.
Using the modified Ramberg-Osgood relation, by keeping a constant, the larger
the hardening exponent, N, the smaller the strain hardening rate and the closer to the
perfect elastic-plastic the case will be. This fact is evident from this plot. As one observes
the curve with open triangles, N=5, is closer to the analytical solution than the curve with
152
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black solid dots with N=2. Moreover, the results due to the modified Ramberg-Osgood
relation with N=2 and a=14 approximate the results due to Ludwigson’s model in
Vasinonta and Beuth’s study (2001) fairly well. Besides all the points we have made, the
hardness with various fixed hardening parameters is also almost a constant providing that
the contact radius is reasonably large. This is to say, with the same rate of strain
hardening (fixed N and a), the hardness is essentially constant. This finding is found to
be consistent with the statement seen in the literature by Bhattacharya and Nix (1998).
They found that the response of a material with a high rate of strain hardening is
essentially the same as the response of a material with a higher yield strength.
Figure 4.6 presents the results due to a 90 degree sharp conical indentation. The
trends of those curves are fundamentally the same as presented in the previous plot for the
standard conical indentation. Regardless of the strain hardening behavior, once the strain
rate is fixed by the hardening parameters of a and N, the hardness is roughly a constant
providing sufficient penetration depth. Again we see the agreement between the results
due to Ludwigson’s model and those due to the equivalent Ramberg-Osgood relation for
N=2 and a=14. Moreover, the hardness for each of the fixed parameters compared to that
due to the standard conical indentation, the magnitude becomes larger in each case. This
is apparent from the analytical solution from the Johnson’s cavity model, which indicates
the hardness increases with the decrease of the conical indenter tip angle while the
material properties are fixed.
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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5000
a
4000
II
CA
(/}
(O
c
3000
No Hardening
Johson's model
N=5, a=14
N=2, a =14
0 —TR substrate
1000
0
0
0.1
0.2
0.3
Contact Radius, a (mm)
0.4
0.5
Figure 4.5: Indent Load vs. Contact Radius Compared with the Analytical
Predictions due to a Standard Conical Indentation, Illustrating the Role of
Hardening Behavior on the Effects of load vs. contact radius a
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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5000
4000
<N
as
3000
or)
2
2000
No Hardening
~ Johnson's mode]
N=5, a =14
N=2, a =14
TR substrate
1000
0
0
0.1
0.2
0.3
0.4
0.5
Contact Radius, a(mm)
Figure 4.6: Indent Load vs. Contact Radius Compared with the Analytical Predictions
due to a 90° Conical Indentation, Illustrating the Role of Hardening Behavior on
the Effects of load vs. contact radius a
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It is also found useful to consider the hardness, H, to be the effective hardness
since the material is not single but consisting of two layers of material: bondcoat and
superalloy substrate in the contact on an EB-PVD TBC specimen without a TBC coating
on top. The effective hardness, H, for a bi-layer substrate with a hard film on top of a
softer substrate can be evaluated from an empirical equation by analyzing the numerical
results and fitting with various forms of equations done by Bhattacharya and Nix (1988).
The expression can be rewritten as follows:
exp
H bc/H ,
"a
"
(4.6)
V^ Bc y
Where, Hs and
H bc
are the substrate hardness and bondcoat hardness, respectively, CTys
and CyBc are the yield stresses of substrate and bondcoat, respectively. Eys and EyBc are
Yong’s modulus for substrate, and bondcoat, respectively, tsc is the thickness of
bondcoat and 6i is the penetration depth without considering the round at the conical
indenter tip.
This formula can be used to evaluate the effective hardness when the penetration
is not sufficiently deep. When the indent depth surpasses by about one and half times the
bondcoat thickness, however, from our experience for the currently involved TBC
system, the bondcoat properties become insignificantly small on the quantities we are
most interested in such as the surface displacements and strains away from the
indentation region. Interestingly, the formula (4.6) also predicts the effective hardness H
-5% higher than the substrate hardness Hs at 6i/tBc =2 and -10% higher at 5i/tBc =1-5 for
all conical indenters investigated thereof. This prediction not only supports the
observations from our numerical results, but also it simplifies the analytieal analysis
significantly since the hardness values are necessary for the evaluation of the surface
strain or displacement from the analytical formula as stated in the subsequent section.
When the penetration is sufficiently deep, the bondcoat properties become insignificant
and the analytical evaluations of the surface strain or displacement can be based solely on
the substrate’s material properties.
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For the bulk single substrates, the hardness was found to be 9.2 Oys MPa, and 5.2
CTys MPa for the bondcoat and the nickel superalloy substrate, respectively. Those
hardness results are obtained from the numerical results including the actual contact
radius due to the standard conical indentation on a standard EB-PVD TBC specimen
without a TBC coating on top. The properties of the nickel superalloy substrate and the
bondcoat are those used most frequently in this study as described in the previous section.
One may see that these hardness values are much larger than their yield stresses compared
to the metal hardness work hardening. The hardness for an ideally plastic metal is about
3ay (Tabor 1951). Moreover, the hardness keeps roughly constant for fixed hardening
parameters with the load levels of interest. This observation is also discussed previously
and it agrees with the statement by Bhattacharya and Nix (1988), i.e., the response of a
material with a high rate of strain hardening is essentially the same as the response of a
material with a higher yield strength and strain hardening does not produce qualitatively
significant effects on hardness.
Now we are ready to present the results of the indent load vs. the contact sizes for
the contact on a standard EB-PVD TBC specimen without a TBC coating on top. Figure
4.7 shows the load vs. contact radius for a conical indentation with diverse conical tip
angles. The contact radius herein again refers to the ideal contact radius, not the actual
contact radius reported from the sticking status in the finite element contact simulation.
These curves are practically always used in this study for evaluations as well as providing
insight for further indentation tests on various EB-PVD TBC specimens. Furthermore,
the results of the load, P, vs. the contact radius, a, of the conical indentation with a tip
angle of 120° are found to be in excellent agreement with the finite element simulation as
well as experimental tests presented by Vasinonta and Beuth (2001). As a general trend,
one may have noticed that it requires a larger load for a sharper indenter than a blunter
one of the same contact radius. As mentioned previously, this is due to the fact that for
the sharper indenter it is neeessary to displace more substrate materials in order to reach
the same eontaet radius. At the same time, the eontact radius is smaller for a sharper
indentation than a blunter one at the same indent load level. However, this does not mean
the indent depth would be smaller for the sharper conical indentation than a blunter one at
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the same indent load level. In fact, the sharper indenter penetrates much deeper than the
blunter one which will be clear as we move to the next Figure 4.8.
Sufficient indentation depth is not only necessary, but also mandatory in this
study. The purpose of deep penetration is to avoid the significant effect of bondcoat
properties as well as to get self-similar surface field solutions such as surface
displacement and surface strain. Figure 4.8 presents a plot of indent load, P, vs. the indent
depth, 6. From this plot, it is seen clearly how the penetration depth varies at each load
level for various conical indentations. As indicated in the plot, it can be very hard for a
blunt cone to get sufficient penetration to surpass the bondcoat layer. As for the 150°
cone, it requires 60Kg to surpass the bondcoat thickness of 50p.m and 150Kg load to
reach a depth two times larger than the bondcoat thickness. However, to reach a depth of
two times larger than the bondcoat thickness can be easily done by a standard conical
indenter or other special sharp indenters of 90° to 60° cones. Actually, the 90° conical
indentation can penetrate about 30% deeper than the standard conical indentation at each
available load level on the Rockwell hardness tester. In Figure 4.7, the load curves are
pretty compact. This means it does not require an extremely large load level for one type
of conical indenter to reach the same contact radius as others do within a reasonable
contact size of less than 250p.m. However, unlike the load vs. contact radius curve in
Figure 4.7, Figure 4.8 shows that much more discrepancy exists between each load curve
as it departs from the shallow indent region. This indicates that it may be extremely hard
to reach a certain indent depth as required by a blunter conical indentation. For instance,
to reach a depth of three times the bondcoat thickness, i.e., 150 pm, it requires the indent
load level of 150Kg for the standard conical indentation, and 60 Kg for the 90° conical
indentation. However, it may require the 150° conical indenter about SOOKg to reach the
same depth, whieh can not be performed on a standard Rockwell hardness tester.
Besides all the points that have been made, attention will be paid to the shapes of
the load vs. contact radius curves in the two plots of Figure 4.7 and 4.8. The relation
between load and contact radius adheres strictly to the second order power law such that
P°= a^ for an elastic perfect plastic material is indicated in (4.5). From another
perspective, the relationship between the contact radius and the indent depth holds linear.
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i.e.,
a. Therefore the plot of Figure 4.8 retains the same order between P and 5 as
between P and a, i.e., P°<= 5^. This behavior is very different from that of spherical
indentation as will be clear in the subsequent section
300
- O Cone 60°
250
Cone 90°
U)
w
Cone
p^
’d '
O
Cone
200
+->
c
CD
C
0.2
0.3
0.4
Contact Radius, a (mm)
Figure 4.7: P vs. a due to Various Conical Indentation Geometries Considering
Typical EB-PVD TBC Properties
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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300
250
bX)
cj
O
200
150
■4— >
(U
C
100
50
^ Cone 60°
^ Cone 90°
-+ - Cone 120'
Cone 150'
X /
•XF*2^
0
0.1
0.2
0.3
0.4
0.5
Penetration Depth, 8 (mm)
Figure 4.8: P vs. 6 due to Various Conical Indentation Geometries Considering
Tj^ical EB-PVD TBC Properties
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4.4.2 Surface Displacement Profiles
As for the axisymmetric indentation, the surface displacements or the surface
strains must be extracted from the finite element simulation. These field solutions are
essential for further evaluations of the interfacial fracture mechanics issues. Based on the
finite element algorithm described in the previous sections, various conical indentations
were performed on the standard EB-PVD TBC system substrates comprised of bondcoat
and superalloy substrate bi-layers. The surface displacements vs. the normalized distance
from the contact region are extracted directly from finite element modeling and presented
in Figure 4.9.
For the displacement field away from the conical indentation region, the analytical
approximation can be found by correlating the numerical results (Drory and Hutchinson,
1995, 1996). For most cases of interest in the TBC systems, the range of R/a is roughly
between 2 and 12, i.e., 2 < R/a < 12. A polynomial approximation of the following (Drory
and Hutchinson, 1995, 1996) can be adopted and it is found the approach is both
excellent for conical as well as the spherical indentations.
Ln(UVa) = bo + bi (R/a) + ba (R/a)^ -i- bs (R/a)^
(4.7)
The coefficients in (4.7) can be correlated from the finite element solution presented in
Figure 4.9. They are listed in table 4.1. These results are easy to use and can capture with
the numerical results excellently within the space in which we are interested. In Figure
4.9, each dotted curve adjacent to a solid curve represents the results from (4.7), which is
fitted from the numerical results shown by the solid curve. The agreement between the
numerical results and the fitting results are apparent in the space of interest.
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Table 4.1: Correlated Coefficients for Eqn. (4.7) due to Different Conical Indenters
Cone Angle
bi
bo
b2
b3
60°
-2.9318
-0.503
0.0232
-0.0004
90°
-2.9963
-0.6583
0.0399
-0.0009
120°
-3.2116
-0.7905
0.0568
-0.0014
150°
-3.7928
-0.918
0.0793
-0.0023
Correlation valid range for 60°: 3 < R/a < 12; 2.5 < R/a < 12.for 90°, 120° and
150°.
0.016
- - Cone
Cone
— Cone
Cone
0.014
0.012
a
(U
O
a
0.01
60°
90°
120^
150^
Predicted
0.008
XS
cj
PiJ
X3
<D
0.006
0.004
N
a;-i
O
;zi
0.002
0
2
4
12
14
Normalized Radial Distance, R/a
Figure 4.9: U/a vs. R/a due to Various Conical Indentation Geometries Considering
Typical EB-PVD TBC Properties
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4.4.3 Surface Strain Profiles
•
Approach from the Surface Displacement Profile
The radial displacement extraction from the numerical model is considered the
most important field solution to obtain. The strain in axial and circumferential directions
due to the indentation event can be easily obtained due to the relationship between the
radial displacements and the strains as given in (2.25) and (2.26).
The calculated surface strains due to (2.25) and (2.26) are found to be in excellent
agreement with the surface radial and hoop strains output directly from the numerical
simulations providing a reasonable distance away from the contact region. Though the
radial strain calculation from the displacement field may yield significant errors in the
region just beneath the indenter extending to R/a<2, since it is very hard to capture the
accurate displacement gradient due to the non-smooth numerical radial displacement at
each nodes in this region. This will not cause any problem for tbe current study since we
are not interested in the solution of this region. As in the case of in-need of the strain
solutions in or near to the indentation region, the current author would suggest extracting
the strains directly from the numerical simulation to reduce the errors. Also, more careful
meshing resolutions and other techniques may be necessary to capture the strain reversals
beneath the contact region due to the fact of non-proportional loading conditions just
beneath the indenter and the near surface as described elsewhere (Begley et al., 1999).
•
Asymptotic Approach of Surface Strains
For a blunt conical indentation, i.e., (3<30°, an asymptotic approximation for the
surface radial strain was solved recently (Begley et al., 2000), and we present it as
follows:
e! = - ( l + v)
Y£^an(3V'V„^3
a
v*^Y y 6 ( l - v )
(4.8)
vRy
where - indicates the strain is compressive, H is the hardness.
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Considering R '^ oo, u '
0, and the effective hardness H is not a function of R/a, the
corresponding integration gives another way for the evaluation of surface displacement
profiles.
U'
(1 + v)
a
H
j 6(1 - V
(4.9)
vR y
)
Further, the circumferential displacement can be easily expressed as:
.1
-e
(1 + v)
2
tan (3^
1/3
a^
fV*^Y
^ 1y[ 6 ( l - v ) J rUJ
(4.10)
Formula (4.10) indicates that the radial strain is 2 times larger than the circumferential
strain in magnitude for a blunt conical indentation. By a rough comparison, this is
remarkably true from the numerical solutions conical indentation with tip angles of 120°,
150° within a reasonable region on the surface away from the indentation region, but it is
not valid for sharper cones, such as those with tip angles of 60° and 90°.
Figure 4.10 and Figure 4.11 provide plots of the surface strain distributions vs. the
normalized distance away from the indentation region. The substrate is taken as the single
bulk material consisting of the nickel based superalloy properties only. The hardness H is
taken individually for each individual indenter. Specifically, the hardness from the 90
degree conical indentation is 6.2cTyBc MPa and 4.8 OyBc MPa for the standard conical
indenation and 3.5ayBc MPa for the 150 degree conical indentation. Those values are
again evaluated from the finite element simulation and not from the direct calculation
from the Johnson’s solution. Since Johnson’s analytical hardness formula does not
consider the strain hardening, it may underestimate the hardness significantly.
Figure 4.10 presents the compressive strain vs. R/a due to various indentation
geometries. Comparisons are made in this plot between the strains from the asymptotic
solutions and those from the calculations based on the surface displacement field. First
we may see all the curves approach to zero very quickly and the significant strain
magnitude is only found in a relative small region at about R/a<8. At the same R/a, the
compressive strain magnitude is larger due to a sharper conical indentation than a blunter
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one. Also, we may see the 90 degree, the standard and the 150 degree conieal indentations
correlate fairly well between the asymptotic approximation and the finite element results.
Figure 4.11 presents the tensile hoop strain vs. R/a due to various conical
indentations. The points just discussed in Figure 4.10 also hold for the results presented
in this Figure. However, we may see that now the magnitudes of strains are relatively
smaller than those is in Figure 4.10. This is one of the reasons why the tensile hoop strain
distribution is much less significant to the contributions of the energy release rate
evaluations. Again we see that asymptotic approximations give a fairly good approach to
the numerical results. Although discrepancies exist between the asymptotic approaches
and the numerical results, the asymptotic approach does provide a good means for the
quick evaluation of the surface strain distributions on the evaluation of interfacial fracture
issues.
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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Normalized Radial Distance, R/a
4
6
8
10
12
14
16
0
-
-
0.001
0.002
-0.003
//:/' 1II */
/j /• Ir »!^/
/ ' r V
r / Y
Vt
r
-0.004
-0.005
-0.006
-0.007
-0.008
90° Cone FEA
■1 • n
'/I
;l1 if
-J1 irIf
" " " 90° Cone Approx.
120° Cone FEA
120° Cone Approx.
150° Cone FEA
150° Cone Approx.
( ,'h
yi
VM
#*
*
*1
Figure 4.10; Axial Compressive Strain vs. R/a as a Function of Conical Indenter
eometry Compared with the Analytical Solution for a Single Material
(Substrate Properties only)
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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0.01
C3
(D
Vh
o
•fH
90° Cone FEA
90° Cone Approx.
120° Cone FEA
120° Cone Approx.
150° Cone FEA
150° Cone Approx.
0.008
0.006
0.004
U
0.002
0
4
6
8
10
12
14
16
Normalized Radial Distance, R/a
Figure 4.11: Circumferential Strain vs. R/a as a Function of Conical Indenter Geometry
Compared with the Analytical Solution for a Single Material (Substrate Properties
only)
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4.5
Mechanics of Spherical Indentation
4.5.1 Loading Curves vs. Contact Sizes
Compared to the characteristics of the conical indentation mechanics, the
spherical impression behaves distinctly. Due to the geometrical non-similarity, a
generalized analytical solution for hardness due to spherical indentation seems more
difficult to derive than that due to a conical or a wedge indentation. However, as the
indentation depth increases, the indentation response becomes dominated by plastic flow
and elastic parameters become irrelevant. Therefore, at the stage of full plastic
indentation, where the plastic zone envelops the contact region, the non-dimensional
contact size, a/Rb, and the contact mean pressure, or the hardness, P/7ia^, will depend only
upon the material plastic parameters such as its yield stress and hardening exponent. Hill
et al. (1989) found a similar solution in the fully plastic regime of spherical indentation.
The similarity solution states that the relationship between hardness and the normalized
contact size a/Rb follows:
1 p
Tia
a
l/N
(4.11)
2 8y Rb
This relation is derived based on the deformation theory and the assumptions of a
rigid spherical indenter contacting a half-space with a pure power-law constitutive
relation as described in (4.1). Following Tabor (1951)’s experimental results for pure
power-law materials, the values of (|) and P are close to 2.8 and 0.4, respectively. Biwa
and Storakers (1995) modified the similarity solution by a numerical analysis with a J 2
flow theory and the corresponding numerical results for (j) and P are 3.07, 0.32,
respectively. In the case of indenting a half-space with a Ramberg-Osgood relation, (4.11)
it can be considered still valid by multiplying [l/a]'^ on the right hand side (Begley et al.,
1999). A limitation for the validity of the formulation expressed in (4.11) is studied by
Mesarovic and Fleck (1999). They found the regime of validity of a similar solution is
restricted by both elastic effects for small contacts, and by finite-deformation effects for
large contacts. Though it is not a task of this study to provide a detailed analysis of (4.11),
168
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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we may expect the same dependence among the parameters as expressed in (4.11) to be
valid if the different flow rules are used. However, the universal constants may be
expected to be different as found by Biwa and Storakers (1995) based on the pure powerlaw hardening rule of J 2 flow theory. For instance, for the currently involved substrate
properties as described by the modified Ramberg-Osgood relation, the fitted universal
contacts of ^ and |3 are found to be no longer valid as compared with those of 0 and P
obtained by Biwa and Storakers (1995), which underestimates the load values with the
same contact radius.
Figure 4.12 presents the numerical results of the hardness (H=P/7ta^) vs. the
normalized contact radius a/Rb- The material properties are the same as mentioned
previously for the standard EB-PVD TBC system without the TBC coating on top. The
bondcoat/substrate size is the same as that of a standard TBC specimen. In this
presentation of numerical results, the sinking-in effect is again ignored so that the contact
radius may be taken as a rather than ac. From this plot, we see that the relationship
between the hardness H and the normalized contact radius a/Rb is independent of the size
of the spherical indenters. The simulation results of the indentation load as a function of
contact radius all collapse into one single curve (drawn by hand) in the expression of H
vs. a/Rb. This demonstrates that the similarity solution as expressed in (4.11) is also valid
for a spherical indentation on the EB-PVD TBC system.
In this figure, we also have the hardnesses of the various conical indentations
plotted. These hardnesses of different conical indentations are expressed as a single line
since they are not a function of a/Rb as discussed previously. Nevertheless, the
comparison between the hardness curve of spherical indenters and those values of
hardnesses due to various conical indenters is meaningful. From this plot, we may be able
to tell when a spherical indenter can perform like a conical indenter for the toughness
tests. Since the contact radius a is a purely geometric parameter, therefore we may also
tell how deep a spherical indenter has to penetrate to be like a specific conical indenter.
For example, for a 1.59mm diameter (Ib^** inch ball) spherical indenter, the hardness
curve intersects with the hardnesses of 150°, 120° and 90° cones at a/Rb = 0.31, 0.62 and
0.87 respectively. These values are at the contact radii of a ’s at 0.25mm, 0.49mm and
169
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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0.69mm respectively, and the penetration depths of 39pm, 171pm and 423pm
respectively. This shows that the 1.59mm diameter spherical indenter has to penetrate
more than 3 times deeper than the bondcoat thickness to induce debonding that may be
equivalently due to a 120° conical indentation. This is practical for the indentation
performed on a Rockwell hardness tester since the penetration depth at 150Kg for the
1.59mm diameter ball is about ~ 100pm, which is twice deeper than the bondcoat
thickness. However, if the spherical indenter size increases to 3.18mm in diameter, the
contact radii at the intersections of a/Rb = 0.31, 0.62 and 0.87 are 0.49mm, 0.98mm and
1.38mm respectively. The relevant penetration depths are 49pm, 343pm and 810pm
respectively. The penetration depth for the 3.18mm diameter ball at 150Kg is about
60pm, which indicates it just slightly passes the bondcoat layer. This means that it is
almost impossible for a 3.18mm diameter ball to perform like a 150° cone and it is not
likely to be like a standard cone at all since the required penetration depth is too far too
reach for such a large spherical indenter.
Regarding the expression of (4.11), it is also clear that the relationship between
the indentation load, P, and the contact radius, a, for the spherical indentation does not
only depend on the contact radius, but also depends on the spherical size for the case of
contacting on a substrate with certain material properties. Furthermore, with a fixed size
for the spherical indenter, the relationship between the indentation load, P, and the
contact radius, a, follows P
a^^’^ as indicated in (4.11). Therefore the indent load is not
dependent on the contact radius, a, in a second order relationship anymore.
From the experimental point of view, the relationship between the indentation
load and the indentation depth is just as important as the relationship between the
indentation load and the contact radius. This is due to the fact that a certain depth of
indentation must be reached for the validity of the analysis due to the unknown properties
of the bondcoat layer, which makes the relationship between P and 6 more practical and
more important. The full geometric relation between the contact radius, a, and the
impression depth, 5, follows:
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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\2
(4.12)
R.
V^b
J
Substituting (4.12) into (4.11), we obtain:
1/2N
2(pa,
7t 5 R ,
1-
2R,
1V^Y y R.
2R b y
(4.13)
In case of small penetration, taking 6 /R b « l:
a=V2 8 R^
(4.14)
By substituting (4.14) into (4.11), we obtain:
1/2N
7E5 R.
= 2(pCT,
p
(4.15)
v^Y y R.
Figure 4.13 presents the results of P/7i5Rb vs. 5/Rb as a function of the
indentations of different spherical indenter sizes. Analogous to the previous plot, this plot
shows that the indentation load P vs. the indentation depth due to different sizes of
spherical indenters collapse to a single curve (drawn by hand). This behavior can be seen
in the expressions of (4.13) and (4.15), which indicates a single function between P/7i6Rb
and 6/Rb under fixed material properties. The significance of this plot is not only to
validate the claims indicated in the expressions of (4.13) and (4.15), but also the apparent
relationship between the indentation load P and the penetration depth 5 can be easily
evaluated by a specific spherical indenter and the indentation depth.
Even more interesting sides exist on the distinct behavior of P vs. 5 as expressed
in (4.15) compared to the conical indentations. The relationship between P and 5 as
shown in (4.15) follows P
spherical indentation size and material
properties. Since the hardening exponent N is bigger than a unit, 1/(2N) is usually much
less than a unit, therefore, the P vs. 5 follows approximately a linear relationship. This is
evident from the results shown in Figure 4.13 if the plot is converted to be as P vs. 5 for
each size of the spherical indenters. The results of the standard conical indentation show a
very different behavior from those of the spherical indentation since the indent load is
171
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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related to its contact size in the same order as with its indent depth for the conical
indentation.
From another point of view, the relationship between P and the spherical radius
Rb follows P
Rb'~’^^^ while keeping the same indent depth. Since (1-1/2N)>0, therefore,
at the same indent depth, we will expect a larger load for a larger size of spherical
indenter. This is almost self-evident since a larger size of spherical indenter must displace
more material to have the same impression depth as that made by a smaller spherical
indenter. If we look more closely, it is not hard to find that the curves of P vs. 5, which
can be converted from Figure 4.13, distributes more sparsely than those curves of P vs. a,
which can be converted from Figure 4.12. This behavior shows that it is much more
difficult for a spherical indenter with an 8'*’ inch diameter to have the same penetration
depth as one with a 16* inch diameter. More insights on how spherical indenter size may
affect the debonding behavior compared to that of conical indentations have been
discussed in the previous part of this section from Figure 4.12. Nevertheless, the practical
indentation tests, which are to be presented in the subsequent sections, show that only
when the spherical indenter diameter equals or is less than 1.59mm can it be practically
used for inducing debonding due to the indentation load level available in a standard
Rockwell hardness tester. This is because at the same load level and the same location,
the largest size spherical indenter imparts the least stress intensity and this will be clear
when the relevant results are presented in the subsequent sections.
172
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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60° Cone
c3
Ph
90° Cone
K
120" Cone
C /)
CD
c
150° Cone
O
DO.79mm
O
D1.59m m
□ D S.lSm m
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
N ormalized Contact Radius, a/Rb
Figure 4.12: H vs. a/Rb due to the Spherical Indentation of Various Diameters on a
Typical EB-PVD TBC System without TBC on Top
173
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1
Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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8000
7000
6000
5000
X)
CO
4000
Oh
3000
2000
O D0.79m in
O D 1.59m m
1000
□ DB.lSm m
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Indent Depth, 6/Rb
Figure 4.13: P/7i5Rb vs. 6/Rb due to the Spherical Indentation of Various Diameters on a
Typical EB-PVD TBC System without TBC on top
174
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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4.5.2 Surface Displacement Profiles
As mentioned previously, the surface displacement profiles are crucially important
in the determintation of the stress intensity factor distribution at the interface for the
indentation induced axiymmetric debonding. For a conical indentation with a fixed
geometry, the uVa vs. R/ a curve is uniquely determined due to the characteristics of
geometrical similarity upon the indentation process. However, a spherical indentation
gives a very distinct behavior compared to that by a conical indentation. This is because
the geometrical similarity does not exist for the spherical indentation. As the indent
deepens, the values of uVa vs. R/a become larger in magnitude. Considering a spherical
indentation on a single substrate with a fixed friction, dimensional considerations dictate
that the surface displacements must depend on a dimensionless function F r according to
fL
a
= F
Y
va
E R,
-,v,N ,a
(4.16)
,
As is seen from (4.16), it is clear that the uVa depends on a/Rb. This dependence
provides a strong load as well as size effects on the normalized displacement distribution
of a spherical indentation. To illustrate what the implications are in (4.16), Figure 4.14
presents uVa vs. R/ a at various magnitudes of a/Rb. Three sizes of spherical indenters
were used to perform indentations on a large substrate with a single substrate material
property, which is the same as that of the nickel based supperalloy as currently involved
in EB-PVD TBC systems as listed the Appendix I. At the same a/Rb, three spherical
indenters of different sizes of 0.79mm, 1.59mm and 3.18mm in diameter were used and
each indentation produces a curve of uVa vs. R/a by overlapping the other ones of
different size indenters.
It was found to be crucial to obtain an overlapping behavior for the indentation of
different spherical indenters at the same a/Rb. The single substrate size used here is 5
times larger than the standard specimen size in the horizontal direction and the vertical
size was taken the same as the horizontal. The enlarged model was done by adding extra
elements along the side and the bottom of the standard model. This indicates the edge
effect is not negligible for this type of investigation since much larger load or indent
depth may be required to accomplish this type of analysis. However, the edge effect is not
175
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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significant if the indent depth is shallow or the ball size is small. Moreover, it was found
that the edge effect becomes negligibly small as on the curves of K vs. R/a even for the
deep indent depth as shown in Fig. 4.14. For instance, the edge effect is negligibly small
for U /a vs. R/a as the 1.59mm diameter ball penetrates less than about 50pm, but it is not
negligible after it passes this depth. However, it may penetrate more than lOOpm to still
have negligible edge effects on the K vs. R/a curve. This is due to the fact that the slope
of u V a vs. R/a does not change significantly as R/a becomes larger. And the slope of u V a
vs. R/a determines the compressive strain distribution along the surface, which is the
dominant factor in the evaluation of the stress intensity factors. At the same time, the
tensile strain determined by the magnitude of UVa vs. R/a has only a minor influence on
the evaluation of the interfacial stress intensities. Therefore the contact results on a
standard specimen size model can be still considered valid regarding the evaluation of the
stress intensity factors as those from the large substrate. This will become clearer as the K
vs. R/a results are presented.
In Figure 4.14, the comparison was also made with the results of UVa vs. R/a of
the standard conical indentation. The implications of these curves are: (1) under a fixed
load level, by using a certain spherical indenter, the uVa vs. R/a curve may reach or
surpass that due to the standard conical indentation; (2) under a fixed spherical indenter
size, as the indent load increases, the curve of uVa vs. R/a due to spherical indentation
may reach or surpass that due to the standard conical indentation. This behavior makes
the spherical indentation different from the conical ones. Moreover, the trends seen here
for U/a vs. R/a for the conical vs. spherical indenters will also be true for the trends of K
vs. R/a due to various shapes of indenters. Because the strains depend on the slope and
magnitudes of U/a, the trends in the results of Figure 4.14 are also seen later in the plotted
K vs. R/a as shown in the later plot of Figure 4.18.
Figure 4.15 presents the results of U/a vs. R/a due to the indentation on the
standard EB-PVD TBC system without TBC on the top. At the same load level of 150Kg,
indentations were simulated by three different sizes of spherical indenters of 0.79mm,
1.59mm and 3.18mm in diameters. For the sake of convenience and comparison with
those from the large substrate, three different values of a/Rb were labeled relative to each
176
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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size of the spherieal indenters. Those curves have the same trends and implications as
those presented in Figure 4.14. But now those results are produced by considering the true
bondcoat/substrate system as seen in a standard EB-PVD TBC specimen. Therefore, these
results are expected to be more realistic and more useful regarding the applications on the
quantification of interfacial fracture toughness on a standard EB-PVD TBC system.
0.016
c3
P
a
D
a
<D
U
cd
'H h
C«
0.014
0.012
0.008
0.006
(D
N
13
a
»
o
;zi
0.002
4
6
8
10
12
14
16
Normalized Radial Distance, R/a
Figure 4.14: U/a vs. R/a as a Function of a/Rb for the Spherical Indentation on a Large
Single Material (nickel based superalloy properties) to Illustrate its Size or Load
Dependence (3 sizes of ball used: 0.79mm, 1.59mm and 3.18mm
in diameter and U/a vs. R/a overlaps at the same a/Rb of different size ball)
177
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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0.016
— Cone 120°
cd
0.014
§
0.012
(D
O
cd
'H.
C/D 0.01
rH
Q
0.008
cd
0.006
(D
_N
Id 0.004
g
Vh
O
iz; 0.002
-
.
.
.
D0.79mm, a/Rb=0.81
““ ■D 1.59mm, a/Rb=0.48
a
— D3.18mm, a/Rb=0.27
•
0
\\\^
\ \ \
\v\
1
i
1
4
6
8
------:— -------- 1
1
1
10
12
14
16
Normalized Radial Distance, R/a
Figure 4.15: U/a vs. R /a as a Function of a/Rb for the Spherical Indentation on a
Standard EB-PVD TBC System without Bondcoat on Top (3 sizes of ball used:
0.79mm, 1.59mm and 3.18mm in diameter at the same load level of 150Kg)
178
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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4.6 Interfacial Stress Intensity Factor Distribution Due to Various
Shapes of Indenters
In this section, the results of K vs. R/a are presented from the indentation
simulation on a standard EB-PVD TBC specimen considered frequently in this study. The
K vs. R/a curves due to the conical indentations with various indentation geometries are
to be presented first and then those of various spherical indentations follow.
4.6.1 K vs. R/a due to Conical Indentation
Figure 4.16 presents a plot of K vs. R/a due to conical indentations with various
indenter cone angles under as-processed conditions in an EB-PVD TBC system. From
this plot, the following trends may be observed: (1) in all cases, K vs. R/a curves
converge to the same value at distances far away from the indentation center,
corresponding to the K value due to residual stresses only. (2) K vs. R/a curves shift to
the right as the cone angle decreases. This indicates that for the same value of toughness
and contact radius, the debonding radius increases with a decrease in cone angle.
Interestingly, results also suggest that the opposite is true for the case of a fixed value of
toughness and a fixed indenter depth. In that case, a conical indenter with a smaller
included angle will yield a smaller debond radius. (3) The maximum value of K is seen
for a cone angle of 90°.
However, the increase in the peak K value is not large.
Collectively, the results of Fig. 12 suggest that the control of debond size may be possible
by simply using conical indenters having different included angles.
The goal of
increasing peak K values to allow the testing of very tough interfaces may require the use
of other indenter shapes.
As it shows in the simulation analysis as well as the practical indentation tests
considered in this study, the indenter penetration depth is often of more concern than the
contact radius. Sufficient penetration depth is not only required to produce the similarity
solution in the conical indentations, but also it is required to pass the bondcoat thickness
in order to avoid the effects of the bondcoat properties, which are not exactly known.
179
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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Therefore, it is important to present the results of K vs. R/5 for the application of the
indentation tests - the conical indentations as well as the spherical indentations.
Figure 4.17 shows the numerical results of K vs. R/8 for different conical indenter
tip angles. We see that: (1) regardless of different tip angles, K vs. R/6 curve always
approaches to the same value as R/5
Infinity. This makes sense since the stored elastic
energy in the undebonded portion is irrelevant to the indentation. This also indicates that
the currently received standard TBC specimen size is large enough for the standard
conical indentation tests to be considered as indentation on an infinite substrate. (2) From
this plot, we may see that the curves of K vs. R/5 move to the right side as the tip angle
increases. Thus, the apparent toughness measurement may be benefited for BOTH asprocessed specimens as well as exposed specimens by selecting a proper indenter.
180
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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5
a
Plh
O
o
a
P-H
c/5
■ Cone 60°
- Cone 90°
- Cone 120'
- Cone 150
4
3
2
a>
c/5
C /5
1
0>
0
4
6
8
10
12
14
Normalized Radial Distance, R /a
Figure 4.16: K vs. R/a for Different Shapes of Conical Indenters Based on the
Indentaiton Simulation on a Standard EB-PVD TBC system.
181
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16
Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
Fracture
5
a
—Cone
—Cone
” Cone
—Cone
4
60°
90°
120'
150'
3
o<
-I—
o
a
2
(A
c
0)
1
c/2
c/3
(D
C/D
0
6
10
14
18
22
26
N orm alized R adial D istance, R /6
Figure 4.17: K vs. R/5 for Different Shapes of Conical Indenters Based on the
Indentation Simulation on a Standard EB-PVD TBC system.
182
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30
Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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In summary, it appears that using different shape indenters may extend the
capacity of measuring interfacial toughness of various systems. Special attention should
be paid to the peak values of Figure 4.16 and 4.17, which are sensitive to substrate
material properties and contact conditions. For example, softer materials with small initial
yield strain and contact surfaces with partial or entire slip conditions may raise much
larger peak values while the peak values may be much smaller for materials undergoing
significant hardening or substrate materials with large initial yield strain. More insights
on delamination due to indentation on softer materials, where the deformation is more
concentrated near the indenter, and the K vs. R/a will be steeper, compared with Figure
4.16. For such cases, a sharper indenter may help to get a more distinguishable debond
area, or larger R/a, which may be essential for such cases.
4.6.2 K vs. R/a due to Spherical Impression
Figure 4.18 presents the results of K vs. R/a curves for various sizes of spherical
indenters at the same indent load level of 150Kg, along with a comparison to the standard
conical indentation. Again the curves converge as the R/a is sufficiently large at about
R/a>12. The value of the converged stress intensity factor is found to be about 1.0 MPa
Vm away from the indentation region in the undebonded portion. The converged stress
intensity factor at the sufficiently large R/a (R/a>12) indieates the available energy release
rate for driving the propagation of the delamination in the undebonding portion far away
from the indentation region.
This plot indicates that the K vs. R/a eurves may reach and surpass that due to the
standard eonical indentation providing a sufficiently small size rigid ball at the same load
level. This is the size effect of spherical indentation on the K vs. R/a eurves. This plot
also indieates that eurves of K vs. R/a are load dependent for spherical indentation.
Providing the same size of a rigid ball, at the same R/a, the stress intensity factor, or the
stress intensity factor to cause the debonding may increase with the applied indentation
load levels. This is a distinguishing behavior of the spherical indentations. Again the K
vs. R/a behavior of Figure 4.18 is consistent with the U/a vs. R/a behavior of Figure 4.14
and 4.15.
183
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
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Figure 4.19 presents the results o f K vs. R76 curves for various sizes o f spherical
indenters at the same indent load level o f 150Kg along with a comparison to the standard
conical indentation, analogous to those shown in Figure 4.18. The behaviors shown in
this figure are much like those presented in Figure, 4.18. However, now the K vs. R/§
curve due to the standard conical indentation becomes the lowest curve among all the
results presented for the spherical indentation. This indicates the spherical indentations
considered herein may produce larger debonds at the same toughness level by providing
the same indent depth. At the same time, the peak values due to the spherical indentations
manifest more difference from each other. This indicates a sufficiently small rigid ball
may become the most suitable one for inducing debonding on very strong interfaces.
Moreover, we may also see that it would be very hard to perform indentation and induce
debonding by a larger size spherieal indenter such as the 1/8 inch diameter ball. One
difficulty is the sufficient penetration depth, and the other is no valid value available for
R/6 < 14. Therefore, careful considerations o f spherical indenter geometry become
crucially important on the real debonding tests. In fact, the largest size ball considered
here, i.e., 1/8 inch diameter ball, will not be able to induce debond on the standard EBPVD TBC system by the available load level on a Rockwell hardness tester. And this will
be shown in the part o f the experimental work on a well exposed specimen.
184
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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5
— Cone 120°
a
Ph
+o
->
— D0.79nim, a/Rb=0.81
■D 1.59mm, a/Rb=0.48
D3.18mm, a/Rb=0.27
4
3
o
cd
Ph
2
c/:)
C
(D
C/3
C/2
<D
1
0
4
6
8
10
12
14
16
N orm alized R adial D istance, R/a
Figure 4.18: K vs. R/a for a Spherical Indentation on a Standard EB-PVD TBC System
(3 sizes of ball used: 0.79mm, 1.59mm and 3.18mm in diameter at the same load
level of 150Kg)
185
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
Fracture
5
Ph
— Cone 120°
D0.79mm, a/Rb=0.81
— D1.59nim, a/Rb=0.48
D3.18nim, a/Rb=0.27
4
3
O
4— '
o
2
oo
G
<D
ly)
oo
<D
1
0
14
18
22
26
N orm alized R adial D istance, R/5
Figure 4.19: K vs. R/5 for a Spherical Indentation on a Standard EB-PVD TBC System
(3 sizes of ball used: 0.79mm, 1.59mm and 3.18mm in diameter at the same load
level of 150Kg)
186
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
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4.7 Effects of Unloading for Various Indenter Shapes
4.7.1 Effects of Unloading for Various Conical Indentations
Figure 4.20 presents a plot of K vs. R/a that includes unloading effects due to
indentation by various conical indenters. This plot is analogous to Figure 4.16, which
presents the results due to loading only. In this plot, each line type is used four times to
represent the four cone shapes considered in this thesis. From the uppermost to the
lowermost curve of the same line type, the results of K vs. R/a are due to the 60°, 90°,
120° and 150° conical indenters, respectively.
Again the “LU Simulation” curves
represent the results from the direct finite element combined loading and unloading
simulations, while the “Superposition” curves are from superimposing the results of
elastic-plastic loading and elastic unloading finite element simulations. The “Loading
Only” curves are included for comparison. In all cases, the increases in K values due to
the unloading step are not large, but are significant enough that they should be included in
the analysis of test data.
Also, in all cases, the results from both types of
loading/unloading models agree and are essentially independent of the maximum applied
load.
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
Fracture
7
LU Simulation
6
Superposition
OS
Oh
Load Only
5
5
U
OH
H
o
Oh
60° Cone
4
90° Cone
3
4->
C /5
c
c/5
C/5
2
1
io
CO
0
2
4
6
8
10
12
14
Normalized Radial Distance, R/a
Figure 4.20; K vs. R/a for Different Shapes of Conical Indenters
Including Unloading Effects
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16
Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
____________Fracture
________________________________________________________________________
4.7.2 Effects of Unloading for Spherical Indentations
Figure 4.21 presents K vs. R/a due to various spherical indentations, including
unloading effects. This plot is analogous to Figure 4.18, which presents the results due to
loading only. In this plot, each line type is again used three times to represent the three
types of spherical indentations considered in this thesis. From the uppermost to the
lowermost curve of the same line type, the results of K vs. R/a are for a/Rb = 0.81, a/Rb =
0.48 and a/Rb = 0.27, respectively.
Again the “LU Simulation” curves represent the
results from the direct finite element loading and unloading simulations, while the
“Superposition” curves represent the results by superimposing the results from separate
elastic-plastic loading and the elastic unloading finite element simulations. The “Loading
Only” curves are included for comparison with loading/unloading curves. As was shown
for the conical indentation tests, in all cases of spherical indentation, the increases in K
values due to the unloading step are not large. They are significant enough, however, that
they should be included in the analysis of test data. Also, in all cases, the results from
both types of loading/unloading models agree.
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
Fracture
7
LU Simulation
c3
CIh
S
u
O
■4— >
o
aj
tin
•+-•
^
C/3
(D
CZ)
CZI
6
Superposition
Loading Only
5
D0.79mm
4
3
2
1
D3.18mm
is
c/5
0
2
4
6
8
10
12
14
Normalized Radial Distance, R/a
Figure 4.21: K vs. R/a for Spherical Indentations Including Unloading Effects
at the Same Load Level of 150 kg
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16
Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
____________ Fracture _______________________________________________________________________________
4.8 Quantification of Interfacial Fracture Toughness
This section is to demonstrate how special conical and spherical indenters may be
utilized for the purpose of interfacial fracture toughness measurements on a standard EBPVD TBC specimen. The idea of using different shapes of indenters will be discussed as
to the benefits of multiple indentation techniques, which were utilized for most of the
currently tested specimens. More specifically, how the special shapes of indenters can be
used for the benefit of indentation tests on a well exposed specimen will be demonstrated.
The specimens are the tested cyclic specimens of #3 (6A) and #2 (8A). The cyclic thermal
condition is applied such that each cycle of thermal exposure consists of 10 minutes
heating, 45 minutes at 1100°C and 10 minutes cooling. Both specimens are all wellexposed and have undergone multiple indentations at five different locations in the asprocessed state, as well as after 50, 170, 270 and 470 cycles, respectively, by the standard
conical indenter. The new indentation tests by the special shapes of indenters have been
done after 470 cycles.
4.8.1 Results due to the Conical Indentation Tests
Figure 4.22 demonstrates how a sharper indenter causes a different debond size
compared to the standard Indentation at the same penetration depth. The tested specimen
is the cyclic specimen #2 (8A) after 470 cycles of exposure. At the same penetration
depth, about 100 micrometer, which is twice the depth of the bondcoat thickness, a 30Kg
indent load was applied by the 90 degree conical indenter and a 60Kg indent load was
necessary to be applied by a standard conical indenter. We see that the sharp indenter
caused a much smaller debond size. The reduced debond radius compared to the standard
one is about 27%, while the predicted difference is about 24% reduction in debond size
from the numerical results, considering the interfacial toughness at 1.4MPa Vm., which is
about the same as that after 470 cyclic exposures.
Table 4.2 provides a list of the measured quantities of the debonding radii and
contact sizes as well as the interfacial toughnesses due to the 90 degree conical indenter.
The results of toughness values due to the standard conical indentation were quoted for
comparison. The simulation results presented in the Figure 4.16 were used to map the
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
____________Fracture _______________________________________________________________________________
toughness results with the normalized debonding size R/a. We may also see that the
sharper conical toughness value is very consistent with the indent load of 30Kg compared
to the result of the standard conical indentation with the 60Kg load.
(b) Standard Cone at 60Kg
(a) 90° Cone at 30Kg,
Figure 4.22: Debonding Behavior Upon the Same Indentation Depth of 0.1mm Caused
by Different Shapes of Indenters. Debonding Size and Pattern Are Seen
Differently for Different Cones at the Same Penetration Depth (cyclic specimen
#2 (8A) at 470cycles)
Table 4.2: Measurements of Interfacial Toughness due to the 90 Degree Conical
Indentation and Comparison with the Results of the Standard Conical Indentation
INDENTER
TYPE
90 degree
120 degree
Load
(Kg)
30
60
R
(mm)
1.50
2.05
a
(mm)
0.16
0.21
R/a
9.38
9.76
Kc
[MPa (m)'^^]
1.3
1.2
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
____________ Fracture _______________________________________________________________________________
It is also expected that the blunt indenter with a 150° tip angle can also be used to
induce small size debonding while keeping sufficient penetration depth as indicated in
Figure 4.8. Once the penetration depth is sufficient, the blunter indenter can be used to
yield a smaller debond at the same indentation load level as applied by a sharper indenter
just because the blunter indenter does not penetrate so far. Figure 4.23 demonstrates how
a blunt cone, the 150° cone, can be used to induce a smaller sized debonding at the
150Kg indent load level. The tested specimen is the cyclic specimen #3 (6A) after 470
cycles of exposure. At 150Kg, the 150° cone penetrates about 0.1mm, two times deeper
than the bondcoat thickness as indicated from the simulation results presented in Figure
4.8, while the standard 120° cone penetrates three times of the bondcoat thickness at the
same load level. Therefore, this blunt indenter can be used for the tests without worrying
about the penetration depth at 150Kg load level. It is clear that the blunter indenter yields
a smaller debond radius as compared to that of the standard conical indenter. The
deduction of the debond radius is about 19% less than that by the standard conical
indenter as indicated in the results listed in Table 4.3. At the same time, we see that the
toughness values presented in Table 4.3 agree with each other amazingly well.
However, some discrepancies exist for the toughness values presented in Tables
4.2 and 4.3 although both tested specimens are at the same cyclic exposure history and
have approximately the same apparent interfacial toughness. The differences are mainly
caused by the difference of the applied loads. Such phenomenon has also been observed
for the case of the same indenter indenting at the same location multiple times with
increasing indent load as stated elsewhere in this thesis. Therefore, we conclude that the
differences in Kc with indenter shape are smaller than the difference in Kc with applied
load. This further confirms that interfacial toughness values measured by different shapes
of indenters are consistent.
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
Fracture
2 mm
(b) Standard Cone
(a) 150° Cone
Figure 4.23: Debonding Behavior Upon the Same Indentation Load of 150Kg
Debonding Size and Pattern Are Seen Differently for Different Cones
at the Same Indent Load Level (cyclic specimen #3 (6A) at 470cycles)
Table 4.3: Measurements of Interfacial Toughness due to the 150 Degree Conical
Indentation and Comparison with the Result of the Standard Conical
INDENTER
TYPE
120 degree
150 degree
R
(mm)
2.19
1.78
a
(mm)
0.35
0.39
R/a
6.26
4.56
Kc
[MPa (m)'^^]
1.5
1.6
From the above experimental results, it is clear that a sharper conical indenter or a
blunter one all can be used for the benefit of multiple indentation tests on a standard EBPVD TBC specimen. Several main factors that limit the capability of a standard conical
indenter to be used successfully include: (I) to avoid extremely large debonding size or
obtain optimum debond size for indenting a well exposed specimen; (2) to avoid
satisfying the critical buckling criteria upon indentation; (3) to have sufficient penetration
depth to avoid the contributions from the unknown properties of the bondcoat; (4) to have
larger debonds so that the test may have a better resolution, such as for the tests on an asprocessed specimen. For such cases, we hope the small changes in Kc may result in
measurable changes in debond size. Then one can imagine choosing an indenter shape
that will yield large debonds for short thermal exposures, where the fall-off in toughness
is great. In this case, increased resolution would be very helpful while the debond size is
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
____________ Fracture _______________________________________________________________________________
not a concern. These considerations limit the usage of the standard conical indenter and
make the special shaped indenters the best alternative method to use.
4.8.2 Results due to the Spherical Indentation Tests
Two sizes of carbide balls are considered for the spherical indentation tests. They
are 1.59mm and 3.18mm in diameter, respectively. However the 3.18mm ball did not
induce any clear debonding even under the largest available load level on the Rockwell
hardness tester. The 1.59mm ball causes a nice axisymmetric debonding upon a 150Kg
indent similar to those seen due to the conical indentations.
Figure 4.24 shows the
backscattered images due to the 1.59mm ball and the 3.18mm ball. We see that the
smaller sized carbide ball caused a clear damage and clear penetration imprint on the
TBC coating while the larger one did not cause clear damage.
From the currently
involved impact tests, very similar phenomenon was also observed on the larger sized
carbide ball, i.e., the TBC was not damaged in the low speed impact tests. Figure 4.25
shows the debonding behavior upon the indentation of the 1.59mm diameter carbide
spherical indenter at the indent load level of 150Kg. This demonstrates that the smaller
size and sufficient penetration depth are the keys for a successful debonding in a spherical
indentation event.
Table 4.4 summarizes the results of interfacial toughness due to the indentation
tests of different shapes of indenters at the same load level of 150Kg. The spherical
indentation results appear in the first row of the table. The consistency of the results is
very apparent. This makes us have more confidence in performing the indentation tests
for the purpose of measuring interfacial toughnesses using different shapes of indenters.
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Chapter 4. Indenter Shape Effects on the Delamination Mechanics o f Interfacial
Fracture
A 200 Lim
(a) 1.59mm Ball
(b) 3.18mm Inch Ball
Figure 4.24: Backscattered SEM Photographs to Illustrate the Debonding Behavior for
Different Spherical Indenters at the Load Level o f 150Kg (cyclic specimen #3
(6A) at 470cycles)
Fiure 4.25: Debonding Behavior Upon upon a 1.59mm Diameter Spherical Rigid
Indenter at the Load Level o f 150Kg (cyclic specimen #3 (6A) at 470cycles)
Table 4.4: Summary o f the Measurements o f Interfacial Toughness due to Various
apes o f Indenters at the Inc ent Loac Level o f 150Kg
R
a
R/a
INDENTER
Kc
[MPa (m)''^l
TYPE
(mm) (mm)
5.36
1.5
D1.59mm
1.93
0.36
1.7
1.97
0.30
6.57
90° Cone
1.5
0.35
2.19
6.26
120° Cone
1.6
1.78
0.39
4.56
150° Cone
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Chapter 4. Indenter Shape Ejfects on the Delamination Mechanics o f Interfacial
____________ Fracture _______________________________________________________________________________
4.9
Chapter Summary
In this chapter, the limitations of interfacial toughness measurements due to the
standard conical indentation were first addressed. The constitutive behavior used to
describe the EB-PVD TBC system considered in the previous study by Vasinonta and
Beuth (2001) was revisited and a more general description, namely, the modified
Romberg-Osgood hardening law, was provided to be suitable for more general studies of
the effects of substrate hardening behavior. The existing indentation method was enriched
by including the indenter shape effects and indentation results at its unloading state. The
ideas of using various shapes of indenters to control the debond size were illustrated
through the experimental studies on an exposed speeimen. The measured values of
interfaeial toughnesses due to different shapes of indenters have been found in excellent
agreement.
In summary, it was found necessary to identify optimal indenter shapes such that
an indentation provides an acceptable debond behavior.
Specifically, special-shaped
indenters may be beneficial and valuable in the following cases: (I) for a very adherent
interface, such as exists in some as-processed EB-PVD TBCs and in some oxide scale
systems. For both types of systems, a special indenter may be used to cause a more
distinguishable debond. For an oxide system or other thin coatings, special indenters can
be used to provide larger energy release rates, resulting in clearer debonding and/or
debonding to larger radial distances; (2) for the case of a very thick coating, such as a
TBC with a thickness greater than 200 pm. In such cases, the penetration by a standard
cone may not be deep enough to induce debonding. A sharper indenter may be used to
cause deeper penetration and debonding; (3) for cases of multiple indents on the same
specimen.
A special indenter may be needed to cause debonding without causing
coalescence with other indentation-induced debonds or buckling driven delamination; (4)
for tests simulating the failure of applied thermal barrier coatings in hot sections of gas
turbine engines, which is often caused by impact events from ballistic foreign objects. A
contact analysis of spherical indentation may provide insight into quantifying adhesion
loss in high-speed spherical impact tests.
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
CHAPTERS. CONTACT AND
FRACTURE ANALYSIS
OF DELAMINATION ON
CURVED SUBSTRATES
5.1 Chapter Overview
Previous research has focused on the axisymmetric delamination of coatings on
flat substrates. However, in practice, ceramic thermal barrier coatings are deposited onto
turbine engine blades and other components with curved surfaces. Compared with the
phenomena of delamination of compressed films on flat substrates, the delamination of
compressed films on curved substrates is expected to be either enhanced or suppressed by
the curvature of the substrate (Hutchinson, 2001).
Recent research at the German Aerospace Center Institute of Materials Research,
involving thermal gradient mechanical fatigue (TOME) tests on EB-PVD TBC systems
(Bartsch et a l , 1999, 2002), has considered indentation testing on curved substrates to be
highly relevant. The specimens used in these tests are hollow cylinders with various
inner and outer diameters. Much thicker PtAl bond coats of llO pm and TBC layers of
220pm to 290 pm are applied in the cylindrical TBC systems compared with the flat
specimens tested in this research. These specimens are used to simulate the real-life
exposure of gas turbine blades by imposing simulated mechanical fatigue loads in
addition to thermal cycles. Cooling air is circulated in the hollow cylinders to induce a
thermal gradient similar to that seen in air-cooled turbine blades.
After some TGME specimens were tested, they were indented at room
temperature by a standard conical indenter to induce debonding, so that the debond size
could be related to the interfacial toughness of the TBC.
It was observed that the
delamination, caused by the combination of biaxial residual stresses in the TGO and TBC
layers, and the induced stresses due to a standard conical indentation, yields an unsymmetric butterfly-shaped debonding pattern, as shown in Figure 5.1. The butterflyshaped pattern may be explained as being caused by a series of events. First, tbe axial
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
strain induced by indentation in the circumferential direction is larger than in the
longitudinal direction. Because of this, the energy release rate for crack extension in the
circumferential direction is expected to be much greater than for crack extension in the
longitudinal direction.
Due to this, the crack extension will be greater in the
circumferential direction, resulting in an elliptically-shaped debond.
However, as the
propagation continues, the debond size may reach its critical value for buckling to occur
in the circumferential direction.
Once buckling occurs, delamination becomes much
easier in the longitudinal direction. The result is the formation of the “wings” of the
butterfly, at the top and bottom of the elliptical delamination.
Figure 5.1: Delamination Pattern of TBC Coating on a Cylindrical Specimen with Outer
Diameter = 14.7mm, Inner Diameter = 6mm, NiCoCrAlY Bond Coat
Thickness = 110pm, and EB-PVD TBC Thickness = 220pm. Indentation
Performed with a Rockwell Hardness Tester by a Standard Brale C Diamond
Conical Indenter (Bartsch, et.al, 2002)
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
The purpose of this study is to provide a quantitative analysis of strain
distributions in each direction that will allow the determination of steady state advanced
energy release rates and interfacial toughness for this type of test.
Guidance for
performing indentation tests on curved specimens without causing buckling driven
delamination will also be addressed.
The concept of geometrical similarity may simplify the analysis of this test.
Although the longitudinal and circumferential strains are coupled, it is expected that
results for strains in the longitudinal direction may be roughly load-independent because
there is no curvature in this direction.
However, geometric similarity would not be
expected in the circumferential direction; thus the strain from indentation in the theta
direction will not be self-similar and the strain distribution would be load-dependent.
To quantify interfacial toughness debonding on curved substrates, indentation and
delamination mechanics on a curved substrate are analyzed first. Next, finite element
models are used for quantitative analysis of surface strain distributions in the normal
distance from the indentation region, and to determine the necessary indent load vs.
indentation sizes. More specifically, two hollow cylindrical specimens, seen in the TGMF
tests, will be chosen as the application pattem for the FE models. A solid cylindrical
specimen, received from the University of Califomia at Santa Barbara (UCSB), will be
analyzed through the FE model. This specimen will then be tested and the interfaeial
fracture toughness will be provided quantitatively.
200
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.2 Indentation Mechanics on a Curved Substrate
5.2.1 Geometrical Consideration
Figure 5.2 gives a schematic plot of the indentation geometry for a conical
indentation impressing on the top surface of the cylindrical substrate vertically. Since the
geometrical dimension of the cylinder is much larger than the indentation size to be
performed, to simplify the analysis, we may imagine another indenter operating from its
opposite side. Therefore, it is only neeessary to simulate one-eighth of the specimen to
obtain the surface strain results.
Attention will be given to some geometric notations. As the indentation force P is
applied vertically from the top surface of the cylindrical specimen, the conical indenter
penetrates an actual depth of 6. We denote 5i , shown in Figure 5.2, as the imaginary
depth associated with the actual penetration depth 6, without the roundness at the indenter
tip. At the same time, the contact radius in the axial direction is denoted as az, while the
contact radius in the circumferential direction is denoted as ae. Note that the contact radii
of az and ae, considered the pure geometric parameters, are directly associated with the
indentation depth 5, similar to the consideration stated in chapter 4. In general, the
relationship among the geometric parameters shown in Figure 5.3a and 5.3b is derived as
follows:
The contact radius in the axial direction:
a , = V 5 (2 r-6 )
fo r 5 < 5 ^ ^
(5.1)
a,
forS>8„
(5 .2 )
tanp
where the imaginary indentation depth 5j is defined from the geometry as:
5. = 5 + r
cosp
(5.3a)
/
Penetration depth at the turning point in the axial direction:
SjA = r( l-c o s p )
(5.3b)
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
where p is the inclination of the cone surface to the surface of the cylinder in the axial
direction, r is the round radius.
The contact radius in the circumferential direction:
ag = P g A rcco s
Po + ( P o
-5 )(2 r + po
-S)
for 6 < 6 T C
(5.4)
for 5 > 5 T C
(5.5)
2 p o ( r + Po - S )
(%
Po'
^
- Arcsin
v2
(
5. ^
1---- ^ cosp
V Po y
where:
^TC
Po
1
sK
P + Yt )
siny.j.
(5.6a)
X
(5.6b)
y.j. = arcsin — sinp
Po
J
where po is the outer radius of the cylinder.
From these expressions, it can be seen that the contact radii in the axial direction
and the circumferential direction are pure functions of the geometry of the indenter and
the cylinder, as well as the penetration depth. As for a shallow indentation, the contact
radii—either in the circumferential direction or in the axial direction—are dominated by
the effect of rounding each indenter tip, as seen in the expressions of (5.1) and (5.4). As
penetration deepens, the effects of the rounding at the indenter tip will be diminished and
the contact radii are dominated primarily by the indenter tip angle and penetration depth.
In the practical analysis, the penetration depth is much larger than 5r (the turning point
depth), due to the roundness at the indenter tip, as indicated in Figure 5.3. Nevertheless
expressions of the contact radii for the shallow indentation are included in the analysis
when 5 < 6.
^TC •
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
cone
iiollow cylindfical substrate
X, Y -g lo b a l
r, 0 ~ local
(a) Schematic View of the Curved Contact Side
cone
hollow cylindrijcal substrate
(b) Schematic View of the Straight Contact Side
Figure 5.2: Schematic of Indentation on a 3-D Curved Substrate
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
'^TA
I
I
Cylindrical Substrate
(a) Schematic View of Straight Contact Side for the Determination of
TC
Cylindrical Substrate
(b) Schematic View of Curved Contact Side for Determination of ae
Figure 5.3: Schematics of Indentation Geometry on Determination of Contact Radius in
the Axial Direction az and Circumferential Direction ae
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
Figure 5.4 provides a plot for the contact radii in the axial, as well as for the
circumferential direction vs. the penetration depth. In this plot, solid curves represent the
results from the standard conical indentation; dashed curves represent results from the 90°
sharp conical indentation. Each line type has been used three times from thick to thin. The
thickest curve represents the results for the contact on a cylinder in the axial direction,
labeled as “Flat ...”. The thinnest curve represents the results of the contact on a cylinder
with the smallest outer radius. From this plot, it is clear that three major factors play a
very important role on the determination of the contact radii for a contact on a curved
substrate, compared to a contact on a flat specimen. One factor is the conical tip angle;
the sharper the cone, the less curvature effects are expected on the contact radius. The
other factor is the cylindrical outer radius. The bigger the cylinder, the fewer curvature
effects are expected for a fixed conical geometry. The third factor is the penetration
depth; while maintaining other factors at constant, the deeper the penetration, the more
curvature effects are expected.
For the load level of interest on a standard Rockwell hardness tester, the
penetration depth for using a standard cone is less than 200pm; using a sharp 90 degree
cone, penetration is less than 300pm. For these practical cases, the contact radius in the
circumferential direction is about 5% less than the contact radius in the axial (flat)
direction for the larger cylinder considered here, and about 8% less for the smaller
cylinder considered here for the standard conical indentation at a penetration depth of
200 pm. If the 90 degree conical indenter is used, the difference between the contact
radius in the axial (flat) direction and in the circumferential direction reduces to less than
3% for the larger cylinder and 4% for the smaller cylinder at a penetration depth of
300 pm. As will be clarified later in this thesis, for the experimental results of contact on
a curved substrate, this is why the difference between the contact radii measured from the
axial and the circumferential direction is insignificantly small.
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.7
0.6
0.5
(D
0.4
---- Flat, std. cone
R c-5.11m m , std.
Rc=3.08mm, std.
— Flat, 90° cone
Rc=5.11mm, 90°
Rc=3.08mm, 90°
cone
cone
cone
cone
N
•1-H
'Td
cd
0.3
O
+-1
c
O
U
0.2
■
0.1
0
0.00
0.05
0.10
0.15
0.20
0.25
Indent Depth, 5 (mm)
Figure 5.4: Curvature Effect of Contact Radii a© Compared with a^ at the Same
Penetration Depth
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0.30
Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.2.2 Dimensional Analysis for Surface Strains
For the convenience of analysis, the modified Romberg-Osgood relationship is
used here to describe the uniaxial behavior of the substrate materials, as stated in the
previous chapter. A conical indentation on a single cylindrical substrate is examined.
Under the same contact conditions, the conical indentation on a long solid cylindrical
substrate, the compressive—as well as the tensile biaxial strains on the contact surface in
both the axial direction and the circumferential direction—must be functions (fa and fc), of
all the independent governing parameters, namely. Young’s modulus (E), Poisson’s ratio
(v), yield toughness ay, the inclination of the cone face to the surface of the cylinder in
the axial direction P, the distance away from the contact center, Rz, Re, and the contact
size, az ae :
= fa(E, a y ,
£* = fc (E,
V,
a y , V,
Rz, az, po, P, a, N)
(5.7)
Re, ae, po, P, a , N)
(5.8)
Applying the Pl-theorem in dimensional analysis (Barenblatt, 1996), the following
dimensionless functions, fa and f c , were obtained, according to:
<=fa
E
Gy
—
E
^\P,v,a,N
(5.9)
Po a
,— ,
Rn
„
(5.10)
,p,v,a,N
Po a,
It can be seen that the in-plane strains in each direction on the cylindrical surface
are expressed in (5.9) and (5.10). More specifically, (5.9) expresses the indentationinduced biaxial in-plane strain state at each point on the cylindrical surface in the axial
direction. The biaxial in-plane strain in the axial direction includes s ’^ands^^in the local
r-0-z coordinate. (5.10) expresses the indentation-induced biaxial in-plane strain state at
each point on the cylindrical surface in the circumferential direction. The biaxial in-plane
strain in the circumferential direction also includes c'^ands^^in the local r-0~z
coordinate. It is emphasized that the indentation-induced strains 8 and
207
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, in a different
Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates_________
direction on the cylindrical surface, indicate different meanings or different dimensionless
functions.
5.2.3 Energy Release Rate
From the experimental observations, the primary area of interest is the crackdriving intensity in the z and 0 directions on the cylindrical surface, based on the local
coordinate system. For simplification, the main assumptions used in 2-D contact fracture
analysis will be adopted in this study, mainly: (1) The top composite plate, consisting of
TBC and TGO layers, will be deformed upon indentation in such a way that it only
follows the deformation occurring on the top bondcoat surface, and no variation at any
cross section; (2) breaking occurs for each contact event and only a narrow strip is left
behind each crack front; (3) delamination must satisfy quasi-steady-state conditions so
that energy release rates can be calculated using steady state formulas.
Based on the above assumptions, the total energy release rate in each direction
along the interface of TGO and bondcoat of the cylindrical specimen may be formulated
the same as those in the 2-D flat specimen. That is, the total energy release rate can be
expressed as the sum of Gj and Gn , such that G = Gj -i- Gn. In this expression, Gn is the
energy release rate due to the bending effects caused by the difference of residual stresses
in the TBC layer and in the TGO layer, which can be computed using the same method as
presented in formulations of (2.35) to (2.36). The formulation of Gican still be expressed
in a familiar way (Vasinonta and Beuth 2001), with distinctions in each direction as
follows:
Gi expression in the axial direction:
2G,(l-v^)
I
!----------------= Ie
E
ft
^ e f f V '-T B C
~
-I-1
‘• T G O
J
' zz
\z
+v£Q„f
.c , ^
(5.11a)
00''
Gi expression in the circumferential direction:
}2
where:
(5 .U b ,
s,, = 8 f + e ' ,
(5.12a)
208
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates_________
+e;
(5.12b)
where tjBC and troo are the thicknesses of the TBC and the TGO layers, respectively, Eeff
is defined in the same way as (2.30).
5.3
Finite Element Modeling
5.3.1 Model Description for Contact on 3-D Curved Substrates
Two 3-D cylindrical FE contact models have been built with outer radii of
3.08mm and 5.11 mm, respectively, and inner radii of 0.97mm and 3.00mm, respectively.
The length of each half cylinder used in the models is 10mm. By considering sufficiently
small deformation by the contact events, two indenters may be placed on the opposite
sides of the cylinder, such that the FE model can be reduced to one-quarter of the
specimen considered. The cylinder is made of a nickel-based superalloy with an EB-PVD
PtAl bondcoat on top. The bondcoat thickness is 110pm, the same as the specimens used
in the real life tests.
For the sake of consistency with studies performed in the flat specimens, the
elastic-plastic behavior of the polycrystalline PtAl bondcoat at room temperature was
taken to be the same as used in the 2-D studies. Therefore, a power law hardening
behavior is assumed for the bondcoat material, such th at,a = ce", where n is about 3.4,
and c is 4780MPA for a yield stress at 900MPA (Vasinonta and Beuth, 2001;
Wasilewski, et a l, 1967). However, the yield stress of the bondcoat can vary by a large
range with extreme values of 480 MPa and 900 MPa, regardless of whether the 900 MPa
is adopted, unless otherwise specified. The hardening behavior of the nickel substrate was
taken as the Ludwigson modified power law, so that: ct = Kj8"‘ -1-e‘^^e"-', where Ki =
2.88X10^, ni = 0.44, K 2 = 19.9, and n 2 = 25, and a and e are the true stress and
logarithmic strain, respectively (Vasinonta and Beuth, 2001).
By using the modified Ramberg-Osgood relation, the uniaxial stress-strain
relations can be easily obtained. If this relation is used, relative parameters are a=14 and
N=2 for the nickel superalloy substrate and oc=1.7 and N=2.87 for the PtAl bondcoat, as
indicated in the previous chapter.
209
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
A 3-D isoparametric element type of 8-node linear brick with incomplete modes,
C3-D8I, has been chosen for the 3-D contact finite element analysis. For using
isoparametric elements, special attention will be paid to the element regularity, whieh
consists of measuring the element distortion with respect to an ideal cubic shape. The
distortion is measured by the angle between isoparametric lines of the elements.
According to the accuracy of the numerical integration in the element, this angle should
be greater than 45“ deg. or less than 135“. Such types of element distortion are carefully
avoided in the present FE analysis.
Nonslip conditions between the indenter and the substrate are ensured by taking p.
= 0.7. Load is calculated using reaction force at the rigid reference point of the cone,
unless otherwise speeified. All other contact mechanisms necessary in FE simulation are
the same as stated previously and will not be repeated here.
The cases considered here for the finite elements are listed in Table 5.1. A typical
FE mesh used in this study for contact analysis on a hollow cylindrical specimen with
boundary eonditions labeled on each relevant surface, is given in Figure 5.5. Special
attention will be paid to the boundary conditions on the inner surfaee of the cylinder
considered. The inner surface of the test specimens considered by Bartsch et al. (1999,
2000) is not constrained, and is subject to a traction-free boundary condition. A
simplified model considers the inner constraints, as specified by Ur=0, and will be
detailed in later sections. A typical mesh consists of 43,200 user-defined elements and
266,431 nodes. The total number of variables defined in the model, consisting of the total
degree of freedom plus the Lagrange Multiplier variables, is 707,853. Two coordinate
systems used in this modeling are set up; the global coordinate was used to establish the
proper solid model. The local coordinate was a cylindrical coordinate system and was set
up to map the solutions in the proper directions, using the commands available from
ABAQUS code, ^ORIENTATION and ^TRANSFORM. It is very expensive to run such
3-D simulations because it takes about 80 hours CPU time to finish one job at a standard
load on a Dell precision machine with 1GB standard memory.
A typical FE mesh used for the UCSB speeimen is given in Figure 5.6. This
typical mesh consists of 54,020 user-defined elements and 330,995 nodes. The total
210
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
variables defined in the model consisting of the total degree of freedom, plus the
Lagrange Multiplier variables, are 880,817. At least one GB memory is required to run
the job created from this model; 130 hours of CPU time are required to finish the job.
Table 5.1: Cases Considered in the FEA Simulations
Cylinder
Type
Substrate
Diameter
(mm)
Substrate
Inner
Diameter
(mm)
Substrate
Material
Bond Coat
Thickness
ilim)
Bond Coat
Material
Big
hollow
cylinder
Small
hollow
cylinder
10.2
6.0
Ni based
Superalloy
110
NiCoCrAlY
(EB-PVD)
6.16
1.95
Ni based
Superalloy
110
NiCoCrAlY
(EB-PVD)
NiCoCrAlY
110
Ni based
11.0
Solid
(EB-PVD)
Superalloy
cylinder
Note:
The substrate diameter includes the bondcoat thickness
The hollow cylinders are simulated with or without bondcoat on top.
The big hollow cylinder with or w/o inner constraints are considered.
211
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Half
Cylinder
Length in
simulation
(mm)
10.0
10.0
15.0
Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
U. =0
L y, 0
or
Traction-Free
U r=0
w
a m
r
Figure 5.5: A Simplified 3-D FEA Contact Model o f a Hollow Cylindrical Specimen
212
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
Figure 5.6: FEA Contact Analysis of a Sharp 90° Conical Indentation on the UCSB
Specimen with Bondcoat/Substrate System
213
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates __________
5.3.2 Model Verification for Contact on a 3-D Flat Substrate
A convergence study was performed for the problem of contact on a 3-D flat
substrate. The main purpose of this study is to verify and confirm the number of elements
in contact which are adequate for converged results. One widely held opinion is that the
surface displacement and surface strain away from the contact region are not sensitive to
mesh resolution (Begley et a l, 2000). However, it is not clear how coarse the mesh can
be in order for this conclusion to be maintained. If the mesh resolution is too coarse, it
will inevitably fail to capture the contact events and result in inaccurate results.
Therefore, it is important to perform a convergence study to confidently determine the
number of elements to be used in the contact region to achieve the converged solution of
displacement and strain away from the contact region. Convergence was tested here from
two perspectives. The first method is through contact on a 2-D flat specimen; the results
can be compared with those of standard 2-D specimens. The other method utilizes
insights from the dimensional analysis, and this will be presented in the next subsection.
This 3-D flat substrate is equivalent to an example when the radius of a cylindrical
substrate is infinitely large. Fig.5.7 shows the FE model of a flat specimen with a typical
mesh resolution used in the convergenee study. Two mesh densities were eonsidered to
obtain the displacement U/a in the longitudinal direction in comparison with the standard
2-D solution (with bondcoat thickness changed to llOjim, to match this 3-D study). Mesh
I consists of 17640 user-defined elements and 19779 user-defined nodes, while mesh n
eonsists of 32338 user-defined elements and 35569 user-defined nodes. The mesh
resolution in the contact region is roughly two times denser in model n than in model 1.
Figure 5.8 presents the results of the surface compressive strain vs. R/a from the
3-D flat FE model, as compared to those from the 2-D standard mesh resolution. It ean
be seen that the results show some improvements from mesh n at the region beneath and
near to the indentation, compared with that obtained from the standard 2-D model.
Moreover, the mesh 1 was found to have five elements in contact, and mesh 11, nine
elements in contaet when reaching the contact load of 150Kg. Therefore mesh H
resolution is adopted as a reference mesh for the cylindrical FE models.
214
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
Indenter
r^ jS ^ r'T l l i- i- h T T tV i! 'ii-H tiH H i‘"—i .
1
l ^ '. V f - A f .
'
—
/.-,-rT w I I L r r h t T T ^ f I ! i iT ~ r i-4 -4 - —1 i ^ —‘—^ -L
-' ti+
4 -+ttTJZW+‘f rfflSW IrlHith-.4^4ltrn'-fH
Uy=0'
XYZ: global coordinate
Figure 5.7: Contact on a 3-D Flat Substrate with Results Compared to the 2-D Standard
Analysis to Show the Validation of 3-D Mesh Resolution
215
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.000
-
-
!/5
-
0.001
0.001
0.002
<
-
0.002
n M esh 1, 5 Elems
X M esh 2, 5 Elems
A M esh 2, 7 Elems
-0.003
•
M esh 2, 9 Elems
— 2-D Std. M esh, 51 Elem^
-0.003
6
8
10
12
14
N orm alized Distance, Rz/az
Figure 5.8; Compressive Strain vs. Rz/az for a Standard Conical Indentation on a Flat
Substrate with Comparison to Standard 2-D Results
216
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16
Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.3.3 Model Verification for Contact on 3-D Hollow Cylinders
This section serves as the validation of the finite-element models of the contact on
hollow cylindrical substrates. One single substrate material is assumed for all the results
presented here. Besides the single-material assumption,it is also assumed that the length
of the cylinder is sufficiently long so that edge effects are essentially negligible.
Furthermore, the inner surfaces of the hollow cylinders investigated herein are
constrained so that the displacements along at the inner surface in the radial direction in
the local coordinate r-0-z system are set to be zeroes (roller constraint). The importance
of the constraint in the modeling of some cylindrical specimens will be discussed later in
this chapter.
The material properties of the substrates are the same as routinely used, in
this research, the nickel based superalloy substrate.
From the previous dimensional analysis, it can be seen that the surface biaxial
strains in the axial direction are dependent on az/po and Rz/az , and the surface biaxial
strains in the circumferential direction are dependent on ae/po and Re/ae ^by providing the
same contact condition and material properties. Therefore, validation of the FE model can
be fulfilled by recognizing that the compressive, or tensile strain in a certain direction
must be the same at the same R/a on different sizes of cylinders, but with the same a/po.
Figures 5.9 and 5.10 illustrate this fact and serve as validation of the finite element
models from this perspective.
Figure 5.9 presents two sets of compressive strain distributions vs. a normalized
distance away from the indentation region. These results are obtained from the contact
analysis performed on the two cylinders; The larger cylinder with an outer radius of po
=5.11mm, and an inner radius of Pi =3.00mm, the smaller cylinder with an outer radius of
Po =3.08mm and an inner radius of p; = 0.97mm. Each of the two hollow cylinders has
the same thickness of 2.11mm.
The curves of the strain vs. R/a overlap each other at the same a/po for the two
different cylinders.
On one hand, the compressive strain distribution in the
circumferential direction vs. Re/ae , due to the contact on the large cylinder, overlaps the
compressive strain distribution in the circumferential direction because for the same ae/po
217
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
=0.071. On the other hand, the compressive strain distribution in the axial direction vs.
Rz/dz , due to the contact on the large cylinder, overlaps the compressive strain
distribution , due to the contact on the small cylinder, in the axial direction for the same
a^/po =0.076. For the same a/po, contact on a different sized cylinder may result in a
significant difference in penetration depth and indent load. For the properties used in this
study, at the same az/po=0.076, the contact on the small cylinder requires a penetration
depth of about 100 pm, and an indent load approximately 60K, while the contact on the
large cylinder requires a penetration depth of about 200 pm and an indent load
approximately 170Kg.
Figure 5.10 presents the same points as illustrated in Figure 5.9. Here however,
another two sets of surface tensile strain results are provided, which are directly relevant
to the compressive strains shown in Figure 5.9. These tensile strains do not exist
independently, but are associated with the compressive strains at the same point in the
cylindrical surface in either the axial direction or the circumferential direction. Again it is
evident that tensile strain distribution vs. normalized distance in the circumferential
direction, Re/ae, overlap each other due to the contact on the large and small cylinders for
the same value of
a e /p o = 0 .0 7 1 .
At the same time, the tensile strain distribution vs. the
normalized distance in the axial direction, Rz/az, overlap each other for the results of the
contact on the two different hollow cylinders for the same value of
a z /p o = 0 .0 7 6 .
From the above analysis, the validity of the contact model on the hollow cylinders
is evident; therefore these models will be adopted on the numerical studies of contact on
the cylindrical specimens.
218
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.000
-
0.002
C3
Vh
00
<u
1/5
-0.004
CD
CD
O
o
U
-0.006
Small
"X- - Large
Small
Large
cylinder, ae/po=0.071
cylinder, ae/po=0.071
cylinder, az/po=0.076
cylinder, az/po=0.076
-0.008
4
6
8
10
12
Norm alized Distance, Rz/az,
Figure 5.9: Compressive Strain vs. R/a for a Standard Conical Indenter Contact on
Hollow Cylindrical Substrates with Roller Constraints at Inner Surfaces and
at the Same ae/po in the Circumferential Direction and the Same az/po in the
Axial Direction
219
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
8.0
Sm all
“X" Large
Sm all
Large
7.0
6.0
a
id
<u
C/!5
id
o
H
f ' ■*H
•^
cylinder,
cylinder,
cylinder,
cylinder,
a0/po=O.O71
ae/po=0.071
aJpo=0.076
ajQo=0.016
5.0
4.0
3.0
2.0
1.0
0.0
4
6
8
10
12
N orm alized Distance, Rz/a^, Re/ae
Figure 5.10; Tensile Strain vs. R/a for a Standard Conical Indenter Contact on Hollow
Cylindrical Substrates with Roller Constraints at Inner Surfaces and at the
Same ae/po in the Circumferential Direction and the Same a^/po in the Axial
Direction
220
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.4
Numerical Results and Discussion
In this section, the numerical results are presented for the cases listed in Table 5.1.
The relevant 2-D results presented for comparison are based on the 2-D simulations with
the same material properties considered in the 3-D cases and with the same bond coat
thickness of llOpm.
5.4.1 Indentation Results on Hollow Cylinders without Roller Constraints
In the TGMF tests in Germany by Bartsch et al. (1999, 2002), the tested
specimens are hollow cylinders, which are not subject to any inner surface constraints.
Therefore, the traction-free boundary condition at the inner surface is first kept in order to
simulate the real tests. In this subsection, numerical results for contact on the large hollow
cylinder will be presented first, and results for contact on the small hollow cylinder
follow.
Figure 5.11 provides a plot of the compressive strain vs. the normalized distance
away from the indent region in both the axial and the circumferential directions for
contact on the large hollow cylinder, subject to the traction-free boundary condition at the
inner surface. From this plot, it can be seen that the axial compressive strain distribution
almost overlaps the relevant 2-D results, while the circumferential strain distribution
departs from the 2-D results. In fact, the circumferential strain is much larger than the
axial strain in magnitude at the same R/a. This is especially true at the region near to the
indenter. In addition, crossing effects occur over the strain distribution due to the larger
load level vs. the lower load level; this is caused by the bending strain at the top and
bottom of the cylinder in the circumferential direction. Briefly, as the indent load
increases, the bending strain in the circumferential direction also increases with a
maximum value located at the intersection of the r-z plane and r-0 plane on the
cylindrical outer surface. However, the bending strain in the circumferential direction at
the outer surface is tensile. When this tensile strain finally dominates and exceeds the
value of the compressive strain in magnitude due to the indent load, then the effective
strain becomes tensile. Thus the compressive strain distribution in the circumferential
direction may experience a transitory point from the indent center to the comer point at
221
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates_________
the intersection of the r-z plane and r-6 plane on the outer surface of the cylinder. The
transitory point also separates the region from the indent center to the comer point into
two: the compressive area, from the indent center to the transitory point and the tensile
area, from the transitory to the comer point at the intersection of the r-z plane and r-0
plane on the cylindrical outer surface. Furthermore, the transitory point moves closer to
the indent center as the load increases. Nevertheless, we do not see the tensile portion in
Figure 5.11, simply because the results are plotted only in the interested space of R7a<12
and the tensile portion falls off the range of R/a larger than 12. This is essentially the
cause of the crossing effect; more details will be explained at the end of this subsection.
Figure 5.12 presents the results of the stress intensity factor distribution of the
large hollow cylinder vs. the normalized distance away from the indent region. These
results are evaluated from the compressive strain distribution and the tensile strain
distribution in both the axial, as well as in the circumferential directions. The tensile
strain distributions are not shown here since they do not contribute significantly to the
stress-intensity factor distribution. Again it can be seen that the crossing effect also exists
in this K vs. R/a plot similarly to that observed in the compressive strain vs. R/a. That is,
the stress intensity factor vs. the normalized distance away from the indent region at the
150Kg load level crosses that at the lOOKg load level. Although the crossing effect occurs
for both the stress intensity factor distributions in the axial—as well as in the
circumferential directions, the stress intensity factor distribution in the axial direction of
two different load levels are close to the 2-D results, but slightly higher, suggesting that
the 2-D results may be a good approximation to the 3-D axial results.
222
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.000
-
0.001
a
OQ
(D
>
C/!5
C/D
(D
-
0.002
•
-0.003
O
U
— Flat 2-D (150Kg)
-0.004
-0.005
^
Axial (lOOKg)
^
Axial (150Kg)
Circumferential (lOOKg)
Circumferential (150Kg)
-0.006
2
4
6
8
10
12
Normalized Distance, Rz/az, Re/ae
Figure 5.11: Compressive Strain vs. R7a for a Standard Conical Indenter Contact on a
Hollow Cylinder (po=5.11mm, Pi=3.00mm) Traction-free at Inner Surface
223
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
5.0
PlH
-IO
—•
o
a
00
Ch
(U
C/D
IZ)
(D
ts
oo
Flat 2-D (150Kg)
Axial (lOOKg)
O -A xial (150Kg)
Circumferential (lOOKg)
Circumferential (150Kg)
4.0
3.0
2.0
1.0
0.0
4
6
8
10
12
N orm alized Distance, Rz/a^, Re/ae
Figure 5.12: K vs. R/a for a Standard Conical Indenter Contact on a Hollow Cylinder
(Po=5.11mm, pi=3.00mm) in the As-processed Condition and Traction-free at
the Inner Surface
224
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
Figure 5.13 provides a plot of compressive strain distribution for the contact on
the small hollow cylinder, subject to the traction-free boundary condition at its inner
surface. The crossing effects are reduced compared to the results of the large hollow
cylinder in Figure 5.11; this is because the smaller the hollow cylinder, the greater is the
rigidity for the same thickness, and the smaller the effect on the strain caused by the
bending. Furthermore, while the strain distribution in the circumferential direction departs
from the 2-D results, the compressive strain distribution in the axial direction of the two
load levels are again close to the 2-D results, similar to those in Figure 2.11. At the same
time, it can be seen that the circumferential strain is much larger than the axial strain in
magnitude at the same R/a.
Figure 5.14 presents the final results of the stress intensity distributions for
contact on the small hollow cylinder. Similar trends observed in the compressive strain
distribution are also observed in the distribution of the stress intensity factors. First, the
stress intensity distributions in the axial direction of the two different load levels are close
to the 2-D results, but slightly lower than them. Although there is still a crossing effect
between the two curves of different load levels, this crossing effect is insignificant
compared to the 2-D results, and it can be approximately approached by the 2-D results in
the axial direction. Second, the stress intensity distributions in the circumferential
direction of the two load levels depart from the 2-D results with much larger values.
Therefore, crack initiation and propagation are first expected to occur in the
circumferential direction, since stress intensity is much greater at the same distance away
from the indent region in the circumferential direction than in the axial direction. At the
same time, this also indicates that the specimen may experience a larger delamination size
in the circumferential direction than in the axial direction for the same level of interfacial
toughness. We also see that the load dependence of the stress intensity distribution is
more evident in the circumferential direction than in the axial direction.
225
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.000
-
d
-t—>
-
0.001
0.002
GO
(D
'
go
cn
(D
u
CG
O
U
-0.003
-0.004
-0.005
— Flat 2-D (150Kg)
Axial (lOOKg)
^ Axial (150Kg)
Circumferential (lOOKg)
Circumferential (150Kg)
-0.006
8
10
12
N orm alized Distance, Rz/az, Re/a©
Figure 5.13: Compressive Strain vs. R/a for a Standard Conical Indenter Contact on a
Hollow Cylinder (po=3.08mm, pi=0.97mm), Traction-free at the Inner
Surface
226
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
5.0
— F lat2 -D (1 5 0 K g )
^
Axial (lOOKg)
Axial (ISOKg)
4.0
Circumferential (lOOKg)
Circumferential (150Kg)
+o
->
o
a
CO
c;
<D
CO
CO
<D
u
00
3.0
2.0
1.0
0.0
2
4
6
8
10
Normalized Distance, Rz/az, Re/ae
Figure 5.14: K vs. R/a for Contact on the Small Cylinder at the As-processed Condition
for a Standard Conical Indenter Contact on a Hollow Cylinder (po=3.08mm,
pi=0.97mm), Traction-free at the Inner Surface
227
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12
Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
Several important conclusions may be drawn from the numerical results above.
First, numerical results—either strain distributions or stress intensity distributions—in the
axial direction are close to the 2-D results. Moreover, the axial results for the small
cylinder are even closer to the 2-D results than results for the large cylinder, indicating
the 2-D analysis may be a good approximation for the 3-D in the axial direction. Second,
the numerical results in the circumferential direction possess much larger values than
values in the axial direction, indicating a reasonable explanation for the large
delamination size in the circumferential direction in the real tests. Third, a distinct
behavior is exhibited for the contact on a hollow cylinder when its inner surface is subject
to the traction-free boundary condition. This behavior is the crossing effect, and it is not
observed from any previous simulations. The crossing effect occurs over the strain
distribution due to the larger load level vs. the lower load level, and it is caused mainly by
the bending effect. This behavior will be explained in more detail below.
The finite element modeling, at 150Kg load level, shows that the nodal point
immediately below the contact center, at the inner surface of the cylinder, indicates a
downward displacement of 8.5 micrometers for the large hollow cylinder, and 2.6
micrometers for the small hollow cylinder. The displacement at the comer intersecting the
r-z plane and r-0 plane, at the inner surface in the X direction in the global coordinate, is
about +4.4 micrometer for the large hollow cylinder and about +1.2 micrometer for the
small hollow cylinder. These values indicate that a bending event is taking place. It can
also be seen that those displacements caused by the bending effect in either direction are
much smaller than the penetration depth, which is about 200 micrometers. Although the
magnitudes of these displacements are not large, they are responsible for the crossing
behavior of the surface strain distributions, as well as the outcome stress intensity factor
distributions.
The bending effect caused by the indentation is similar to that of a hollow cylinder
under line loads, acting at the opposite side of the cylinder. As the indent load increases,
the bending strain at the surface of the symmetrical plane (defined by the r-z plane in the
local r-O-z coordinate system), may dominate and yield much larger values than that
caused by the direct axial load from the indentation event at the locations of interest. The
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
strain caused by the bending effect from the indentation is tensile. When this tensile
strain is larger than the compressive strain, the effective strain then becomes tensile
instead of compressive. Thus, from the near indent region to the point intersecting the r-z
plane and r-0 plane in the circumferential direction, there is a transitory point from
compressive to tensile. The transitory point moves closer to the contact center as the
indent load increases. Notice that within the space range of interest, the strains presented
in Figures 5.11 and 5.13 are all compressive and the tensile area is not shown on the plot
simply because it falls in the range of R/a larger than 12.
From the above analysis, it can be seen that the crossing effect can be fairly well
explained from the bending contribution due to indentation. Attention must be given to
the fact that the bending strains at the top and bottom of the cylinder in the
circumferential direction and in the axial direction will disperse as soon as the indentation
load is released. This is because the bending strains are expected to be purely elastic and
can be fully recovered upon unloading. During unloading, the bending effects will
disperse, lowering K values. At the same time, the unloading of the indented area will
increase the indentation-induced strains, increasing K. Therefore the maximum K after
local unloading, i.e., at the final unloaded state, may still be expected to be close to the
maximum K for the loading process only. Thus the numerical solution, acquired from the
entire process of indentation on a hollow cylinder—with its inner surface subject to the
traction-free boundary condition, is expected to be identical to the problem of contact on
the same hollow eylinder after the full event of the loading and unloading process with
the elimination of any bending effect caused by the indentation.
One method to eliminate the bending effect is to add radial constraint (roller type)
at the inner surface of the cylinder. For better insight into the loading problem, the next
subsection presents the results from a series of solutions, using radial constraint at the
inner surface of the cylinder to eliminate bending effects.
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.4.2 Indentation Results on Hollow Cylinders with Roller Constraints
As mentioned previously, the contact analysis on a hollow cylinder may be
simplified by adding constraints in such a way that the radial displacements at its inner
surface in the r-0-z local coordinate system are set to zero, referred to here as the “inner
surface roller constraints”, or “roller constraints” .
Two hollow cylinders, typically
involved in the TGMF tests on EB-PVD TBC systems by Bartsch et al. (1999, 2000), are
investigated using the finite-element method. The load vs. contact sizes and the in-plane
strain distributions, in both the axial as well as the circumferential directions, are
presented. Finally, the stress intensity factor vs. the normalized distance away from the
indent region are evaluated following the procedure mentioned in the previous sections
and in the analysis developed in chapter 2 of this thesis. Care will be taken on the
cylindrical substrate system, comprised of two layers similar to those performed in the 2D analysis of a standard EB-PVD TBC specimen. However, the thicknesses of the
bondcoat considered for the hollow cylinders are 110 micron meters instead of 50 micron
meters. Therefore, contact on the 3-D curved substrate has a much thicker bondcoat. This
fact may require significant indent depth to avoid the effect of the bondcoat properties.
Additionally the length of the hollow cylinder in the finite element simulations is chosen
in such a way that free-edge effects are insignificant. Here, 10 mm as half length is
chosen in the finite-element model.
Figure 5.15 presents the indentation load vs. contact sizes with comparison of the
2-D flat specimen results. It can be seen that the contact sizes presented include the
indentation depth, 5, and its associated contact radii in the axial direction
, and in the
circumferential direction ae. The geometrical relationships among 5, az and ae are the
same as described in the equations of (5.1-7), and presented in Figure 5.4 for the two
hollow cylinders currently involved. Compared to the 2-D results, it is clear that load
values are very close at the same indentation depth, due to 3-D contact on the large
hollow cylinder and the contact on the flat 2-D specimen. Nevertheless, at the same
indent depth, the load for the 3-D contact on a hollow cylinder is slightly less than that of
the contact on the 2-D flat specimen. This is simply due to the fact that less material is
necessary to be displaced at the same penetration depth, because of 3-D contact, rather
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates __________
than a 2-D flat contact. The insignificant difference between the loads of the 3-D contact
and the 2-D contact indicates that the currently involved indent load level is sufficiently
small and the load vs. indent displacement relation can be approximated from the contact
analysis of the 2-D flat specimen.
Another important conclusion we may draw from this plot is that the difference between
az and ae is not great, ae being slightly smaller due to the curvature of the substrate.
Figure 5.16 shows that compressive strain distribution vs. R/a, for a standard
conical indenter contact, on a hollow cylinder with outer radius of po=5.11mm and inner
radius of Pi=3.00mm (the big hollow cylinder), with roller constraints at the inner surface.
The results of the contact on the 2-D flat specimen are used as a comparison. The surface
strain results are presented at two load levels of lOOKg and 150Kg, to ensure sufficient
contact elements beneath the indenter. We see that the axial strain distribution, vs. the
normalized distance away from the indent region Rz/az at the two different load levels,
overlap and are very close to the 2-D results. At the same time, the circumferential strain
distribution vs. the normalized distance away from the indent region Re/ae at the two
different load levels, are found to have some distance from each other, which is especially
evident at the nearby region of their peak values. Also, the circumferential compressive
strain curves are away from the compressive strain curve of the 2-D flat specimen. This
indicates
that the indentation
event causes
larger compressive strains
in the
circumferential direction than in the axial direction, at the same normalized distance away
from the indentation region. Since compressive strains dominate in the analysis of the
stress intensity distribution, this will inevitably cause large stress intensity at the same
normalized distance. This will be evident when the results are presented.
For completeness, as well as for more accurate evaluations of the stress intensity
factors, the tensile strains are given in Figure 5.17. More obviously, the tensile strains in
the axial direction for both load levels overlap with those of the 2-D flat specimen results
almost perfectly. At the same time, the tensile strains in the circumferential direction
depart from the 2-D results and give a much larger value at the same R/a.
The results presented in Figure 5.18 are based on the strain values presented in
Figure 5.16 and 5.17. It is now apparent that the stress intensity factor in the axial
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
direction is also very close to those from the 2-D analysis. This indicates that the
curvature effects on the stress intensity factors in the axial direction are negligibly small,
with the currently applied load level. And at the same time, the stress intensity factors in
the circumferential direction are much larger at the same normalized distance away from
the indent region. It can also be seen that the stress intensity distributions of different load
levels bear approximately the same characteristics as that of the 2-D flat specimen results
in the axial direction. However, the stress intensity distributions of different load levels
bear more evidence of load dependence in the circumferential direction. That is to say, the
curvature effects do not significantly influence the axial stress intensity distribution. But,
the curvature effect has been significantly manifested in the circumferential stress
intensity distribution.
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Chapter 5. Contact and Fracture Analysis of Delamination on Curved Substrates
200
150
"d
J
100
B
'd
fn
— Flat 2-D 5
-A - Axial a^
Circumferential ae
0.00
0.10
0.20
0.30
Contact Size (mm)
0.40
0.50
Figure 5.15: Indentation Load as a Function of Contact Size for a Standard Conical
Indenter Contact on a Hollow Cylinder (po=5.I Imm, Pi=3.00mm), with
Roller Constraints at the Inner Surface
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Chapter 5. Contact and Fracture Analysis of Delamination on Curved Substrates
0.000
0.001
-
0.002
in
CO
CO
(D
O
U
-0.003
F lat 2-D (150K g)
-0.004
- -X - A xial (lOOKg)
- O - A xial (150K g)
-0.005
- X - C ircum ferential (lOOKg)
—
Circumferential (150K g)
0.006
2
4
6
8
10
12
N orm alized Distance, Rz/az, Re/a©
Figure 5.16: Compressive Strain vs. R/a for a Standard Conical Indenter Contact on a
Hollow Cylinder (po=5.11mm, Pi=3.00mm), with Roller Constraints at the
Inner Surface
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.008
F lat 2-D (150K g)
X
A xial(lO O K g)
-O - A xial (150K g)
0.006
C ircum ferential (lOOKg)
C ircum ferential (150K g)
0.004
• 1— (
(D
H
0.002
0.000
4
6
8
10
12
N orm alized Distance, Rz/az, Re/ae
Figure 5.17: Tensile Strain vs. R/a for a Standard Conical Indenter Contact on a Hollow
Cylinder (po=5.11mm, Pi=3.00mm), with Roller Constraints at the Inner
Surface
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
5.0
F lat 2-D (150K g)
X ■ A xial (lOOKg)
4.0
-<3)- A xial (150K g)
C ircum ferential (lOOKg)
C ircum ferential (15OKg)
3.0
O
o
4 —>
Ph
•4^— >
C/D
c
<D
c/o
<D
2.0
1.0
00
0.0
4
6
8
10
N orm alized Distance, Rz/az, Re/ae
Figure 5.18: K vs. R/a for a Standard Conical Indenter Contact on a Hollow Cylinder
(po=5.11mm, Pi=3.00mm) At the As-processed Condition, with Roller
Constraints at the Inner Surface
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12
Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
Similar to the previous analysis. Figures 5.19 to 5.21 provide numerical results for
the standard conical indentation on the small hollow cylinder with an outer radius of
Po=3.08mm and inner radius of Pi=0.97mm. Surface roller constraints are again applied at
the inner surface of the cylinder. Since the size of this cylinder is much smaller (almost
half the size) than the larger cylinder, the curvature effects would be more evidently
manifested if any significant influence exists on the load distribution, as well as the strain
distributions, and eventually the stress intensity distributions.
Figure 5.19 provides a plot of load vs. contact sizes for the contact event on the
small cylinder; they display very similar behavior to Figure 5.15. Without repeating the
details, the load vs. indent depth is again approximately the same as the contact on a 2-D
flat specimen. However, since the curve is larger for this small cylinder, the load is
somewhat lower at the same indent depth, compared to that of contact on the large
cylinder. On the other hand, the load vs. az is approximately the same as presented in
Figure 5.15, since this quantity is without the cylinder size involved and is a pure function
of indent depth while maintaining the same indenter shape. Therefore the difference of az
away from 6 at the same indent load level is approximately the same as shown in the large
cylinder. However, the difference of ac away from 6 at the same indent load level is
affected by the curvature and the difference is larger than that presented in the large
cylinder. This is because the quantity of ae is not only a function of the indenter
geometry, but also that of the cylindrical radius. As the outer radius of the cylinder
becomes smaller, at the same load level, the value of ae becomes smaller. In summary,
compared to Figure 5.15 (although there are some differences due to the curvature
effects), two major conclusions drawn from the previous Figure 5.15 are still valid. One
is that the load vs. 5 for the 3-D contact results are close to the 2-D results; the second
validated conclusion is that the difference between ae and az is rather small in the space
range of interest.
Figure 5.20 provides a plot of compressive strains vs. the normalized distance
from the indent in both axial and circumferential directions at two indent load levels of
lOOKg and 150Kg; there are more similarities than differences compared with those
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
presented for the large cylinder in Figure 5.16, It is clearly seen that the compressive
strains in the axial direction of two load levels are very close to the 2-D flat results, while
the strains in the circumferential direction depart from those of the 2-D contact results of
the flat specimen. At the same time, the circumferential strain distribution manifests more
evidence of curvature effects, which means less self-similar behavior and more load
dependence of strains in the circumferential direction than in the axial direction.
Figure 5.21 provides a plot of the tensile strains vs. the normalized distance away
from the indent in both the axial and the circumferential directions at two indent load
levels of lOOKg and 150Kg. The argument just made can be seen more clearly from this
plot. The tensile strains in the axial direction of the two load levels overlap the 2-D
results almost perfectly. At the same time, the tensile strains in the circumferential
direction of the two load levels are away from the 2-D results and express load
dependence.
Based on the in-plane equi-biaxial strains in the axial, as well as in the
circumferential directions, the stress intensity factors are evaluated and plotted as
provided in Figure 5.22. We see that the stress intensity distribution in the axial direction
is close to the self-similar results of the 2-D analysis results and the stress intensity
distribution in the circumferential direction is away from the 2-D results. It is clear that
the stress intensity factor in the circumferential direction departs further away from the 2D results than that presented in Figure 5.18. This is because the cylinder involved here is
smaller and thus more curvature effects can be seen from this plot compared to the
previous one.
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
200
150
100
HCH
— Flat 2-D 6
-♦-5
-A- Axial az
-X- Circumferential a©
0.00
0.10
0.20
0.30
0.40
0.50
Contact Size (mm)
Figure 5.19: Indentation Load as a Function of Contact Size for a Standard Conical
Indenter Contact on a Hollow Cylinder (po=3.08mm, Pi=0.97mm), with
Roller Constraints at the Inner Surface
239
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.000
-
i
0.001
-0.002
<D
■
>
C/5
c/5
D
-0.003
Flat 2-D (150Kg)
^
IO -0.004
U
Axial (lOOKg)
O - Axial (150Kg)
-0.005
X—Circumferential (lOOKg)
Circumferential (150Kg)
-0.006
4
6
8
10
12
N orm alized Distance, Rz/az, Re/ae
Figure 5.20: Compressive Strain vs. R/a for a Standard Conical Indenter Contact on a
Hollow Cylinder (po=3.08mm, pi=0.97mm), with Roller Constraints at the
Inner Surface
240
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.008
Flat 2-D (150Kg)
Axial (lOOKg)
Axial (150Kg)
Circumferential (lOOKg)
0.006
C3
Circumferential (150Kg)
cn
(D
i<u 0.004
H
0.002
0.000
4
6
8
10
12
Normalized Distance, Rz/az, Re/ae
Figure 5.21: Tensile Strain vs. R/a for a Standard Conical Indenter Contact on a Hollow
Cylinder (po=3.08mm, pi=0.97mm), with Roller Constraints at the Inner
Surface
241
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
5.0
— Flat 2-D (150Kg)
a
4.0
^
Axial (lOOKg)
^
Axial (150Kg)
Circumferential (lOOKg)
Circumferential (150Kg)
3.0
5-h
o
-I— '
o
tin
•tH
C /)
c
<D
-I— I
GO
2.0
<
1.0
C/3
O
c/D
0.0
2
4
6
8
10
Normalized Distance, Rz/az, Re/ae
Figure 5.22; K vs. R/a for a Standard Conical Indenter Contact on a Hollow Cylinder
(po=3.08mm, Pi=0.97mm), with Roller Constraints at the Inner Surface
242
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12
Chapter 5. Contact and Fracture Analysis of Delamination on Curved Substrates _________
5.4.3 Indentation Results on a Solid Cylinder
In this subsection, the simulation results are based on the contact analysis of a
solid cylinder. The building of the finite-element model is based on the received EB-PVD
TBC cylindrical specimen, taken from the burner rig at the University of California,
Santa Barbara (UCSB). The half-simulation length of the specimen is taken as 15mm and
the radius of the cylinder is taken to be 5.5mm. Therefore this specimen is somewhat
larger than that of the big hollow cylinder in the TGMF test specimens. The bondcoat
thickness is assumed to be 110 pm, which is the same as that used in the hollow
cylinders. The material properties of the bondcoat, as well as the nickel based superalloy,
are taken to be routinely the same as addressed previously. The sharp conical indenter
with a 90 degree tip angle is used to provide sufficient penetration depth while
maintaining debonding under the necessary buckling-driven criterion.
Figure 5.11 provides the plot of the indentation load vs. contact sizes with a
comparison of the 2-D flat specimen results. The 2-D simulation uses a 90 degree conical
indenter and the bondcoat thickness of the flat specimen substrate is also 110 pm. We see
again that the difference between ae and az is very small. Furthermore, it is clear that the
load values are very close at the same indentation depth, due to the 3-D contact results
and the 2-D contact results, indicating that the load vs. indent displacement relationship
for the 3-D contact can be approached from the 2-D contact analysis.
Figure 5.14 shows the compressive strain distribution vs. R7a for the 90 degree
sharp conical indenter contact on the solid cylinder. The results of contact on the relative
2-D flat specimen are used for comparison. The surface strain results are again presented
at two load levels of lOOKg and 150Kg. The axial strain distribution vs. the normalized
distance away from the indent region Rz/az at the two different load levels overlap, and
are very close to the 2-D results. At the same time, the circumferential strain distribution
vs. the normalized distance away from the indent region Re/ae at the two different load
levels are found to have some distance from each other, especially evident at the nearby
region of their peak values. The circumferential compressive strain curves are also away
from the compressive strain distribution from the 2-D flat specimen results. This indicates
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
that the indentation event causes the compressive strains in the circumferential direction
to depart further than those in axial direction at the same normalized distance away from
the indentation region. Since compressive strains dominate the analysis of the stress
intensity distribution, considerable stress intensity will inevitably occur at the same
normalized distance; this will be evident in the results presented. These observations are
similarly apparent in the analysis of the contact on the hollow cylinders with inner surface
roller constraints.
In the interest of completion, the tensile strains in both the axial and the
circumferential directions are given in Figure 5.25. More apparently, the tensile strains in
the axial direction for both load levels overlap those of the 2-D flat specimen results; and
the tensile strains in the circumferential directions simultaneously depart from the 2-D
results, giving a much larger value at the same R/ai.
The results in Figure 5.26 are based on the strain values in Figure 5.24 and 5.25. It
is now possible to see that the stress intensity factor in the axial direction is also very
close to those in the 2-D analysis. This indicates that the curvature effects on the stress
intensity factors in the axial direction are-again-negligibly small, with the load levels of
interest. At the same time, stress intensity factors in the circumferential direction are
much greater at the same normalized distance from the indent region. It can also be seen
that the stress intensity distribution of different load levels in the axial direction has
nearly the same characteristics as the results of the 2-D flat specimen. However, the stress
intensity distribution of different load levels shows greater load dependence in the
circumferential direction. Curvature effects do not significantly influence the axial stress
intensity distribution, but greater influence can be shown in the circumferential stress
intensity distribution. Once again, these observations are found to be the same as those
stated previously in the contact analysis on the hollow cylinders with roller constraints.
Therefore, we conclude once more that the interfacial stress intensity factor in the axial
direction can be approximated by the 2-D results. In other words, the available 2-D
analysis results can be valid for the determination of the interfacial fracture toughness of
the 3-D curved substrate by specifying the characteristic dimension of delamination in the
axial direction.
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
200
— Flat 2-D 5
OJ)
cd
O
hJ
'(— I
c
CD
T3
C
Axial a^
Circumferential ae
150
100
50
0
0.00
0.10
0.20
0.30
0.40
Contact Size (mm)
Figure 5.23; Indentation Load as a Function of Contact Size for a 90° Conical Indenter
Contact on a Solid Cylinder (po=5.50mm) (UCSB Specimen)
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.000
-
a
tl
00
<D
-
0.001
0.002
>
{/}
cn
V
Flat 2-D (150Kg)
-0.003
X- Axial (lOOKg)
o
U
-0.004
©■ Axial (150Kg)
X—Circumferential (lOOKg)
Circumferential (150Kg)
-0.005
10
12
N orm alized Distance, Rz/az, Re/ae
Figure 5.24: Compressive Strain vs. R/a for UCSB Specimen for a 90° Conical Indenter
Contact on a Solid Cylinder (po=5.50mm)
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
0.008
Flat 2-D (150Kg)
-X- Axial (lOOKg)
©■ Axial (150Kg)
0.006
X—Circumferential (lOOKg)
a
a
00
•^
c/:}
Circumferential (ISOKg)
0.004
<D
H
0.002
0.000
4
6
8
10
N orm alized Distance, Rz/az, Re/ae
Figure 5.25: Tensile Strain vs. R/a for UCSB Specimen for a 90° Conical Indenter
Contact on a Solid Cylinder (po=5.50mm)
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12
Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
5.0
a
Flat 2-D (150Kg)
--X -A x ia l (lOOKg)
- O- Axial (150Kg)
X—Circumferential (lOOKg)
Circumferential (150Kg)
4.0
Ph
3.0
O
o
•-If—
H>
C/!)
c
<D
2.0
1.0
00
D
b
C/)
0.0
2
4
6
8
10
N orm alized Distance, Rz/az, Re/ae
Figure 5.26: K vs. R/a for UCSB Specimen at the As-processed Condition for a 90'^
Conical Indenter Contact on a Solid Cylinder (po=5.50mm)
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12
Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.5
Guidelines for Indentation Tests on Curved Substrates
5.5.1 Onset Buckling and Valid Indent Load Range
In this subsection, performing a valid indentation test on a curved substrate will be
described. Two concerns are to be addressed regarding this issue: (1) a sufficient
indentation depth to achieve the self-similar solution and prevent the dominance of the
bondcoat properties in the axial direction, and (2) a maximum load level that can be
applied without causing buckle-driven delamination. The latter is the major concern in
the problem of indentation on the cylindrical specimens. The first concern is in fact
efficiently addressed in the 2-D analysis and can generally be applied to 3-D cases.
Therefore a solution for the latter concern is first addressed, and valid tests are attempted
to balance these two issues.
To simplify the analysis, a single layer delamination on a flat substrate only, will
be considered first. In this case, delamination is considered as a straight-sided blister
occurring along the interface of the TBC layer and the TOO layer. The next consideration
is the reasoning in the case of buckle-driven delamination on a flat substrate, growing at
its curved front while its sides remain stationary, as examined by Hutchinson et a l,
(1992) and Hutchinson (2001). In this case, at the onset of buckling, the value of the half­
width bo of the blister, under the uniform equi-biaxial compressive residual stress CTtbc ,
can be determined by:
b„ =
,
7T
'•
.
jE.
,1 ^
(5.13)
TBC
where txBC L the TBC thickness, axBC is the compressive pre-stress in the TBC layer,
E xbc and VxBC are the Young’s modulus and Poisson’s ratio of the TBC layer,
respectively.
For delamination of the top layer(s) of the 3-D cylindrical specimen due to
indentation, bo as expressed in (5.13) may be taken as the half-width of the blister in the
circumferential direction at the onset of buckling, as shown in Figure 5.27. Thus formula
(5.13) may serve as an indicator for buckle-driven delamination to occur in the axial
direction. The validity of the formula (5.13) can be argued as follows: Since the
delamination considered on the cylindrical specimen is induced by the event of
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
indentation, indentation causes the material beneath the substrate to be displaced. The
displaced substrate material tends to stretch the debonded portion and causes the release
of some stress in the debonded area, resulting in slightly reduced pre-stress in the TBC
layer. Therefore, the critical value of bo, determined by (5.13), is the smallest value
possible for buckle-driven delamination to occur by including the effect of the indentation
event. Thus the indentation provides a conservative contribution to the critical half-width
evaluated by (5.13). However, care must be taken in the use of (5.13) so that the curvature
effect is neglected and consideration of the curvature effect takes the opposite effect of
the indentation, which provides a non-conservative contribution to the critical half-width
determined by (5.13). Overall, formula (5.13) can be regarded as a valid means to achieve
evaluation of the half-width as the buckle-driven criterion in this analysis; however, its
accuracy depends on whether the effect of the indentation or the curvature dominates the
determination of the critical half-width.
If delamination starts at the interface of the TOO layer and the bondcoat layer,
then a composite blister will be considered on the cylindrical specimen, and the formula
(5.13) must be modified by considering Young’s modulus and the residual stress to be
effective, neglecting Poisson’s mismatch. Then (5.13) becomes;
bo = (txBc + tTGo ) 1 .............................................................................................(5.14)
^12(1- v " ) V o
where
and Eeff are the effective residual stress and the effective modulus, as
expressed in (2.29) and (2.30), respectively. Care should be taken in the use of (5.14).
Similar to the previous analysis, the indentation again provides a conservative
contribution to the evaluated value of bo, while the curvature effect provides a non­
conservative contribution to the analysis. Additionally, the net-bending moment, due to
the mismatch of oxide residual stresses, tends to reduce the possibility of buckle-driven
delamination.
Therefore the net-bending
moment also provides
a conservative
contribution to the analysis, similar to that of the indentation event itself.
Figure 5.28 provides a plot based on the formulation (5.14), considering the asprocessed material properties in the EB-PVD TBC system, as listed in Appendix I, except
that the TBC and the TOO layers may vary in thickness. In this plot, three thicknesses of
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates_________
the TBC layer are considered. It is clear that the TBC thickness dominates the magnitude
of the bo in this analysis. As the TBC thickness increases, the critical half-width bo
increases. The thicker the TBC layer, the larger the bo, and the more difficult it appears to
experience buckle-driven delamination.
At the same TBC thickness, the critical half-width bo decreases with the increase
of the TOO layer thickness; this is because the residual stress in the TGO layer is 70
times larger than in the TBC.
At the same time, TGO thickness is negligibly small
compared to the TBC thickness, and the stiffness of both layers can be considered
comparable to the difference between their residual stresses. These facts cause an overall
increase in pre-stress in the blister by considering the TBC layer only, thus decreasing the
critical half-width bo. From this plot, it can be seen that the critical factor in determining
the bo is still the thickness of the TBC layer. The critical half-width, bo , for the single
TBC layer delamination can be determined at the zero thickness of the TGO layer.
Figure 5.27: Convention for Delamination in the Circumferential Direction
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
10
9
8
o
X)
-t—'
• l-H
7
6
5
4
ffi
3
o
2
u
1
0
0
1
2
3
4
5
6
7
8
9
10
T GO Thickness, Itgo (M-ni)
Figure 5.28: Critical Half-Width for Buckle-driven Delamination as a Function of
TGO thickness
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
Tables 5.2 and 5.3 illustrate the determination process in a valid test. To achieve a
valid indentation test performed on a cylindrical substrate, two major concerns have been
addressed and must be resolved. As mentioned previously, the first concern is a
necessarily sufficient penetration depth so that a similar solution can be achieved in the
axial direction, and the effect of bondcoat properties may be avoided. The second
problem is the limitation on the applied indent load level so that the buckle-driven
delamination criterion cannot be satisfied, i.e., the half-width b, debonded in the
circumferential direction, must be less than its critical value bo.
Table 5.2 lists the indentation depth at each indent load level for different cone
types and different bondcoat thicknesses. Although those results are from the 2-D
simulation of the flat specimens, they are also valid for the 3-D cases, as was concluded
in the previous sections. For the 50pm bondcoat substrate, the penetration depth is
considered to be sufficient if the conical indenter is over about one and half or two times
the bondcoat thickness. However, in the 110pm bondcoat substrate, the 2-D simulation
results show that similarity can be effectively achieved and the results approach those of
50pm bondcoat simulation results just after the indenter passes the bondcoat thickness.
Therefore, penetration depths by the two types of cones at the standard available load
levels on the Rockwell hardness tester, are quite satisfactory except in the case with a
shaded entry. The load level determined from this aspect can be regarded as the lower
limit that can be applied for the tests if a larger load can be applied without causing a
buckle-driven problem.
To illustrate valid tests for avoiding buckle-driven delamination, we will consider
the case in the beginning of section 5.4—conical indentation on the large hollow cylinder
that does not impose inner surface constraints. As discussed in the previous section
regarding this case, the increase in the K values due to the bending effects during the
loading process will be reasonably close to the results which consider the whole
indentation process: Only the results of K vs. R/a for the indentation on the large hollow
cylinder-which is traction-free at its inner surface due to the loading process—may
resemble the results at its final unloading state. This is because the bending effect will not
occur during the unloading process; but the increase of K values due to the bending
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
effect will be replaced by the local unloading process. So the whole process may he close-at least in this case, only to the loading process. Nevertheless, the accuracy of those
results is not important in this analysis; the goal is to illustrate management of a valid test
when the toughness value at the interface is roughly known.
Delamination occurring at the interface of the TGO layer and the bondcoat layer
will he considered here: TGO layer thickness will he 0.25pm; other properties remain as
listed in Appendix I. The critical half-width ho is found to he 2.58mm—also as shown in
Figure 5.28. Table 5.3 lists the results of the evaluated half-width at the three toughness
levels of 2.5, 2.0 and 1.5 MPa Vm , from Figure 5.12. It can he seen that the dehonding
radii are determined from the K values in the circumferential direction, and the contact
radii ae are determined from the 3-D simulation. A test is valid if the evaluated dehond
half-width in the circumferential direction h is less than ho ; most of the cases are valid
from this aspect except the example with a shaded entry. Combining the information
provided in Tables 5.2 and 5.3 indicates that the standard conical indenter can he used for
tests in most of the cases listed in the table. But care must he taken to include some
interactions to limit the validation. For example, the standard conical indentation at
150Kg is valid in terms of penetration depth, hut it is not valid at the toughness level of
1.5 MPa Vm , since the buckle-driven criterion is satisfied.
In summary, to prevent buckle-driven delamination, a critical indent load (leading
to a critical value of dehond size), must he determined, and this may he obtained through
a quantitative analysis of the indent event along with the critical buckling solutions, as
presented in (5.13) and (5.14). This will set an upper boundary on the indent load that
can he used in such tests.
A rigorous mapping of test parameters is beyond the work of this thesis. The
purpose of this section is to provide a general guide for checking and planning valid
indentation tests on cylindrical specimens.
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
Table 5.2: Indentation Depth as a Function of Cone Type and Bondcoat Thickness at the
Loads of 60Kg, lOOKg and 150Kg
Load Level
tBc (itm)
Cone Type
60Kg
lOOKg
I50Kg
5 (pm)
50
90°
153
210
267
110
120°
90°
120°
96
143
92
133
200
130
171
258
166
Table 5.3: Half-width Determination at a Certain Toughness Level with bo=2.58mm by a
Standard Conical Indentation
lOOKg
b
b< bo
Kc(MPa Vm)
Re/ae
ae
2.5
2.0
1.5
4.43
5.64
8.36
2.5
2.0
1.5
4.72
5.90
8.28
1.22
1.55
2.31
150Kg
1.61
2.02
2.83
0.276
0.342
Y
Y
Y
Y
Y
N
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates_________
5.5.2 Effects of Unloading on the Toughness Measurement
Two very important conclusions have been drawn from the 2-D unloading
analysis presented in chapter 4. First: The increases in K values due to the unloading
step are significant and will be included in the analysis of test data. Second: The results
from both types of loading/unloading models agree and are essentially independent of the
maximum applied load. In this subsection, the toughness curves, K vs. R/a are presented
by including the unloading effects for the valid 3-D results approached from the 2-D
analysis. Thus, we may have a complete set of results for the interfacial toughness
measurement of the 3-D indentation induced delamination, without performing the actual
3-D unloading simulations.
The most important information from the analysis in section 5.4, that the 3-D
results closely resemble the 2-D results in the axial direction for all the cases considered
here; this conclusion is essentially independent of the boundary condition imposed at the
inner surface of the hollow cylinder. In addition, the 3-D results in the axial direction are
also load-independent, or self-similar. Therefore the only need for obtaining the 3-D
results in the axial direction is to perform a 2-D analysis of loading/unloading in order to
extract the Kc values which serve as the 3-D results.
Figure 5.29 presents a plot of K vs. R/a that includes the unloading effects due to
the indentation of two types of conical indenters - the 120° and the 90° cones. These
results are obtained from the 2-D simulation of contact on the flat specimen, with its size
and properties identical to the relevant 3-D cylindrical specimens. Moreover, the
thicknesses and properties of the TBC layer and the TGO layer are taken to be identical to
those listed in Appendix I. In this plot, each line type is used twice to represent the two
cone shapes considered here. From the uppermost to the lowermost curve of the same line
type, the results of K vs. R/a are due to the 90° and 120° conical indenters, respectively.
Again the “LU simulation” curves represent the results from the direct finite-element
combined loading and unloading simulations, while the “superposition” curves occur
from superimposing the results of elastic-plastic loading and elastic unloading finiteelement simulations. The “loading only” curves are included for comparison. The results
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates_________
presented in this figure can be used for the toughness measurement of indent on the 3-D
cylindrical specimens, as indicated from the previous discussion.
5
LU Simulation
d
Ph
Superposition
4
Loading Only
5
90° Cone
3
o
120
-I— >
o
a
Um
2
c
(D
GO
GO
I
CD
in
4
6
10
8
N orm alized Distance,
12
R/a
Figure 5.29: K vs. R/a for the 90° and 120° Conical Indentation on a Flat EB-PVD TBC
System with llO pm Bondcoat Thickness Including Unloading Effects
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.6
Toughness of a Typical EB-PVD TBC Fabricated on a Curved
Substrate
5.6.1 Specimen Analysis
The TBC specimen received from UCSB, as shown in Figure 5.30, was reportedly
taken from the base of a burner rig bar, where the TBC system was most intact. From the
direct measurement, the specimen diameter is found to be ~11 mm and the TBC portion
length is about ~5 mm; the total length is ~16mm. The specimen reveals a nice polished
cross section at the coated end, allowing determination of the bondcoat and TBC coating
thicknesses, as well as analysis of the composition of each layer through BSE SEM and
EDS techniques.
Briefly, the thickness of the TBC is roughly between 90-100 jttm, with a typical
image shown, as in Fig. 5.31. The TBC structure of the cylindrical specimen is somewhat
different from that of a standard 2-D flat specimen; the difference appears on the TBC
grains. The columnar structure of the currently-received cylindrical TBC specimen is
constructed of several short nonuniform grains, while the 2-D flat TBC grains are straight
with relatively uniform grain sizes. However, there is no special information concerning
the differences in the TBC columnar structures which would cause other discrepancies in
TBC properties, or TGO growth at the interface of the TBC and the bondcoat. And, the
structural difference also reveals some TBC damage at the top of the specimen that might
be due to the cutting process. The bond coat thickness is -110 pm , as shown in Fig. 5.32.
It can be seen that there is a mixed region of bondcoat and nickel substrate at -2 0 pm
thick in magnitude. The current measurement is taken from the middle of the intermixed
zone to the top of the bondcoat surface. The TGO thickness is measured at multiple
locations and the averaged value is about 1.7pm , with a typical image as shown in Fig.
5.30.
The composition of the bondcoat was analyzed using the EDS techniques. It was
found that the bondcoat is composed of NiCoCrAlY with 44.4%Ni, 26.07%Co,
19.25%Cr, 9.47%A1 and 0.8%Y (in wt. %). The TGO was found to be aluminum oxide.
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
The TBC was found to be Yittria Stabilized Zirconia (YSZ) and the substrate to be a Nibased superalloy. The following gives a brief summary of the received specimen:
Table 5.4: Characterization of the UCSB Solid Cylindrical Specimen
Averaged Thickness of the TBC Layer:
90-100 jxm
Thermal Barrier Coating Material:
YSZ
Average TGO thickness:
1.7jUm
TGO:
Aluminum oxide
Bond coat thickness:
95-110 pm
Bond coat material:
NiCoCrAlY
Substrate material:
PWA 1484, similar to N5
Specimen diameter:
-11.00 mm
TBC portion length:
-5.00 mm
Specimen Length:
-16.0m m
259
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
Figure 5.30: TBC Specimen from UCSB, for Interfacial Toughness Measurement
i-
A,
"
i
I
i f i
to/
'3
j
*]
'
lioiul ('oat
BO tim
Figure 5.31: Typical TGO Morphology and TBC Thickness Measurement
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
7
r(;b
Bond Coat
SO |im
Substrate
Figure 5.32; Typical TGO Morphology and Bondcoat Thickness Measurement
%
TBC
f
Bond Coat
Figure 5.33: Typical TGO Thickness Measurement
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.6.2 Indentation Tests
The indentation tests were performed on a standard Rockwell hardness tester, with
major load levels of 60, 100 and ISOKg. A 10 Kg minor load was applied to seat the
specimen before an additional load was added. A 90 degree conical indenter with a
0.1mm round tip radius was used to perform the tests. This special indenter was used to
penetrate a sufficient depth into the substrate while avoiding the buckle-driven
delamination condition being satisfied.
The method of multiple indentations at the same location was used. The indent
location was roughly at 3.1 mm away from the free edge and 1.9mm away from the inner
edge of the TBC coating. In this way, the free-edge effect may be avoided while the
nonuniform nature of the TBC coating at the inner portion—away from the free edge-is
also considered.
At the major load level of 60Kg, the indentation induced a clear debonding area,
shown in Figure 5.34a, with some irregularity similar to a butterfly wing-shaped
debonding, observed elsewhere on the hollow cylindrical specimen. It can be seen that
debonding propagates much more in the circumferential direction than in the axial
direction. At the lOOKg load level, the debonding shown in Figure 5.34b propagates
further in both circumferential as well as axial directions. At the 150Kg load level, the
debonding size is not much different from that induced at the lOOKg load level, which
was also observed and explained using the 2-D test specimens.
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates
■
0»^A i
f/
C '- .
f
a) at 60Kg
d) at 60Kg
b) at lOOKg
e) at lOOKg
c) at 150Kg
f) at 150Kg
Figure 5.34: Typical SEM Images for Delamination Patterns and Contact Regions due to
Indentation at Three Standard Load Levels, Available From a Rockwell Hardness Tester
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
As was concluded in the previous discussion regarding load vs. contact radius for
the indentation on the cylindrical specimens, the difference between ae and a^ is
essentially very small. The experimental results shown in Figure 5.34 d-f) reveal that the
difference between the contact radii in the circumferential direction and the axial
direction is not distinguishable. This proves that the indentation is shallow compared to
the cylindrical radius. Therefore, the contact radii in both directions can be regarded as
identical at the same load level. Table 5.5 lists the experimental results on the
measurement of the contact radius compared to the FE results in both directions. The
agreement between the measured values and the simulated results is evident.
Some TBC peeling occurred at the event of indentation. The exposed interface
was analyzed through the SEM and the EDS to reveal the cracking interface. A typical
image is shown in Figure 5.35. This image shows that the debonding location is either at
or near the interface of the TBC and the TGO layers. The debonding on the flat TBC
specimen—cracking within the TBC coating, or along the interface between the TBC and
the TGO layers—indicates it is unlikely that the specimen experienced lengthy isothermal
exposure. However some cyclic exposure could explain the cracking near the interface of
the TBC and TGO layers. Therefore, determining toughness values may only be necessary
at the interface of the TBC and the TGO layers. In the meantime, it is also important to
include toughness values at the interface of the TGO and the bondcoat in order to have
some reference for further exposures.
The last task for this test is to determine whether the indentation induced buckledriven delamination. The critical half-width at the residual stress level of the TBC
coating, to avoid buckle-driven delamination in the axial direction, can be determined
from (5.13). The formula (5.13) was used to determine the critical half-width, since the
actual test in this specimen shows that the cracking interface occurs only along, or near
the interface of the TBC layer and the TGO layer. Moreover, the estimate in (5.13) is
again a conservative estimate, as discussed previously. The value of bo should actually be
greater, because the indentation strains reduce the compressive stress in the debonded
area of the TBC layer. Using the thickness and the properties of the TBC layer as listed in
Appendix 1, it was found bo = 2.76 mm. The half width of debond in the circumferential
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
direction is less than 1.5mm (satisfying b< bo). Therefore, currently applied load levels do
not appear to cause buckle-driven delamination.
Table 5.5: Contact Radius due to 90 Degree Cone at Various Load Levels
Load (Kg)
60
100
150
Experiment
a (mm)
0.180
0.236
0.286
EEA
ae (mm)
0.190
0.247
0.303
az (mm)
0.193
0.252
0.311
m
I
%
1 .^
a) low resolution
b) high resolution
Figure 5.35: SEM Images Reveal the Cracking Interface at or Near the Interface of TBC
and TGO
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.6.3 Critical Energy Release Rate and Interfacial Fracture Toughness
The 2-D numerical simulation considers a 90 degree cone contacting on a 2-D flat
specimen with a PtAl bondcoat/Ni-based superalloy substrate system, including the
unloading effect. The bondcoat was taken to be 110 pm in thickness, with properties the
same as in the previous work by Vasinonta and Beuth (2001). For the evaluation of the
stress intensity factor, or energy release rate, the properties of the TBC layer and the TGO
layer are the same as listed in Appendix I. However, when the energy release rate is to be
evaluated at the interface of the TGO layer and the bondcoat layer, the measured TGO
thickness of 1.7pm is adopted.
The debonding, R, seems more difficult to obtain than that of the indent radius in
2-D analysis, since the delamination length in the axial direction is not well defined. But
the delamination extension in the circumferential direction is clear and can be measured
accurately. Therefore, the debonding characteristic dimension in the axial direction might
be reasonably found via an effective elliptic axis length, which considers the actual
debonding area.
By measuring the actual debonding area. A, and the debonding size in the
circumferential direction, Dc, the effective characteristic length in the axial direction can
4A
be obtained from: D^ = ------ . Then, the debonding radius in the axial direction is Rz=
jrD^
Dz/2. Table 5.6 lists the results of the effective delamination geometric parameters at the
three load levels performed on the solid UCSB specimen. The effective debond radii in
the axial direction, listed in the last column in Table 5.6, are then utilized for the
evaluation of the Kc and Gc values at its final unloading state, with or without
considering the TGO thickness. The results of the Kc and Gc values, with and without
consideration of the TGO layer, are different. In this test, the results without the TGO
layer are the necessary toughness values for debond at the interface of the TBC and the
TGO layers. However, the results after consideration of the TGO layer are taken as
references.
Furthermore, the UCSB specimen has a NiCoCrAlY bond coat, which is different
from the Pt-aluminide bond coat. The observation for this type of TBC system under
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
higher temperature cyclic exposures at the University o f Pittsburgh shows that the
toughness values were actually rather high compared to a PtAl specimen if it had been
exposed to a significant number o f high temperature cycles. Although the exposure
condition for the UCSB specimen is not known, the results listed in Table 5.7 are
reasonable regardless o f whether the specimen has experienced thermal cycles or not. The
toughness values o f Kc with or without considering TGO thicknesses listed in Table 4.7
are higher than those o f the PtAl bond coat specimens presented previously after even a
short thermal exposure history. Therefore, these results support the observation at the
University o f Pittsburgh for this type o f bond coat specimens compared to the PtAl bond
coat specimens. However, if this UCSB specimen did not experience any thermal
exposure, the toughness values listed in Table 4.7 are comparable to those measured in
the PtAl bond coat specimens at their as-processed states.
Table 5.6: Effective Delamination Sizes from the Tests on the UCSB Specimen
Load
(Kg)
60
100
150
A
(mm^)
3.26
4.67
4.85
Dc
(mm)
2.50
2.85
2.82
Dz
(mm)
1.66
2.09
2.20
Rz
0.83
1.05
1.10
Table 5.7: Kc and Gc at the Final Unloading State for the UCSB Specimen
Load
(Kg)
60
100
150
Average
Rz
az(mm)
Rz/a
0.83
1.05
1.10
0.180
0.236
0.286
4.61
4.45
3.85
4.30
w/o TGO
Kc
Gc
2.5
23
2.7
26
3.2
37
2.8
29
1.7 pm TGO
Kc
Gc
3.8
51
54
3.9
4.5
71
4.1
59
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
5.7
Chapter Summary
In this chapter, analysis of indentation on the eylindrical substrates reveals a few
very crucial points regarding measurement of interfacial toughness and performance of
valid indentation tests on the 3-D cylindrical specimens. The analysis reveals first that the
contact radius in the circumferential direction, and in the axial direction, are not much
different within the load levels of interest. Analysis further proves that the load is very
close to the 2-D results at the same penetration depth, and that indentation on all the
hollow cylinders shares a common characteristic - the results in the axial direction are
close to those of the 2-D results. In the meantime, the results in the circumferential
direction are away from the 2-D results with higher magnitudes. The analysis also reveals
that indentation tests can be performed on a hollow cylinder with its inner surface subject
either to roller constraints, or traction-free boundary conditions. The insight gained is that
the bending effect, caused by indentation when the inner surface is not constrained, will
disappear during the unloading process. The final unloaded state, then, is the same as if
the bending effect never occurred.
The most important conclusion to be drawn is that the toughness measurement for
indentation tests on the 3-D cylindrical specimens can be approached via the 2-D
analysis. The toughness curve of Kc vs R/a can be obtained from the 2-D results at the
unloading state. However, it is clear that the importance of the 3-D analysis is not
negligible for a valid test. This is because the stress intensity in the circumferential
direction can be a measure of the debonding size as the half-width at a certain toughness
level. Thus the results in the circumferential direction can be very useful for analysis of
preventing buckle-driven delamination. Therefore, the actual 3-D analysis can be
essential for a valid test on the cylindrical specimen.
Regarding actual testing on the UCSB specimen, the debonding was observed to
occur at the interface of the TBC and the TGO layers; therefore, the critical energy release
rate and the interfacial toughness, with delamination only in the TBC layer, are
quantified. These values are found to be 2.8MPa m
for the interfacial toughness and
29J/m^ for the
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Chapter 5. Contact and Fracture Analysis o f Delamination on Curved Substrates _________
critical energy release rate. The toughness and energy release rate for craeking at the
interface of the TGO and the bondcoat layers are also obtained as references.
This is the first attempt to perform this type of contact and fracture analysis. Findings in
this researeh will provide a valuable guide for similar contact and interfacial fracture
analyses of curved substrates.
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Chapter 6. Conclusions
CHAPTER 6. CONCLUSIONS
6.1 Contributions of This Thesis
This thesis has addressed a number of issues relating to the loss of adhesion in EBPVD TBC systems caused by thermal exposures. These issues include the methods of
measuring the critical energy release rate, toughness, and mode mixity of interfacial
fracture caused by indentation; the mechanism-based tests in different types of thermal
exposures; the indentation and delamination mechanics of different shapes of indenters
on a flat TBC specimen; and the indentation and delamination mechanics on a curved
TBC specimen. The specific contributions to this thesis regarding each of the issues are
summarized below.
6.1.1 Fracture Analysis of Indentation Tests
•
Analytical derivation of energy release rate of an annular plate delamination on a
substrate due to the presence of equi-biaxial stresses. The derived results confirm that
the energy release rate of an annular plate debonding on a substrate is independent of
the stress parallel to the crack front. This derivation further provides a clear insight
into more complex problems.
•
Eormulation of energy release rate with the grown TGO thickness in EB-PVD TBC
systems. The energy release rate with a complete consideration of the bending effects
was formulated to correct the previous formulation without consideration of the
neutral axis relocation due to the variation of TGO thickness.
•
A numerical model with the capability of both contact and fracture analysis to verify
the energy release rate formulation and extract the mode mix for interfacial cracks.
•
Confirmation of mode II cracking dominance for practical oxide thicknesses in EBPVD TBC systems.
6.1.2 Application of Conical Indentation Tests
6.1.2.1
Mechanism-Based Tests for Isothermal Dry Air Exposures
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Chapter 6. Conclusions
•
Toughness degradation as a function of isothermal exposure time and temperatures
(with Roy Handoko).
•
Establishment of a set of models on the oxide thickening and sintering based on the
thermally activated mechanism.
•
Degradation of toughness in EB-PVD/PtAl TBC systems under the dry air isothermal
exposure conditions for including the in-situ oxide thickening, sintering properties in
TBC coatings at each exposure time.
•
Ranking on the mechanisms causing the apparent toughness degradation. Oxide
thickening is the most important mechanism leading to spallation of the isothermally
exposed TBC systems.
Sintering appears to be less important.
Chemical or
mechanical damage at the interface appears to be the least important and could be
considered to be insignificant for this isothermally exposed industry-grade TBC
system.
•
Arrhenius analysis not only giving insight into mechanisms behind toughness loss, but
allowing the generation of predicted toughness loss curves (and life) for these systems
under isothermal conditions.
6.1.2.2
•
Mechanism-Based Tests for Exposures with Water Vapor
Toughness degradation as a function of isothermal exposure time and water vapor
pressure of O.latm and 0.3atm at 1100°C.
•
Microstructure comparison for oxide morphologies and fracture paths between dry air
exposure and exposure with water vapor.
•
Isothermal exposures with water vapor having little effect on the EB-PVD/PtAl TBC
system tested as the final conclusion.
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Chapter 6. Conclusions
6.1.2.3
•
Mechanism-Based Tests for Cyclic Thermal Exposures
Toughness degradation as a function of thermal cycles.
• Discovery of the fact that the difference of apparent toughness degradation between
the cyclic exposure and isothermal exposure is insignificant while a significant
difference exists between the cyclic microstructure and the isothermal microstructure.
•
Improved evaluation and better understanding of toughness degradation at the
interface during thermal cycles by integration between the destructive and the non­
destructive methods.
•
Toughness measurements from indentation including oxide thickening and residual
stress relaxation during thermal cycles.
6.1.3 Indenter Shape Effects
•
Numerical analysis of indentation mechanics and results comparison with the
analytical solutions for contact on a single substrate.
•
Loading curves due to conical indentations with various tip angles and spherical
indentations with different sizes in the EB-PVD TBC system.
•
Distributions of the surface displacements and strains due to conical indentations with
various tip angles and spherical indentations with different sizes in the EB-PVD TBC
system.
•
K vs. R/a for conical indentations with various tip angles in the EB-PVD TBC system
at unloading states.
•
K vs. R/a for spherical indentations with various a/Ri, in the EB-PVD TBC system at
unloading states.
•
Experimental validation on the idea of using different shapes of indenters to obtain
the optimal shapes for debonding on an exposed EB-PVD TBC specimen.
6.1.4 Conical Indentation on a Curved Substrate
•
Finite element modeling and geometric analysis of a conical indenter contact on a
three dimensional cylindrical substrate.
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Chapter 6. Conclusions
•
Dimensional analysis for surface strains in the axial direction and in the
circumferential direction due to indentation.
•
Guidelines provided for determination of the onset of buckling and valid indent load
range for contact on an EB-PVD TBC cylindrical specimen.
•
Surface strain distributions in the axial and in the circumferential directions due to a
conical indentation on the cylindrical specimens.
•
K vs. R/a in the axial direction and in the circumferential direction for contact on a
hollow cylindrical specimen and on a solid cylindrical specimen.
•
Quantification of the interfacial toughness of a solid cylindrical TBC specimen.
6.2 Recommendations for Future Work
6.2.1 Tracking Material Properties with Thermal Exposures
In the studies of mechanism-based tests in chapter 3, the sintering effects on
change of the TBC modulus with exposure time were modeled based on the thermally
activated mechanism. It is also known that the TBC sintering affects the toughness
degradation even though it is not as significant as the oxide thickening. However, the
properties of a TBC with sintering are not known. This demonstrates a need to track the
TBC properties, especially its stiffness modulus, with the increase of thermal exposures.
Accurate measurement of TBC properties not only improves the modeling, but also
provides a better source of TBC properties that can be trusted for the evaluation of the
toughness degradation at each exposure time and its durability before it experiences
spontaneous spallation.
As stated elsewhere in the chapters 4 and 5 in this thesis, the unknown properties
of the bond coat create some uncertainties and difficulties for the measurement of
interfacial toughness in EB-PVD TBC systems. More recent studies on the bondcoat
properties indicate that there are profound changes in bondboat properties at elevated
temperatures during thermal exposures (Deng Pan, 2003; Pan et ah, 2003). However, the
properties of the bondcoat layer are still not available at room temperature. Nevertheless,
the properties of the bondcoat at room temperature, especially the yield strength as well as
the strain hardening behavior, are crucially important in this research. This again
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Chapter 6. Conclusions
demonstrates a need o f a more careful study on the bondcoat material properties in EBPVD TBC systems. The measured properties may integrate with the methods and models
developed in this thesis to evaluate the TBC toughness degradation and durability more
precisely. Recently received equipment o f a nanoindentation system provides an essential
tool to accomplish this task.
6.2.2 Toughness Measurement for Low Speed vs. High Speed Impact Test
How would the delamination behavior be manifested by a spherical particle
impact on the EB-PVD TBC specimen at an elevated temperature? What will happen if
there are spherical particles impacting on a turbine blade under working conditions? The
simulation o f a spherical indentation performed in this thesis is characterized as under the
static or quasi-static condition. Some experimental work has been done during this
research on the low speed impact by a carbide spherical object impact on a standard EBPVD TBC specimen. It was found that the debonding behavior is analogous to that of
static indentation. However, more complex analysis is necessary to be performed on high
speed impact tests on TBC specimens. Studies on foreign object damage (FOD) have
been mostly focusing on the damage o f substrates due to high speed impact on a turbine
blade (Steif et a l, 1998; Chen and Hutchinson, 2002). There is very little literature
dealing directly with the TBC damage mechanism due to the FOD involved (Chen and
Hutchinson, 2002; Chen et a l, 2004). Therefore, the first focus on this topic envisioned
by the Pis is to develop a plan for the high-speed impact testing o f TBC systems with
collaborators at GE Aircraft Engines in Evendale, Ohio.
In this plan, the elevated
temperature tests will be performed at GEAE using a pressurized gas gun impact system,
to relate the losses in toughness measured in room temperature indentation tests to losses
o f resistance to high-speed impacts occurring at gas turbine operating temperatures.
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Appendix
APPENDIX
Table 1: As-processed Properties and Each Layer Thickness o f the EB-PVD/PtAl TBC
Property
Bondcoat
Ni 5 substrate
(PtAl
TGO (a -
TBC (Zr02)
AI2O 3)
Young’s modulus (GPa)
189.3
137.9
393
44
Poisson’s
0.313
0.38
0.22
0.22
Yield stress (MPa)
900
775
—
—
3500
50
0.25
100
Compressive residual
stress (MPa)
Thickness (pm)
50
3130
25.4
System Diameter (mm)
285
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