EFFECT OF OXYGEN ON CREEP CRACK
GROWTH IN NICKEL-BASE SUPERALLOYS
by
Kenneth Rees Bain
B.M.E., General Motors Institute
(1980)
S.M., Massachusetts Institute of Technology
(1982)
SUBMITTED TO THE DEPARTMENT OF
MATERIALS SCIENCE AND ENGINEERING
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS OF THE
DEGREE OF
DOCTORATE IN PHILOSOPHY
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 1983
@ Massachusetts
Institute of Technology 1983
Signature of Author:
Department odfMaterials Science and Engineering
August 5,1983
Certified by:
Crii
-Regis
by:
M. Pelloux
Thesis Supervisor
Accepted by:
pm .)_Bernhardt J. Wuensch
Chairman, Depatrntal
Graduate Committee
ArchiveS
MASSACHUSETTS
INSTITUTE
OFTECHNOLOGY
OCT 14
1983
LIBRARIES
EFFECT OF OXYGEN ON CREEP CRACK
GROWTH IN NICKEL-BASE SUPERALLOYS
by
KENNETH REES BAIN
of Materials Science and
to the Department
Submitted
Engineering on August 5, 1983 in partial fulfillment of the
requirements for the Degree of Doctorate in Philosophy.
ABSTRACT
(CCGR) of four PM/HIP
The creep crack growth rates
nickel-base superalloys are measured in the range of CCGR
from 10 -9 m/s to 10-5 m/s and a range of stress intensity,
K, from 10 to 120 MPa/F at 7040 C in air and in 99.999% pure
The alloys tested are Low Carbon Astroloy, Merl-76,
argon.
(60 and 120 mesh size
Low Carbon IN-100, and Rene-95
Crack length was measured on single edge notched
powders).
specimens using the D.C. potential drop technique. Crack
growth rates were observed to accelerate up to 1000 times in
an air environment over the CCGR measured in 99.999% pure
argon.
The fracture path was totally intergranular in all the
The fracture path in argon follows grain
CCG tests.
boundaries which coincide with prior powder boundaries
for PPB grain boundary
There was no preference
(PPB).
cracking in CCGR tests in air.
The CCGR behavior of the Ni-base alloys tested was
shown to correlate with the stress intensity factor, K. The
CCGR versus K curves exhibit three stages of behavior which
respectively with an initial transient in
are associated
damage accumulation ahead of the crack, power law dependent
CCGR on K and fast fracture at KIC. The measured CCGR for
an alloy
is shown
to be significantly
affected
by changes
in
test procedure, specimen design, and initial K.
A comparison of the notched stress rupture results
gives a qualitative measure of the CCGR behavior observed
for the nickel-base alloys.
Tensile, creep, and creep rupture tests at 704C for 4
alloys were performed to obtain the constitutive equations.
These relationships along with the microstructure were used
to model the CCGR behavior of the alloys based on the
accumulation of damage ahead of the crack tip. The computer
model predicts the effect of microstructure, mechanical
properties, and load history on creep crack growth rates.
Thesis Supervisor:
Title:
Dr. Regis M. Pelloux
Professor of Materials Engineering
3
TABLE OF CONTENTS
CHAPTER
TITLE PAGE
PAG
1
ABSTRACT
2
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
3
6
11
ACKNOWLEDGEMENTS
12
1.
INTRODUCTION
13
2.
LITERATURE
16
REVIEW
2.1.
Metallurgy of Ni-Base Alloys
2.1.1. Chemistry of Ni-Base Alloys
2.1.2. Strengthening Mechanisms
2.1.3. Grain Boundary Morphology
2.1.4. Heat Treatment
16
16
22
25
28
2.2.
Environmental Embrittlement of Ni-Base
Alloys
2.2.1. Determination of Embrittling
Elements
2.2.2. Theories for Environmental
Embrittlement
2.2.3. Effect of Grain Boundary Chemistry
on Environment Embrittlement
29
Creep Crack Growth
2.3.1. Analysis of CCGR Testing Methods
2.3.2. CCGR in Various Alloys
2.3.3. Air Embrittlement of Ni-Base
Alloys
2.3.4. Effect of Microstructure on CCGR
in Ni-Base Alloys
42
43
48
52
Theories of Creep Crack Growth
2.4.1. Crack Tip Stress Distribution
2.4.2. CCGR Models
2.4.2.1. Diffusional Creep Models
2.4.2.2. Creep Constrained Cavity
57
57
63
63
65
2.3.
2.4.
33
38
54
Deformation Controlled
2.4.3.
CCGR Models
Iterative CCGR Models
66
4
TABLE OF CONTENTS (cont'd)
CHAPTER3.
EXPERIMENTAL PROCEDURES
3.1.
69
Materials
69
3.3.
3.1.1. Chemistry and Processing
3.1.2. Microstructural Characterization
Mechanical Testing
3.2.1. Tensile Testing
3.2.2. Smooth Bar Creep Testing
3.2.3. Notched Stress Rupture Testing
3.2.4. Creep Crack Growth Rate Testing
3.2.4.1. D.C. Potential Drop Technique
3.2.4.2. Data Analysis
Pre-exposure Oxygen Penetration Tests
70
72
77
77
79
79
81
83
91
93
3.4.
Fractography
93
3.2.
4.
PAGE
EXPERIMENTAL
4.1.
4.2.
4.3.
4.4.
RESULTS
95
Tensile Properties at 7040C
Smooth Bar Creep Results
4.2.1. Minimum Creep Rate Results
4.2.2. Creep-Rupture Results
Notched-Rupture Results in Air
4.3.1. Constant Load Results
4.3.2. Air Pre-exposure Results
Creep Crack Growth Rate Results
4.4.1. CCGR for Five Ni-Base Alloys
4.4.1.1. CCGR of PM/HIP Low C Astroloy
4.4.1.2. CCGR of PM/HIP Merl-76
4.4.1.3. CCGR of PM/HIP Low C IN-100
4.4.1.4. CCGR of PM/HIP Rene-95
95
96
96
98
100
100
100
102
102
102
104
106
106
(60 mesh)
4.4.1.5.
CCGR of PM/HIP Rene-95
(120 mesh)
4.4.2. Effect of Initial Stress Intensity
Factor
4.4.3. Comparison of CCGR in Air
4.4.4. Comparison of CCGR in Argon
4.4.5. Validity of K Correlation of CCGR
4.4.6. Fractography of CCG Tests
4.4.6.1. Argon Tests
4.4.6.2. Air Tests
4.5.
G. B. Penetration
of Oxygen
Results
109
109
112
112
115
116
117
118
118
5
TABLE OF CONTENTS (cont'd)
CHAPTER
5.
AN ITERATIVE MODEL FOR CREEP CRACK GROWTH
130
5.1.
'Introduction
130
5.2.
Numerical Procedures
5.2.1. Calculation of Stress and Strain
5.2.2. Accumulation of Strain
131
131
136
5.3.
Effect
140
5.4.
5.5.
143
Predictions of Creep Crack Growth Rates
148
Effect of Critical Parameters
5.5.1. Effect of Critical Strain to Fracturel 48
5.5.2. Effect of Grain Size
149
149
Constant K Calculation of CCGR
153
Effect of dK/da on CCGR
155
Effect of Temperature and Yield Strength
Predictions of Creep Crack Initiation Times 158
5.6.
5.7.
5.8.
5.9.
6,
PAGE
of Oxygen
159
DISCUSSION
6.1.
CCGR Modelling
6.1.1. Effect of Triaxiality
6.1.2. Effect of Oxygen Concentration
6.1.3. Limitations of the CCGR Model
62.
CCGR of PH/HIP
6,2.1. Effect
6.2.2. Effect
Notched-Stress
6.3.
Ni-Base Alloys
of Test Procedures
of Oxygen
Rupture versus CCGR Tests
159
164
165
167
169
169
170
173
7.
CONCLUSIONS
177
8.
RECOMMENDATIONS FOR FUTURE WORK
179
8.1.
8.2.
Grain Boundary Chemistr,y Variations
Effect of Test Procedures and Specimen
Design
179
180
APPENDIX I Table of CCGR Test Results
181
APPENDIX II Computer Program for CCGR Prediction
183
APPENDIX III Calculation of Ductile-Brittle Creep
186
Transition Times
References
190
6
LIST OF FIGURES
FIGURE
2.1.
PAGE
Alloying elements in Nickel-Base alloys.
19
(ref. 6)
2.2.
Gamma prime volume fraction versus weight
percent Al + Ti in Ni-Base Superalloys.
(ref.
2.3.
Comparison
21
8)
of reduction
in area for tensile
tests on Ni-270 following 10000 C, 200 hour
exposure to various gaseous environments.
31
(ref. 34)
2.4.
Fracture ductility versus temperature for
both inert and air exposure at 100 0 °C for
200 hours.
2.5.
(ref. 34)
Effective diffusivity of oxygen in pure Nickel
versus
1/T.
32
34
(ref. 30)
2.6.
Effect of alloying additions on the rupture
40
life of IN-738. Results given as stress
versus the Larson-Miller Parameter. (ref. 22)
2.7.
Creep strain versus time in PE16 at 6500 C
with and without Boron and Zirconium
additions.
2.8.
2.9.
(ref. 32)
Typcial CCGR behavior found in Nickel-Base
alloys.
41
46
(ref. 64)
Effective of initial K on CCGR results on .5%
Cr-.5%Mo-.25%V steel at 565 0C. (ref. 41,66)
2.10. CCGR versus K for several Ni-base alloys at
47
50
7040 C.
2.11. The effect of temperature on CCGR in PM/HIP
low carbon Astroloy. (ref. 63)
51
2.12. Comparison of CCGR results in an air
environment and in an inert environment for
Ni-Base alloys at6500 C.
53
2.13. Initial K versus time to failure for CCGR
tests on IN-792 in air at 7040 C. (ref. 35)
55
2.14. Effect of heat treatment on CCGR results on
56
IN-100
in air at 700 0C. (ref. 57)
7
2.15. Calculated stress field ahead of a crack tip
for PM/HIP low carbon Astroloy. (ref. 63)
62
2.16. Stress and Creep Strain ahead of a crack tip
versus time, used in modelling CCGR.
68
3.1.
Microstructure of PM/HIP Low Carbon Astroloy.
73
3.2.
Microstructure of PM/HIP Merl-76.
74
3.3.
Microstructure of PM/HIP Low Carbon IN-100.
75
3.4.
Microstructure of PM/HIP Rene-95.
76
3.5.
Specimen geometry used for both tensile
and creep-rupture testing.
78
3.6.
NSR specimen geometry
80
3.7.
Single Edge Notched specimen geometry used
for CCGR testing.
82
3.8.
Theoretical and experimental d.c. potential
drop calibration of SEN specimen geometry.
85
3.9.
Schematic
test system.
87
of CCGR
3.10. Variation in the calculated a/w from the
d.c. potential drop technique with varying
load spacing, Y.
90
4.1.
Stress versus minimum creep rate results
at 70°0 C for 4 Ni-Base Alloys.
97
4.2.
Stress versus time to rupture for NSR tests
on 4 alloys in air at 704C.
99
4.3.
CCGR results for PM/HIP Low Carbon Astroloy
103
at 704C in both air and 99.999% pure argon.
4.4.
CCGR results for PM/HIP Merl-77 at 704 0 C
in both air and 99.999% pure argon.
4.5.
CCGR results for PM/HIP Low Carbon IN-100
107
at 7040 C in both air and 99.999% pure argon.
4.6.
CCGR results for PM4HIP Rene-95 (60 mesh
powder) at 704 C in both air and 99.999%
pure argon.
108
4.7.
CCGR results for PM/HIP Rene-95 (120 mesh
powder) at 7040 C in both ari and 99.999%
pure argon.
110
105
8
4.8.
CCGR results for PM/HIP Merl-76 in air
at 7040°C with varying initial K.
111
4.9.
CCGR results for five PM/HIP Ni-Base
113
in air at 7040 C.
alloys
4.10. CCGR results for five PM/HIP Ni-Base
alloys in argon at 7040 C.
114
4.11. Fractograph of the Fatigue precrack creep crack growth transition in Rene-95
(120 mesh) and in IN-100.
120
4.12. Fractograph of the creep crack - Fast
121
fracture
transition
in In-100
at 704 C in air.
4.13. Fractograph of the CCG - Fast fracture
transition
at 7040 C.
in IN-100
in pure
122
argon
4.14. S.E.M. Fractographs of CCG fracture
surface for PM/HIP Astroloy in air and in
99.999% pure argon. Tests performed at
704°C.
123
4.15. S.E.M.Fractograph of a typical creep
crack fracture in arson for PM/HIP Low
Carbon In-100 at 704 C.
124
4.16. S.E.M. Fractograph of a typical CCG fracture
surface for Rene-95 (60 mesh) tested in
argon at 7040 C.
125
4.17 S.E.M.Fractographs of the typical creep
crack fracture surface in argon at 704°C
for the four Ni-Base alloys tested.
126
4.18. Cavity like features observed on Rene-95
(60 mesh) and Merl-76 fracture surfaces at
127
10,000x.
Tests
run at 704 C in argon.
4.19. S.E.M. Fractographs of typical creep crack
fracture surfaces in air at 7040C for the
four Ni-Base alloys tested.
128
4.20. S.E.M. Fractograph of a creep crack
fracture surface tested in air for PM/HIP
Low Carbon Astroloy.
129
5.1.
135
Graphic illustration of the stress field
ahead
5.2.
Graphic
of a creep
illustration
advance.
crack
at t=0.
of the Dt for crack
139
9
5.3.
Ratio of critical creep ductility in air
142
and argon versus the ratio of grain boundary
concentration of Boron to that of Astroloy.
5.4.
Predicted and Actual CCGR results for
PM/HIP Low Carbon Astroloy.
144
5.5.
Predicted and Actual CCGR results for
PM/HIP Merl-76.
145
5.6.
Predicted and Actual CCGR results for
PM/HIP Low Carbon IN-100.
146
5.7.
Predicted and Actual CCGR results for
PM/HIP Rene-95 (60 mesh).
147
5.8.
Plot of predicted constant K CCGR versus
critical strain for Astroloy at 7040 C in
air.
150
5.9.
Plot of predicted constant K CCGR versus
grain size for Astroloy at 7040 C in air.
150
5.10. Effect of grain size on predicted CCGR curves
for PM/HIP Low Carbon Astroloy at 7040C,
and actual CCGR results.
151
5.11. Predicted CCGR versus the number of crack
advances for constant K tests. Results
based on constitutive relationships for
Astroloy in air at 7040 C.
152
5.12. Effect of dK/da on the predicted CCGR for
PM/HIP Low Carbon Astroloy in air at 7040 C.
154
5.13. Comparison of Predicted and Actual CCGR
versus K data obtained by Huang (63) for
PM/HIP Low Carbon Astroloy in air.
156
5.14. Predicted constant K CCGR versus yield
strength for Astroloy in air at 7040 C.
157
5.15. Plot of initial K versus predicted time
to first crack advance. Prediction based
on data for Astroloy in air at 7040 C.
157
6.1.
Graphic
illustration
of the effect
of
162
dK/da on measured CCGR.
6.2.
Predicted effect of plane stress on the
CCGR for Astroloy in air at 704 0C.
166
6.3.
CCGR measured
172
in air at K = 30 MPa/im
704 C for 4 Ni-base alloys versus the
10
product of the effective diffusivity of
oxygen along the grain boundaries and the
grain size.
6.4.
CCGR
in air at K = 30 MPa/ii at 704 C
for 4 Ni-Base alloys versus the NSR time
to failure.
175
11
LIST OF TABLES
TABLE
2.1.
PAGE
Chemical Composition of selected Nickel-Base
superalloys.
18
(ref. 9)
2.2.
Ratio of rupture strength for various additions
of solid solution strengtheners to pure
nickel at 6150 C and 815 C.
23
2.3.
Creep Rupture properties of U-500 at 8700 C with
additions of Boron and Zirconium. (ref. 15)
27
2.4.
CCGR Results for Ni-Base alloys in published
literature.
49
3.1.
Powder size before HPing
alloys studied.
for the Ni-Base
69
3.2.
Thermal Processing used on Ni-Base alloys
studied.
70
3.3.
Alloy chemistries and microstructure for 4
Ni-Base alloys studied.
71
4.1.
Tensile
95
4.2.
Minimum creep rate results at 7040 C.
96
4.3.
Creep-rupture results for 4 Ni-Base alloys
in air at 7040 C and 801 MPa.
98
4.4.
Notched stress rupture results on Rene-95
(60 mesh) in air at 7040 C, following
pre-exposure to air at 7040 c with and
without a load.
101
4.5.
Grain boundary embrittlement study results.
100 hour air pre-exposure in air at 704C.
119
5.1.
Comparison of Critical strain ratio to average
141
concentration of Boron on the grain boundary
in Ni-Base alloys.
test results
at 704 G.
12
ACKNOWLEDGEMENTS
The author gratefully acknowledges the support of the
following people and institutions. Their encouragement and
assistance greatly contributed to the completion of this
thesis.
Professor Regis Pelloux, the author's thesis advisor
whose guidance, encouragement, and assistance throughout the
author's graduate studies were invaluable.
Professor Andre Pineau whose many discussions and
critiques on modelling of creep crack growth were very
helpful.
Professor F.A. McClintock and Professor R. Ballinger
for their reviews and comments of the final thesis.
Mr. Lenny Sudenfield for his help in operating and
later teaching the operation of the scanning electron
microscope at M.I.T.
The author would like to thank Philippe Bensussan and
Bill Moshier, graduate students at M.I.T., for their help
and discussions on occasions too numerous to count. The
author would also like to acknowledge all the members of the
creep and fatique research group for their interesting
discussions and assistance throughout the author's graduate
career.
My wife, Amy, who typed this document and without whose
love and constant support this research would have been
impossible.
The author would like to acknowledge the financial
support given by the Air Force Office of Scientific Research
and the Cabot Corporation in the form of a Cabot Fellowship.
The author would also like to acknowledge the Center
for Material Science and Engineering for support from a
NSF-MRL grant, and the AT-1, High Temperature Fracture,
group for their many interesting discussions.
13
1.
INTRODUCTION
Creep crack growth is a process in which a single crack
advances
intergranularly
tensile
stress
at
is
inert
environment
growth
possible
consist
a
material
under a constant
temperatures where at least local creep
deformation
test
in
of
(T>.4 Tm; melting point).
In an
the micromechanisms of creep crack
nucleation,
growth, and coalescence of
grain boundary cavities.
The
forms
the
recent
of
interests
high temperature mechanisms for crack advance are
result
concepts
of the desire to incorporate fracture mechanics
into
advanced
retirement-for-cause
life
of
in creep crack growth and other
as
design
a
criteria.
The concept of
method for extending the useful
of many high temperature components is but one example
these
area
of
gas
advanced
concern
turbines
criteria (1).
Creep crack growth is an
in nickel-base superalloys used in modern
hot section components and stainless steel in
nuclear and conventional power plants.
Current
based
on
design
are
statistical
chance
inch
for
gas turbine engines are
bulk creep deformation and crack initiation.
components
1/32
criteria
crack.
removed
that
from
one
service
when
there
The
is
a
part in 1000 has developed a
This conservative life limit results in
the
retirement of 999 out of 1000 components, many of which
may
have
replacing
up
to
10
times
more useful life.
The cost of
these components may reach $100 million a year by
14
The
1985.
life
of
these
components
critical
could be
by periodically inspecting the part for cracks and
extended
replacing
spacing
those parts in which cracks are found.
only
the
of
inspection
of
understanding
the
periods
requires
both
limits of detection
reasonable
The
an
of a
and of the rate at which this flaw or crack propagates
flaw
The accuracy required in the prediction
to
final fracture.
of
a creep crack propagation time is critical since failure
cf a component such as a turbine disk could be costly.
Creep is time-dependent deformation of a material under
stress.
The
mechanisms
of
creep and creep fracture have
The notched stress rupture
extensively studied (2-4).
been
test is a simple test designed to measure the time to
(NSR)
rupture
to creep processes in the vicinity of a stress
due
concentration
site.
Extensive
NSR
and
smooth
bar test
have 'indicated that the time to rupture is reduced
results
in the presence of the high stresses at the root of a notch.
The
creep
severe
crack
NSR
growth
test
test
can be thought of as a more
in which the time to form the macroscopic
crack is eliminated.
The test environment has been shown to
significantly affect the results of smooth bar and NSR tests
(5),
environment will also have an effect on the
the
and
creep crack growth rate (CCGR).
crack
Creep
severe
tip
form
acts
produces
as
of
a
locally
growth
testing
can
be
thought of as a
notched stress rupture testing.
severe
stress
concentration
The crack
site
which
large stresses, which may relax with time
15
due
to
creep
advances
as
deformation
a
time-dependent
and
result
crack
and
fracture.
The crack front
of creep damage which is due to the
tip
stresses.
Crack tip plasticity,
environmental embrittlement ahead of the crack tip play
an important role in controlling CCGR.
This
current
Then
thesis
includes
a
brief
review
of the
literature on the metallurgy of nickel-base alloys.
the
Ni-base
literature
alloys
and
literature
review
mechanical
test
Finally,
presented,
given.
first
a
and
on
environmental
creep
crack
growth is reviewed.
of
The
is followed by a detailed description of
procedures,
computer
a
embrittlement
materials,
model
of
creep
discussion
of
the
and test results.
crack
growth
is
critical results is
16
2. LITERATURE REVIEW
2.1.
Metallurgy of Ni-Base Alloys
Nickel-base superalloys are the material used in almost
every modern gas turbine disk and blade.
outstanding
low-cycle
these
tensile
fatigue
alloys
> 6000 C)
Typical
modern
100,000
hr.
stability.
strength,
at
which
properties,
the
are
high
common
turbine
lives
capability
weight
and
creep-rupture
and
corrosion
operating
strength,
resistance of
temperatures
(i.e.
in modern gas turbine engines.
engines
are
designed for 5000 to
which therefore require long time alloy
Turbine
maximum
This is due to the
operating conditions are pushed to the
of the alloy in the interest of minimum
maximum
operating
efficiency.
All
these
requirements are generally fulfilled by Ni-base superalloys.
The following sections detail the chemistry, microstructure,
strengthening
mechanisms
and heat treatment of nickel-base
superalloys.
2.1.1.
Chemistry of Ni-Base Alloys
The
chemistry
of
nickel-base
superalloys is complex
with at least 12 carefully controlled alloying elements.
In
general these alloys contain 10-20 percent chromium, up to 8
percent
aluminum
zirconium,
specific
and titanium, and small amounts of boron,
and carbon.
properties,
other properties.
Other elements are added to enhance
but
usually
at
the expense of some
17
The alloying elements can be divided into three classes
which are:
Elements which prefer to form the face-centered
1.
cubic (FCC) austenite (gamma,y ) matrix
(i.e. nickel, iron, chromium, cobalt, molybdenum,
tungsten, and vanadium)
2.
Elements which form the gamma prime phase (y ')
(i.e., aluminum, titanium, columbium, and tantalum)
3.
Elements which segregate to the grain boundary
(i.e., magnesium, boron, carbon, zirconium, and
undesirable impurities).
2.1.
Table
chemical
gives
superalloys
nickel-base
compositions
for several
currently being used in modern gas
turbine applications (9).
The
most
common
alloying
additions
in
nickel-base
alloys and the area of their greatest influence in the alloy
is shown
in Figure
The
(gamma, Y
MC
).
boundaries
of
a
consists mainly of
microstructure
large
and
2.1. (6).
solid
embedded
carbides
in
' precipitates
the austenite matrix
y' precipitates are also found at the grain
along
with M 2
solution
of
molybdenum, and tungsten.
6 carbides.
nickel
The matrix consists
with
cobalt,
chromium,
This combination of phases allows
the utilization of the alloys at up to .8
(melting point)
18
C-
0
\O
\O
O
0
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- -.AF-
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49 _;
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066
N,
n Atomic
Difference
o.
DiameterfromNickel
5.66 1,.66
+13
Ta
-
O
+12
Nb
+18 -.
+1
Fe
Cr
5 66
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3
.
W
5.66
4.66 ..
.
.
.
!,
AtomicDiameter
of Carbon.Soron.Zrcni
Magnesum
- Goldschmidt
forCN12
AtomicDianeterof OtherElements
from tticeParameterEffectn NickelBinaryAlys
"
El~ement
Partitions to
FIGURE 2.1)
D
Element
Partitions
to '
1
Partitions
to GrainBoundary
3 1 Element
Periodic table of alloying elements in Nickel-Base
Superalloys. (ref. 6)
20
for times as long as 100,000 hrs (6).
attack
down
slow
or
inhibit
which
Al203 oxides at the surface
and
Cr203
form
aluminum
and
Additions of chromium
by oxygen, nitrogen,
sulfur, and other aggressive atmospheric elements (7).
main precipitate phase in the gamma matrix (y ) is
The
( y').
gamma-prime
"B"
and
a
phase with the general
FCC
with "A" being either nickel, iron, or cobalt
A 3 B,
formula
is
It
aluminum,
either
being
titanium,
or columbium.
precipitates were initially spherical in early alloys
These
treatments
heat
advanced
but
result
in
shape
cube
a
precipitate which enhances strengthening.
The
tantalum.
aluminum,
of
percent
atomic
y' is a function of the combined
percent
weight
The
result
of
y'
columbium,
ti
tanium,
analyses of 15I
superalloys are summarized in Figure 2.2(8).
It
and
nickel-base
can be seen
that additions of aluminum, titanium, columbium and tantalum
will
increase
Y'
formation.
The presence of Cobalt and
Vanadium will also enhances the formation of
y' from the y
matrix.
are
Carbides
(usually
boundary
boundary
phases
in Ni-base alloys.
microstructure
grain
major
sliding.
M23C6)
of
the
grain
boundary
Carbides, located at the
markedly
inhibit
grain
These grain boundary carbides, however,
can and will serve as nucleation sites for creep cavities.
One
the major problems with Ni-base superalloys is
of
the
formation
TCP
phases
of topologically closed-packed phases (TCP).
usually
have
body centered tetragonal crystal
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i
22
A Laves phase has the chemical formula
structure.
and
cobalt
"B" being either Mo or Ta.
(Ni,Co)y where
phase is generally of the form (Cr,Mo
Sigma
x
being
usually
"A"
and
can vary from 1 to 7, but usually are both around
y
as hard flat plates or needles
form
phases
These
unity.
B with
which will reduce alloy ductility (10).
The
Fe
to
the
matrix
enables
the
of y" , eta, and delta phases which strengthen
precipitation
Columbium
When
alloy.
the
of
addition
IN-718,
the
primary
centered
tetragonal
is
present, such as in alloy
strengthening
phase
is
",
phase with the composition Ni 3Cb.
body
y"
can degenerate into the orthorhombic delta phase.
The third phase enabled by iron is called eta, which is
Ni 3Ti and has a hexagonal close packed (HCP) structure.
is
a
IN-901,
strengthening phase in alloys such as A-286,
primary
and Pyromet 860. However, the frmation
IN-706,
brittle
large
Eta
particles
of
of either eta or delta phase will
reduce rupture life and ductility.
2.1.2.
Strengthening Mechanisms
Several
Ni-Base
strengthening
alloys
give
to
mechanisms
are usually used in
high short and long time strength
over a wide range of operating temperatures.
Several
alloys
as
harden
the
between
the
elements are added to the
solid
solution
alloys
solute
strengtheners.
matrix of Ni-base
These elements
as a result of the atomic size mismatch
atoms and the nickel matrix.
The most
23
potent
solid
elements,
Rene-95
solution strengtheners are the slow diffusing
such
has
as
both
molybdenum and tungsten.
Mo and W additions.
The effect of solid
solution strengtheners is shown in Table 2.2.
10%
additions
Ni is reported
The
most
The effect of
of Mo, Cr, and W on rupture strength of pure
(12).
most
temperatures
For instance,
up
common
(Ni,Co)3 (Al,Ti).
important
to
mechanism
for
7600C is precipitation hardening.
The
and
This
strengthening
effective
precipitate
phase
a
has
face
is ¥
',
centered cubic
24
structure which is compatible with the FCC
a
0
1%
to
latice
mismatch.
homogeneous
nucleation of the
stability.
Other
also
on
The
mismatch
allows
y' precipitate and long time
such
as
y", eta, and delta can
effect of the precipitates on strength depends
The
the size, shape, and volume fraction of the precipitate.
strength
optimum
third
The
of
formation
act
to
The
formation
from
strengthening
a mixture of coarse and
(7, 13).
mechanism
involves
the
beneficial carbides at grain boundaries which
inhibit
grain
of
boundary migration and hence creep.
blocky MC and M23C 6 carbides along grain
lock the grain boundaries and decrease the creep
boundaries
at
comes
y' precipitates
shaped
fine, cubic
rate
low
from the matrix and act to strengthen the
precipitate
alloy.
phases
The
matrix and has
high
temperature.
The carbides can also form as
M6C, Cr7C3, and as a film of M23C 6 along the grain boundary,
all
of which will embrittle the grain boundaries and result
in premature fracture.
The above effects (and others) can be summarized in the
following
improve
guidelines for alloy design and heat treatment to
the
balance
struck
tensile and creep strength:
between creep, ductility, and
25
1.
Solid solution strengthen y
2.
Increase volume percent
3.
Increase coherence strains for less than 0.6 Tm.
4.
Decrease ripening rate for greater than 0.6 Tm.
5.
Solid solution strengthen
6.
Minimize formation of TCP embrittling phases such
as Ni 3Nb, Laves, and a phases.
7.
Control carbides and grain boundary
rupture strength.
8.
Careful control of heat treatment to develope
y'.
'.
y' to enhance
microstructure.
2.1.3. Grain Boundary Morphology
Creep
fracture
crack
and
growth
therefore
is
a
process
of
intergranular
the control of the composition and
microstructure of the grain boundaries is of great interest.
Several
alloying
magnesium,and
elements
carbon
such
segregate
as
boron,
zirconium,
to the grain boundaries in
Ni-base alloys.
Addition
zirconium
have
properties.(7)
times,
of
less
been
These
elongation
than .1 weight percent of boron and
shown
additions
to
increase
increased
creep-rupture
lifetime by 13
by 7 times, rupture stress by 1.9 times,
and
they
law
creep. (7, 12) Magnesium also is thought to improve the
creep
also increased the stress exponent, N,
properties,
element.
for power
but it is not widely used as an alloying
26
While
it
beneficial
not
effect, the mechanisms by which B and Zr act are
clearly
grain
is known that these B and Zr elements have a
understood.
boundaries
B
because
and
Zr will segregate to the
of their atomic sizes 21 percent
undersize
and 29 percent oversize, respectively.
zirconium
have been shown to retard grain boundary cracking
Boron and
in U-500, and boron alone has been shown to resist oxidation
damage along grain boundaries in IN-738 (14).
Boron
boundary
was
crack
indicates
that
observed
initiation
upon
the
loading
onset
in
of
grain
U-500, which
When the concentration of boron is
120 ppm, it will form M 3 B 2 borides with the "M" being
primarily
as
reduce
it may be a critical element for inhibiting
grain boundary fracture.
above
to
molybdenum
and chromium.
These g.b. borides act
a source of boron as well as molybdenum and chromium for
the grain boundary (7).
It
zirconium
Reduced
has
also
and
diffusion
formation
creep-rupture
(15).
retard
rates
grain-boundary diffusion.
along grain boundaries reduce the
y' nodules around M 2 3 C 6 carbides in U-500.
of
region of fine
strength.
suggested that additions of boron,
magnesium
tendency to form
The
been
y'
nodules depletes the grain boundary
y' which results in a loss of grain boundary
The
effect
life
of
of
boron
Udimet
500
and
zirconium
on
the
is shown in Table 2.3.
27
TABLE 2.3.
Creep Rupture of Udimet 500 at 870 C
Alloy
a =17.6MPa, hrs.
Life at
Base Alloy
+.19% Zr
+.009% B
+.009% B + .01% Zr
Creep Exponent, N
50
2.4
140
400
647
4.0
7.0
9.0
The boron and zirconium additions reduced the number of
y' nodules observed and the number of microcracks.
The
alloys
MC,
M 23 C6,
Cr 7C 3
of
carbon
at grain boundaries in Ni-Base
is generally better understood.
marked
MC
effect
Cr 7 C3
or
tendency
for
carbides
carbides
boundary
M 6 C carbides.
grain
Carbon forms either
M 23 C6
carbides have a
boundaries, as well as M 6 C and
which are observed as grain boundary films.
are
y'
(15)
important
and
M 2 3 C6
for
the
carbides
formation
through
the
of
grain
following
reaction:
6MC + Y
M23C6 +
Y'
This reaction occurs between 7600°C and 9800 C.
Carbides
and
grain
creep
have
crack
growth.
boundaries
reducing
cavitation
creep
positive
and negative effects on creep
Blocky M
inhibit
rates.
They
grain
also
23 C 6
and MC carbides at
boundary
sliding
thus
act as sites for creep
and tend to increase the CCGR as observed by Law
28
(16),
Blackburn
and
in
(18)
al.
of Cr7C 3 or M6C both have a strong negative
grain
the
embrittling
of
effect
Grain
alloys.
Ni-base
wrought
different
films
boundary
Pelloux and Huang (17) and Saegusa et
boundaries and reducing
stress rupture strength.
2.1.4.
Heat Treatment
Proper
for
critical
development
the
Wrought
alloys,
mainly
Y
following
temperature
varies
temperature
this
and
matrix
from
prepares
nickel-base superalloys is
of
treatment
heat
of
strength and ductility.
MC
y', consist of
of
solutioning
Y'
The
carbides.
solvus
10400 C to 12300 C, and aging above
the matrix for precipitation of
y' on subsequent cooling and/or aging.
Following
precipitate
to
given
Rupture
phases.
precipitating
24-hour
solutioning a series of aging treatments are
y'
period.
and
creep
and
in
develop the major strengthening
the
This
resistance
range
is
is
obtained
of 8400 C to 1100 0 C for a
followed
by
an
aging
approximately 7600 C to complete the development of fine
Good
by
at
'.
tensile strength at lower temperatures is developed by
precipitating
fine
y' by aging slowly at 7600 C.
This also
minimizes the formation of carbides at grain boundaries (7).
Several
variations
of the general heat treatments are used
to develop various microstructures.
Alloys
which
depend
on
y"
for
strength,
such as
IN-718, usually require a longer time for precipitation at a
29
temperature.
lower
is
to
used
avoid
The lower temperature (650 C-760 C) age
the
of eta phase which will
formation
reduce creep-rupture life. (11)
Environmental Embrittlement of Ni-Base Alloys
2.2.
degradation in properties of metallic materials in
The
environments
various
long been observed.
Nickel-base
operating at temperatures above 500 C in air exhibit
alloys
a
has
marked
decrease
in their creep-rupture life (24), and a
decrease in notched stress rupture life (16), lower fracture
(34),
ductility
at
increase in fatigue crack growth rates
in creep crack growth rates (17).
and
(19),
an
temperatures
high
in
air
has
been
Embrittlement
observed
for
iron-nickel alloys (21), cobalt alloys (20), and nickel-base
alloys (22-24, 26, 27, 30, 33, 34).
in
strongest
Embrittlement in air is
the nickel-base alloy systems.
Only a slight
of air is observed on cobalt systems and iron-nickel
effect
Air
systems.
embrittlement is not observed in copper base
alloys, and in aluminum alloys (36).
2.2.1.
Determination of Embrittling Elements
Chaka
and McMahon (33) have demonstrated that air will
creep-rupture
life of Udimet 700 at 9250 C by a
reduce
the
factor
of 2 over the creep-rupture life in vacuum.
results
Similar
have been observed by Shahiniam (24) and Prager and
Sines
(23)
Hosoi
and
on several wrought and cast nickel-base alloys.
Abe
(26) indicated that small amounts of oxygen
30
can
rupture
All
of
time
studi'es were performed on Ni-base alloys at
7500 C.
above
Most
Ni-base alloys will have
It has
of their strength at these temperatures.
lost
most
been
shown
pre-exposure
IN-738
9000 C.
causing the initiation of surface cracks.
by
these
temperatures
and
the surface of IN-617 and reduce the creep
decarburize
that
a
to
air
when
(30,
loss
in
at 1000°C is observed for pure nickel
at temperatures between 6000 C and
tested
34)
ductility following
tensile
Exposure
to
air
results
in
brittle
intergranular fracture.
Ni-base
gaseous
elements.
Nimonic
115,
presence
of
are
alloys
embrittled
by a variety of other
Fatigue crack growth rates in IN-718 and
Ni-base
both
gas
hydrogen
alloys,
at
are
increased in the
6500 C (35). The presence of
carbon dioxide was found to embrittle alloy PE 16 and reduce
creep-rupture
lives
the
environments
7000 C
at
presence
(25).
Along with the above
of sulfur containing gases will
ductility and rupture times for nickel-base alloys
decrease
(37).
Recent
is
oxygen
the
temperatures
were
tensile
measured.
species
in
air
at
high
Round specimens .10 inches in diameter
to a variety of atmospheres at 10000C for
These environments included vacuum, N2 , H , CO2,
H20, 02, and air.
time
Ni-270 (99.98% Ni) has shown that
embrittling
(34).
pre-exposed
200 hours.
on
research
test
The specimens were then failed in a short
at
8000C and the reduction in area was
The results (See Figure 2.3) indicate that oxygen
31
NI 270, 1000 C EXPOSURE FOR 200 HRS. IN VARIOUS ENVIRONMENTS
-
VAC
10c
90
C02
I--
80 tm
--
7
I
H2
CO
.-
N2
r
_
70 I-Cu
.-
60
C:
0
'-H
Ii
W
O
o
ad
C0
50
40
.m
30 V20
m
AIR
10
02
I
LI
k./
"I w
FIGURE 2.3)
__
_
__
·
I
w
m
I
m
m
Percent reduction in area for NI 270 following 200 hr.
exposure to various gaseous environments at 1000 C.
(ref. 34)
32
100
90
r
80
:
z-70
E450
z
r
40
"a
30
20
10
0
0
200
400
600
800
TEMPERATURE ( C)
FIGURE 2.4)
Reduction in area results for NI 270 versus test
temperature following a 10000 C/200 hr. exposure
to either air or a vacuum. (ref. 34)
1000
33
is
the
embrittling
embrittling
species.
effect
of
oxygen
Figure
is
2.4
only
shows that the
detectible over a
narrow range of temperatures from 5000 C to 9000 C (34).
Oxygen
penetration
along
grain
boundaries
in
pure
nickel and nickel-base alloys produces severe grain boundary
embrittlement.
The depth of grain boundary embrittlement of
pure Ni in air from 9000 C to 11000 C was measured on fracture
surfaces after tensile tests (30).
generate
a
plot
of
the
The results were used to
effective
diffusivity of oxygen
versus temperature 1l' (K)
of oxygen exposure.
diffusivity
along
of
calculated
as
fracture,
and
plot
D
of
64 Kcal/gm
-10
D=X 2 /t.
t
atom
is
grain
the
depth of intergranular
1/T
gives
an
boundaries
(Figure 2.5).
activation
energy
was
The
of
and values of diffusivity which range from
-9
cm /s to 10
7040 C(977K)
(X
the
is the exposure time)
versus
2
10
oxygen
The effective
2
cm /s.
indicate
Extrapolation of these results to
an oxygen diffusivity along the grain
boundaries of approximately 10-1 4 cm2 /s.
The
results
gaseous
oxygen
reported
is
a
by
many have demonstrated that
severely embrittling element in both
pure
nickel
and nickel-base alloys.
most
severe
along
oxygen
crack
embrittlement
grain
This embrittlement is
boundaries, which indicates that
will
be an important factor in creep
growth at the temperatures of interest in this study.
2.2.2.
Theories of Environmental Embrittlement
While the embrittlement of nickel-base alloys by oxygen
has
been
observed,
the
mechanism
by which oxygen causes
34
0.1
CN
'4
Cn
U
4-
4
0
-ri
Ai
U
0
1/T (K-1)x 104
FIGURE 2.5)
Depth of penetration of oxygen, X, in NI 270 +
0.005% S as a function of exposure temperature.
(ref. 30)
35
forth
put
unknown.
remains
embrittlement
Several theories have been
to explain oxygen embrittlement.
These theories
are:
1.
Gamma prime-oxygen reaction
2.
Reduction of surface energy at
3.
Complex oxide formation along grain boundaries
4.
Carbon dioxide bubble formation
5.
Sulfur
y-y ' interfaces
due to oxidation of grain boundary
release
sulfides.
The first mechanism is the
It
proposed
been
has
grain
boundaries
fine
y'
y'-oxygen reaction process.
oxygen will diffuse along the
that
ahead of the crack tip and react with the
precipitates
oxide particles and
.
along
This reaction is shown below:
Y' + (0)-- + Mxy
0
removal
The
of
fine
(Equ. 2.1)
y'
particles
along
grain
reduce the strength of the boundaries and
would
boundaries
to form
the grain boundaries
promote brittle intergranular fracture.
Oxygen
boundary
grain
heat
has been observed to increase the rate of grain
cracks at
boundary
treated
y' nodules in Udimet 500 (7).
instability
superalloys
A severe
can exist in poorly alloyed or
when aided by an applied tensile
36
Here large M 2 3 C 6 carbides nucleate large nodules of
stress.
Y '
that
hypothesized
and
matrix
the
the
cohesive
nodules (23).
'
Y'
fine
oxygen
atomic
reduces
boundaries
its
of
boundary
grain
which deplete the surrounding
perimeter
their
around
particles.
It
is
diffusing down the grain
strength
between the y
The resulting cracks and
the weakened grained boundaries result in a brittle fracture
along the grain boundaries.
A
mechanism
third
proposed by Woodford and Bricknell
33) involves the formation of complex oxides along the
(30,
grain
by
boundaries
the
mechanism given in equation 2.1.
These complex grain boundary oxides then serve as additional
The formation
nucleation sites for grain boundary cavities.
of
numerous
creep
will greatly accelerate grain
cavities
boundary cracking and promote brittle fracture.
Another
alloys involves the formation of CO 2 bubbles at
nickel-base
grain
proposed mechanism for oxygen embrittlement of
boundary carbides.
(22) This mechanism is similar to
the well known methane bubble formation in Cr-Mo-V steels in
the
diffuses
of
of
presence
the
reacts
hydrogen
at
high
temperatures.
Oxygen
into the material along the high diffusivity paths
grain
with
MC
boundaries.
Once
in the alloy, the oxygen
and M 2 3 C6 carbides to form CO 2 as shown in
equation 2.2:
12(0) + M 2 3C6 -
Y + 6C02
(Equ. 2. 2)
37
thermodynamic feasibility of carbon dioxide bubble
The
has
formation
pressure
will
in
result
growth
of
cavities.
these
These
link and cause a reduction in creep strength
boundary
grain
premature
through
nucleation of bubbles at carbides and
the
early
the
will
cavities
The partial
CO 2 gas is large (approximately 2000 MPa), and
of
accelerate
determined by Dyson (31).
been
fracture.
This theory
that a reduction in carbon content will reduce CO2
suggests
bubble
and
formation
fracture
intergranular
reduction
since
creep
crack
growth
is
an
it will reduce the CCGR. A
process
in carbon content will detrimentally affect other
creep properties and therefore may not be feasible.
mechanism
Another
into
the
sulfur
grain
release
oxidation
involves the release of free sulfur
by a reaction with oxygen.
boundary
to
the
Free
boundaries results from the
grain
MnS particles in the grain boundaries through
of
the following reaction:
(0) + MnS -
The
presence
concentrations
severly
of
as
embrittle
has
MnO + S
free
low
as
sulfur
10
(Equ. 2.3)
in
nickel
alloys
in
to 20 ppm has been shown to
grain boundaries (38).
The oxidation of
been observed in IN-738 and Ni-270 with
MnS
particles
the
use of Auger microscopy (28, 29).
While the release of
38
free
sulfur
affected
was observed, it could not be determined if it
the ductility of these alloys since the formation
of CO 2 bubbles was also observed.
All of the above embrittlement mechanisms depend on the
diffusion
rates of oxygen along grain boundaries.
Elements
which segregate to grain boundaries and reduce the number of
vacancies
oxygen
can
along
be
expected
grain
to
reduce
boundaries.
increase
the
cohesive
interface
will
inhibit
Alloying additions which
strength
the
the diffusivity of
of
nucleation
the
carbide-g.b.
of grain boundary
cavities and reduce the amount of embrittlement in the alloy
by oxygen.
2.2.3.
Effect of Grain Boundary Chemistry on Environmental
Embrittlement
Several' researchers
alloying
nickel
have
investigated
the effect of
additions on the extent of oxygen embrittlement in
base alloys
(22, 28, 30, 32).
Woodford (22) varied the composition of IN-738 in order
to
study
the
susceptibility
effect of boron, hafnium, and yttrium on the
of IN-738 to oxygen embrittlement.
The time
to
rupture was measured in air and in vacuum for four heats
of
IN-738.
reduced
after
200
hours.
for
bars
1000°C
Rupture
lives
of
smooth
bars were severely
pre-exposures to oxygen or air at 10000 C for
A slight decrease in rupture life was observed
exposed
to N 2 gas, while exposure to a vacuum at
for 200 hours resulted in the longest rupture lives.
39
The
lives
rupture
were
severely
reduced
after
oxygen
pre-exposure at 10000 C when tested in a range of temperature
from 7000 C to 8000 C.
Oxygen pre-exposure had no detrimental
effects
on rupture life at 10000 C.
results
are
Larson-Miller
Figure
The
parameter.
2.6
as
stress
versus the
addition of 1.5% hafnium to
The addition
the longest rupture time in air.
gave
IN-738
in
shown
The above creep rupture
of
only
0.1% boron also increased the rupture time in air,
but
the
addition of 0.5% yttrium reduced the rupture times
for
IN-738.
to
time
of the heats gave approximately the same
All
tested in a vacuum.
when
rupture
This indicated
that the addition of these elements affected the interaction
between the alloy and oxygen.
0.005%
Zr
and
.05% zirconium reduced the minimum creep
did
additions
sliding,
boundary
both
cracks
in
strain
versus
for
and
boron
(32) found that the addition of
and increased the time to rupture for alloy PE16.
rate
B
Davidson
and
Floreen
PE16
with
not
reduce
The
the amount of grain
but did inhibit the formation of surface
and
air
helium
environments.
The creep
time
at 6500C measured in air and in helium
and
without B and Zr additions is shown in
Figure 2.7.
The
observed
addition of boron to Ni200 (99.54% pure nickel) is
to
eliminate
grain boundary embrittiement in air
(30).
The fact that Ni200 and Ni270 (99.99% pure nickel) do
show
severe
containing
grain
environments
boundary
embrittlement
by
oxygen
indicate that oxygen embrittlement
40
600
500
400
X
300
rn
O 200
100
n
v16
18
20
22
24
P=T(°K)[20+log (tR(hrs.))]x10
FIGURE 2.6)
26
28
3
Comparison of creep-rupture life of IN-738 with
four alloy variations with a pre-exposure in air
and without a pre-exposure in air. (ref. 22)
41
6
Creep
Elong. 4
2
t
0
200
400
600
800
1000
1200
Time (h)
FIGURE 2.7)
Comparison of smooth specimen creep tests for the
alloy PE16 with both boron and zirconium or with
neither boron nor zirconium. Tests performed in
either air or helium at 650 C and a stress of
380 MPa. All tests interupted at approximately
4% Elongation. (ref. 32)
1400
42
is
a
phenomenon
is
inherent
in
the nickel alloy
Since
boron
additions eliminate embrittlement in
models
based
on
system.
Ni200,
which
'
-
reaction,
oxygen
possible, are not required for embrittlement.
to
while
Boron appears
be very effective in eliminating the effect of oxygen on
a fundamental level.
While
additions
exact
the
role
segregate
which
of
to
boron
and
other alloying
the grain boundaries is not
The effect of boron
clear, some conclusions can be derived.
and zirconium additions on embrittlement of grain boundaries
in
nickel
alloying
these
are
they
the
alloys
pronounced.
The mechanisms by which
work are very fundamental, since
additions
effective in very pure nickel.
of
diffusion
occupying
is
along
oxygen
the
Boron may inhibit
grain
boundaries by
vacancies and slowing grain boundary diffusivity.
(30)
2.3
Creep Crack Growth
Creep
crack
growth
rates
(CCGR)
measured in several alloy systems:
steels
wide
(43-48),
variety
aluminum alloys (39-42),
and nickel base alloys (29, 35, 48-63).
A
of alloys, test specimen geometries, and test
been reported.
Several review papers have
been written (63, 64, 66).
The following section will
conditions
also
have recently been
have
review the published work to date on creep crack growth rate
results and test procedures.
43
2.3.1.
Analysis of CCGR Testing Methods
CCGR
tests
geometries
tension
including
specimens
(DCB),
(64).
performed
center
(CT),
(SEN),
Several
using many specimen
cracked panels (CCP), compact
double
specimen
and
wedge
researchers
specimens
(39,
been
cantilever beam specimens
double edge notch specimens (DEN), single edge notch
specimens
test
have
to
surfaces,
opening
load specimens (WOL)
have added side grooves to the
promote a plane strain condition at the
and
to
eliminate crack tip tunnelling
47, 51, 53, 55, 57, 58, 62, 63).
Crack
tip tunnelling
results from the creep crack growth rate being faster in the
specimen
center
which
specimen
sides.
Side
the triaxiality
has
greater
triaxiality
than the
grooves are often added to increase
at the surfaces
of the specimen.
All of the above specimens have certain advantages, but
the CT specimen and the SEN specimen geometries are the most
widely
used.
stress
intensity with crack advance and the test procedures
and
The
K-calibration
CT
specimen
are
well
affords a low rise in the
documented.
The SEN specimen
allows
a complete CCGR versus K plot to be generated from a
single
test because of a steep dK/da, and the K-calibration
is
been
equally
observed
measurement
CCGR
well known.
of
results
questionable
to
Since the lack of side grooves has
result in crack tip tunnelling, accurate
crack
length
obtained
(39, 59).
from
is impossible, and therefore
ungrooved
specimens
are
44
Crack
length
potential
is usually determined via the electrical
difference technique (58, 59).
compliance
techniques for crack length measurement are also
employed
(47).
accurate
for
of
grooves
side
Optical (47) and
therefore
Optical
crack
length measurement is only
a polished smooth specimen surface.
all
will
result
results
The lack
in crack tip tunnelling and
obtained by optical techniques will
under-estimate the crack length and the CCGR.
Creep crack growth rates have been correlated using the
stress
intensity
(COD),
the
for
time
stress
J-Integral
dependent
the
(41,
correlated
by
determine
crack
from
a
C*
have
the net section
been
published
The CCGR is best
the C* parameter in creep-ductile materials.
however, that the method used to
yields
a
rate.
(64,66)
rate
growth rate.
studies
and
46, 52, 53, 59, 64, 66).
possibility,
growth
the
Several
(C),
(J), the C*-integral
practical applicability of these correlating
parameters
is
for plasticity
plasticity
(anet )
comparing
There
factor (K), the crack opening displacment
of COD.
value of C* which is a function of
The C* parameter is measured
This depends strongly on the crack
Correlations of CCGR data with C* when C* is a
function of the CCGR results in the situation of correlating
CCGR
versus
appear
CCGR
(67).
While
the
correlations with C*
good, the results cannot be used to predict the CCGR
behavior when different initial conditions of load and crack
length are used.
and
IN-100
CCGR tests on IN-718 (52), Udimet 700 (53)
(59), all nickel-base alloys, indicate that the
45
factor,
intensity
stress
K, gives the best correlation of
The definition of creep-brittle and creep-ductile are
CCGR.
given in section 2.4.
The
creep
quickly
K
.
The
function
unique
values
initial
behavior does not appear to be a
stage
I
of
and tests which are started at high
K
of K may only exhibit Stage I and Stage III
Figure 2.9 shows results for .5% Cr-.5% Mo-.25% V
behavior.
at 565 0C by Nikbin
steel
CCGR with K. Stage II is similar to
Stage III corresponds to a rapidly increasing CCGR
growth.
near
increasing
known Paris Law regime observed for fatigue crack
well
the
rate versus K curves usually
three stages (Figure 2.8) (64). Stage I is a region
exhibit
of
growth
crack
et. al.
(41) and Neute
and Siverns
(66), and the effect of initial K on the CCGR behavior of an
are
alloy
obvious.
versus
CCGR
curve.
The
K
and
A higher initial K resulted in a lower
a
steeper slope for the CCGR versus K
higher initial K tests did not have a Stage II
region of CCG.
In
length
reported
complex
general the test procedures, specimen design, crack
measurement
for
CCGR
array
of
technique,
testing
in
and
correlating parameters
the literature result in a
often conflicting and inconsistant data.
These differences reflect the lack of a proper understanding
of the creep crack growth fracture processes.
46
iE
z'U
U
U
TIME
_
Il
I-
0
U
0
ICa
J
I--
I --
LOG STRESS INTENSITY
FiCuRE28)
Schematic illustration of crack growth data. (ref. 64)
47
.- 6
iU
10- 7
da
dt
(m/s)
10- 8
10
10
20
40
60
80
100
STRESS INTENSITY FACTOR,K (PaM)
FIGURE 2.9)
Comparison of CCGR results for 0.5Cr-0.5Mo-0.25V steel
in air at 565 C with different initial K. (ref. 41,66)
48
CCGR in Various Nickel Base Alloys
2.3.2.
have
CCGRs
both
been determined for many Ni-base alloys in
and inert environments from 530 C to 850 C.
air
CCGR
in
the literature for Ni-base alloys are listed in
Table
2.4.
The results in Table 2.4. are for a variety of
test
conditions,
results
techniques.
measurement
designs,
specimen
In
general
and
crack
length
the stress intensity
factor was observed to give the best correlation of the test
results.
Figure
the
CCGRs for these alloys at 704 0C are shown in
The
2.10.
Ni-base
A wide range of results has been obtained for
alloys.
originates
from
conditions
which
appear
Some
inaccurate
of
the scatter in the results
tests
procedures
and initial
result in CCGR versus K data which do not
to be a unique
function
of K.
49
TABLE 2.4.
CCGR Results for Nickel-Base Alloys from Literature
ALLOY
Astroloy
Astroloy
Astroloy
TEMPERATURE (C)
ENVIRONMENT
655, 704, 725, 760
655, 704, 760
Vacuum
704
650, 750, 850
850
850
Udimet 700
Udimet 700
Udimet 700
IN-100
IN-100
X-750
X-750
X-750
X-750
IN-718
IN-718
IN-718
IN-718
IN-718
IN-718
IN-718
NIMONIC 115
AF 115
NIMONIC 105
IN-738 LC
B6
704
540, 650
540, 650
650
538, 650, 704, 760
704
650
650
650
540, 650
540, 650
704
The
48
59
57
61
58, 62
58
50
48
48
55
55
52
50
49
56
56
48
48
50
Air
Argon
Air
Air
Air
Vacuum
Air
Vacuum
Air
Air
Air
Air
Air
Air
Air
704
704
650
650
effect
48
Vacuum
704
750
850
PE16
PE16
53
Vacuum
650
Waspaloy
50
Air
Air
Air
Air
Argon
Air
Air
650, 704, 760
650, 760
Rene-95
Rene-95
51, 63
51, 63
Vacuum
650, 700
704
Rene-95
Air
Air
Air
Air
732
MERL-76
REFERENCE
61
54
54
61
50
32
32
Helium
of temperature on CCGR behavior
in Ni-Base
alloys has been extensivly studied. (48, 51, 52, 58, 62, 63)
The
results for PM/HIP low Carbon Astroloy by Huang
Figure
2.11
temperature
are
on
given
CCGR.
as
an
example
of
(63) in
the effect of
The results of all reported research
50 -
1r -3
Iv
L-
-I
I
I
I
Creep Crack Growth Rate, Air, 704°C
1
2
3
10
ASTROLOY (ref. 63)
IN-100
(ref. 57)
MERL-76 (ref. 61)
4
.-
.- ,
e
,I
e
\
/
5
6
7
10-5
da
dt
8
_
9
6
10- 6
1
(m/s)
10- 7
-8
10
io8
10
M
o-9 -
--
10
-
L-
I
20
I
_
I
40
I
60
I
I
80
100
STRESS INTENSITY FACTOR, K (MPa-i)
FIGURE 2.10)
Typical CCGR data for several Nickel -base alloys
in an air environment at 7040 C.
51
1 --"
.
I
10
II
II
U
i I[' it
L/C ASTROLOY
-
/
i.
Air
Ha o
I
/LD
-d5
700
C
I
I
-6
10
10'E
u
I0 E
E
oIw
-7
10
=o1
-8
0
-g
FIGURE 2.11)
I
I
I-I
20
30
LJ~
II
40
50
.K, MPa j
....
I.
I
70
I
I
I
100
Comparison of CCGR results for PM/HIP low Carbon
Astroloy tested in air at three different test
temperatures. (ref. 63)
52
that in the range of temperatures tested the CCGR
indicates
increases significantly with increasing temperature.
The
surfaces for all the Ni-Base alloy tests
fracture
was totally intergranular, and the tests in air displayed an
fracture
brittle
extremely
mode
with very little visible
ductility or cavitation.
Air Embrittlement of Ni-base Alloys
2.3.3.
The
oxygen on the CCGR has been studied by
of
effect
(63) on Astroloy, Sadananda and Shahinian (49, 51) on
Huang
In-718, X-750, and Udimet 700, Pineau (56) on IN-718, and by
The effect
(32) on PE16, and Bain (58) on Rene-95.
Floreen
of oxygen on CCGR ranges from only a slight increase in CCGR
for Astroloy to a 1000 times increase in the CCGR for IN-718
and Rene-95.
2.12 - shows
Figure
results
environment
The
CCGR
range
of
surprising
creep
results
for
in
well
CCGR
since
range
the
several
of
and
air
inert
Ni-base alloys at 650C.
an inert environment are in a narrow
below
all
the
the
air results.
This is not
alloys have essentially similar
and tensile properties at this temperature.
The CCGR
in air were much faster than in an inert environment but the
amount
alloy
of
to
strongly
increase
alloy.
on
embrittlement.
The
each
The
in
the CCGR varies significantly from
effect
alloy's
of
on
oxygen
ability
to
CCGR depends
resist
oxygen
ability of an alloy to resist CCGR
in
air are probably linked to the same alloying additions which
53
0
da
dt
(m/s)
STRESS INTENSITY FACTOR, K (MPa1m)
FIGURE 2.12)
CCGR results for several Nickel-Base alloys for
both air and an inert environment
54
have been shown to eliminate
oxygen embrittlement in Ni-base
alloys described in section 2.2.
2.3.4.
Effect of Microstructure
Floreen
on
the
(35,
CCGR
increasing
decrease
in
The
the
in
Figure
factor
of
68) has studied the effect of grain size
IN-792 in air
grain
size
the CCGR.
2.13
versus
on CCGR in Ni-Base Alloys
as
at 7040 C.
It was found
that
from 8um to 250um results in a
The results for IN-792 are reported
a plot of the initial stress intensity
time to failure for precracked CT specimens.
finer grain size produced a sharp reduction in the time
to failure.
IN-718
Similar results were obtained by Pineau (67) on
6500°C and by Law and Blackburn (61) on AF 115 at
at
7040 C.
Wu and Pelloux (57) varied the heat treatment of IN-100
and studied its effect on CCGR at 7000 C in air.
are
shown
in
eliminated
showed
a
Figure
grain
2.14.
boundary
reduction
in
The
carbides
heat
The results
treatment
(treatment
C
which
and D)
stage II.creep crack growth rates.
Heat treatment C produced a smaller grain size (3.5 um grain
size),
resulted
than
in
heat
an
treatment
D
(40 um
grain
size) which
increase in the CCGR for treatment C.
The
results indicate that the CCGR of an alloy are significantly
affected by thermal treatment and processing.
55
Un
cc
0
o
%
0
oo
e CU
&l;
CM
C;
_
at
X
X
:D
(Z/.'NW)
4!suolul ss8J4s IO!l!ul
X
I
I - - - Ir
I
I
1
r
1
I
I
I
Iv'
I
1
z
-
id
E
(
4
-A
I0
lot
700'C
A
B
10
-
C
!
r-
zU
I
40
I
.
,,~~~~~~~~~~
60
I
89
!
!
100
I
150
K MPa/m
FIGURE2.14)
Comgarison of CCGRresults for IN-100 in air at
700 C with four different heat treatments (A-D).
(r-f. 57)
57
2.4.
Theories of Creep Crack Growth
Creep crack growth is generally thought to be a process
in which a single macro-crack advances through a material at
growth
the
and
existance
of grain boundary cavities ahead of
coalesence
crack.
Tm) as a result of the nucleation,
(T>.5
temperature
high
and growth result from the
nucleation
Cavity
high stresses and strains in the region ahead
of
of the crack tip.
Cavity
are
theories
growth
based
on
either
the
diffusional growth of cavities by vacancy transport or creep
is
essentially
exception
Creep constrained cavity growth
cavity growth.
constrained
that
as
diffusional
growth with the
the
same
the
cavity growth rates are limited by the
accommodation of the matrix via bulk creep plasticity.
one
of
models
the
above
based
are
been developed on the assumption of
have
models
CCGR
cavity
on
mechanisms.
growth
the
time
dependance
of
These CCGR
crack tip
stresses.
2.4.1.
A
Crack Tip Stress Distribution
study of creep crack growth theories must begin with
a description of the state of stress ahead of the crack tip.
Several
reviews of crack tip stress calculations have
good
been written by McClintock and Bassani (65), Huang (63), and
Bensussan
complicated
et.
by
al. (39).
The stresses ahead of a crack are
the accumulation of creep deformation which
relieves the stresses with time.
-58
the
In
are
dominant,
elastic region where the elastic strains ( e
the
)
stresses, for small scale yeilding, are
given by the usual singular field (69):
KI
fi
(0)
(Equ. 2.4)
aij /2Jrr
Where
KI
is the mode I stress intensity factor, "r" is the
distance ahead of the crack tip, and f(8)is a function which
varies with the angle from the plane of the crack.
In
tip,
plastically deformed region ahead of the crack
the
the
( P ) by
material is assumed to harden with plastic strain
ower law hardening:
sP=Bp (a)NP
where
eP
dependant
where
is
the
plastic
parameters.
plastic
strain
(Equ. 2.5)
strain, Bp and Np are material
The stresses at time=0 in the region
dominates
are
represented
by
the
Hutchinson, Rice, and Rosengren (HRR) singularities (70-72):
J
aij=
(l/(Np+l))
'
Bp
r
(Equ. 2.6)
fij (Np,®)
Np
where
N
p =
the
parameter
loading
is
the J-integral (73), and
X
As time increases creep strain will accumulate ahead of
the
accumulating
The
crack.
creep strain will relax the
crack tip stresses.
The
minimum creep rate with applied stress is given by
the following power law expression:
(Equ. 2.7)
6C=BC (a)NC
where
iC
is
the
creep
dependent parameters.
the
stresses
dominent
in
factor
the
are
rate,
Be
and
N
are material
If the plastic strains are neglected,
region where the creep strain is the
given
by
the
Riedel
and Rice (RR)
singularity (74) which is analogous to the HRR singularity:
60
ai. C(t) )(1/(NC+) )
ij
(B
I
r
fij (Nc,0)
(Equ. 2.8)
where C(t) is given below:
where
the
given
J
t<t tr
C(t) =
t>t tr
C(t)
-- .
(Equ. 2.9a)
C*
(Equ. 2.9b)
(Nc+l) t
C* is the time dependent C* integral (75), and ttr is
creep
transition
time.
The creep transition time is
by:
J
ttr
Another
expression
(N¢+l)
for
(Equ. 2.10)
C*
the
transition time has been
suggested by McClintock and discussed by Huang (63):
-
,e
ttr
where
c
anet
E nc
£
(Equ. 2.11)
is the creep rate in the far field, E is Young's
modulas, and
a
net
is the net section stress.
transition time approximates the time to relax the
The
stresses
the tip of the crack.
at
If t<< transition time,
the stresses have not relaxed significantly and the alloy is
called
If
creep-brittle.
the time/= transition time, the
stresses will have significantly relaxed.
The
for small scale yielding condition can
J-integral
be approximated as for plane strain (73):
J=
(1-v2 ) KT 2
(Equ. 2.12)
E
Therefore,
when the conditions of small scale yielding
apply
in
a creep brittle material the stresses and strains
ahead
of
the
conditions
modern
gas
crack tip can now be described by KI .
generally
turbines,
These
apply for Ni-base alloys operating in
and,
therefore, K I is the parameter
which is being used to correlate CCGR data.
61
- 62
CreeDi n
C_(t ) fia, 1
:=0
~0
()
V)
1
E
I
- in
alostic
field
/*
.4
.
-- -
Log r
--- -
(a)
--
_L
nc > np
O<t t 2 t3
FIGURE 2.15)
Schematic crack tip stress distribution versus time
in a creeping solid. (ref. 63)
63
above relationships are used to calculate
The
of
ahead
(63).
(Figure 2.15)
The
stresses are highest upon loading at t=0 and are
calculated
by
given
crack tip in Astroloy
a
stresses
the
HRR
singularity.
As
time
progresses the
stresses given by the RR singularity slowly relax.
2.4.2.
CCGR Models
There have been several attempts to predict creep crack
The models are based on
growth rates in metallic materials.
either
law
by
diffusional
of cavities (76-79) or by power
growth
creep deformation controlled cavity growth as suggested
(80).
Hancock
law
Power
has
creep
been
diffusional cavity growth by Argon (81) and Chen
2.4.2.1.
coupled to
(82).
Diffusional Creep Models
Diffusion
have
models
been
proposed
by Vitek (83),
Pilkington (84), and Raj. et al. (85):
da
Vitek:
.516 6 DB
4
4
(Equ. 2.13)
)
413
(2
2
D
da
Pilkington: . d
K
s
1
2(
2
1)d)/
Raj et al.:
da
7 x
K
3
)
kT 1s (1-TB/S)
n 6 D
K
(Equ. 2.14)
)(2
(x-Ro)
32
2
(Equ. 2.15)
1 05
E k T x
3
64
where:
- Young's modulus
E
- Grain boundary thickness multiplied by grain
6DB
boundary diffusion coefficient
- Atomic volume of controlling diffusion species
k
- Boltzman constant
T
- Temperature (absolute)
s
- Crack width
K
- Stress intensity factor
Ds
- Surface diffusion coefficient for controlling
species
Ts
- Surface energy of matrix
8B - Surface energy of grain boundary
Ro
- Radius of cavity nuclei
x .One-half cavity spacing.
.
The
diffusional
models predict a CCZR dependance on K
with a slope between 2 and 4.
CCGR tests performed
environments,
however., have
given
higher
in
(63)
strain
is
not
slope
results
which
in inert
have a
the Stage IIregion of creep crack growth.
These models do not account for the effect of plastic
on
the crack tip stress field, environmental damage
considered,
predicted.
and
the
Stage I CCGR behavior is not
65
2.4.2.2. Deformation Controlled CCGR Models
(84)
Barnby, (86) Nix, (87) and Pilkington.
N
da
dt
Barnby:
Nc
B K
da
Nix:
dt
C
net
o r
dt L
=
been proposed by
have
models
controlled
Deformation
(Equ. 2.16)
oo
(d) (-Nc/2 + 1)
(Equ. 2.17)
N /2
ln()
c (N-2)
(rr)
N
da
Pilkington:
dt
BcK c (2A)
-
(RL)°i
ln(R)
(-Nc /2 + 2)
(Equ. 2.18)
N /2
)
(Nc-2)
(2r)
0
"d"
where
the
is
grain size, and
a
net
is the net section
stress ( C=B CNc ).
The deformation models predict
on
K
is
the
approximately
behavior,
predicted.
models
do
by
given
but
the
that the CCGR dependence
N , the creep exponent.
slope
of
the
observed
This.slope
Stage
I
is
CCGR
observed stage two CCGR behavior is not
Again, as in the diffusional CCGR models, these
not predict any effect of environment.
of CCGR models was given by Huang
(63)
A review
66
2.4.3. Iterative CCGR Models
An
iterative
Huang (63).
computer
This model calculated damage ahead of the crack
tip
in
the
grain boundaries
terms of average grain boundary cavity radius along
advances
The crack tip
when the average cavity size
the cavity spacing in the grain immediately ahead of
crack tip.
HRR,
ahead of the crack tip.
by one grain-diameter
equals
the
model of CCGR was attempted by
RR,
and
Huang calculated
the stress field using the
elastic singularities already described, and
the stresses were allowed to relax with time.
The idea of damage accumulation and creep relaxation of
stress
represent
a realistic view of the actual conditions
which are believed to exist during creep crack advance.
slope
of
crack
advance and K.
decrease
model
CCGR
as
damage
proposed
on
decreases
the
the predicted
K
in
CCGR versus K curves will vary with
The slope will be initially large and
accumulates
by Huang
the
The
ahead
of the crack.
The
(63) predicts a high dependance of
region
of
Stage I growth.
The slope
with. increasing K as a result of the increase in
number of grains in the plastic zone ahead of the crack
tip.
The
the
only major problem in the Huang model results from
calculation
loading
rather
direction
than
the
of
stress versus time.
was
used
equivalent
The stress in the
to predict cavity growth rate
stress.
The stress
in the
67
is much larger than the equivalent stress.
loading direction
An adjustable parameter
prediction of stress.
over
relaxation
no
a11 (0) was used to correct for this
The model also assumes there is
of stresses ahead of the crack tip until the
the
RR-singularity
stresses
predicted
by
stresses
calculated
from the HRR-singularity.
the
ahead
of
after
loading
crack
plastic
the
creep
creep
with
tip should begin to relax immediately
The RR singularity is only valid at t=O
strains
are
small when compared to the
strains.
However, This is not the situation ahead of
tip
at t=O in creep crack growth. The stress and
crack
the
The stresses
due to-the high stresses in the plastic zone
ahead of the crack.
when
drop below the
strain accumulation at a point ahead of the crack tip
time
is
shown
schematically
in
Figure
2.15.
The
consequence of assuming the stress relaxation beginning with
t
=
0
is
that
creep strain accumulates too fast and the
creep crack growth rate is over-predicted.
68
HRR
""I
3)
TIME
,-,r
.c
HUANG
CREEP
STRAIN
TIME
FIGURE 2.16)
Stress and strain ahead of the crack tip versus
time from the computer model given by Huang(63)
and the predicted values in the present model.
69
EXPERIMENTAL PROCEDURES
3.1
Materials
Four
/ y'
nickel base superalloys were chosen for this
study.
They
IN-100,
and
varying
susceptibility
oxygen.
alloys
each
are
Rene-95.
The
alloys
into
alloy
Low Carbon Astroloy, Merl-76, Low Carbon
These
alloys were chosen for their
to grain
boundary embrittlement in
were produced by HIP processing of PM
9/16" diameter rods.
is
shown
particle diameter.
in
The powder mesh size for
Table 3.1 along with the maximum
Rene-95 was obtained in two mesh sizes.
Table 3.1
-
Powder
Mesh
S.ize
Particle diameter, pm
Size
Astroloy
100
149
Merl-76
325
45
IN-100
60
250
Rene-95
60
250
Rene-95
120
125
70
Chemistry and Processing
3.1.1.
The
thermal
and
HIP
processing
alloys
are given in Table 3.2.
chosen
to
yield
parameters
for the
The heat treatment used was
similar mechanical properties for all the
alloys.
TABLE 3.2.
--
I
Thermal Processing
--
1.
HIP Cycle
a.
Astroloy - 12320C/4 hours/Furnace cool/15 Ksi
b.
IN-100, Merl-76, Rene-95 - 11770 C/4 hours/
Furnace Cool/15 Ksi
2.
Heat Treatment
Solution:
Age:
1177 C/4 hours/air cool
871°C/8 hours/air cool
982 C/'4 hours/air cool
650 0 C/24 hours/air cool
760C/8
The
alloy
hours/air cool
chemistries
were
determined
adsorption and wet chemistry by Luvac, Inc.
using atomic
The chemistries
71
and
microstructures
The
calculated
given
Table
in
elements
for the alloys are given in Table 3.3.
volume fraction for each alloy is also
y'
3.3.
(3.1)
The
trace
which segregate to the grain boundaries such as B,
Zr, C, O, P and S were determined.
powder
of
concentration
particle
size
were
The grain size and prior
determined
via
linear
the
intercept method. (98)
TABLE 3.3.
Alloy Chemistries and Microstructure
Sample
1
Molybdenum
Columbium
Aluminum
Titanium
Hafnium
Vanadium
Nitrogen
3.97
3.39
14.0
7.71
3.33
3.36
3.31
2.41
12.2
17.8
3.20
1.36
4.71
4.19
.01
.01
.10
12.2
18.3
3.39
<.01
4.88
4.17
<.01
<.001
.,007
.009
.97
.044
.082
.034
.025
.037
.0129
<.001
.014
.0008
.007
.020
.050
.0238
.082
.021
.037
Silicon
Iron
Tungsten
y' Volume Fraction
(Calculated)
Grain Size (um)
Prior Powder
Size (um)
Remainder
0.50
28
I
95
,
.064
.0137
.001
<.001
.0020
I
4
.0111
<.001
<.001
<.001
<.001
.07
.18
.02
.24
Nickel
Sample
IN-100
.004
Carbon
Boron
Zirconium
Oxygen
Sulfur
Phosphorus
3
Sample
Merl-76
14.8
16.3
4.82
Cobalt
2
Rene-95
Astroloy
Chromium
Sample
.0029
.0016
.10
.04
.077
.082
3.42
Remainder
Remainder Remainder
0.52
25 and 24
11
70
and _ 34 _
I,
22
0.58
0.63
23
I
-
35
-
,
-
-72
3.1.2. Microstructural Characterization
in
of heat treated material were mounted
samples
Several
Buehler plastimet, ground on 240, 320, 400, and 600 grit
paper, polished with 3 um diamond paste on
carbide
silicon
with
polished
finally
and
cloth,
nylon
silica ..solution) on nylon cloth.
(colloidal
Nalcoag
1060
The specimens
etched using No. 2 stainless reagent (100 ml methanol,
were
50 1 HC1, and 5 gm FeC1 3 ).
specimens were observed under both a Zeiss
The/ etched
Astroloy have a coarse
a
finer
grain size with large
' particles along the boundaries.
Prior
boundaries
powder
all
in
magnification
usually
have
Rene-95
and
and
carbides decorating the grain boundaries.
with
size
primary
result
were
easily observed at low
the alloys tested.
These boundaries
grain boundaries.
The prior powder
with
coincide
boundaries
the
IN-100
respectively.
Merl-76
AMR-1000 A scanning
an
microstructures of Astroloy, Merl-76, IN-100, and
treatment
Rene-95
and
Figures 3.1 - 3.4 show the after heat
microscope.
electron
grain
microscope
optical
Universal
from
the existence of large carbides on
surface of the powder particles.
These carbides do not
go
into solution on subsequent heat treatment.
In the case
of
Rene-95
are
known to be
and
Columbium
carbides,
probably
are
segregate
to
while
Titanium
during
precipitate
these
Merl-76
the
in
carbides
Astroloy
carbides.
solidification
powder
surfaces.
(3.2)
of
The
and
IN-100
These
the
carbides
powder
prior
they
and
particle
73
(a)
(b)
FIGURE
3.1)
Photomicrographs of PM/HIP low carbon Astroloy.
(a) optical, (b) SEM (etchant: 100ml Methanol,
50ml HC1, and 5g FeC13 )
74
(a)
(b)
FIGURE 3.2)
Photomicrographs of PM/HIP MERL-76. (a) optical
(b) SEM (etchant: 100ml Methanol, 50ml HCl, and
5g FeC13 )
75
(a)
(b)
FIGURE 3.3)
Photomicrographs of PM/HIP low carbon IN-100.
(a) optical, (b) SEM. (etchant: 100 ml Methanol,
50 ml HC1, and 5 gm FeC1 3 )
76
(b)
(a)
(c)
FIGURE 3.4) Photomicrographsof PM/HIP RENE-95. (a) optical
(60 Mesh), (b) optical (120 mesh), (c) SEM.
(etchant:100ml Methanol, 50ml HC1, and 5g FeC13)
7-7
boundaries
grain
have
a
boundaries
higher
which
concentration
are
not
along
of carbides than
the
prior powder
particle boundaries.
3.2.
Mechanical Testing
Different
the
mechanical tests were performed
to determine
high temperature tensile, creep, and creep crack growth
behavior
of
the alloys.
The test procedures are described
in the following sections.
3.2.1.
Tensile Testing
Tensile tests were performed using a screw driven floor
mounted Instron Tensile Tester.
and
An
The tests were run at 7040 C
a crosshead displacement rate of .02 inches per minute.
A.T.S.
three-zone
resistance
heater
with a Leeds and
Northrup Electromax III temperature controller were used for
specimen
a
The
heating.
Load vs. Displacement was recorded
using
strip chart recorder incorporated in the Instron machine.
.2%
yield
stress
measured graphically.
measured
and
ultimate tensile strength were
Elongation and reduction of area were
directly off the failed test specimen.
illustrates
the
Figure 3.5
specimen geometry used in both tensile and
creep-rupture tests.
-78
2 -
-
NF-3A
2 PLACES
FIGURE 3.5)
Smooth bar creep-rupture and tensile specimen
geometry. (Dimensions in inches)
Smooth Bar Creep Testing
3.2.2.
were
tests
Creep
conducted
obtain the power law
to
constitutive equations for the purpose of theoretical
creep
accurate
was
temperature
test
The
determine
the
Creep tests were
within stress range of 600 to 1200 MPa.
704C
at
conducted
the alloys.
of
properties
creep-rupture
to
and
growth,
crack
creep
of
modeling
to
within
4°C.
The
elongation was measured using an extensometer connected to a
tester.
arm
level
data
per
points
mV,
and a
stress versus minimum creep rate
Smooth
specimen.
bars were tested at a
and the time to rupture was recorded as well
load
constant
100
The stress was increased in steps in
several
obtain
to
per
The minimum creep rate was recorded for
several stress levels.
order
range
inch
Tests were conducted on an A.T.S.
1 micron.
of
resolution
.25
a
with
LVDT
dc-dc
as the minimum creep rate.
3.2.3.
Notched Stress Rupture Testing
root
of
radius
air
in
.33 mm,
The notch has 60° flank angles, a
and
factor of 3.2.
concentration
in
3.6.)
(Figure
testing.
an
heater.
recorded.
The
The
tests
a
calculated elastic stress
Tests were conducted at 7040 C
level arm test system with a 3-zone
A.T.S.
resistance
specimens were used for NSR
notched
Circumferentially
time to rupture for each test was
were
performed
in a range of stress
from 400 MPa to 800 MPa. Several specimens of PM/HIP Rene-95
80
2ZO-UF-3A
2 PLACES
I1
FIGURE 3.6)
Notched Stress-Rupture (NSR) specimen geometry.
(Dimensions in inches)
81
pre-exposed to air at 7040 C to determine the effect of
were
oxygen on the notched stress rupture (NSR) behavior.
Creep Crack Growth Rate Testing
3.2.4.
a constant applied load in a level arm tester supplied
with
by
growth rate tests were conducted at 7040C
crack
Creep
was
controlled
using
specimen
System Company (ATS).
Testing
Applied
a
in
4°C
within
resistance
3-zone
retort
argon.
A
tests.
Argon
ATS
by
supplied
gauge section of the
heater.
Tests were
air and 99.999 percent pure
in two environments:
conducted
the
The temperature
was used in the argon
tests were conducted at a pressure of 5 psig
in order to insure no back streaming of air.
A
crack
creep
has
side
grooves
Tunnelling
growth
rate tests.
growth
added
specimen was used in the
test
edge-notched
single
to
(Figure 3.7) The specimen
prevent crack tip tunnelling.
of the crack results from the slower creep crack
rate in the plane stress condition which would exist
on the specimen surface without side grooves.
A
notch
is
cut using a 150 um thick diamond
Specimens were fatigue precracked at room temperature.
saw.
The
starter
maximum
always
stress
K, used in precracking was
intensity,
less than the initial stress intensity in subsequent
0
creep crack growth testing at 704 C.
82
i
2 PLACES
I
I
.I
~.
%A
.
.
I
CHAM.1.5-2.0
x 45APPROX.
2PLACES
25.4
-59 -
-
- -
76.2 REF.
-
P
I
J--
'
"'IA
"
I
-
"
111.7
j
4.76R
4 PLACES
.
I
i
l)
'
H
127-20-UNF-3A
2 PLACES
4 PLACES
1
r
-,4.76R
476~
Y
U--
FIGURE 3.7)
\
0114.4b\
rT7sz2T
I A
r
I
E
Single Edge Notched (SEN) specimen geometry
used in CCGR tests. (Dimensions in mm)
83
3.2.4.1.
D.C. Potential Drop Technique
electrical potential drop method is based on
d.c.
The
the
fact
such
as
in a current carrying body, a discontinuity
that
a crack, results in a disturbance in the potential
field.
order to monitor the crack length, a current is
In
passed
through
across
the
length
causes
either
side
the
mouth is measured.
crack
monitoring
potential
the
of
this
and the electrical potential
specimen
the
crack
(V),
to
two fixed points on
increase.
increase
potential
reference potential
between
An increase in crack
By continuously
and comparing it to a
the crack length to specimen width
ratio (a/w) can be inferred.
Several
potential
solution
theoretical
have
by
solutions for crack length versus
been made by solving Laplace's equation.
Johnson
(88)
developed
A
for a center-cracked
plate specimen with a razor slit starter is as follows:
cosh-l
V
V
Johnson
1
cosh(7Y/W)
cos(lwa/W)
-
cosh
1
cshYW(Equ.
3.1)
cos (raY/W)
later
worked out a similar solution for a SEN
specimen with a razor sharp slit starter notch (89):
84
cosh
1
V 0 = c° h
1
V0
In
both
cosh_
cosh(wY/2W)
(Equ. 3.2)
cos(Tra/2W)
cosh(nY/2W)
1
cos(ao/2W)
equations V is the measured potential, V
is
0
the
measured
potential
for a crack of length a , Y is one
0
half
the
leads,
distance
'a'
specimen
and 2a
is
between
the
crack
length
the
two potential measurement
(for the center-cracked
the crack length and reference crack length are 2a
respectively), and W is the specimen width.
Other
Che-Yu
theoretical
calibrations have been performed by
Li and Wei (93) who modified Johnson's relations for
an elliptical starter notch.
Recent work has been performed
on modeling the potential distributions using finite element
techniques
(94).
The
finite
element
solutions
verify
equation 3.2 by Johnson.
The
shown
to
theoretical
calibration
by Johnson (89) has been
be valid for the SEN specimen geometry in several
experimental calibrations
(63, 90-92, 94).
Figure 3.8 shows
the results of a theoretical and an experimental calibration
for
was
the
SEN specimen shown in Figure 3.7.
accomplished
by
growing
temperature while monitoring
was
measured
a
fatigue
The calibration
crack
at
room
the potential. The crack length
by periodically altering the R-ratio to beach
85
L
-J
I
D.C. POTENTIAL DROP: EXPERIMENTAL CALIBRATION
Linear Approximation
-
-
-Theoretical
-
Calculation (ref. 89)
(W=11.7mm; a=1.05mm;
Y=1.30mm)
5
4
V
-IJ,
v
ao
3
_
/~~~~P
2
]
2
1
3
4
5
a/a O
FIGURE 3.8)
-
Experimental calibration of the d.c. potential
drop technique for crack length measurement for
the SEN specimen shown in figure 3.7.
6
86
fracture
the
mark
surface.
Agreement between the actual
data and the theoretical calculation were obtained.
3.9. shows a schematic for the test system used
Figure
in
creep
was
growth testing.
crack
off-the-sheif
and
did
not
All of the equipment used
have
to
be specifically
manufactured.
There
exists
several
sources
of potential errors in
this method of crack length measurement from both electrical
and configurational
source
A
from
of
sources.
electrical error which is possible comes
the DC power supply used as a constant current source.
A Hewlett- Packard Regulated DC Power Supply Model 6295B was
used in this study.
Possible errors are:
1.)
Current Drift -The current output can drift
by .05% in an 8 hour period
at constant
temperature.
2.)
Temperature Variation -Ambient temperature
variation can cause a variation of .012%/°C
in a range
from 20 to 400 C.
3.)
AC Line Variation -Variation in AC line current
can cause .012% variation in DC output current.
40)
Ripple -Background current fluctuations of
.05% peak to peak are possible with system.
5.)
Insufficient Warm Up Time -Significant variation
in output current and voltages can occur if
the power source is not allowed a 30-minute
warmup.
6.)
Plotter Accuracy -The Omega plotter has an
accuracy of .5% of full scale. With a typical
full scale of 1OmV the error becomes 50 uV.
-87
DC POWER SUPPLY
HP -
G2 59B
O.-- 50AMP O-10V
SOL
__
rEC
DB-2
RECORDER
10 MV± 0.05 MV
'FIGURE
_____
3.9)
Schematic of the d.c. potential drop system
for crack length measurement.
88
In
a
time
24-hour
.33% maximum variation in output current is
a
temperature,
is small and not detectable with
variation
This
possible.
a 100 C variation in
with
period
Using the calibration curve
the recorder used in the study.
in Figure 3.8 and assuming an initial voltage of 2 mV yields
a minimum resolution of 60 microns change in crack length.
of
Analysis
by
performed
of
variation,
electrical
temperature
Electrical
variations.
geometry
and
variation have been calculated to cause a limit
temperature
of
been
The sources
and
variations,
has
several researchers (90-92, 95).
include
error
error
of
sources
potential
in crack length resolution for a compact tension
100 um
specimen
(95).
position
can
Configurational
cause
variations
errors
extreme
such
as lead
and should be tightly
controlled.
The
potential difference method requires careful
d.c.
positioning
measurement
of
both
leads.
leads
current-input
The
and
potential
positioning will affect the
lead
sensitivity and precision.
The current leads should be positioned at a distance of
at
least
of
the
Closer positioning
2w from the crack plane (90).
leads
reproducibility
the
increases
and
increased
sensitivity
insulated
from
the
therefore
is
sensitivity,
demanded.
loading
only
should
frame
but
be
reduces
used when
The specimen must be
in
order to force the
current to pass only through the specimen.
The current lead
be large enough to conduct up to 50 amps d.c.
should
wires
current.
close
as
leads
measurement
potential
The
should be placed as
possible and across the mouth of the crack.
This
has been shown to give the best reproducibility
positioning
sensitivity (90).
while maintaining
The contact area of the
potential lead wires should be small, and wires on the order
of .2 mm in diameter are usually used.
high
creep
in
leads
leads
measurement
discharge
welding
to
is
the
These welds should be strong enough to endure the
environment
oxidizing
and
temperature
during
potential
electrical
by
accomplished
specimen.
the
of
Attachment
crack growth rate testing.
studies
several
have
experienced
The current input
been attached outside the
heating furnace and passing the current through the specimen
grips thus eliminating some problems of attachment.
The calculated value for crack length given by equation
will vary significantly with the potential lead spacing
3.2
The variation in the theoretical calibration is shown
''V.
in
for
3.10.
Figure
three
values of Y which represent a
lower limit, upper limit, and nominal spacing.
errors can be eliminated by stopping the
Configuration
test
before
in
temperature
final
crack
surface.
termination
and
failure
fatigue.
length
can
breaking
An
be
the
accurate
obtained
specimen
at room
measurement of the
from
the
fracture
This along with the potential measurement at test
will
give
a point with which to calibrate the
90
rb
7
6
V
V0
i
4
3
2
.1
a/W
FIGURE 3.10)
-
Comparison of the effect of potential measurement
lead spacing, Y, on the potential versus crack
length curve. SEN specimen geometry. (equation 3.2)
91
The
test.
used
are
and initial crack lengths and potentials
final
to
the
eliminates
the lead spacing Y.
calculate
major
of
source
This procedure
configurational
error in
crack length measurement.
effect
The
crack tip bowing on the d.c. potential
of
drop technique has been analyzed by Druce and Booth
a significant under-prediction
indicate
short
if
cracks
addition
side
of
(39,
researchers
a
length for
of crack
crack front is assumed.
straight
on
grooves
(92) who
SEN
63) eliminates
specimens
by
The
several
the plane stress condition
at the specimen surface and reduces crack tip bowing.
Data Analysis
3.2.4.2.
The
the
crack
potential
potential,
V,
length
versus
to
versus time data is calculated
from
The conversion
from
time
crack
results.
length,
'a', is given by solving
equation 3.2. for crack length:
aljn)
gg
i,(
-1
2
ccosh(crrY/2W)
cV
- l Jo
lrs
C
IVo ~
The
slope
points
of
1=osh(Y/2W)
(Equ. 3.3)
cos(0rao/2W)
crack growth rate is calculated by determining
a
must
least
span
squares fit to 3 data points.
.2 mV
in measured potential
times the limit of resolution).
the
The data
(which is 4
92
The stress intensity factor, K, for the SEN specimen is
given by Brown and Strawly (96):
K = ar
(1.12-.23(a/w)+10.6(a/w)
+30.4 (a/w) 4 )
K
where
is
the
2
-21.7(a/w)
intensity
stress
3
factor, a
(Equ. 3.4)
is the gross
section stress in MPa, 'a' is the crack length, and w is the
of
width
notched
the specimen.
specimen
(SEN)
This equation is for a single edge
which
is free to bend.
The gross
section stress for a notched specimen is given as:
P
a=
(Equ. 3.5)
W V"B*BN
.I,
where
P is the applied load, B is the gross thickness,
and BN is the net section thickness
N
(97).
93
3.3 Pre-exposure Oxygen Penetration Tests
in
of each material was
air at 7040°C for 100 hours with no applied load
to
exposed
3.7)
(figure
specimen
SEN
One
The
order to allow oxygen to diffuse into the material.
were
bars
using
notched
fatigue-precracked
room
at
temperature exposure.
a
150 um thick diamond saw, and
before
temperature
the
high
The bars were pulled to failure in an
0
with extension
screw driven tensile tester at 704 °C
Instron
rate of .2 inches/minute.
The
depth of inter-granular fracture is measured.
fracture
intergranular
of
(30).
alloys
the
The
is a result of oxygen embrittlement
An apparent
diffusivity
of oxygen
is
calculated using the following equation:
D= X2 /t
x
where
exposure
is
time
the
(Equ. 3.6)
depth of intergranular fracture, t is the
(3.6 x 10 seconds),
and
D
is the apparent
diffusivity of oxygen along the grain boundary (30).
3.4. Fractography
The
scanning
fractography
electron
was
performed
microscrope.
using
an
AMR-1000
The specimens were cleaned
-\~~
with
acetone
and
oxidized surfaces.
coated
with
gold
to avoid charging of
~~9
95
4. EXPERIMENTAL RESULTS
4.1.
at 7040 C
Tensile Properties
The
4.1.
tensile
The
results at 7040 C are shown in Table
test
0.2% yield strength, Elastic modulas, and U.T.S.
measured for all the alloys are approximately
total
elongation
Rene-95
to
ductility
exhibited
cracks.
The
(P=
The
varies by a factor of three from 5.0% for
15.4%
for
Astroloy.
The
specimens with low
failure via the propagation
plastic
proportionality
the same.
strain
constant
B
hardening
are
of surface
exponent
Np and
also given in Table 4.1.
(/ B )P )
TABLE 4.1.
704 0C Tensile Test Results
U.T.S.
.2% Y.S.
(MPa)
(MPa)
Rene-95
1199
947
IN-100
1167
MERL-76
Astroloy
.
,
% El.
E
Bp
Np
(GPa)
(MPa)
5.0
167
1785
1012
8.4
162
1454 16.39
1164
1012
13.1
160
1448 16.67-
1200
950
15.4
170
1662
8.93
9.71
i
..
96
4.2.
Smooth Bar Creep Results
Minimum Creep Rate Results
4.2.1.
The
air
7040 C
at
in
a
range
applied stress from 600 to
of
The results are given in Figure 4.1 as a plot of
1200 MPa.
stress
creep rate for each alloy was measured in
minimum
The creep exponents, Nc,
versus minimum creep rate.
constants, Bc, for the-power law equation for secondary
and
creep
rate are given in Table 4.2.
range
from 10 -8 sec
all
-4
to 10
sec
-1
The creep
.
alloys measured is similar.
four
exponent
creep
-1
The minimum creep rates
behavior
of
Rene-95 has a larger
(Nc) and proportionality constant (Bc) than
the other alloys.
TABLE 4.2.
Minimum Creep Rate Results at 7040 C
.
I
gc(sec
I
-1)
I I
=
Bc(a(MPa))
B
I
Ill
I
I
Nc
6.29 x 10
61
18.5
Merl-76
1.66 x 10- 65
20.0
IN-100
7.81 x 10-61
18.5
(60 meesh) 4.03
x
II
c
Astroloy
Rene-95
II
10 - 3 7
10.3
---
97
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4.2.2.
Creep Rupture Results
Four
creep-rupture
performed
at
800 MPa
tests
in air
(one
from each alloy) were
at 704 C. The
results
for the
four alloys were similar with the exception of Merl-76 which
gave
a
longer time to rupture.
The individual results are
shown below:
-
-
Table 4.3.
Creep-Rupture Results, Air, 7040 C, 800 MPa
t (hrs)
ecritical
Rene-95
7.2
.0083
IN-100
4.7
.0068
Merl-76
28.7
.0202
Astroloy
5.8
.0068
- -
Table
failure.
minimum
constant
4.3.
The
creep
also
shows the secondary creep strain at
secondary creep strain is the product of the
rate and the time to rupture.
This value is
for an alloy at a given stress, which is the basis
for the well known Larson-Miller parameter used to correlate
creep-rupture results.
-
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Notched Stress Rupture Results
4.3.
4.3.1.
Constant Load Results
Notched
all
rupture
(NSR) tests were performed on
alloys in air at 704°C.
four
Figure 4.2.
rupture
stress
The results are given in
The results indicate that Rene-95 has a shorter
time
than
the other three alloys tested.
At high
Merl-76 gave the longest time to rupture, but at the
stress
lower stress a crossover occurs and Astroloy has the longest
time to rupture.
NSR results can be interpreted as giving a measure
The
of the relative CCGR behavior of the four alloys when tested
in
Astroloy
air.
had
the longest time to rupture at the
lower stress, but at the higher stress Astroloy'fails sooner
than IN-100 and Merl-76.
4.3.2. Air Pre-Exposure Results
Three
for
100
hours
specimens
were exposed to air at 7040 C
prior to NSR testing.
Some specimens had a
applied load during the pre-exposure.
small
run
Rene-95
to
failure
at
a
higher stress i, air
results are summarized in Table 4.4.
They were then
t 7040 C.
The
101
TABLE 4.4.
Notched Stress-Rupture of Rene-95, 704 C
Pre-exposure
Test Results
408 MPa/403.4 hrs.
675 MPa/<1 min.
No Pre-exposure
591 MPa/137.2 hrs.
0 MPa/73.4 hrs.
591 MPa/237.8 hrs.
338 MPa/69.0 hrs.
571 MPa/153.8 hrs.
The
tests were inconclusive but they did present a few
interesting
tensile
with
no
results:
1)
pre-exposure
in air with a small
stress was more damaging than a pre-exposure to air
stress;
and
2)
a long pre-exposure with a small
stress exhausted the residual life at the higher load.
1C2
Creep Crack Growth Rate Results
4.4.
CCGR for Five Ni-Base Alloys
4.4.1.
air
The
creep crack growth rates were measured at 7040 C in
and
in
low
They were
low carbon IN-100, Rene-95
Merl-76,
Astroloy,
carbon
The
on all five alloys.
argon
were all in the PM/HIP condition.
tested
alloys
pure
99.999%
(60 mesh), and Rene-95 (120 mesh).
could
be
not
made to grow if the
K used in pre-cracking the specimen was higher than
maximum
K
initial
the
cracks
creep
The
CCGR
probably
is
growth
for
to
imposed
stresses
compressive
due
The lack ofcreep crack
testing.
the
by
presence
the
of
residual
larger plastic zone
remaining from the fatigue precracking.
4.4.1.1.
CCGR of PM/HIP low C Astroloy
The
results
of
6 CCGR tests on PM/HIP low C Astroloy
in Figure 4.3.
are
shown
and
exhibited
an
Four tests were performed in air
increasing
da/dt versus K, but the CCGR
not linear over the entire range of K tested.
curve
was
three
stage
creep
crack
growth
curve was obtained.
A
The
lowest initial K in air was 22 MPavi, and the lowest initial
K in argon was 33.2 MPa i.
The
by
a
tests had an initially large rise in CCGR followed
region
of decreasing slope.
The slope in the second
region was approximately 3.5 in air and 7.0 in argon.
103
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o\
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C'#
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s.o
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(S/W) ?P/DP
104
at
argon
CCGR
for
but
K = 70 MPa
i the air and
are the same at 3.5 x 1-6 m/s.
curves
The two
at high crack growth rate indicating that the
merge
curves
100 times faster in air than in
is
air
K = 40 MPa'm-,
argon
was advancing faster by creep fracture with no
front
crack
in
CCGR
The
effect of oxygen embrittlement.
CCGR of PM/HIP Merl-76
4.4.1.2.
Four CCGR curves in air and two CCGR curves in argon at
7040 C
were obtained.
The results in air were
(Figure 4.4)
and an
for gross section stress from 145.6 MPa to 655.0 Ma,
length
1.01 mm
from
to 2.62 mm.
The CCGR
initial
crack
results
in air increased 20 times over the CCGR in argon at
K = 40 MPa-m.
The behavior in air and in argon are similar
Astroloy.
All the tests have an initially fast increase
to
in the CCGR followed by a region of linearly increasing CCGR
on
a
log-log
plot.
slope
The
of the air CCGR versus K
curves
are approximately 3, and the CCGR tests in argon had
a slope
of
A
observed
4.
rise
definite
in
the
CCGR
measured
failure at K = 80 MPa/,
before
in
air was
while in an argon
atmosphere the final K was approximately 110 MPaii.
measured
CCGR
The
in
air
away
from
the
initial
transient was slightly higher in specimens which had a lower
gross- section
change
in
stress.
dK/da
with
This effect is probably due to the
gross stress in the specimen.
result will be discussed later.
This
105
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a,
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1C6
4.4.1.3.
The
CCGR of PM/HIP Low C IN-100
Both air and high purity argon CCGR results are
Figure 4.5.
in
CCGR
The
given.
for PM/HIP Low C IN-100 at 7040 C is shown in
CCGR
air increased to 4 times the CCGR in
The apparent
at K = 40 MPaAH.
argon
for IN-100
KIC
in both
air and argon was 100 MPF/m.
The
effect of dK/da on the CCGR in an argon atmosphere
is easily observed.
The higher the gross section stress the
lower the CCGR for the same stress intensity factor, K.
4.4.1.4.
CCGR of PM/HIP Rene-95 (60 Mesh)
(60
Rene-95
mesh)
showed
the
largest
environment on the creep crack growth behavior.
The
effect
of
(Figure 4.6)
CCGR in air was 300 times higher than the CCGR measured
in argon.
CCGR
KIC at 704 0 C was observed to occur at 80 MPai.
tests in air were performed over a range of gross
91 MPa
from
to
291 MPa, and a range of
section
stresses
initial
crack lengths from 1.40 mm to 3.35 mm.
of
air
the
tests
were
similar,
The results
but the effect of gross
stress on the Stage II CCGR was observed in this alloy as in
all the previous alloys tested.
The
behavior.
and
in
CCGR
CCGR
The
increased
CCGR
was
results
crack
indicate
similar
CCGR
growth rates were initially very low
rapidly with crack advance.
followed
initial
This sharp rise
by a region of gradually increasing
over a broad range of K.
The slope of the CCGR versus
107
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K
II in air was 2, and for purified argon the
Stage
curve
slope was 4.
CCGR of PM/HIP Rene-95 (120 mesh)
4.4.1.5.
change in the CCG behavior at 704 0C between an air
The
and an argon atmosphere was not as pronounced as
atmosphere
was
for
observed
larger mesh size. (Figure 4.7)
The
the CCGR in air over the CCGR in argon is only
in
increase
the
10 times.
The CCGR in air for the finer 120 mesh size is the same
as the larger 60 mesh size Rene-95.
a faster CCGR in an argon atmosphere.
result
The difference is the
size and powder particle size variations.
grain
of
The finer mesh size has
the prior particle boundaries in argon,
follows
The
crack
but
it follows the grain boundaries in air.
The finer mesh
size has a faster CCGR in argon because of the smaller prior
particle size, but the grain size for both mesh sizes is the
same (grain size = 25um.)
Effect of Initial Stress Intensity Factor
4.4.2.
The
from
K
704 C
initial
stress
= 14.2 MPam
in
quickly
43.2 MPaii
air atmosphere.
an
to
to
intensity
factor, Ki, was varied
for PM/HIP Merl-76 at
(Figure 4.8)
The CCGR rises
a region of gradually increasing CCGR versus K.
The initially low CCGR results from the lack of damage ahead
of
the
occurred,
crack.
the
Once the first jump in the crack front has
crack tip encounters material which has been
110
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112
creep
and
oxidation
damaged ahead of the crack tip.
This
damaged material requires less time (and creep ductility) to
fracture
and
increases
ahead
the
until
of
the
crack
growth
increases. The CCGR
the dynamic process of damage accumulation
crack
tip
and
equilibrium.
The *.CCGR depends
history,
stress
the
rate
the
on
intensity
crack
advance
changes
factor,
and
in
reach
the load
dK/da in the
specimen.
4.4.3.
Comparison of CCGR in Air
A comparison of CCGR versus K curves for all the alloys
in
air
indicate
to
in
is
given
in
Figure
4.9.
The results
all the alloys exhibit CCGR between 10 - 7 m/s
that
10-5 m/s
slopes
4.
7040 C
at
in
a
range
of
K from 20 to 100 MPa/i.
The
the stage II region of the curves vary from 2 to
Astroloy
and Merl-76 have the lowest CCGR in air while
Rene-95 (60 and 120 mesh) and IN-100 have the fastest CCGR.
In
all
the
intergranular.
intergranular
alloys
Fracture
the
fracture
surfaces
in
path
is
totally
Astroloy
have
prior particle boundary cracking at K greater
than 60 MPai-.
4.4.4.
A
alloys
in
The
Comparison of CCGR in Argon
comparison
of
the CCGR versus K curves for all the
in argon at 7040C is shown in Figure 4.10.
argon
are
compared
The CCGR
to the air results in Figure 4.11.
CCGR for all the alloys is higher in air than in argon.
113
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The
slopes
of the stage II region of crack growth in argon
is higher than in air and it ranges from 3.5 to 6.
has
Astroloy
the lowest CCGR at low K, but Merl-76 becomes slower at
higher
K
values.
Rene-95
(120 mesh) and IN-100 have the
fastest CCGR in argon at all values of K.
fracture ..path
The
grain
boundaries
which
in
argon
are
also
is intergranular, along
prior
powder
particle
boundaries.
4.4.5.
Validity of K Correlation of CCGR
CCGR curves for Merl-76 in air are shown in Figure
The
These results are for a range of gross section stress
4.8.
from
145.6 MPa
Stage
II
to
and
655 MPa.
The
CCGR for Merl-76 in the
Stage III regions of creep crack growth rate
versus K curves indicate a K-dependancy on crack growth with
a
scatter
of
approximately
of magnitude
in
There
is
higher
crack
growth rate for a lower initial K and a lower
gross
section
value
of
stress.
dK/da
5.
A
trend
an order
CCGR.
chapter
a
half
in
the
in the results which indicate a
This behavior is attributed to the
specimen; it will be explained in
good correlation exists between da/dt and K
for all the alloys tested in both air and argon with scatter
being
result
within
should
creep-brittle
one half an order of magnitude in CCGR.
not
and
characterized by K.
be
the
surprising
crack
This
since the materials are
tip
stresses
are
well
116
initial transient behavior, Stage I cracking, does
The
crack
initial
is
this
not
cracking,
growth rate increases with increasing K, but
but
Tests which are performed at a
true.
always
initial
large
In general it is observed that the
K.
with
correlate
not
intensity
stress
directly
proceed
never
exhibit
stage II
from Stage I to Stage III
crack growth.
I
Fractography of CCG Tests
4.4.6.
fracture path for all the creep crack growth tests
The
was intergranular.
The tests in argon fractured along grain
boundaries which coincided with prior powder boundaries.
In
air the cracks were not limited to prior powder boundaries.
precracking was performed at room temperature.
Fatigue
fracture path of the fatigue precrack
The
crystallographic
can
be seen in Rene-95 (120 mesh) and IN-100. (Figure 4.11)
The
transition
crack
growth to creep crack
as a sharp fractographic transition for all
appears
growth
fatigue
from
the alloy tested.
The transition from creep crack growth to fast fracture
is
also
transition
very
the
which
ductile,
is
transition
more
mixed
between
difficult
surface observed for CCG in air and
fracture
observed
to
The sharp
from the difference between the brittle
results
intergranular
the air tests in air.
for
sharp
intergranular-transgranular
for
fast
fracture
fracture. (Figure 4.12)
The
creep crack growth and fast fracture is
detect
in
tests
performed
in argon.
117
Figure
4.13
for IN-100
4.4.6.1.
in air.
general
the
boundaries..
boundary
Figure
from CCG to fast fracture
Argon Tests
In
powder
shows the transition
The
cavitation
4.14
fracture
for
in
crack
argon
Astroloy.
for
argon
in
argon follows prior
fracture surface shows more grain
in
surfaces
respectively
creep
than
in air as is shown in
Figures 4.15 and 4.16 show the
IN-100
7040 C.
at
and
Rene-95
(60
mesh)
The round prior powder
particles can be easily detected on the fracture surface.
Figure
4.17
shows the typical fracture appearance for
argon CCG tests for the 4 alloys.
are
easily
particles
seen
is
in
all
determined
the
by
The round prior particles
fractures.
the
mesh
The size of the
size used for each
alloy.
High
magnification
argon
revealed
These
cavity
Rene-95
surfaces
(60
fracture
like
mesh)
photomicrographs
features
features
and
are
which
of the alloys in
may be cavities.
shown in Figure 4.18 for
Merl-76 at 10,000 x.
The fracture
in Figure 4.18 were from CCGR tests in argon which
were not oxidized.
118
Air Tests
4.4.6.2.
Figure 4.19 shows the typical fracture surfaces for the
path
fracture
The
the
when
alloys
four
featureless
CCG tests were run in air at 704C.
totally
was
boundaries
intergranular
flat
with
characteristic of brittle fracture.
The surfaces obtained in air tests are heavily oxidized as a
of exposure to oxygen at 7040 C .
result
High magnification
failed to reveal any cavity-like features.
photomicrographs
(Figure 4.20)
CCGR
The
versus
the
intersect
CCGR
results
K
results
for
obtained
Astroloy
in
in
Air
argon
at
K = 60 MPamiii. The fracture surfaces of the CCG tests in air
have a transition at K= 60 MPa-/m from intergranular, brittle
fracture to a predominantly prior particle boundary fracture
which
path
fracture
has
been
surfaces
is
transition
shown
obtained
physical
to
be
characteristic of the
in an argon environment.
This
evidence supporting the conclusion
at high creep crack growth rates in Astroloy the crack
that
grows faster than the embrittling effect of oxygen.
The
tests
fracture
surfaces
for the notched stress rupture
in air are the same as that observed for the air CCGR
tests.
4.5.
Penetration of Oxygqen Results
The
exposure
depth
at
of
7040°C
intergranular fracture following oxygen
varied
from
alloy to alloy.
Astroloy
exhibited the smallest depth of damage and Rene-95 (60 mesh)
119
the
showed
largest
depth
of
intergranular
damage.
The
results are summarized in Table 4.5.
TABLE 4.5
Depth of Intergranular Embrittlement after a 100 hour
Exposure at 7040 C in Air
I
Average Depth of
Embrittlement (um)
Alloy
Effective
Calculated
Diffusivity (m2/s)
D = x2/t
84
1.96 x 10-14
Merl-76
310
2.67 x 10-13
Low C IN-100
720
1.44 x 10-12
Rene-95 (60 mesh)
840
1.96 x 10-12
Low C Astroloy
The results indicate that Astroloy and Merl-76 are only
slightly
crack
embrittled
growth
rates
and
in
therefore should have lower creep
air than either IN-100 or Rene-95.
This result has been verified in section 4.4.3.
120
I
FIGURE4,11) FRACTOGRAPHOF THE FATIGUEPRECRACK-CCG
TRANSITION
0
IN PM/HIPRENE-95 (120MESH POWDER)TESTEDAT 704C
IN AIR,
121
FIGURE 4,12)
FRACTOGRAPH OF THE CCG-FASTFRACTURE TRANSITION IN
PM/HIP Low C IN-100 TESTED AT 7040 C IN AIR.
122
(a)
(b)
FIGURE 4.13)
Fractographs of the CCGR-Fast Fracture transition in
PM/HIP Low C IN-100 tested at 704-C. (a) in 99.97O
pure argon; (b) in air.
123
(a)
(b)
FIGURE
4.14)
Fractogrphs of PM/HIP Low C ASTROLOY at 704 C.
(a) CCGR test in air; (b) CCGR test in 99.999%
pure argon.
124
0
FIGURE4,15) FRACTOGRAPHS
OF CREEDCRACKFRACTURES
IN 99.999%PURE
ARGON,(A)PM/HIPLow C IN-100,(B)PM/HIPRENE-95
(120 MESH POWDER)
125
FIGURE 4.16)
Fractograph of a CCGR specimen tested in air at 7040 C.
(PM/HIP RENE-95 (120 mesh powder))
126
(a)
(b)
(c)
(d)
FIGURE 4.17) Typical fractographsof four PM/HIP Nickel-Basealloys
0
tested in argon at 704 C. (a) Low C ASTROLOY; (b) MERL-76;
(c) Low C IN-100; (d) RENE-95 (60 mesh).
127
(a)
(b)
FIGURE 4.18)
Fractographs of cavity like featurew on creep
crack fracture surfaces from CCGR tests in argon
at 704 0 C.
(a)
PM/HIP MERL-76.
PM/HIP
RENE-95
(60 mesh);
(b)
128
(a)
(c)
(b)
(d)
FIGURE 4.19) Typical creep crack fracture surfaces in air at 704 C in
four PM/HIP Nickel-Basealloys. (a) Low C ASTROLOY; (b)
MERL-76; (c) Low C IN-100; (d) RENE-95 (60 mesh).
129
FAST FRACTURE
PRIORPOWDER
BOUNDARY
FRACTURE
INTERGRANULAR
FRACTURE
FIGURE4.20) TYPICAL FRACTOGRAPH OF A CCGRTEST ON PM/HIPLowC
0
ASTROLOY
TESTED IN AIR AT 704C.
130
5.
AN ITERATIVE MODEL FOR CREEP CRACK GROWTH
5.1.
Introduction
A
a
specimen
conditions
creep
model
for creep crack growth is developed
the accumulation of damage ahead of the crack tip
on
based
for
computer
which
is
creep brittle and satisfies the
of small scale yielding.
The damage is based on
accumulation in elements which are assumed to
strain
have the dimension of the critical microstructural parameter
(i.e.
and
grain size or prior powder size).
primary
contribution
by
advances
of
strain are assumed to make a negligible
creep
to
The plastic strain
the
total
amount
of
damage.
The crack
one element when the element immediately ahead
the crack tip achieves a critical value of creep strain.
After
a crack advance, the stresses in all the elements are
reset to calculated initial HRR stress.
the
stresses
The assumption that
reset to the HRR stress after a crack advance
was done in the interest of simplicity.
However, the actual
stress will be slightly lower as a result of the accumulated
creep
accumulation
and
Rice
crack.
(63)
which
strain
in
gone
before.
Creep
strain
is calculated using the stress given by Riedel
(74)
This
has
in
model
creeping material ahead of a stationary
differs from an earlier model by Huang
placing an upper bound on stress at the crack tip,
and by using the equivalent stress rather than stress in the
y-direction.
relaxing
Crack
tip
stresses
are
assumed
to
begin
from their HRR values immediately after loading as
131
a
result
of
the
accumulating
creep
strain. (See Figure
2.16).
The
effect
of oxygen on crack growth is modelled by a
change
in element size from prior powder size to grain size
and
reduction
a
in
the
value
of
the
critical
strain
necessary for crack advance.
The
function
model
of
strongly
predicts
K-history
dependent
the
and
upon
K.
changes
strength, and critical strain.
the
predicted
CCGR
is
creep crack growth rate as a
CCGR
in
is also shown to be
creep
rate,
yield
The effect of temperature on
accounted
for
in
secondary creep rate and yield strength.
changes
in the
The critical creep
strain is assumed not to change with temperature.
5.2.
Numerical Procedures
5.2.1.
Calculation of Stress and Strain
Stresses ahead of the crack tip at time=O must first be
determined.
with
This
increasing
initial stress distribution then relaxes
time, t>O.
The stress in the far field is
co' Closer to the crack tip, at radius "r"
the stresses are
described by the elastic stress intensity factor, KI (99).
aE
aE
j,
T
fE(a)
fE()
(Eq.-. 5.1)
132
(
f
)
is
a
factor
for
each stress component that
depends only on the angle (O ) from the plane of the crack.
The equivalent stress, aE , in the plastic region ahead
of the crack
at t=O
is given by the HRR singularity
(70, 71,
72):
KJ2(1/(Npi))
E
(Equ. 5.2)
Np is the stress exponent from equation 5.3:
eP = B (a) P
p
where
cp
e
(Equ. 5.3)
is the plastic strain.
The
size
expression
of the plastic zone, Rp, is estimated by the
for
plane
strain
loading
and
non-hardening
plasticity (99):
R
where
Y
is
=
P.
.1
the
P
2
I
(-EC.
Yj
yield
strength.
5.
)
The calculation for the
plastic zone size can be combined with the HRR stress field:
133
~~p~
i(1/
At r-Rp
the
(Eq.
Y .RJ
(
(l/(Np+1))
(Eq.
5.6)
equivalent stress calculated by the model ahead of
crack
tip
at
t=0
is illustrated
in Figure
approximation
of
equation
5.3
and
stresses
which are slightly above the actual
by
5.5)
aEIY, so equation 5.5 gives:
aE
The
(NP+))
the
HRR
corrected
the
stress-strain
substituted
singularity.
into
The effect
5.1.
The
relationship given by
equation
5.6
yields
stresses given
of a lower stress is
by assuming a 10-20% smaller critical strain
than
is obtained from smooth bar creep rupture results.
For
t>O
relax as a
the stresses in the plastic and elastic zones
result of creep
strain ahead of the crack tip.
The relaxation is described by Riedel and
.29 K2
= ,E
r E (Nc+l) B
Rice
(74):
(1/(Nc+l))
t
LY
~~\b](1/(NcCl))
fE (O,NN,) (Eq.
5.7)'
134
are the material constants for Norton's law:
N
where Bc an
ic
Bc(a) c
(Eq.
5.8)
is the minimum creep rate as determined via smooth bar
iC
The term f ( O,N ) is taken as 1.
creep rate measurements.
RR stress calculation indicates that at time 0 the
The
( aE )
stress
impossible
predicted
and
for
upper
an
bound
HRR.
by
t=0
infinity.
at
starts
A
on
This
stress
transition
is
obviously
is the stress
time
can
be
calculated at which the creep-relaxed stress given by the RR
calculation
(5.7)
the same as the stress
is
t=0 given by HRR (5.2).
at=O at r and
(See Figure 2.16)
· 29 i
r (::c+l)r
L-ransition
BcE
(:cO)
)(:"c.
This
calculated transition time does not relate to the real
test
time,
but
it
is only a starting time for subsequent
creep strain calculated according to the RR equation (5.7).
135
PM/HIP low C ASTROLOY, On=
200 MPa, O,=
950 MPa, a=lmm
-1
(1 = -. 093
(Np+l)
0'
r
I
I
I
I
I
1
I
2
I
I
I
I
I
I
I
I
I
I
I
Iv
10- 2
100
102
r/a
FIGURE 5.1)
Equivalent stress ahead of a creep crack at time=0 in
a PM/HIP nickel-base superalloy at 704°C.
136
5.2.2.
The Accumulation of Strain
The
of
time
creep
strain ahead of the crack tip as a function
is found by integrating the Norton Law expresssion
with time using the stress given from the RR analysis.
ec(t)=
tf
tf
f6c dt=
fBc( RR)NC dt
0
0
(Eq. 5.10)
where Ec(t) is the creep strain as a function of time, tf is
the
time
interval
time-dependent
to
stress
advance
given
the
by
crack, and aRR is the
the
RR singularity.
The
result of integrating equation 5.10 is:
=c
EC~)
=[
~ .29 K 2
E r
Equation
crack,
very
but
5.11
for
c
(
+1)
Bc (Nc+l)
predicts
short
t(
(Eq
(
)
the creep strain ahead of the
times the accumulation of strain is
fast resulting from the infinite stresses predicted at
t=0 by the RR singularity.
The
ahead
of
model calculates the creep strain for each element
the
crack tip within the plastic zone.
When the
137
strain
in
an
element
reaches the critical creep fracture
strain ( Crit ) the crack advances by one element.
For
each
calculated
strain.
t=O
element a transition time for
aRR =HRR
is
and this time is used to calculated a transition
This transition time given by equation 5.9 becomes
and
is
combined with the calculation of creep strain
with time in equation 5.11 to calculate a transition strain:
29 K'
r E at=
transition)
(E
It is interesting to note that this strain is independent of
Bc, Nc, and time.
from
the
This transition strain must be subtracted
calculated
over-prediction
in
creep
stress
strain
as
to
compensate for the
short
times
by
the
RR
singularity.
The time increment to advance one element is calculated
as:
(Nc+l)
At =
-t
transition
(Eq., 5.13)
where
the
crit
is the critical strain for fracture and
accumulated
strain
in
that
element
from
ei
is
previous
138
=0
c
(note:
iterations.
for
the
first
jump)
This
is
graphically illustrated in figure 5.2.
The
is
tip
creep
change
K with advances in crack length, and
in
have
will
history
load
The plastic zone
will accumulate.
and
calculated
the
size,
or each element ahead of the crack
f,
strain
a
strong effect on the predicted
creep crack growth rate.
is calculated
[r 2K
Ec(At)
strain in an element ahead of the crack tip
creep
The
as:
2
) - (Eqr(t
N Bc (Nc+l)(t+ ttra
trans.
(Eq.
Creep
strain
plastic zone.
to
accumulate
values
K
of
significant.
stresses
crack
at
length.
for
elements
5.14)
within
the
Elements outside the plastic zone are assumed
creep
negligible
stresses
smaller
only
accumulates
5.14trans.
in
in
creep
The
stresses
given
Once
the
However, at low
elastic region.
the
the
t=O
strain as a result of the
the elastic region may become
are
reset
to
the calculated
by the HRR singularity for the new
stresses
are
reset
the entire
process begins again for the next jump in crack length.
139
1n
c
(E
cri;-
Ei )
I
5
I
I
I
10
_
.At
~ ~ ~ ~ ~ ~~~~~I
_
I
I~_
III
-
I
I
I
I
I
I
I
0
6
tran
8
TIME (sec)
FIGURE 5.2)
Schematic representation of the time for a
crack advance in CCG, &t.
I
140
5.3.
The Effect of Oxygen
Oxygen
diffuses
grain boundaries.
ahead of the crack and embrittles the
This results in a loss of creep ductility
and an increase in creep crack growth rate.
fracture
alloy.
The decrease in
ductility in air is observed to vary from alloy to
In
fracture
addition
path
to a change
in ductility,
a change
in
occurs from prior powder boundaries to grain
boundaries.
This decreases the element size and results in
an
in the creep crack growth rates.
increase
strain
The critical
for an inert environment is obtained from short time
creep-rupture
tests
by
and
the time to failure.
by
the
Monkman-Grant
multiplying the minimum creep rate
This is the critical strain given
relationship
(100).
In
air
the
ductility is determined by fitting the predicted CCGR to the
actual
CCGR.
The
allpo.yis given
required
in table
change
in ductility for each
5.1.
--
TABLE 5.1
crit/air
Alloy
w/o B in G.B.
crit/argon
Astroloy
1.0
MERL-76
IN-100
0.2
0.71
RENE-95
1.0
.30
.70
0.1
.
I
II
w/o B in G.B. Astroiov
.26
.II
1.
141
ratio of the grain boundary concentration of Boron
The
to
the grain boundary concentration of Boron in Astroloy is
also
of
This expression shows the relative amount
presented.
per
boron
unit
of
grain boundary volume.
The weight
B per unit grain boundary volume is proportional to
percent
the
w/o
by
the
B in the bulk times the average grain size divided
grain
boundary
thickness
(6).
Table
5.1
is
graphically illustrated in Figure 5.3.
Woodford
and
(22, 30, 101) have shown that
Bricknell
additions of as little as .1 w/o B added to Ni-200 or IN-738
will
totally
The
than
on
with
alloys
grain
a
the
embrittling effect of oxygen.
large amount of boron per unit area of
have less of a reduction in creep ductility
boundary
alloy with less boron.
an
The concentration of boron
grain boundaries was found to be 1000 times greater
the
than
eliminate
the bulk for PM/HIP Rene-95 as determined by Auger
in
Spectral
analysis.
segregates
to
the
segregate
to
grain
zirconium
should
This
indicates
grain
boundary.
boundaries
that
most
of
Boron
Other elements which
such as carbon, sulfur and
also have an influence on the creep crack
growth rates which is a process of grain boundary fracture.
Predictions of Creep Crack Growth Rates
5.4.
The
alloys
for
model
studied.
both
was
used
o predict the CCGR for the four
The predicted and actual results are shown
the air and the argon CCGR results in figures 5.4
142
1.
0.
0.1
crit.
air
crit.
argon
0.
0.2
o.(
0.0
0.2
0.4
0.6
I[W/oB*GS/6/6
]/[w/oB*GS//6
FIGURE 5.3)
0.8
1.0
ASTROLOY
Ratio of the critical strain in air to the critical
strain in argon versus the ratio of the grain boundary
concentration of boron in the alloy to that in ASTROLOY.
(6=Grain Boundary Thickness,assumend to be a constant
for all the alloys; GS=Grain Diameter). Assuming the
boron in the bulk segregated to the grain boundaries
the amount of boron will form a zone 17 mono-layers
thick in PM/HIP Low C ASTROLOY.
143
to
5.7 for Astroloy, MERL-76, IN-100, and RENE-95 (60 mesh)
respectively.
The
factor
an
model
predicts
the experimental results within a
of 2 for all the alloys.
The predicted results show
initial transient until damage is established throughout
the
plastic
versus
K
plot
elements
size
is
The variation in the slope of the da/dt
a
accumulating
increases.
because
the
zone.
result
of
strain
(damage) as the plastic zone
This
effect
the increasing
varies
number
of
from alloy to alloy
the variation in grain size leads to a variation in
number
Damage
is
of
elements
assumed
to
within
the plastic zone changes.
accumulate
only
in
the region of
plastic deformation.
5.5.
Effect of Critical Parameters
5.5.1. Effect of Critical Strain to Fracture
Increasing
in
the
critical strain results in an increase
the time to accumulate this ( Ecrit) strain and therefore
decreases
the
predicted
CCGR.
The
model
predicts
the
relationship between critical strain and da/dt is non-linear
and
for
larger
values
of
the
critical
strain the CCGR
becomes exponentially smaller.
Figure
strain
K=50 MPa
K
test
on
5.8
the
.
shows
CCGR
the
effect of varying the critical
predicted
for
Astroloy
in
air, at
The CCGR is determined for a simulated constant
after a sufficient number of crack advances for the
144
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148
CCGR to become constant.
The number of crack advances is on
the
order
of
the
plastic zone divided by the grain size.
The
slope
of
the
steady
(da/dt)ss
versus
steeper
increasing
with
fracture
-1
strain
results
rates
state
critical
creep
strain
strain.
crack growth rate
plot
For
a
becomes
small
the slope of figure 5.8 is -1.
from
ever
critical
A slope of
the fact that for fast creep crack growth
the stresses at the tip of the crack have little time
to relax.
5.5.2. Effect of Grain Size
The
into
effect
account
size.
of grain size on CCGR predictions is taken
by
changing
the
element size or crack step
This will cause changes in both the slope of the CCGR
versus K curve and in the magnitude of the CCGR predicted as
a
result
the
of stress at each element node.
effect
Figure 5.9 shows
of grain size on the predicted constant K CCGR.
The curve is similar to figure 5.8 with the constant K creep
crack
growth
rate exponentially decreasing with increasing
grain size.
The predicted effect of changing grain size on the CCGR
versus K curve for PM/HIP Astroloy tested in air is shown in
figure
slope
5.10.
and
The
a
larger
grain size resulted in a higher
lower creep crack growth rate.
The change in
slope resulted from the number of elements which accumulated
damage.
within
The CCGR will increase with the number of elements
the
plastic
zone.
However, the CCGR is lower as a
149
result
of
a
decrease
in
the
rate
of
creep
strain
accumulation with increasing r as given by equation 5.11.
5.6.
Constant K Calculations
The
been
creep
predicted
Astroloy
of
crack
in air.
strain
growth
transient
occurred
of
The
until
to
a
bring
accumulation
is
in
figure 5.11. for PM/HIP
the crack tip affects the creep crack
crack
the
should
growth
curves
have
an initial
sufficient number of crack advances has
process
equilibrium
shown
The plot illustrates how the accumulation
ahead
rate.
creep
and
growth rate for constant K tests has
crack
to
a
growth
dynamic
correspond
to
an
rate and the damage
equilibrium.
upper limit for the
crack growth rate in an increasing K test.
constant,
longest
an
time
element
ahead
in
region
the
of
of
This
When K is
the crack experiences the
plastic
deformation and
therefore accumulates the most creep strain.
5.7.
Effect of dK/da on CCGR
The
of
creep
crack growth has been modelled as a process
damage accumulation ahead of a crack tip. Therefore, the
load
history
an
element
experiences
before
advances through it will become important.
or
decreasing
intensity
important.
crack
K
factor
A
advance
CCGR
with
situation
test
the
crack
in
the
crack
In an increasing
rate of change of stress
advance,
dK/da,
becomes
which the rise in K with each
becomes so large as to not allow the dynamic
15i
)4°C, air
=50 MPaS
10
-6
(m/s)
1-7
10
,^-8
-
---
.0 01
I
I
.01
0.1
Ecritical
FIGURE 5.8)
10
M
Predicted effect of Ecritical on the CCGR of a PM/HIP
Superalloy at 7040 C.
Z_
m
PM/HIP low C ASTROLOY,
704°C, air, K=50 MPaYm
---
ass
(m/s)
-6
10
-
10
1
I
10
I
100
GRAIN SIZE (um)
FIGURE 5.9)
Predicted effect of grain size variations on the
CCGR of a PM/HIP nickel-base superalloy at 7040 C.
151-
0o
o
.0
0
C-,
3
0
v-I
P-I
U
U
~
N
o
U)
-0v'p0r
1-I
n
c:I
9-4
t
loI
-0
lo
Ic~
o
tn
co
Io
tl-
(S/W) 7p/lop
DCDDi-
oI
CC:
152
d1o
_
I
__
I
I
I
I
._
I
I
I
1
=70 MPa-F
K:=50
MPa-m
-6
10
d
aim
da
dt
(m/s)
Pa-i
1-7
10
0
I
1
I
2
II
.
3
I
4
5
I
6
I1
7
8
I
9
NUMBER OF CRACK ADVANCES (X)
FIGURE 5.11)
Predicted CCGR versus the number of crack advances
for a constant K test. (based on data for PM/HIP
low carbon ASTROLOY at 704°C in air.)
10
153
process
will
of
strain accumulation to reach equilibrium.
result
in
the
prediction of a different creep crack
growth rate than is actually possible at a given K.
illustrated
Astroloy
in
specimens
dK/da
in
and
or
figure
air
at
This is
5.12 for CCGR predictions on PM/HIP
704 C.
procedures
a
This
large
A careful
is
examination
of test
recommended to avoid a large
initial
K
which
will
give
a
non-conservative creep crack growth rate.
The
load
effect
history
prediction
of not reaching equilibrium as a result of
will
of
temperature.
become
extremely
creep-fatigue
This
process,
important
interactions
though
noted,
in
at
will
the
high
not
be
discussed here.
5.8.
Effect of Temperature and Yield Strength
The
K
curve
obtained
effect of temperature on the predicted CCGR versus
is
illustrated
in
figure
5.13 with the results
by Huang (63) for PM/HIP Astroloy at 650 0C and 760
C. Temperature changes result in changes in the creep strain
rate
and
a
change
will
maintain a high yield strength at high temperature and
will
increasethe
This
will
result
in the yield strength.
secondary
in
creep
rate
Ni-base alloys
with temperature.
a large increase in CCGR.
rate for Astroloy is given below (Huang(63)):
The creep
154-
0
o
-T
I0
-J
0
It
-o
0A
00)
·
0)
P4
Ec
44
'I<
I
ct
~~
Ila
I
c:
-(S/W)
1
a
l
I
O
I
p
I
w
H
/p//p
X
155
12.31
=0-(MPa)
(sec-l)
exp -122.2
(Kcal-mole -1
(Eq.
The
changes in
s
5.15)
for Astroloy account for the change
in CCGR between 650 C and 760 C.
As
yield
decreases
ahead
strength
decreases
the predicted CCGR also
as a result of a lower stress in the plastic zone
of
the
illustrated
crack.
The
effect
of
varying
Y.S.
is
in figure 5.14 for the predicted CCGR of PM/HIP
Astroloy
at
a constant K=50 MPa/m.
strongly
on
stress, and a small decrease in yield strength
results
been
in
a
observed,
groups.
creep
The creep rate depends
large decrease in the CCGR.
but
not
reported,
This result has
by industrial research
The
process of reducing yield strength to decrease
crack
susceptibility is refered to as "de-tuning" an
alloy.
The
with
yield
strength
from
hot tensile tests will vary
strain rate at temperatures where creep deformation is
possible.
Faster
yield strength.
strain rate tests have a larger value of
Therefore, the value of yield strength from
tensile tests used in the model may not be totally accurate.
However,
all
the tensile results were obtained at the same
strain rate and should be self-consistant.
156
16
~_
---- ----------
- -
- --
rI
I
I
1
I
Js
r
1
L/C ASTROLOY
Air
C
760
--- p
o65
0
/
700 OC _
.
10
0
10
650
C
i
IL
-
3
U
E
1/I,
E
-7
10
Cy +j
!
'IA
-8
-9
0
l
!I
20
FIGURE 5.13)
_
I
_I
X
30
I.
I'
40
I
-C
50
'
-LI
7
/U
II !
---
~
t
l
--
r
IUU
K, MPaclm
Predicted and actual CCGR results for PM/HIP low
carbon Astroloy (ref. 63) for different temperatures.
157
PM/HIP low C ASTROLOY; .704°C; air; K=50 MPa~Y
10-
5
asS
(m/s
10- 6
855
FIGURE 5.14)
.
950
YIELD STRENGTH (MPa)
Predicted effect of yield strength on the steady state
CCGR of a nickel-base superalloy.
An
IUU
mm
PM/HIP low C ASTROLOY; 7040C; air
60
Kinit.
(MPaVffi)
20
a
0
I
100
10
_
,I
I
104
f
___
,,,
106
-
108
I
1010
INITIATION TIME (sec)
FIGURE 5.15)
Predicted time to begin CCG in a nickel-base superalloy.
158
5.9.
Predicted Creep Crack Initiation Times
The
effect
initiate
creep
specimen
has
of initial stress intensity on the time to
crack
been
Charpigny
(103).
the
to
time
growth
reported
It
initiate
from
by
a
fatigue
precracked
Floreen (50), Bain (102),
is found that as initial K decreases
a creep crack becomes exponentially
large.
The
crack
the
model
can be used to predict the time to initiate
growth from a sharp notch by determining the time for
first
results
versus
crack
obtained
time
advance.
for
Figure 5.15 shows the predicted
PM/HIP
to initiation.
Astroloy in air as initial K
At low values of K the time to
initiation becomes extremely long as a result of the rapidly
reducing
stresses at the crack tip.
is similar to what is observed.
The behavior predicted
159
6.
DISCUSSION
6.1.
CCGR Model
The computer model presented in chapter 5 predicts some
surprising
results
for
creep-brittle materials in a small
scale yielding condition.
1)
The
apparent
These predictions are:
lower
limit
for creep crack growth
occurs when the plastic zone ahead of the crack becomes less
than half an average grain diameter;
2)
The CCGR in the stage II region depends on the rise
in K with crack advance;
3)
The
stage
I CCGR observed is an initial transient
and is not a unique function of K;
4)
The
CCGR
of
an alloy
is a strong
function
of the
yield strength and creep strain rate of a material;
5) Load history can affect creep crack growth rate; and
6)
function
The
function
The time to initiate creep crack growth is a unique
of K.
lower
limit
in
K
of the grain size.
for
CCG is predicted
to be a
This lower limit, K threshold,
for CCG is given below:
KTH
Y
GS
(Equ. 6.1)
where
KTH is the threshold stress intensity for creep crack
growth, Y is the yield strength, and GS is the average grain
16
diameter.
Floreen
for
intensity
function
(104) has shown that the initial stress
in 100 hours at 704°C
failure
GS
A
in IN-792
is a
true threshold may not exist for creep
crack growth since there will always be some yielding at the
tip
a
crack
and
for
creep
crack
of
limit
therefore some damage.
growth
(K
)
should
The apparent
be given by
equation 6.1.
The
region of Paris Law type growth is affected by the
dK/da for a specimen geometry.
A Paris type relationship is
given below:
da/dt = AKd
(Equ. 6.2)
where
A
and
variation
are
CCGR
material
dependent
constants.
an
in
increase
dK/da
a
crack
element
drawn
characterized
ahead
for
constant
The CCGR
is determined by the stresses ahead of the
material
as
At a given
results in less time for damage
accumulation in an element ahead of the crack tip.
for
The
with dK/da results from a change in the
history for an element ahead of the crack.
load
K,
in
N
by K, and the load history for the
of the crack tip.
the
K test.
CCGR
A series of curves can be
versus number of crack advances for a
The CCGR increases with each jump until a
dynamic equilibrium occurs between the rate of crack advance
and the rate of damage accumulation ahead of the crack.
The
161
equilibrium value represents the CCGR for a given constant K
without any history effects.
In actual CCGR tests the value
for K increases with each crack advance. The CCGR at a value
of
K
depends
cin the K-history which results
from the dK/da
This process is graphically
illustrated in
in the specimen.
Ais the dK/da increases within a specimen, the
6.1.
Figure
CCGR
K; curve
versus
grained
large
in
pronounced
decreases.
This
effect
materials
and
will
be
should
be
considered when measuring the CCGR for a material.
The
I
stage
transient
CCGR
behavior
jumps.
results
an initial
undamaged
material
for the first
Thi s results in a lower CCGR upon loading which
quickly
will
is
whichI results from the fact that the crack tip is
advancing throug;h initially
few
measured
rise
reported
to
in
the
stage
II region.
Many of the
the literature reflect primarily this
initial transient, and any conclusions based on Stage I CCGR
data are questionable.
The
be
CCGR
measured for all materials has been shown to
a strong function of the stress at the crack tip and the
of creep strain accumulation (Chapter 5).
rate
Any changes
in heat treatment or processing which alters either of these
material
properties
will
result in a marked affect on the
observed CCGR behavior in a material.
The
the
measured
amount
of
CCGR at a value of K depends strongly on
creep deformation accumulated
just ahead of the crack tip.
of
a
Variations
in the grains
in the load history
specimen or component which will affect the amount of
162
K
KK
X
a
_
1
I
I
I
I
I
I
I
1
Ki
FIGURE6.1)
!
_ _
I _
I
K2
Schematic showing the effect of dK/da on CCGR results.
163
crack
creep
strain
ahead of a crack will affect the
growth rate.
The crack growth rate depends on
creep
accumulated
the amount of damage a grain receives from previous loadings
which
gives
study
on
the
the
a "memory" of past loadings.
material
effect
of
load
history
is
vital
A
if the
between fatigue and creep crack growth are the
.interactions
be understood.
shown in chapter 5, the time to initiate creep
was
As
from
growth
crack
initial
a
crack depends strongly on the
sharp
This result is important when one considers the
K.
between
interaction
creep
crack growth and fatigue.
If a
fatigue crack advances through the damaged zone ahead of the
in
crack
tip
crack
growth
exhibit
time
less time than is required to initiate creep
for
a sharp crack, then the crack should not
significant time dependent behavior.
becomes
important
when
The initation
considering whether or not a
fatigue crack will advance during a tensile hold period at a
high temperature.
Tensile hold periods are common in modern
aircraft gas turbine components during flight.
164
Effect of Triaxiality
6.1.1.
It
much
often been observed that creep crack growth is
has
slower in the plane stress condition than in the plane
strain condition.
any
show
growth
shown
stress
rate
critical
that
can
be
to change the creep crack
shown
a material via changes in the value of the
of
strain
function
The affect of a triaxial
effect of stress state.
of
state
in section 5 does not
The model presented
for
fracture.
Rice and Tracey (105) have
the critical strain to fracture a material is a
of
the
state
of stress.
The expression for the
critical strain is given by:
e
where
"C"
is
hydrostatic
plane
have
plane
A
material,
cH
is
the
aE is the equivalent stress.
The
The ratio of the
strain for plane stress to the critical strain for
strain as given by equation 6.3. is approximately 18.
in
smooth
significant
75 0 C.
the
worked out by Hutchinson (72).
been
reduction
versus
and
for
(Equ.6.3)
and plane strain stress fields at a crack tip
stress
critical
constant
stress,
[(.
C expI 23Ja
rtcal
by
the
creep
Dyson
creep ductility for notched specimens
rupture
specimens
was
shown
to be
and Loveday (106) for Nimonic 80A at
165
The
effect
increasing
of
critical
of 18 for PM/HIP
plane
stress CCGR is shown in Figure 6.2.
is
much
behavior
The plane stress
than the CCGR in plane strain.
slower
accounts
strain by a
at 704 0 C in air to simulate
factor
CCGR
Astroloy
the
This
the crack tip tunnelling phenomenon
for
observed in CCGR tests without side grooves.
6.1.2.
Effect of OxygenConcentration
model
The
the
strain and a change in the element size.
critical
in
reduction
critical
mechanism
element
size
change
in
in
air
assumes
tests.
mystery.
A
reduction in the
path from predominantly prior particle
argon
CCGR
in
air
tests
to
CCGR tests.
predominantly
The change in
crack
crack
runs
This
to
The model
growth rate which is not observed in all
in air on PM/HIP Astroloy indicate that the
Tests
out
growth rate for Astroloy.
constant reduction in the critical strain in air
creep
da/dt.
CCGR
a
CCGR tests results from the observed
fracture
creep
a
alloys.
crack
will result from any of the
size alone is sufficient to explain the increase in
element
with
air
in
intergranular
the
remains
fracture
boundaries
strain
The
mechanisms suggested in section 2.2., but the
embrittlement
exact
the CCGR in air by a reduction in
predicts
the
embrittling
effect of oxygen at high
change is reflected in the transition at fast
a prior particle boundary fracture path in the air
166
to
cn
co
0
co
-
co
0
.-4
t0
uC
P4-
UI
.;4 .h
0
00
cV
0oI
I
0-
C0
-
I!
(
(IS/ W)
I
'0
?P/OP
II
i
0C
-4
I
-
0
I
-
P
167
6.1.3.
Limitations of the CCGR Model
There
are
several
points in the model which may give
rise to errors in calculating the CCGR of a material.
include:
crack
These
1) The procedure used to update the stresses upon
advance;
2) The effect of strain rate on plasticity;
3) The estimation of the plastic zone size; 4) The effect of
time
independent plastic strain on CCGR; and 5)
The effect
of strain rate on yield strength.
The
stresses ahead of the crack tip are updated to the
calculated values given at t=O which are by an approximation
of
the
HRR singularity.
result
of
creep
iterations.
stresses
of
creep
strain
accumulation
from
previous
This may result in an slight over-estimation of
at
CCGR.
The stresses are not reduced as a
the crack tip and therefore an over-estimation
This
strains
over-estimation
are
generally
should
be small since the
small when compared with the
plastic strain.
At high temperatures the strain hardening behavior of a
material
The
becomes a function of both strain and strain rate.
measured
increasing
yield
strain
strength
rate.
of a material increases with
A change in yield strength would
result in a considerable effect on the predicted CCGR for an
alloy.
at
All
the tensile tests in this study were performed
the same strain rate, and therefore should be comparible
and self consistant.
The
scaling
plastic
zone
is
calculated
as
.1 (K2 /y 2).
parameter for the plastic zone is 0.1.
The
Estimations
168
of plastic zone size vary with angle ahead of the crack tip,
For mode I loading in
state of stress, and mode of loading.
plane strain estimates for the scaling factor vary from .018
to
.32.
scaling
0.1 is a good estimate
While
(69)
factor,
it
may
not
be
the
best.
of the average
Changing the
of the plastic zone will affect the slope of the
estimation
CCGR versus K curve, but such changes will be minor.
model does not calculate any damage as a result of
The
the
time independent plastic strain ahead of the crack tip.
Plastic
strain
has
been
shown
strain by Nix (107).
fracture
reduce
to
the
critical
The effect of plastic strain
on the critical strain may be a source of error in predicted
CCGR results. At this time there exists no consistant way of
predicting this damage.
The
yield
0.2%
strength
for
temperature varies with strain rate.
a
strength
will
affect
tested
were
at
high
Any change in yield
The yield strength of the
the CCGR.
obtained
material
The yield strength has
affect on the predicted CCGR.
large
alloys
a
at
the
same
strain
rate
(2%/minute) and should be self-consistant.
The
various sources of error in CCGR prediction can be
significant,
but
hopefully these errors are systematic and
therefore
act only as scaling factors which will adjust the
predicted
CCGR
in a self-consistant manner.
The fact that
model
predicts the CCGR for the alloys tested based on
measurable
input parameters indicates that these errors are
the
systematic.
169
CCGR of PM/HIP Ni-Base Alloys
6.2.
for a PM/HIP Ni-base alloy has been shown to
CCGR
The
considerably. from alloy to alloy in both air and inert
vary
measured
The
environments.
CCGR will vary as a result of
test procedure, and environment.
and
creep-brittle,
tip
crack
well
are
conditions of small scale yielding
the
III) Therefore, the stresses ahead of the
(Appendix
apply.
The alloys tested were all
characterized
by
K, and K becomes a
natural parameter against which CCGR behavior is correlated.
Effect of test procedures
6.2.1.
CCGR
The
and
load
initial
the
in
air for an alloy varied with the applied
K.
The
stage
II
CCGR decreased with
The effect of applied load is a result of
load.
increasing
changes
in
dK/da
associated with changing load.
The
dK/da for the SEN specimens tested is given by:
dK/da
/7;P
OF
N
(.56-.345/w+26.5(a/W2 )-76.0(a2/W 3 )
/W3 4 ))
+136.8(a
(Equ
6 4)
The dK/da varies only with load, "P", for a fixed a/w.
The
tests exhibit a region of sharply increasing
CCGR
CCGR upon initial loading.
This stage I region of growth is
not unique and occurs for any initial K.
high
initial
CCGR
versus
K
K.
resulted
Tests performed at
in the lack of a stage II region
This indicates that the condition required
17C
at
equilibrium
reach- dynamic
to
crack tip were not
the
acheived before the value of KIC was reached.
fact that the applied load and initial K will have
The
a profound effect on the CCGR results coupled with the
such
effect of triaxiality on the CCGR indicates that most of the
CCGR
on
results
published
for
Ni-base
alloys
high
Systematic tests
may have significant errors.
temperatures
at
with low dK/da, low initial K, and specimens which have been
to avoid crack tip tunnelling are required to
grooved
side
achieve accurate CCGR results.
6.2.2.
Effect of Oxygen
presence of oxygen acted to significantly increase
The
the
In addition to
measured CCGR in all the alloys tested.
increasing
the
path
fracture
CCGR,
from
oxygen
resulted
to
boundaries
particle
prior
in a change in the
grain
boundary cracking.
hour
100
that
indicated
the
grain
results
air
exposure
at
been
to
a
considerable
of
also
on 4 alloys
depth.
Similar
obtained by Woodford and Bricknell (30)
and Pineau (56) using Ni-base alloys.
that
7040 C
the oxygen diffuses into the material along
boundaries
have
tests
The results indicated
the alloys which had the highest effective diffusivity
oxygen
had
were IN-100 and Rene-95 (60 mesh).
the
embrittlement
fastest
in
the
CCGR
time
in
for
The depth of oxygen
air.
one
These alloys
crack advance can be
calculated from the following expression:
171
(Equ. 6.5)
is
X
where
the
Assuming a minimum depth of oxygen
grain diameter.
average
a" is the CCGR, and "GS" is the
in section 4.5,
determined
embrittlement
ahead
is the
of oxygen along the grain boundaries
diffusivity
effective
of oxygen embrittlement, D
depth
the
of
crack
tip
is
required
for
accelerated fracture in air, equation 6.5 indicates that the
CCGR
maximum
at
air
Figure 6.3
7040 C and K = 30 MPami versus
A good correlation of the CCGR data is observed, but
DO GS.
the
air is proportional to Do-GS.
in
CCGR
the
shows
in
slope of the line is -.5 indicating the depth of oxygen
embrittlement is not the only criteria for fracture.
CCGR
rate
the
CCGR
the
Stage
observed
Merl-76.
limited by the diffusion of oxygen and
embrittlement, then when the diffusion of oxygen
subsequent
becomes
is
oxygen
in
If the
the slope of the stage II region of
limiting
versus
K curves will be reached.
A reduction of
II CCGR slope from the predicted slope in air is
in
Rene-95
to a lesser degree in IN-1OQ and
and
While the change in slope may be partially due to
the change in fracture path, these results indicate that the
of
rate
limiting
similar
diffusion
oxygen
rate
to
and embrittlement does become a
step for CCGR in air.
the
well
known
stress
This behavior is very
corrosion
phenomenon observed in aquious environments.
cracking
172
. -5
_
'U
_ _
_
I
I
da
dt
I
(m/s)
-6
10
1
I v
-7
-
- -
_
l
_
10-18
_
_
_
_._
_
I
7-
_
10-17
10
-j
10
10
D *GRAIN SIZE (m3/s)
0
FIGURE 6.3)
Comparison of the CCGR in air at 7040 C, K=30 MPa-f
versus the effective diffusivity of oxygen * grain
size for four PM/HIP Nickel-Base Superalloys.
10
173
Alloying
magnesium
additions
which
such
as
boron,
zirconium,
and
inhibit the embrittlement of oxygen can be
expected to reduce the CCGR measured in an oxygen containing
environment.
The
predicted
over-predicted
preditions
by
for
over-prediction
reduced
CCGR
the
upon
model.
Rene-95
comes
initial
(60
from
before
boundaries
neglected
oxygen
in air is
This is most obvious in the
mesh)
the
critical strain in air.
required
loading
can
in
air at 7040C.
The
assumption of a constant,
Actually some time will be
diffuse
and embrittle the crack tip.
along
the
grain
Since this time is
in the model, an over-prediction of the CCGR will
occur.
Some
indicate
crack
CCGR
results
in
air
for IN-718 by Pineau (56)
that the diffusion of oxygen down the crack to the
tip may limit the availability of oxygen.
These CCGR
results indicate that as the initial crack length increases,
the
would
creep
crack
occur
growth rate decreases for a given K. This
if diffusion of oxygen to the crack tip became
the rate limiting step in oxygen embrittlement.
In general,
these effectswere not observed in the alloys tested.
6.3.
time
Notched Stress Rupture Tests versus CCGR
The
notched
stress
to
failure
for an alloy from creep mechanisms in the
rupture
presence
of a stress concentration.
involves
the
(NSR) test indicates the
The fracture mechanism
initiation of cracks in the specimen followed
174
by
propagation of a single dominant crack until KIC is
the
and
reached
At high stresses the
occurs.
fracture
fast
net section of the notched specimen goes plastic and
entire
failure usually occurs from subsurface cracks which initiate
The
failure.
stress
lower
fractures.
intergranular
to
These
to from one dominant crack which propagates to
link
cracks
surface cracks.
from
results
failure
the
stress,
shown
At lower net section
center of the specimen. (106)
the
in
fractures are usually brittle
The
presence
reduce
significantly
the
of oxygen has been
time
to
failure
in
nickel-base alloys. (5)
of
a
as
crack.
test at low net section stress can be thought
NSR
The
which measures the time to initiate a creep
test
If crack initiation in the NSR test results from the
nucleation, growth and coelescence of cavities in the stress
field
at
tests
can
root
the
the notch, then the results of NSR
of
the relative CCG behavior of different
indicate
alloys and/or different heat treatments.
6.4
Figure
for
air
from
have
while
highest
performed at 675 MPa in air at 704°C.
tests
results
CCGR
be
of the alloys tested versus the time to rupture
4
results
NSR
to
NSR
compares the CCGR at 704 0 C, K=30 MPa/-m, in
the
Rene-95
CCGR.
for
The
the alloys follow the same ranking as the
for the same 4 alloys.
longest
gave
time
the
Astroloy was observed
to rupture and the lowest CCGR
shortest
time to rupture and the
These results indicate that the NSR test may
a quick, simple and inexpensive test to compare the CCGR
175
S
10
_
_
da
dt
(m/s)
-6
10
l A-7
LU
10
100
1000
RUPTURE TIME (HRS.)
FIGURE 6.4)
Comparison of the CCGR in air at 7040 C, K=30 MPa-i
versus the time to rupture a NSR specimen.
176
behavior
changes.
of
various alloys, heat treatments and processing
177
7. CONCLUSIONS
1.
Creep crack growth rates were measured for 4
Ni-base, y -'; strengthened Ni-base superalloys at 704 C in
both air and in a 99.999% pure argon environment. The four
alloys tested were all PM/HIP alloys and they included low
Carbon Astroloy, Merl-76, Low Carbon IN-100, Rene-95 (60
mesh powder), ad
Rene-95 4(120 mesh powder). The CCGR
ranged from 10- m/ s to 10
m/s and the stress intensity
ranged from 10 MPa-m- to 120 MPaii: The presence of oxygen
during CCG resulted in an increase in the measured CCGR for
a given K in all the alloys tested. The increase in CCGR
varied for the alloys tested, but Rene-95 (60 mesh) had the
largest increase in CCGR and Low Carbon IN-100 had the
smallest increase in CCGR. CCGR increases for the alloys
ranged from 10 times to 1000 times in air over the CCGR
measured in pure argon.
2.
The increase in the measured CCGR in air resulted
from a change in fracture path and a decrease in creep
ductility. The CCG fracture path was intergranular for both
the air and the pure argon environments, but the creep crack
followed grain boundaries which were coincident with prior
particle boundaries in argon tests. The predominantly PPB
cracking in argon can be attributed to the increased number
of carbides which segregate to the PPB in PM/HIP alloys. In
air the fractures followed the nearest grain boundary,
regardless
of whether
it was a PPB or not.
3.
The CCGR behavior of
Ni-base alloys exhibited
three stages. Stage I is an initial transient, which is not
a
unique function of K, and results from the crack
propagation through initially undamaged material. Stage II
is a region of gradually increasing CCGR with K, and stage
III is associated with KIC and fast fracture.
178
4.
A computer model was developed to predict the CCG
The model is based on the
of the alloys.
behavior
accumulation of damage in the form of creep strain ahead of
the crack tip. The results of the model were in excellent
agreement with actual CCGR results, and the model provided
some insights into the CCG process. The model predicts that
grain size, critical strain, and creep rate will all
significantly affect the CCGR. The model also predicts that
load history effects will significantly alter the CCGR
measured.
5.
CCGR behavior depends on both the stress intensity
factor and the load history applied to the specimen. The
intensity factor, K I, describes the crack tip
stress
stresses and therefore the CCGR for creep-brittle materials
when the conditions-of small scale yielding are satisfied.
The CCGR measured depends strongly on the load history. The
effect of load history on CCGR was observed with the effect
of dK/da on CCGR. The initial transient in CCGR upon loading
also indicates the importance of load history.
The CCGR test procedures and the specimen geometry
6.
used in CCGR testing will have a strong effect on the
measured CCGR behavior of an alloy. In all cases the errors
in CCGR measurements resulting from improper test procedure
lead to a non-conservative estimate of CCGR, and in a large
over-prediction of actual component life.
Notch stress rupture test can be used to evaluate
7.
the CCG resistance of a material when the net section stress
is low.
8.
The grain boundary chemistry of an alloy is
in determining it's susceptibility to oxygen
critical
Alloys with high concentrations of boron
embrittlement.
tend to have a smaller reduction increep ductility and lower
increase in CCGR in air than alloys with a low B content.
179
8.
RECOMMENDATIONS FOR FUTURE WORK
following
The
are
for research that
recommendations
extend the understanding of creep crack growth and the
will
effects of alloy chemistry on CCG behavior.
Effect of Test Procedures and Specimen Design
8.1.
It
by
has been shown that the CCGR results are influenced
rise
the
a
with crack advance and thevalue of the
K
The development of general testing criteria and
K.
initial
in
standard
geometry
specimen
used in creep crack
be
to
rate measurement are required to insure accurate and
growth
test
repeatable
These
results.
results
can
then
be
incorporated in a design criteria for operating components.
tests
CCGR
such
geometries
edge
single
varying
on several specimen
performed
cantilever beam specimen,
double
double
specimen,
specimen
notched
from
obtained
the
as
tension
compact
be
should
notched specimen,
edge
and
others.
The
results
specimens with a specific alloy while
these
the specimen dimensions should be analyzed to
only
determine if such parameters as grain size to specimen width
ratio
and
dK/da
Since
CCGR
is
a
boundaries
ahead
surprising
if
measured
dK/da
CCGR.
are
size
ratio are important.
process
of damage accumulation on grain
of
crack
the
affected
boundaries
grain
versus
Once
analyzed,
the
number
by
the
of
tip,
it
randomly
would
oriented
not
be
grain
crack tip would influence the
the effects of specimen geometry and
a
coherent
test
procedure could be
180
conceived
repeatable
insure
would
which
comparible
and
results.
Grain Boundary Chemistry
8.2.
The
of
chemistry
boundary
grain
alloys is
Ni-base
strongly affected by minor alloying additions. Elements like
C, B, and Zr segregate to the grain boundaries, and have the
potential
of
strongly
the creep crack growth
influencing
behavior of an alloy.
A
of
study
the effect of elements which segregate to
grain boundary should be attempted.
the
commercial
Ni-base
systematic
alloying
elements.
The
oxygen
such
be
can
procured
ofgrain
additions
which
have
specific
boundary
selected for the study should have a
alloy
eff ect of environment on CCGR, since the interaction
strong
of
alloy
Several heats of a
as
acceptable
and
Rene-95,
IN-718,
in
regard.
additions of
yttrium,
those elements is also of interest.
which
this
INCONEL
Different
X-750
are
all
heats should have
like boron, zirconium, hafnium, and
elements
are
and
Alloys
known
to affect sensitivity to oxygen
embrittlement.
The
alloy
is
changes.
development
of a new creep crack growth resistant
conceivable
The
by making only minor alloy chemistry
development
commercial applications.
of
such
an
alloy has obvious
181
APPENDIX
I
CCGR TEST RESULTS
182
TABLE I.1
LIST OF CCGR TESTS
GROSS
STRESS
TES
ALLOY
tP
Kinitial
(PROPAGATION TIME)
(hours)
Ao (mm) (MPa m)
(MPa)
_
.
.
tf
(FAILURE TIME)
(hours)
.
236.(
2.40
29.0
1.5
1.5
135
145.6
2.68
19.4
68.6
117.3
137
191.1
2.28
22.1
20.9
20.9
149
191.1
3.52
34.6
1.9
1.9
150
191.1
2.36
23.0
2.1
2.1
153
236.
1.78
22.6
28.0
31.6
140'
141.1
3.48
33.2
63.6
63.6
145'
291.2
2.45
35.6
70.0
70.0
655.C
1.01
43.2
2.1
71.6
132
155.C
1.81
15.1
1.5
7.4
138
200.2
2.62
26.2
2.3
2.3
139
236.6
1.87
23.3
2.1
2.1
152
145.6
1.84
14.2
12.1
12.1
141*
291.2
2.48
36.0
41.0
84.3
144*
241.2
2.32
33.8
31.5
51.2
528.0
1.03
35.4
5.5
5.5
131
164.0
2.08
17.6
7.6
30.2
148
182.0
2.13
20.0
4.6
22.8
142*
291.2
2.13
31.7
7.5
7.5
147*
145.6
2.54
18.3
23.7
23.7
241.0
1.40
23.6
6.5
124.9
145.6
1.42
12.0
2.1
4.6
151
91.0
3.35
15.3
1.2
1.2
154
164.0
1.91
16.5
1.0
26.2
143*
236.6
2.03
24.9
36.2
36.2
441.0
1.01
32.4
2.8
71.3
145.6
1.57
13.2
6.8
58.2
236 . 6
1.37
18.6
43.7
66.0
130
128
127
Low C Astrolo:
MERL-76
Low C IN-100
Rene-95
(60 mesh)
133
136
129
Rene-95
(120 mesh
134
146*
* 99-999%pure Argon;**
time to failure includes time spent at lower loads
183
APPENDIX
Computer Program:
II
CCGR Prediction Model
(Written for the IBM-PC in -BASICA)
Portions of the text
on the following page(s)
are not legible in the
original.
184
I
2
.
4
5
6
REM t*S**t**
REM *
REM *
F:EM *
REM *
REM *
7 REM*
X*t***
*
*************
CCGRMOD9
WRITTEN :)4-14-EWRITTEN BY: ENJETH R. EAIrJ
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
THIS PROGRAM CLCULATES da/idt vs
FOR SPECIFIC
INPUT VALUES RAND MATE:IALS FARAMENTERS
t**
*******s
****
*******YIB$t$ttt
***trW
****
****
i':,DIM EG (2':~,:)
DADTS
2') W=.0117
21 0=')
22 FOR Z=1 TO ZOO)C:)
O. EG(Z) ='
24 C02(Z)=':
25 NEXT Z
26 CLS
S (50)
,C02
5
$
*
*
(2'C:,::)
29 RESTORE
.0 GOSUB 2(:,":)'
40 Tl=O
50 A=AO
60 I=1
65 PI=5.14159
7') K=SI*SOR(PI*A)*(1.12-.2*A/W+10).6*(A/W) "2-21.7*(A/W)' 7-+.4*(A/W)
72 RP=(K/SY)2/10
76 IF I=1 THEN A2=A
77 IF I=1 THEN T2=O
'4)
IF K'=K:IC THEN GOTO 250
90 IF A(.6*W) THEN GOTO 20
91 NC1=(NC/(1+NC)):ECCON=(.29*K'2/BC/E*(l+NC)'(l/NC))'NC1
95 EP1=ECCON/GSNC1
96 R=GS
99 GOSU 1000
106 T=((EPC-EG(I)+ECTR)/EP1)"(NC+I)-TTRAN
1JO> N%=RP/GS
140 FOR J=2 TO N%
150 R=GS*J
152 GOSUS 1000
155i L-I+J-1
159 TT=T+TTRAN
160I EG(L)=EG(L)+ECCON*(TT'(1 /NC)/R)"NC1-ECTR
170 I NEXT J
180 I A=A+GS
190 I TI-TI+T
191 IF I-1 THEN GOTO 201
195 IF K (S1.5*K1) THEN GOTO 210
201 Q=Q+
202 DADTS () = (A-A2)/(T1-T2)
20.:
KS(Q)=(K1+K)/
2
204 KI=K
205 IF I=1 THEN KS(Q)-K1
206 A2-A
207
208
210
220
2.0
T2:=T1
PRINT D ADTS(Q):KS(Q);A;T1
I=I+1
GOTO 70
GOSUBP
000
INPUT "DO YOU WANT ANOTHER RUN (Y/N)"; Q09
9
2J3 IF 09$-"Y" OR Q0
$"y" THEN GOTO 20
240 END
1000)TTRAN=NC.LOG(BC)+LOG(.29*K-2/E/R/(NC+1))-(NC+1)*LOG(SY(RP/R)(1/(NP+I))I
1010i TTRAN=EXP(TTRAN)
1020 ECTR=ECCON*(TTRAN (1/NC)/R)"NCI
1050 F
PETURN
200: i PRINT "WELCOME TO CCGRMOD9:
2010 i PRINT "'INPUT ALLOY: ASTROLOY
PRTNT_"
_- _
R_-7_
WRITTEN BY KENNETH BAIN":PRINT
1"
185
:040
2050
2060
2070
PRINT "
IN-t100
PRINT "
RENE-95 (60 mesh)
4"
PRINT "
RENE-95 (120 mesh) 5"
INPUT "
OTHER
6":02
IF 02, 1 OR 02;5 THEN GOTO 2100
2075
FOR
Z=l TO 02
READ
C,NC.BP.NP.GS,PPS,E,fIC.EPCK:ICAR.SY.D02
2085 NEXT Z
2090 GOTO 2210
INPUT "ENTER BC (MPa); (creep rate=(stress/BC)'NC)";BC
2110 INPUT "ENTER NC" :NC
2120 INPUT "ENTER NP";NP
2140 INPUT "ENTER GRAIN SIZE (um)";GS
2145 GS=GS / 1 0004:
:C) '
2160 INPUT "ENTER MODULUS (MPa)";E
2170 INPUT "ENTER KIC (MPa*sqrt(m))":KIC
2180 INPUT "ENTER CRITICAL STRAIN";EPC
2190 INPUT "ENTER YIELD STRENGTH (MPa)":SY
2200 INPUT "ENTER DUCTILITY REDUCTION IN OXYGEN";D02
221 0 INPUT "ENTER INITIAL STRESS (MPa)":SI
:21':0
2220 INPUT "ENTER INITIAL CRACK LENGTH (mm)";AO
AO=AO/1000
2225
INPUT "IS OXYGEN PRESENT (Y/N)";Q8$
2240 IF Q8$="Y" OR 085="y" THEN GOTO 2270
2247 IF 02=6 THEN GOTO 2270
2250 GS=PPS
2260 KIC=I ICAR
2270 INPUT "ENTER TITLE";TITL$
2272 DATA 1795,18.4,1662,9.70,28E-6 95E-6,17E+4,88..008,88,.95(:0.1.0)
2275 DATA 1734,19.9,1448,16.6,11E-6,22E-6,16E+4,84,.05.120,1012,.2
2274 DATA 1774.18.5,1454, 16.3,23E-63,.
5E-6, 16E+4,72. 007,105.1012,.714
2275 DATA 416,10.3.1785,8.90,25E-6,7E-6,167E+3.,71..00.90.950j,. _-...5
2276 DATA 416.10..-.1785,8.90:,22E-6,
:-.:)50,.
00.9,95
34E-6,167E-43 71 ..
2278 IF Q8$="Y" OR oes="y" THEN EPC=EPCtDO2
2280 RETURN
5000 LPRINT TITLS:LPRINT "
1c000
5005 AOOAO
LPRINT "INITIAL CRACK LENGTH (mm)=";AOO
3015
o15 LPRINT "INITIAL STRESS (MPa)=";SI
3020 LPRINT "OXYGEN (Y/N)=":$SS
LPRINT
30.5
"BC="
;
C;"
LFRINT " ":LPRINT " "
LPRINT "da/dt (m/s)
3.040 FOR 0Q=1
"
YS="; SY;"
GS = ": GS
"
K (MPatsqrt(m))":LPRINT
TO
3050 LPRINT USING " ##.##.
3060 NEXT Q1
5070 RETURN
=
NC ":NC
"':DADTS(O),.KS(01)
186
APPENDIX
III
CALCULATION OF DUCTILE-BRITTLE TRANSITION TIMES
187
The
tested
alloys
to
time
assumption
the
can
creep-brittle condition for the
be verified by comparing the total test
calculated transition time.
creep-brittle
the
a
of
time
transition
Calculations for
have been suggested by
Riedel and Rice (74) and by McClintock (108).
The C*-integral must be calculated for the SEN geometry
calculate the transition time from Riedel and Rice (74).
to
The
C*-integral
can
inferred
be
calculation of Shih (63).
from
the
J-integral
The expression for C* is:
(1+N)
C=
N )c
(r~Ea a hh(a/wN)
(a/w
l
a a
n
1
+wa2]
(w-a)
m= 1.455 for plane strain
m= 1.072 for plane stress
N
)
(Equ. A.3.1)
188
e=( C/Bc)
Cr is the gross section stress,
where
c, and
h1 (a/w,N ) is a geometric constant which is equal to .96 for
a/w = .25 and N
When
= 10; and .23 for a/w = .15 and Nc = 20.
CX=
specimen
is
a/w = .25,
300 MPa,
in
plane
strain,
w = 11.7 mm,
the
and
calculated
the
value for
transition time is given in Table A.3.1.
The calculation in
Table
tested
A.3.1.
are
for
the
constituative relationships
alloy
using
the
at 704°C.
TABLE A.3.1.
Transition Times for Several Ni-base Alloys at 7040 C
ttrans (sec)
C*(MPa'm-s )
ttrans (RR)(sec) McClintock
-14
ASTROLOY
8.2 x 10 14
MERL-76
1.6 x 101
IN-100
8.8 x 10
Rene-95
1.3 x 10
1.1 x
_
15
105
2.3
9
x 1010
5.1 x 1015
1.2 x 109
1.0 x
2.3
x 106
9.4
x 10
10
1.2 x 10
(60 mesh)
K = 43.5 MPa-m
which
corresponds
results
indicate
for the conditions used in Table A.3.1.
to
an
average, K in CCGR testing.
The
that the transition time calculation
from
McClintock is more conservative,
time.
CCGR
tests
lasted
giving a shorter transition
only
4 x 10 5
seconds
for
Astroloy, and less time for alloys which have a faster CCGR.
The
total
a
longer
transition
times are much larger than the
CCGR test time which indicates that the assupmtion of
creep-brittle
condition
is a valid assumption.
When the
189
total
test time is on the order of the transition time then
no conclusions are possible.
190
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