Grain Size Effects on the Fatigue Response of
Nanocrystalline Materials
by
Timothy Hanlon
B.S., Materials Science and Engineering,
Rensselaer Polytechnic Institute (1999)
Submitted to the Department of Materials Science and Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in Materials Science and Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2004
c Massachusetts Institute of Technology 2004. All rights reserved.
°
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Materials Science and Engineering
March 30, 2004
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Subra Suresh
Ford Professor of Engineering
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Carl V. Thompson II
Stavros Salapatas Professor of Materials Science and Engineering
Chair, Departmental Committee on Graduate Students
2
Grain Size Effects on the Fatigue Response of
Nanocrystalline Materials
by
Timothy Hanlon
Submitted to the Department of Materials Science and Engineering
on March 30, 2004, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy in Materials Science and Engineering
Abstract
The resistance of metals and alloys to fatigue crack initiation and propagation is
known to be influenced significantly by grain size. Based on a wealth of experimental results obtained from microcrystalline metals, where the grain size is typically
greater than 1 µm, it is widely recognized that an increase in grain size generally
results in a reduction in the fatigue endurance limit. On the other hand, a coarser
grain structure can lead to an increased fatigue threshold stress intensity factor range,
as well as a decrease in the rate of fatigue crack propagation. The relevance of these
trends to ultra-fine-crystalline metals (grain size between 100 nm and 1000 nm) and
nanocrystalline metals (grain size less than 100 nm) is relatively unknown. Such lack
of understanding is primarily a consequence of the paucity of experimental data on
the fatigue response of metals with very fine grains. In this work, the fatigue behavior
of electrodeposited, fully dense, nanocrystalline pure Ni, with average and total range
of grain sizes well below 100 nm, was examined. The fatigue response of nanocrystalline Ni was also compared with that of ultra-fine-crystalline and microcrystalline
Ni wherever appropriate. It was found that grain refinement to the nanocrystalline
regime generally leads to an increase in resistance to failure under stress-controlled
fatigue whereas a deleterious effect was seen on the resistance to fatigue crack growth.
To explore the generality of the above trends, similar experiments were performed on
additional ultra-fine-crystalline material systems, produced using alternate processing
techniques such as cryomilling and equal channel angular pressing.
Contact fatigue behavior was also examined down to the nanocrystalline grain
size regime. Friction and damage evolution was monitored as a function of the number
of unidirectional sliding contact fatigue cycles introduced at the surface of several material systems. Critical experiments were performed to isolate the effects of grain size
and material strength. Over the range of materials investigated, strength rather than
grain size dominated the contact fatigue response, with substantial improvements in
strength resulting in reduced damage accumulation, and a lower steady state friction
coefficient. Conversely, grain size was found to govern the rate of crack growth under
mechanical fatigue, with all other structural factors approximately held fixed.
In addition, the cyclic deformation behavior of nanocrystalline materials was
also investigated. Experiments designed to extract the strain response at a constant
range of imposed cyclic stresses provided the first evidence of cyclic hardening in a
nanocrystalline material. This behavior was observed over a broad range of loading
conditions and fatigue frequencies.
Thesis Supervisor: Subra Suresh
Title: Ford Professor of Engineering
This work is dedicated to the loving memory of my brother, Michael Hanlon.
Because I would give it all back for just one more day,
Because I know he would never let me.
Acknowledgements
It is impossible to adequately convey the appreciation I have for the people who
supported (and sometimes carried) me through what has been the most academically
challenging years of my life. Any successes that I might claim will have found roots
in their sacrifice, their selflessness, and their unwillingness to let me fail. It is my
distinct pleasure to acknowledge here my coworkers, friends, and family, without
whom I would not be writing this today.
Thanks are due first to my advisor, Professor Subra Suresh, for providing me with
the opportunity and means to grow under his guidance. He has an exceptional ability
to inspire, and I have truly valued his advice and encouragement over the course of
my studies. He has taught me that limits are self-imposed, and should always be
challenged. He leads by example in this respect, and I am sincerely grateful for the
direction he has provided.
In addition, I extend my sincerest thanks to Professor Lorna J. Gibson and Professor Ronald G. Ballinger for their willingness to serve on my thesis committee. Their
generosity with their time, and their invaluable suggestions are greatly appreciated.
I am exceptionally grateful to all of the sources of funding for this work. Three
years of support were obtained through a National Science Foundation Graduate
Research Fellowship. Additional grants from the Office of Naval Research, as well as
General Electric were critical to the completion of this thesis.
I would also like to acknowledge the support I received from all of my colleagues in
the Suresh Group. First and foremost, I express my deepest gratitude to Mr. George
LaBonte, who has single-handedly kept our lab running since its inception. I consider
myself extremely fortunate for having had the chance to know and work with him
these last few years. Above all, I am grateful for his friendship and his patience, as I
desperately needed them both on several occasions.
Mr. Kenneth Greene is quite simply the finest assistant in all of MIT. Regardless
of his schedule, he always found time whenever I needed his help. I enjoyed trading
stories in his office, even (or maybe especially) when we were both pressed for time.
His laugh may be the most contagious I’ve ever heard.
Dr. Nuwong (Kob) Chollacoop, with me from the start, has been one of my closest
friends over the past four years. I am in awe of his intellect, and the way in which he
chooses to share it. Help is a one-way street with Kob. He gives but refuses to accept
it. I am especially grateful for all of his ABAQUS assistance, and for his tireless
efforts as our system administrator. The lab has not been the same without him.
John Mills is a success waiting to happen. He has shown me the meaning of taking
risks in research, and I look forward to seeing him write one of the most unique theses
ever to leave our department. Friends from the first day he arrived, I’ve enjoyed our
countless meandering conversations, which always seemed to finish at the furthest
possible point from where they started.
Working with Dr. Benedikt Moser for the past twelve months has been the equivalent of having a second advisor. He has the strongest desire to teach that I have ever
seen, and the knowledge of a scientist ten years his senior. I am truly grateful for all
of his contributions to this thesis, and for his endless patience in answering my daily
barrage of questions.
To all remaining members of the Suresh Group, both past and present, I express
my warmest thanks and gratitude for helping to shape the last four years of my
life. I especially thank my friends from the basement office, Simon Bellemare, Bruce
Wu, and In-Suk Choi. Others who have graciously contributed to this work include
Prof. Sharvan Kumar, Dr. Ruth Schwaiger, Prof. Krystyn Van Vliet, Prof. Andrew
Gouldstone, Dr. Yoonjoon Choi, Dr. Tae-Soon Park, Prof. T.A. Venkatesh, Dr.
Yong-Nam Kwon, Dr. Ming Dao, Dr. Brett Conner, and Mr. Laurent Chambon.
Within the Materials Science Department, Kathleen Farrell, Gerald Hughes, and
Stephen Malley have all helped in various ways to make my stay at MIT all the more
enjoyable. I also owe a deep debt of gratitude to Peter Morley, Andrew Gallant, and
all of the machinists at the MIT Central Machine Shop. They have come through for
me time after time.
Whether they knew it or not, my friends outside of MIT were responsible for
keeping a large portion of my sanity intact during my nine year college trek. Ronald
Jensis, Daniel Fiore, David Cooper, Joseph Hayes, Corey Richard, Travis Spalding,
and David Sweenor are the type of friends anyone would feel lucky to have. I look
forward to catching up with all of them upon the completion of this document.
Dr. Don Lipkin is the standard to which I hold myself as a scientist and an
engineer. He has given me some of the soundest advice I have ever received, and his
influence played a major role in my decision to attend MIT. He and Elena Rozier
made my tenure at General Electric one of the most memorable periods of my life.
To the best of my ability, the words that follow represent the level of appreciation,
admiration, and gratitude that I have for my family, who have sacrificed so much to
put me here today.
All that is good in me comes directly from my parents, Margaret and William
Hanlon. If I am half as successful at raising a family, I would consider that to be my
greatest achievement. Without a second thought, my parents bore the unreasonably
heavy financial burden of my education, for which I am eternally grateful. The lessons
I learned before I ever left their house are the ones that I value most, however. It is
their unconditional love and support that drives me to do everything in my power to
make them proud. There is no one in this world that I admire more.
My brother, Daniel Hanlon, and sister, Teresa Hebert, are role models whose
shoes are impossible to fill. Dan, who protects his daughter like he once watched over
his little brother, gives so much of himself without asking or expecting anything in
return. As far back as I can remember, I have strived to be like him in every way,
and he has never let me down. From the bottom of my heart, I thank him for setting
the bar just out of my reach. I am, without a doubt, a better person for it. To his
incredible wife, Paula Hanlon, I extend my deepest thanks for all her encouragement
and support. Never without a smile, she is the type of person that makes everyone
around her feel good, a quality that I both envy and admire.
My sister, Teresa, has been such an inspiration for my entire life. She is the most
caring individual I have ever met, and she is the reason I started down this career
path. I can remember, even at an early age, marveling at her math and science
abilities, wishing that someday I could be as smart. I still carry the same wish. She
has given me more than she will ever know, and she is one of my closest friends. The
term ‘in-law’ has never applied to her husband, Paul Hebert. He has been a brother
to me for sixteen years, and for that, the privilege is all mine. Nobody could ever
replace my brother, Mike, but he is the closest anyone has ever come.
To my nephews and niece, Owen Michael Hebert, Luke William Hebert, and Julia
Mary Hanlon, I thank for providing some much needed perspective in my life. Their
presence alone lifts me.
I am especially grateful to my uncle and aunt, Daniel and Ellie Snyder. Without
their financial support, none of this would have been possible. Their extreme generosity is matched only by their love for their family. I am so blessed for the overwhelming
support that I have received from all of my relatives.
Last, I thank the one who will come first for the rest of my life. Elizabeth Hardy,
my fiancé and future wife, who has unselfishly given more of herself than I ever had
the right to ask. Without her support, I would have surely fallen long ago. I am
grateful to her parents, Thomas and Teresa Hardy, and her siblings, Trisha and Greg,
for making me feel like part of their family. They have raised Liz with such love and
compassion, and it shows in the fullness of her heart. After eight years, I am still
stunned by her beauty, both inside and out. She is my light. I am hopelessly lost
without her, and I am hopelessly lost within her.
Contents
1 Introduction
25
2 Materials and Experimental Methods
35
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
2.2
Materials Investigated . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.2.1
Model Material: Electrodeposited Pure Nickel . . . . . . . . .
36
2.2.2
Mechanical Attrition: Cryomilled Al-7.5Mg . . . . . . . . . . .
39
2.2.3
Severe Plastic Deformation: Equal Channel Angular Pressed
2.3
Pure Titanium . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . .
44
2.3.1
Fatigue Testing of Thin Foils . . . . . . . . . . . . . . . . . . .
44
2.3.2
Fatigue Crack Growth: ufc Al-7.5Mg . . . . . . . . . . . . . .
48
2.3.3
Fatigue Crack Growth: ufc Equal Channel Angular Pressed Ti
50
2.3.4
Cyclic Deformation: Electrodeposited Ni . . . . . . . . . . . .
52
3 Total Fatigue Life and Fatigue Crack Growth
57
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.2
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
3.2.1
Model Material System: Pure Ni . . . . . . . . . . . . . . . .
59
3.2.2
Cryomilled ufc Al-7.5Mg . . . . . . . . . . . . . . . . . . . . .
63
3.2.3
Equal Channel Angular Pressed Pure Ti . . . . . . . . . . . .
65
11
3.3
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1
3.4
67
Theoretical Background: Model for Crack Deflection Induced
Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
3.3.2
Grain Size Effects on Crack Path and Morphology . . . . . . .
72
3.3.3
Effects of Particle Reinforcement on Fatigue Crack Growth . .
80
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
4 Early Stage Contact and Contact Fatigue of Nanocrystalline Materials
85
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
4.2
Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
4.3
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
4.3.1
Electrodeposited Pure Ni . . . . . . . . . . . . . . . . . . . . .
87
4.3.2
Equal Channel Angular Pressed Cu . . . . . . . . . . . . . . .
90
4.3.3
Equal Channel Angular Pressed Ti . . . . . . . . . . . . . . .
94
4.3.4
SiC Reinforced Electrodeposited nc Co . . . . . . . . . . . . .
94
4.4
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
4.5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5 Cyclic Deformation Response of Nanocrystalline Materials
105
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2.1
Cyclic Deformation Behavior of Electrodeposited Pure Ni . . . 107
5.2.2
Rate Dependence on Total Fatigue Life . . . . . . . . . . . . . 111
5.2.3
Failure Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.3
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.4
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6 Concluding Remarks and Suggested Future Work
12
131
6.1
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.2
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A Cyclic Deformation Response of ufc Ni
137
B Fatigue Response of Functionally Graded Electrodeposited Pure Ni141
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
B.2 Material and Experimental Methods . . . . . . . . . . . . . . . . . . 143
B.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 144
B.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
13
14
List of Figures
1-1 (a) Schematic illustration depicting the typical resolved shear stressresolved shear strain response of an FCC metal oriented for single slip
cycled at a constant resolved plastic shear strain amplitude, γpl . (b)
‘Saturation’ hysteresis loops at varying levels of applied γpl , with the
cyclic stress strain curve drawn through their tips. (c) Typical regimes
observed within the cyclic stress strain curve of an FCC metal oriented for single slip. (Figures courtesy of S. Suresh [27]. Copyright
Cambridge University Press. Reprinted with permission.) . . . . . . .
29
1-2 (a) TEM image of a Cu crystal cyclically loaded at γpl = 10−3 at room
temperature. The matrix veins and persistent slip bands are labeled
‘M’ and ‘PSB,’ respectively. (b) TEM image of a Cu crystal cyclically
loaded to saturation at γpl = 1.45 x 10−2 , showing the cell structure
formed in the latter portion of the cyclic stress strain curve (region C).
(Figures courtesy of Mughrabi, Ackermann, and Herz [28] by way of
S. Suresh [27]. Copyright Cambridge University Press. Reprinted with
permission.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
1-3 (a) Extrusions, intrusions, and protrusions in a Cu crystal after 120,000
fatigue cycles at γpl = 2 x 10−3 at room temperature. (b) Nucleation
of a fatigue crack at the interface between the matrix and a PSB in
a Cu crystal after 60,000 fatigue cycles at γpl = 2 x 10−3 at room
temperature. (Figures courtesy of Ma and Laird [33, 34] by way of S.
Suresh [27]. Copyright Cambridge University Press. Reprinted with
permission.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
30
2-1 Grain size distribution of the electrodeposited pure nc Ni, illustrating
the relatively narrow range of grain sizes, as well as the confinement of
all grains below the 100 nm range. . . . . . . . . . . . . . . . . . . . .
37
2-2 Transmission electron micrographs showing the grain structure of (a)
nc Ni [11] and (b) ufc Ni [54]. . . . . . . . . . . . . . . . . . . . . . .
38
2-3 Optical micrograph illustrating the grain structure of the mc Ni investigated [54]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
2-4 Characteristic monotonic tensile tests of pure nc, ufc, and mc Ni. 0.2%
offset yield strengths were measured at 930 MPa, 525 MPa, and 180
MPa, respectively. A measurable decrease in ductility with grain refinement was also observed. . . . . . . . . . . . . . . . . . . . . . . .
40
2-5 (a) Optical micrograph showing the grain size distribution of the Grade
2 pure mc Ti investigated. (b) TEM image depicting the grain size
distribution of ufc ECAP Ti, subjected to 8 pressing cycles at a temperature of 425o C. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
2-6 Schematic illustration of the imposed loading conditions for (a) pinloaded grips and (b) rigid grips. In the latter, the specimen experiences
a fixed displacement at each end, which generates a closing moment at
the crack tip, thereby reducing the effective stress intensity factor. . .
47
2-7 (a) Validation of the finite element model used to calculate the shape
¡ ¢
factor, f Wa , over a wide range of a/W. The model is in close agreement with the standard formula (Equation 2.2) when constant stress
conditions are imposed. (b) Comparison between Equation 2.2 and the
finite element model for the fixed end displacement condition used in
all current experiments.
. . . . . . . . . . . . . . . . . . . . . . . . .
16
49
2-8 Schematic illustration of (a) the dimensions and orientation of the ufc
Al-Mg compact tension specimen and (b) the pre-cracking methodology. (i) The specimen (excluding the through-holes) is machined and
polished down to 0.25 µm. (ii) The sample is loaded between a fixed
and a ‘floating’ platen in a servohydraulic testing machine. (iii) Cyclic
compression loading is imposed. (iv) Through-holes are machined following pre-crack formation. . . . . . . . . . . . . . . . . . . . . . . .
51
2-9 Schematic illustration of the dimensions and orientation of the mc and
ufc Grade 2 pure Ti compact tension specimens. . . . . . . . . . . . .
52
2-10 Geometry of the electro-discharge machined dog-bone specimens utilized for all cyclic deformation investigations. . . . . . . . . . . . . . .
53
2-11 (a) Testing facility for fatigue crack growth studies on thin metallic
foils. Changes in crack length are monitored in-situ with a telescopic
CCD camera module. (b) Clevis used to pin load compact tension
specimens of ufc Al-7.5Mg as well as mc and ufc Ti. Crack growth is
monitored optically using a traveling microscope. (c) Tabletop servohydraulic machine utilized in all cyclic deformation studies. Data is
acquired from strain gages on either side of the specimen. . . . . . . .
55
3-1 A comparison of the S-N fatigue response showing the stress range
versus number of cycles to failure for nc, ufc and mc pure Ni [54]. . .
59
3-2 Variation of the fatigue crack growth rate, da/dN, as a function of ∆K
for pure electrodeposited ufc, and nc Ni at load ratios (a) R = 0.1, (b)
R = 0.3, and (c) R = 0.7, at a fatigue frequency of 10 Hz at room
temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
3-3 Variation in crack length as a function of the number of imposed fatigue
√
cycles for mc, ufc, and nc Ni subjected to an initial ∆K of 9.5 MPa m,
load ratio R = 0.3, and cyclic frequency of 10 Hz at room temperature. 62
17
3-4 Scanning electron micrographs of mc, ufc, and nc Ni subjected to sinu√
√
soidal fatigue loading at initial ∆K values of 10 MPa m, 6.2 MPa m,
√
and 8.5 MPa m respectively. A cyclic frequency of 10 Hz and load
ratio, R = 0.3 were used in all cases. Crack path tortuosity clearly
decreases with decreasing grain size. Images (d) through (f) are higher
magnification images of (a) through (c), respectively, and the magnification of (f) is 10 times that of (d) and (e). . . . . . . . . . . . . . . .
64
3-5 Variation of fatigue crack growth rate, da/dN, as a function of the
stress intensity factor range, ∆K, for ufc cryomilled Al-7.5Mg at R =
0.1 - 0.5 and fatigue frequency of 10 Hz at room temperature. Also
shown are the corresponding crack growth data for a commercial mc
5083 aluminum alloy at R = 0.33 [54]. . . . . . . . . . . . . . . . . .
66
3-6 Scanning electron fractograph showing the fatigue fracture features
of the Al-7.5Mg alloy. Transgranular crack growth is accompanied
by cracking of inclusion particles (indicated with arrows) introduced
during the mechanical alloying process. . . . . . . . . . . . . . . . . .
66
3-7 Scanning electron fractograph illustrating the catastrophic fracture
surfaces of two separate ufc Al-7.5Mg compact tension specimens. A
ductile dimpled failure was observed in both cases. The measured
toughness was considerably lower than that in mc Al-5083, however. .
67
3-8 Variation in fatigue crack growth rate as a function of ∆K for commercially pure mc Ti and ECAP ufc Ti at a fatigue frequency of 10 Hz at
room temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
3-9 Schematic illustration of a kinked crack and the relevant terminology.
70
3-10 Schematic illustration depicting a segment of a periodically deflected
crack subjected to global mode I fatigue loading (a) in its fully opened
state at the peak fatigue load and (b) at the first point of contact upon
unloading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
71
3-11 Schematic illustration of the relevant segment lengths for the repeat
unit of a periodically deflected crack. . . . . . . . . . . . . . . . . . .
73
3-12 Fatigue crack growth trends, depicted as broken lines, predicted from
the crack deflection/closure model described in Section 3.3.1, superimposed on the data from Figure 3-2. The nc Ni growth rate is assumed
tantamount to the linear crack growth rate in Equation 3.15. . . . . .
75
3-13 Scanning electron micrographs of the fatigue fracture surface features
of (a) mc Ni, (b) ufc Ni, and (c) nc Ni. Each sample was subjected to
√
similar loading conditions, with an initial ∆K = 7 MPa m, load ratio
R = 0.3, and a cyclic frequency of 10 Hz at room temperature. The
direction of crack propagation is left to right in each image. White
outlines represent regions examined at higher magnification, with increasingly magnified views arranged in a clockwise fashion. . . . . . .
76
3-14 Field emission gun scanning electron micrographs of the fatigue frac√
ture features of nc Ni subjected to an initial ∆K = 7 MPa m, load
ratio R = 0.3, and a cyclic frequency of 10 Hz at room temperature.
Clusters of features measuring ∼ 60 nm in size (or one to two grain
diameters) are indicated with arrows in (b). . . . . . . . . . . . . . .
77
3-15 Illustration of the crack path tortuosity in (a) commercially pure mc Ti
√
subjected to an initial ∆K of 6.5 MPa m, and the lack thereof in (b)
√
ufc ECAP Ti subjected to an initial ∆K of 5 MPa m. Each sample
was loaded with a fatigue frequency of 10 Hz and load ratio of R = 0.3
at room temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
3-16 Fatigue crack growth rate predictions, based on the deflection/closure
model defined in Section 3.3.1, for commercially pure mc Ti at load
ratios of (a) R = 0.1 and (b) R = 0.3. The crack growth rate data for
the ufc ECAP Ti is assumed to correspond to the linear undeflected
growth rate in Equation 3.15. . . . . . . . . . . . . . . . . . . . . . .
19
79
3-17 SiC particle size and spatial distribution in an electrodeposited nc Co
metal matrix (a) in cross-section and (b) in plane. . . . . . . . . . . .
81
3-18 Variation in fatigue crack growth rate as a function of ∆K for nc electrodeposited pure and SiC (10 vol.%) reinforced Co at a fatigue frequency of 10 Hz and load ratio R = 0.3 at room temperature. . . . .
81
4-1 Instrumented microindenter used for all repeated sliding contact fatigue experiments. A modification of the indenter tip (see the inset
magnified view) facilitated the monitoring of tangential loads during
scratch experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
4-2 Early stage friction evolution as a result of repeated unidirectional
scratching of nc, ufc, and mc pure Ni, at a normal load of 1.25 N.
An apparent improvement in the ‘steady state’ friction coefficient with
grain refinement was observed. . . . . . . . . . . . . . . . . . . . . . .
89
4-3 SEM images of the scratch paths produced in nc, ufc, and mc Ni at
a normal load of 1.25 N after (a-c) 10 passes and (d-f) 98 passes.
Debris accumulation within the boundaries of the wear region exhibits
a positive grain size sensitivity. . . . . . . . . . . . . . . . . . . . . .
91
4-4 FIB images of scratches produced in nc Ni at a normal load of 1.25 N
after (a) 1 pass, (b) 10 passes, and (c) 98 passes. Similar FIB images
for ufc Ni subjected to (d) 50 passes and (e) 98 passes, at a normal
load of 1.25 N. Local increases in grain size were observed with an
increasing number of sliding contact fatigue cycles. . . . . . . . . . .
92
4-5 Friction evolution during unidirectional sliding contact fatigue of ECAP
pure Cu in its as-received and annealed (473 K for 1 hour) conditions.
93
4-6 Damage introduced following 98 passes of repeated unidirectional sliding contact between sapphire and (a) annealed ECAP pure Cu and (b)
as-received ECAP pure Cu. . . . . . . . . . . . . . . . . . . . . . . .
20
94
4-7 (a) Hardness variation as a function of position across the damaged
and undamaged regions of (b) annealed and (c) as-received ECAP Cu.
Each row of indents contains 15 measurements, labeled ‘1’ through ‘15’
for reference in (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
4-8 Early stage friction evolution as a result of repeated unidirectional
scratching of ufc ECAP and mc pure Ti with a 1/16-inch diameter
sapphire spherical indenter at a normal load of 1.25 N. . . . . . . . .
96
4-9 Wear debris produced after 98 passes of unidirectional sliding contact
between a 1/16-inch diameter sapphire spherical indenter and (a) mc
pure Ti and (b) ufc ECAP pure Ti, at a normal load of 1.25 N. . . .
97
4-10 Friction evolution during unidirectional sliding contact fatigue of electrodeposited pure and SiC (10 vol.%) reinforced nc Co. . . . . . . . .
98
4-11 Damage accumulation following 98 passes of unidirectional sliding contact fatigue at a normal load of 1.25 N in (a) electrodeposited pure nc
Co and (b) SiC (10 vol.%) reinforced electrodeposited nc Co. . . . . .
99
4-12 Alloying effects on the friction evolution of nc Ni. Only minor variations in the friction coefficient were observed between pure and tungsten alloyed nc Ni. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5-1 Strain amplitude as a function of cycle number for electrodeposited nc
Ni under a constant range of applied loading, with peak stresses of (a)
800 MPa, (b) 850 MPa, and (c) 1000 MPa. A load ratio of R = 0.25
was used in all experiments. . . . . . . . . . . . . . . . . . . . . . . . 109
5-2 Strain amplitude response from Figure 5-1, normalized by the applied
stress amplitude. A constant rate of hardening is observed throughout
the duration of each test, over a wide range of cyclic frequencies. . . . 110
21
5-3 Stress-strain hysteresis loop width as a function of the number of fatigue cycles at R = 0.25 for nc Ni, at peak stresses of (a) 800 MPa,
(b) 850 MPa, and (c) 1000 MPa. Values reported were extracted from
the center of the hysteresis loop. Widths measured at 30% above and
below center displayed the same trends. . . . . . . . . . . . . . . . . . 112
5-4 Maximum sample strain as a function of cycle number at R = 0.25 for
nc Ni, at peak stresses of (a) 800 MPa, (b) 850 MPa, and (c) 1000
MPa. In all cases, lower frequency testing resulted in a measurably
higher amount of accumulated strain. . . . . . . . . . . . . . . . . . . 113
5-5 Strain amplitude as a function of cycle number for electrodeposited ufc
Ni under a constant range of applied loading, with peak stresses of (a)
475 MPa, (b) 500 MPa, and (c) 550 MPa. A load ratio of R = 0.25
was used in all experiments. . . . . . . . . . . . . . . . . . . . . . . . 114
5-6 Stress-life diagram depicting the variation in number of cycles to failure
with maximum applied stress for electrodeposited nc and ufc pure Ni
at a load ratio of R = 0.25. A clear beneficial effect, in terms of total
life, with increasing fatigue frequency (i.e. strain rate) is apparent. . . 115
5-7 SEM images illustrating the fracture surfaces after (a-b) monotonic
tensile testing, (c-d) fatigue testing with a sinusoidal waveform at a
cyclic frequency of 0.2 Hz, load ratio R = 0.25, and maximum stress
of 850 MPa at room temperature, and (e-f) fatigue testing with a
sinusoidal waveform at a cyclic frequency of 20 Hz, load ratio R =
0.25, and maximum stress of 850 MPa at room temperature. . . . . . 117
5-8 Stress versus strain response for electrodeposited pure nc Ni as a function of strain rate.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5-9 Fracture surface images of a nc Ni sample loaded to failure monotonically at a strain rate of 3.5 x 10−7 sec−1 . A ductile (dimpled) failure
mode prevailed, and no apparent regions of brittle fracture were observed.119
22
5-10 Creep strain accumulated in electrodeposited pure nc Ni as a function
of time at 900 MPa, 1100 MPa, and 1300 MPa. Steady state creep
rates are indicated on the figure. . . . . . . . . . . . . . . . . . . . . . 121
5-11 TEM images depicting the relative lack of dislocation debris and faulted
material in samples cycled to failure at (a) 0.2 Hz and (b) 20 Hz. TEM
samples were extracted from the gage length of failed specimens, far
from the fillet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5-12 Electrodeposited pure nc Ni specimens loaded in fatigue to 100, 1000,
5000, and 7500 cycles (e.g. 1 %, 10 %, 50 %, and 75 % of their total
fatigue lives, respectively), unloaded, and then reloaded monotonically
to failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5-13 Fracture surface examination of the samples depicted in Figure 5-12,
illustrating the change in dimple morphology with increasing numbers
of fatigue cycles. A transition from an elongated dimple morphology
(indicating extensive shear deformation) to a more symmetric dimpled
failure mode (indicating a hardened state) is apparent with increasing
numbers of fatigue cycles. . . . . . . . . . . . . . . . . . . . . . . . . 125
5-14 Schematic illustration of an imperfect grain boundary with several peripheral defects. It is assumed that sites ‘1’ through ‘5’ act independently, requiring different stress levels for dislocation emission from
each site. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6-1 Cross-sectional view of a three-layer electrodeposited plastically graded
pure Ni specimen. From top to bottom, the layers are composed of
mc, ufc, and nc grains, respectively, with a concomitant increase in
hardness through the thickness. . . . . . . . . . . . . . . . . . . . . . 134
23
A-1 Average stress-strain hysteresis loop width as a function of the number
of fatigue cycles at R = 0.25 for electrodeposited ufc Ni at peak stresses
of (a) 475 MPa, (b) 500 MPa, and (c) 550 MPa. Values are reported
for mid-loop width, measured directly at the center of the hysteresis
loop. Widths measured at 30% above and below center displayed an
identical trend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
A-2 Maximum sample strain as a function of cycle number at R = 0.25 for
electrodeposited ufc Ni at peak stresses of (a) 475 MPa, (b) 500 MPa,
and (c) 550 MPa. No conclusive rate effect on the strain accumulation
with fatigue cycling was observed. . . . . . . . . . . . . . . . . . . . . 139
B-1 Cross-sectional indentation across the grain size gradient of an electrodeposited pure Ni, illustrating the variation in hardness from the
mc top layer, to the ufc and nc layers beneath. All indents were performed to a maximum load of 1 N. . . . . . . . . . . . . . . . . . . . 144
B-2 Load versus depth response of the mc and nc faces of a grain size
graded electrodeposited pure Ni at a maximum load of (a) 1 N and (b)
15 N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B-3 Load-controlled indentation of the (a) mc face and (b) nc face of an
electrodeposited pure Ni foil, with a through thickness grain size gradient. The maximum indentation load was 15 N in each case. . . . . . 145
B-4 Effect of (a) a negative grain size gradient and (b) a positive grain size
gradient on the load versus depth response of an electrodeposited pure
Ni. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
B-5 A comparison of the total fatigue life, as a function of maximum applied
stress at a constant load ratio of R = 0.25, for electrodeposited pure Ni
with a through-thickness grain size gradient. A single controlled notch
was introduced (to a depth of 50 µm) on either the mc or nc face of
electro-discharge machined tensile specimens. . . . . . . . . . . . . . . 149
24
Chapter 1
Introduction
The interest in nanocrystalline (nc) materials, with average and total range of grain
sizes typically below 100 nanometers (nm = 10−9 m), has increased significantly over
the past several years. The unique advantages associated with grain refinement to
the nc regime, such as increased strength, hardness, resistance to tribological damage,
and the potential for enhanced superplasticity at low temperatures and high strain
rates [1–10], have promoted such interest. Their mechanical behavior and general
structural and functional applicability have been the topic of discussion during at
least two international conferences (Nano2000 in Sendai, Japan, and Nano2002 in
Orlando, Florida), and the focus of a large number of journal publications.
The apparent flourish in interest has been stimulated by recent advancements
in both fabrication and characterization technologies, where materials of ultra-high
purity and full density can now be processed with narrow grain size distributions in
the nc regime. In addition, the ability to probe the grain structure with Angstrom
(0.1 nm) resolution, and the mechanical response with nm and picoNewton (pN =
10−12 N) resolution, has provided unprecedented means to systematically characterize
these materials.
Currently, there are no strict conventions in place for categorizing the various
regimes of grain size (e.g. microcrystalline (mc), ultra-fine-crystalline (ufc), and nc).
Throughout this study, the following classification scheme will be employed:
• nc: Average and total range of grain sizes are below 100 nm.
25
• ufc: Average grain size is between 100 nm and 1 µm, with the total range of
grain sizes below 1 µm.
• mc: Average grain size is above 1 µm.
The mechanical behavior of nc metals under monotonic loading conditions, specifically nc Ni, Cu, and Pd, have been characterized previously [11–16]. The yield
strength, σy , and hardness are generally found to increase with decreasing average
grain size, down to at least 20 nm. Here, grain boundary strengthening is typically
considered to result from the difficulty associated with transfer of slip between grains,
and the additional obstacles to dislocation motion presented by the boundaries themselves [17]. Conversely, the strain to failure generally decreases with grain refinement
to the nc regime. This reduced ductility is typically believed to result from local
plastic instability events [14, 18–20]. Below an average grain size of ∼ 15 nm, there
have been reports of decreasing strength with further reduction in grain size [21–24].
It is assumed that deformation is accommodated by grain boundary sliding in this
regime [25, 26]; however, no experimental evidence has been obtained to substantiate
this claim.
Kumar, et al. [11] have proposed a deformation mechanism for monotonically
loaded nc Ni, whereby deformation is initiated by dislocation emission at grain boundaries. As a result, void formation occurs at boundaries and triple junctions due to slip
and unaccommodated grain boundary sliding. The attendant void growth results in
constraint relaxation. Ultimately, monocrystalline ligaments separating these voids
experience significant plastic deformation, finally failing in a chisel-point fashion. This
theory, developed through extensive tensile testing of nc Ni, monitored in-situ within
a transmission electron microscope (TEM), accounts for the observed local plasticity
(dimpled fracture surfaces), despite the reduced global ductility (decreased strain to
failure with decreasing grain size).
While the mechanical properties and deformation mechanisms of nc materials
under monotonic loading conditions have received considerable attention, their fatigue
behavior has been relatively unexplored up to this point. The difficulty associated
26
with characterizing the fatigue properties of fully dense nc materials of relatively
uniform purity and grain size stems from current limitations in the processing of
samples with sufficient dimensions for ‘valid’ fatigue testing. Laboratory specimens
are often limited to a few hundred micrometers or less, which severely complicates
conventional fatigue testing and analysis. Due to the paucity of experimental data,
the relevance of fatigue trends extracted from mc materials to ufc and nc metals and
alloys is largely unknown. A more complete understanding of the fatigue properties of
nc and ufc materials is therefore critical to the overall assessment of their usefulness
in service applications involving structural components. Inadequate fatigue behavior
would likely overshadow the abovementioned attractive characteristics of fine-grain
materials.
In general, cyclic deformation mechanisms have been most successfully defined in
high purity single crystal face-centered cubic (FCC) metals. Such mechanisms are
difficult to quantify in most commercial materials, as they are often dependent upon
the level of impurity, as well as the processing technique employed. The macro- and
micromechanisms of cyclic deformation, fatigue crack initiation, and subsequent crack
propagation are described briefly below. A full treatment of this subject matter can
be found in [27].
Upon the application of fully reversed cyclic loading with a fixed amplitude of
plastic shear strain (γpl ), the flow stress of an annealed FCC single crystal, oriented
for single slip, will increase substantially over the first few cycles. Subsequently, a
diminishing rate of hardening is observed until the deformation reaches a quasi-steady
state, often referred to as ‘saturation.’ Here, the resolved shear stress (τR ) - resolved
shear strain (γR ) hysteresis loop becomes stable, and does not vary with further
cycling (Figure 1-1a).
If the value of γpl is incrementally increased following saturation, a series of saturation hysteresis loops (Figure 1-1b) can be used to construct a ‘cyclic stress-strain
curve,’ which relates the peak resolved shear stress at saturation (τs ) to the plastic
shear strain (Figure 1-1c). The regions labelled A, B, and C in Figure 1-1c represent
27
unique hardening characteristics observed in the material.
Region A consists of work hardening as a result of the accumulation of primary
dislocations. In region B, deformation is localized along ‘persistent slip bands,’ (PSBs)
so termed because they continually appear at the same location, even after being
polished away (Figure 1-2a). Secondary slip occurs in region C, where PSBs are
converted into a cell structure (Figure 1-2b), and secondary hardening commences.
Because PSBs are significantly softer than the surrounding matrix, deformation
occurs almost entirely within their bounds. As a result, roughening, by way of intrusions, extrusions, and protrusions (i.e. conglomerations of intrusions and extrusions)
often occurs where PSBs intersect the surface of a material (e.g. Figure 1-3a). The
generally accepted mechanism for the formation of such surface defects entails some
level of slip irreversibility during cyclic loading [29–32]. Intrusions and extrusions
effectively act as micronotches, concentrating stress at their roots, which leads to
fatigue crack nucleation. In addition, the density and distribution of dislocations experience a sharp gradient across the interface between the PSB and matrix material.
It has been shown experimentally that fatigue crack initiation at such an interface is
favored (Figure 1-3b) [33–36]. The total fatigue life is comprised of the number of cycles required for crack initiation, as well as the number required for crack propagation
to a critical length, whereupon catastrophic fracture occurs.
For ductile polycrystalline metals and alloys, one can generally apply the mechanisms of cyclic deformation described above to grains in close proximity to the surface.
While PSBs cannot traverse high angle grain boundaries, they have been observed
to pass through low angle boundaries in coarse grain materials [37, 38]. For fine
grain materials, however, the orientation of primary slip planes in adjacent grains is
typically different, and multiple slip dominates. Their cyclic deformation response
therefore correlates more closely with single crystals oriented for multiple slip, where
the size of the plateau region in Figure 1-1c is significantly reduced or eliminated.
Once a fatigue crack has initiated, its rate of growth is measured by the incremental increase in crack length per loading cycle (da/dN ). This crack growth rate
28
(b)
(a)
(c)
Figure 1-1: (a) Schematic illustration depicting the typical resolved shear stressresolved shear strain response of an FCC metal oriented for single slip cycled at a
constant resolved plastic shear strain amplitude, γpl . (b) ‘Saturation’ hysteresis loops
at varying levels of applied γpl , with the cyclic stress strain curve drawn through
their tips. (c) Typical regimes observed within the cyclic stress strain curve of an
FCC metal oriented for single slip. (Figures courtesy of S. Suresh [27]. Copyright
Cambridge University Press. Reprinted with permission.)
29
(a)
(b)
Figure 1-2: (a) TEM image of a Cu crystal cyclically loaded at γpl = 10−3 at room
temperature. The matrix veins and persistent slip bands are labeled ‘M’ and ‘PSB,’
respectively. (b) TEM image of a Cu crystal cyclically loaded to saturation at γpl
= 1.45 x 10−2 , showing the cell structure formed in the latter portion of the cyclic
stress strain curve (region C). (Figures courtesy of Mughrabi, Ackermann, and Herz
[28] by way of S. Suresh [27]. Copyright Cambridge University Press. Reprinted with
permission.)
(a)
(b)
Figure 1-3: (a) Extrusions, intrusions, and protrusions in a Cu crystal after 120,000
fatigue cycles at γpl = 2 x 10−3 at room temperature. (b) Nucleation of a fatigue crack
at the interface between the matrix and a PSB in a Cu crystal after 60,000 fatigue
cycles at γpl = 2 x 10−3 at room temperature. (Figures courtesy of Ma and Laird
[33, 34] by way of S. Suresh [27]. Copyright Cambridge University Press. Reprinted
with permission.)
30
is characterized in terms of the stress intensity factor range (∆K = Kmax − Kmin ),
where Kmax and Kmin refer to the maximum and minimum values of the stress intensity factor during a fatigue cycle [39, 40].
Typically, two stages of microscopic fatigue crack growth can be identified [41].
Stage I growth takes place when the crack and its associated plastic zone are confined
within a few grains. Here, crack growth occurs primarily by single slip along the
primary slip system. For Mode I loading, the crack must propagate (on average)
in a direction perpendicular to the tensile axis, leading to a zig-zag crack path. At
higher levels of ∆K, the crack tip plastic zone size becomes large, relative to the
characteristic grain dimension, and crack growth occurs via duplex slip (Stage II). In
this case, the crack propagates in a planar fashion between slip bands, normal to the
tensile axis.
Based on the above analyses and experimental results obtained primarily in mc
metals and alloys, one can speculate about the effects of grain size on total fatigue life,
as well as the resistance to subcritical fatigue fracture. It is known that a reduction
in grain size leads to an increase in strength. Therefore, assuming all other structural
factors are held approximately fixed, the fatigue endurance limit of initially smooth
surfaced specimens is expected to scale inversely with grain size. On the other hand,
a coarse grain structure can lead to an increase in the fatigue crack growth threshold
stress intensity factor range and a decrease in the rate of crack growth owing to such
mechanisms as periodic deflections in the path of the fatigue crack at grain boundaries
during crystallographic fracture [42], especially in the near-threshold regime of fatigue
crack growth (e.g., [43]).
The motivation for this study was to determine the relevance of these broad trends
to ufc and nc metals. Although they appear valid in mc metals and alloys, it has
been found that nc materials exhibit several abnormalities with respect to their deformation and failure processes. For materials with average grain sizes less than 100
nm, Hall-Petch type strengthening is typically not observed with grain refinement.
In addition, for FCC metals with exceedingly small grain sizes (<15 nm), hardness
31
and strength have been reported to decrease with further grain refinement [21–24].
This divergence from the strengthening behavior observed in mc metals is typically
thought to occur as a result of the converging defect spacing and grain size length
scales in nc materials. Traditional Hall-Petch strengthening is assumed to involve
dislocation pile-up at grain boundaries, which has not been observed in nc materials.
Additionally, there is evidence that the strain rate dependence of the yield strength
in nc metals is different from that in mc materials, as is the strain to failure [44]. Finally, it is unclear to what extent nc materials, with grain sizes less than 100 nm, can
support the dislocation substructures described above (PSBs, cell structures, etc.),
whose characteristic dimensions can approach the micrometer range. A suppression
of such structures is expected to strongly influence fatigue behavior. These trends
clearly reinforce the need for experimental results pertaining to the cyclic deformation
and fatigue behavior of nc materials. Such is the motivation for this thesis, which is
arranged in the following sequence:
§ Chapter 2 describes in detail the material systems investigated, as well as the
experimental methods employed. The strengths and limitations of the processing and testing techniques are discussed.
§ Chapter 3 presents total life and fatigue crack growth results obtained in electrodeposited nc, ufc, and mc pure Ni. The latter trends are then compared
with results from a ufc cryomilled Al-7.5Mg alloy and a pure mc and ufc equal
channel angular pressed Ti system to explore their overall generality. A crack
deflection/closure model is used to account for the observed deleterious effects
of grain refinement on the resistance to subcritical fatigue fracture.
§ Chapter 4 describes experiments developed to probe the contact fatigue resistance of a variety of material systems, down to the nc grain size regime. Testing
was performed using an instrumented microindenter, modified to monitor the
friction evolution over many fatigue cycles. Critical experiments designed to
separate the effects of grain size and material strength are described.
32
§ Chapter 5 discusses the grain size dependence of the cyclic deformation behavior
of electrodeposited pure Ni. Several mechanisms are described to justify the
observed cyclic hardening, as well as the strain rate sensitivity of the total
fatigue life, in nc and ufc Ni.
§ Chapter 6 provides a brief summary and conclusions, and addresses pertinent
future areas of investigation.
33
34
Chapter 2
Materials and Experimental
Methods
2.1
Introduction
The materials examined herein, and all associated experimental techniques are described in full detail below. The structure and mechanical properties of each system
were thoroughly characterized prior to initiating fatigue testing. Strict guidelines to
determine the general acceptability of all ‘as-received’ materials were set forth a-priori
to eliminate artificial processing induced effects on the fatigue response.
As-received structures of all nc and ufc materials were examined via transmission
electron microscopy (TEM), and in some cases X-ray diffraction. It should be noted,
however, that X-ray diffraction is typically unreliable in terms of grain size characterization [45]. Measurements of diffraction pattern peak broadening can be used to
estimate the grain size, with broader peaks corresponding to finer grains. However,
intrinsic defects, twins, and stacking faults can also affect peak width, which generally
results in an underestimation of the grain size. TEM image analysis was therefore
employed to identify the average and range of grain sizes in each nc and ufc material
tested. All mc materials were mechanically and/or electropolished to expose the grain
structure, which was subsequently observed optically.
In order to develop quantitative trends regarding the effects of grain size on fatigue
behavior, it is necessary to compare materials of nearly identical composition, purity,
35
and density, with grain size variations spanning several orders of magnitude. It is
therefore sensible to develop a ‘model material system’ of ultra-high purity and full
density, with attainable grain sizes ranging from the mc to the nc regime. To explore
the generality of trends extracted from such a system, similar fatigue experiments
were performed on additional materials produced via alternate commercial processing
techniques, with somewhat relaxed constraints on the level of purity.
The following materials were systematically investigated to probe the effects of
grain size on fatigue behavior:
• Fully dense, electrodeposited pure Ni
• Cryomilled Al-7.5Mg
• Equal channel angular pressed Ti
Electrodeposited Ni was selected as a model material system, the results from
which were compared with those from commercially produced Al-7.5Mg and pure Ti.
2.2
Materials Investigated
2.2.1
Model Material: Electrodeposited Pure Nickel
In this investigation, the choice of a model material system, and corresponding fabrication technique, were predicated upon the following requirements:
§ The attainability of a true nc grain structure, where the average and total range
of grain sizes are both well below 100 nm.
§ The ability to achieve an ultra-high level of material purity, with sufficient
reproducibility.
§ The capability to produce a fully dense structure.
Such requirements ensure that the material produced can accurately be described
as nc. Particular attention was paid to maintaining a range of grain sizes well below
36
0.25
Fraction of Grains
0.2
0.15
0.1
0.05
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70
Grain Size (nm)
Figure 2-1: Grain size distribution of the electrodeposited pure nc Ni, illustrating the
relatively narrow range of grain sizes, as well as the confinement of all grains below
the 100 nm range.
100 nm to avoid having larger ‘outlier’ grains dominate the deformation and fatigue
response of the material.
While there are a number of methods currently available to fabricate nc materials
[46–53], electrodeposited Ni was selected as the model material system. It can be
produced over a broad range of grain sizes, from nc to mc, and is capable of satisfying
the abovementioned requirements. Two notable advantages of the electrodeposition
process are the ability to produce relatively large (in-plane) quantities of uniform,
fully dense material (80 mm x 80 mm), and the capacity to confine the grain size
to an extremely narrow distribution (Figure 2-1). Although the attainable thickness
resides in the millimeter range, samples deposited for this investigation were limited
to a thickness of approximately 100 - 150 µm, to ensure through-thickness grain size
uniformity and to limit processing induced residual stresses.
37
50 nm
270 nm
(a)
(b)
Figure 2-2: Transmission electron micrographs showing the grain structure of (a) nc
Ni [11] and (b) ufc Ni [54].
Ni foils with two substantially different grain sizes were produced using similar
processing methods: an nc material with an average grain size of 20-40 nm and a ufc
equiaxed structure with an average grain size of approximately 300 nm. The former
had a columnar grain structure with an aspect ratio of 7-10, whereas the ufc material
was nearly equiaxed. The as-received structures of both materials were characterized
by electron microscopy (Figure 2-2) and/or x-ray diffraction. The micrographs in
Figure 2-2 depict relatively defect-free initial structures, a critical factor in assessing
the role of grain size on the overall fatigue response. All electrodeposited Ni foils were
of 99.9% purity, and were procured from Integran Corporation, Toronto, Canada.
For comparison purposes, a mc pure Ni with an equiaxed grain size of 10 µm
(procured from Goodfellow, Berwyn, PA) was also studied. The grain structure was
exposed by way of electropolishing, and is illustrated in Figure 2-3.
Position controlled monotonic tensile tests were performed on nc, ufc, and mc Ni
‘dog-bone’ specimens in a servo-hydraulic testing machine, fitted with a 1 kN load
cell. Strain was measured directly with an extensometer, up to 2.5%. The concurrent
38
25 µm
Figure 2-3: Optical micrograph illustrating the grain structure of the mc Ni investigated [54].
stroke displacement data was adjusted for machine compliance by matching the elastic
portion of the stress-strain curve obtained from the extensometer, with that obtained
from the displacement of the crosshead. Because the strain to failure was typically
above 2.5%, the curves depicted in Figure 2-4 incorporate the compliance corrected
stroke displacement data, in place of extensometer measurements. Results for the
nc and ufc Ni revealed 0.2% offset yield strength values of 930 MPa and 525 MPa,
respectively, and strain to failure values of 3% and 10%, respectively. The mc Ni had
a yield strength of 180 MPa, tensile strength of 450 MPa and tensile strain to failure
of 35%.
2.2.2
Mechanical Attrition: Cryomilled Al-7.5Mg
Mechanical attrition (MA) is a processing technique that enables the production of
large quantities of nc powders, which can subsequently be consolidated into bulk form.
Typically, coarse-grained powder feedstock is interspersed with hardened steel or
tungsten carbide coated spheres in a container, which is then violently agitated. Grain
refinement is considered to occur in three stages. First, the deformation of the powder
39
1400
Stress (MPa)
1200
nc Ni
1000
800
ufc Ni
600
400
mc Ni
200
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Strain (-)
Figure 2-4: Characteristic monotonic tensile tests of pure nc, ufc, and mc Ni. 0.2%
offset yield strengths were measured at 930 MPa, 525 MPa, and 180 MPa, respectively.
A measurable decrease in ductility with grain refinement was also observed.
40
particles, resulting from the energy imparted by the hardened pellets, is localized
within shear bands that are approximately 1 µm in width. Second, with increasing
levels of strain and dislocation density, dislocation annihilation and recombination
results in the formation of small angle grain boundaries, which separate (refine) the
original grains. Finally, grain boundary sliding and grain rotation lead to a completely
random structure [47, 48].
MA is often considered attractive due to its relative simplicity, the inexpensive
nature of the required equipment, its applicability to any material class, including
brittle materials, and the ease with which the process can be scaled to produce large
quantities of powder. It is limited, however, with respect to the level of processing
induced contamination (from the milling chamber and milling media), as well as
the difficulty associated with consolidating the resulting powders, without inducing
significant grain growth.
Alloys produced using MA can exhibit an extended range of solid solubility, which
is often attributed to the severe state of plastic deformation imposed on the milled
powder. As previously described, this deformation is responsible for refining the
grain structure via defect annihilation and recombination. In addition to grain size
reduction, however, the particle size of the milled material is also reduced, as a result
of repeated particle fracturing during the agitation stage of the process. Together,
the increased grain boundary volume and reduced diffusion distances, ascribed to the
refined grain and particle sizes respectively, facilitate increased interdiffusion of the
alloy components, which subsequently leads to extended solid solubility [55]. Elevated
defect densities inherent to the process also contribute to the enhanced diffusion
characteristics. Even powders with a positive heat of mixing can be mechanically
milled to form a (non-equilibrium) solid solution. With a few limited exceptions,
however, only those powders that closely follow the Hume-Rothery rules have been
found to exhibit very large extended solubility ranges [55].
One variant of the mechanical attrition process is a low energy/low temperature
form of MA known as cryomilling. The final grain structure is generally independent
41
of the milling energy, assuming the milling time is sufficiently long to compensate
for the inherently slower kinetics associated with low energy mills [47]. Typically,
powders are cryomilled in a liquid nitrogen environment, which increases the rate
of grain refinement and decreases the minimum achievable grain size [47, 56]. In
addition, the liquid nitrogen medium reduces the tendency for ductile materials to
sinter and/or adhere to the container walls during the milling process [57].
To assess the overall generality of the trends observed in electrodeposited Ni,
the fatigue properties of a ufc cryomilled Al-7.5Mg (wt%) alloy, for which larger
bulk specimens could be produced, were evaluated. The Al-7.5Mg was fabricated
in billet form, 50 mm in diameter, and several inches in length. This choice was
motivated by the fact that grain size effects could be assessed in the ufc regime using
specimens whose dimensions are sufficiently large (35 mm x 35 mm x 5 mm) to meet
the requirements of conventional standards for fatigue testing of bulk materials. In
addition, the mechanical properties of this alloy system have been the subject of
considerable experimental research, although its fatigue crack growth response has
not been assessed to date.
A complete review of the Al-7.5Mg powder production and consolidation techniques is given in [57, 58]. Briefly, aluminum powder, with high magnesium content, and commercially pure aluminum powder were combined and subsequently cryomilled. The resulting product was then consolidated by degassing in aluminum cans
at high temperature, followed by hot isostatic pressing (HIP), and finally extrusion of
the hipped billets to eliminate porosity. Milling contaminants include nitrogen, oxygen, carbon, iron, nickel, chromium, manganese, silicon, copper, zinc, and titanium,
the relative proportions of which are given in [58]. TEM images show that the Al-Mg
alloy investigated has a relatively equiaxed grain structure, with an average grain size
of ∼ 300 nm [58]. Its yield and tensile strengths were measured experimentally to be
540 MPa and 551 MPa, respectively.
42
2.2.3
Severe Plastic Deformation: Equal Channel Angular
Pressed Pure Titanium
Equal channel angular pressing (ECAP) is a severe plastic deformation process used to
refine the grain size of a material, without significantly altering its cross section. The
ECAP technique utilized in this study was first described by Segal [59], before which,
forging, extrusion, and rolling were the commonly employed methods to introduce elevated levels of plastic deformation. In general, sufficiently severe deformation occurs
only after several processing cycles, regardless of the technique employed. Extrusion,
forging, and rolling result in significant cross-sectional reductions with each pass, limiting the total number of cycles and therefore the total strain induced. ECAP, on the
other hand, is capable of retaining the initial billet cross section within a few percent
over many processing cycles.
While conventional large deformation processing techniques require substantial
load capacity equipment, ECAP is a relatively low pressure technique, making it
an attractive commercial alternative. The ECAP process entails extruding a well
lubricated billet through two intersecting channels of equal diameter, both of which
having comparable diameters to the initial work piece. Deformation of the entire billet
then occurs via uniform simple shear at the intersection plane between the channels.
The pertinent processing variables are the angle between intersecting channels (a
die angle of 90o is typically considered most effective), number of pressing cycles,
operating temperature, and lubrication choice.
The material investigated in this study was a Grade 2 commercially pure Ti, the
chemical and mechanical requirements for which are listed in [60]. Commercially
pure Ti is chemically inert and often considered more attractive than Ti-6Al-4V for
biological implant applications. Untreated, its strength is considerably lower than
that of Ti-6Al-4V, however. Methods of strengthening commercially pure Ti are
therefore receiving considerable attention.
Billets of pure mc Ti, 40 mm in diameter and 150 mm in length, were subjected
to eight pressing cycles at a temperature of 425o C using a molybdenum disulphide
43
(a)
(b)
Figure 2-5: (a) Optical micrograph showing the grain size distribution of the Grade 2
pure mc Ti investigated. (b) TEM image depicting the grain size distribution of ufc
ECAP Ti, subjected to 8 pressing cycles at a temperature of 425o C.
lubricant and a die angle of 90o . The resulting grain structure was relatively equiaxed,
with an average grain size of approximately 250 nm (Figure 2-5). Full details of the
processing technique are described elsewhere [61].
The unique advantage of studying such a system is the ability to compare the ufc
material directly to its mc counterpart, from which it was formed. Image analysis of
the mc Ti, mechanically polished and etched in Kroll’s reagent (2 mL HF, 4 mL HNO3 ,
1000 mL H2 O), revealed an average grain size of ∼ 22 µm (Figure 2-5). The yield
strengths of the ufc and mc Ti were measured at 635 MPa and 430 MPa, respectively.
2.3
2.3.1
Experimental Methods
Fatigue Testing of Thin Foils
Due to self-imposed restrictions on the thickness of electrodeposited Ni foils, (to
foster grain size uniformity) fatigue specimens were typically on the order of 100 µm
thick. In order to minimize processing induced residual stresses, all fatigue samples
were extracted from the electrodeposited foils by way of electro-discharge machining.
44
Both low- and high-cycle fatigue experiments were carried out in a laboratory air
environment, using a sinusoidal waveform in all cases.
For the purpose of investigating the stress-life response, nickel foils were machined
into “dog-bone” type specimens, 25 mm in length. After mechanical polishing, these
specimens were subjected to zero-tension-zero (R = 0) loading at a frequency of 1.0
Hz. Because of obvious thickness constraints, compression loading was not a viable
option. Multiple samples of the nc and ufc specimens were tested to failure at a given
stress range, and the number of cycles to failure was recorded.
High cycle fatigue crack growth experiments for the nc, ufc, and mc Ni foils were
conducted using single edge-notched specimens, where fatigue cracks were initiated
in cyclic tension at load ratios ranging from 0.1 to 0.7 at a cyclic frequency of 10
Hz at room temperature. The specimens were 39 mm long, 9.9 mm wide, and 100
µm in thickness. The edge-notch was machined to a depth of 1 mm, and its tip was
sharpened using a razor blade sprayed with a 0.25 µm diamond polishing suspension.
Changes in crack length as a function of the number of fatigue cycles were monitored
optically with a traveling microscope. The crack growth rate da/dN was calculated as
a function of the stress intensity factor range, ∆K, as the length of the crack increased
under a constant range of imposed cyclic loads. To ensure small-scale yielding conditions prevailed, all data was truncated such that the remaining uncracked ligament
length was always at least twenty times greater than the maximum plastic zone size
at the crack tip.
Shape Factor Considerations
In order to characterize the variation of the fatigue crack growth rate as a func¡ ¢
tion of ∆K, a proper evaluation of the shape factor, f Wa , specific to the present
specimen geometry (single-edge-notched tension specimen) and loading configuration
was required. For a rectangular plate of width, W, containing a through-thickness
edge crack of length, a, it is commonly known that the stress intensity factor can be
45
expressed by:
√ ³a´
KI = σ af
,
W
(2.1)
where
³a´
³ a ´2
³a´
³ a ´3
³ a ´4
= 1.99 − 0.41
+ 18.7
f
− 38.48
+ 53.85
,
W
W
W
W
W
(2.2)
However, the above expression is limited to loading configurations capable of producing a uniform stress throughout the specimen. Typically, this can be accomplished
by utilizing proper sample geometry (i.e. height, H > 2W ). Equation 2.2 must be
modified when a non-uniform stress is applied.
In order to conduct experiments at a sufficiently high frequency, it was necessary
to load the edge-notch specimens using rigid, as opposed to pin-loaded grips. In the
latter, there exists a rotational degree of freedom, which produces an opening moment
at the crack tip during tensile loading (Figure 2-6a). Upon loading with such grips, a
significant degradation of the imposed sinusoidal waveform occurred at approximately
3 to 5 Hz. This was accompanied by machine resonance, which rendered the system
unstable. Conversely, when specimens were loaded with rigid grips (i.e. ‘fixed end
displacement’ loading), where the ends of the specimens were displaced by a constant
amount (Figure 2-6b), a clean sinusoidal waveform at the desired frequency of 10 Hz
was easily achieved.
Several authors [62–65] have previously recognized that the application of Equations 2.1 and 2.2 to a fixed end displacement loading configuration can substantially
overestimate the mode I stress intensity factor. The boundary conditions associated
with this type of loading are such that a closing bending moment is imposed on the
crack, even during tensile loading, due to the lack of rotational freedom in the grips.
This imposed closing moment effectively reduces the stress intensity factor, lowering
the driving force for crack propagation.
To account for this relative reduction in ∆K, the shape factor, f
¡a¢
W
, was eval-
uated via finite element analysis for the specific loading geometry used in this investigation. In the analysis, the J-integral was calculated for a/W values ranging from
46
P
θ/2
P
M
θ/2
M
δ/2
θ=0
δ/2
θ=0
M
M
P
P
(a)
(b)
δ/2
δ/2
Figure 2-6: Schematic illustration of the imposed loading conditions for (a) pin-loaded
grips and (b) rigid grips. In the latter, the specimen experiences a fixed displacement
at each end, which generates a closing moment at the crack tip, thereby reducing the
effective stress intensity factor.
47
0.1 to 0.7, fully encompassing the range investigated experimentally. Because the
J-integral is proportional to the square of the stress intensity factor under small-scale
yielding conditions, any error associated with the determination of J in the finite element analysis is significantly reduced (by a power of 1/2) upon relating J to f(a/W).
Assuming the stress intensity factor, KI , has the form given in Equation 2.1, the
shape factor can be expressed as follows:
³ a ´ r JE
=
f
,
W
aσ 2
(2.3)
By applying a prescribed load, J can be systematically solved for over a range
of crack lengths. In this manner, the shape factor can be fully characterized for the
loading configuration and specimen geometry of interest.
To confirm the accuracy of the analysis, a constant stress loading configuration
was modeled, and the resulting shape factor was compared to the standard formula
given in Equation 2.2. Figure 2-7a clearly illustrates the validity of the analysis.
¡ ¢
Figure 2-7b compares f Wa for the constant stress and fixed end displacement loading
configurations. The shape factor from the latter was used in all calculations of the
stress intensity factor below.
2.3.2
Fatigue Crack Growth: ufc Al-7.5Mg
In addition to the crack growth experiments conducted on the electrodeposited Ni
foils, the fatigue crack growth response of a ufc Al-7.5 wt% Mg alloy was also studied.
An extruded Al-Mg billet was sectioned to obtain 5 mm thick compact specimens in
the C-R (circumferential-radial) configuration (e.g. Figure 2-8a). The notch tip was
machined to a radius of 0.09 mm, and the specimen faces were polished to a mirror
finish, with a final 0.25 µm polishing step. The through-holes, located on either side
of the notch to pin-load the specimens, were machined after the fatigue pre-crack was
introduced.
Fully compressive far-field cyclic loads were used to introduce a self-arresting
fatigue pre-crack in each sample [27, 66, 67]. These loads were transmitted through
48
15
Standard Formula (Constant Stress)
FEM Calculation (Constant Stress)
f(a/W)
10
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.6
0.7
a/W
(a)
15
f(a/W) Constant Stress
f(a/W) Fixed End Displacement
f(a/W)
10
5
0
0
0.1
0.2
0.3
0.4
0.5
a/W
(b)
Figure 2-7:
¡ ¢(a) Validation of the finite element model used to calculate the shape
factor, f Wa , over a wide range of a/W. The model is in close agreement with the
standard formula (Equation 2.2) when constant stress conditions are imposed. (b)
Comparison between Equation 2.2 and the finite element model for the fixed end
displacement condition used in all current experiments.
49
two parallel plates fitted in a servohydraulic test frame (e.g. Figure 2-8b). The
lower platen was ‘floating,’ in that it maintained a small degree of rotational freedom
throughout the duration of the test. This assured the plates remained parallel and in
intimate contact with the sample. Each specimen was cyclically loaded at 10 Hz in
compression with an incrementally increasing stress range, ∆σ, until a crack initiated
and grew from the notch to a distance of at least fifteen times the notch radius.
Crack growth was monitored in-situ with a telescopic video camera module, and
ex-situ with an optical microscope. Following the pre-cracking stage, tension-tension
fatigue experiments were performed at load ratios ranging from R = 0.1 to R = 0.5, at
a frequency of 10 Hz. Crack growth was sufficiently slow to facilitate load-controlled
rather than K-controlled experiments. The initial ∆K imposed on each sample was
well below the anticipated threshold stress intensity factor range, ∆Kth . ∆K was
increased in 10% increments until measurable crack growth had occurred, at which
point ∆Kth could be determined. Data for the remainder of the crack growth curve
were collected in a similar fashion. The fracture surfaces were subsequently examined
under a scanning electron microscope (SEM).
2.3.3
Fatigue Crack Growth: ufc Equal Channel Angular
Pressed Ti
Compact tension specimens, 3 mm in thickness, were electro-discharge machined in
the R-L (radial-longitudinal) configuration from Grade 2 commercially pure Ti billets subjected to zero (mc Ti) or eight (ufc Ti) ECAP cycles. In plane dimensions
measured 33 mm x 31.75 mm (Figure 2-9). The notch tip was machined to an initial
radius of 0.12 mm, and subsequently sharpened to a radius of 0.03 mm with a razor
blade sprayed with a 0.25 µm diamond polishing suspension. Specimen faces were
polished to a mirror finish, with a final 0.25 µm polishing step.
A fatigue pre-crack was introduced in cyclic tension at load ratios of R = 0.1 and
R = 0.3, at a cyclic frequency of 10 Hz (sinusoidal waveform) at room temperature.
Subsequent crack growth was monitored in-situ with a telescopic video camera module, and ex-situ with an optical microscope, in a similar fashion to that described in
50
φ 6.35
35
4.5
*all units in mm
Sample thickness: 5.0mm
Notch length: 12.5mm
35
φ 50
(a)
Load cell
∆ σ
(i)
(iii)
(iv)
Actuator
(ii)
(b)
Figure 2-8: Schematic illustration of (a) the dimensions and orientation of the ufc
Al-Mg compact tension specimen and (b) the pre-cracking methodology. (i) The
specimen (excluding the through-holes) is machined and polished down to 0.25 µm.
(ii) The sample is loaded between a fixed and a ‘floating’ platen in a servohydraulic
testing machine. (iii) Cyclic compression loading is imposed. (iv) Through-holes are
machined following pre-crack formation.
51
Diameter = 6.61mm
15.865mm
7.27mm
Billet Axis
7.27mm
15.865mm
6.61mm
5.29mm
3mm
33.05mm
Figure 2-9: Schematic illustration of the dimensions and orientation of the mc and
ufc Grade 2 pure Ti compact tension specimens.
Section 2.3.2.
2.3.4
Cyclic Deformation: Electrodeposited Ni
The electrodeposited pure Ni described in Section 2.2.1 was selected as a model
material system to investigate the cyclic deformation behavior of nc materials. The
specimen geometry chosen was a sub-sized ‘dog-bone,’ measuring 53 mm in total
length, 20 mm in gage length, 5 mm in gage width, and 100 µm in thickness (Figure
2-10). The as-received state of the nc Ni consisted of a flat foil, electropolished
to a mirror finish on both sides. The ufc Ni foils were identically electropolished,
however a slight curvature generally existed in one plane. Samples extracted from
these foils were machined with their long axis oriented perpendicular to the direction
of curvature, such that each dog-bone specimen was relatively flat over its entire gage
length.
Samples were thoroughly cleaned in an ultra-sonic bath of acetone, followed by a
52
All units in millimeters
52.94
12
R
6
5
9
20
Figure 2-10: Geometry of the electro-discharge machined dog-bone specimens utilized
for all cyclic deformation investigations.
rigorous swabbing of both surfaces with a water based acidic surface cleaner (M-Prep
Conditioner A) containing phosphoric acid. A neutralizing cleansing step, using a
water based alkaline surface cleaner (M-Prep Neutralizer 5A) containing ammonia
water, was subsequently performed. Strain gages were mounted to both sides of the
specimen with an adhesive certified for strain gage usage (M-Bond 200 Adhesive).
Additional contact points (solder tabs) were mounted beneath each strain gage to
facilitate an electrical connection for data acquisition, without introducing an artificial
strain on the gages due to the weight of the required cables. Fine wires were then
soldered between the strain gages and solder tabs. Each terminal required less than
3 seconds of contact with the soldering iron to complete the connection. The relative
position of the strain gage and solder tab assembly is depicted in Figure 2-11c. The
stiffness of the assembly was negligible, relative to that of the sample, and the stressstrain response was not dependent upon the method of strain measurement (i.e. strain
gage or extensometer characterization). The influence of the strain gages on the
mechanical response was therefore assumed negligible.
Fully strain gaged samples were loaded into a tabletop servohydraulic testing
machine, fitted with a 1000 N (dynamic) capacity load cell. Rigid as opposed to pin
loaded grips were utilized to avoid machine instability at high testing frequencies.
53
Samples were loaded in tension to 5 N, prior to soldering data acquisition cables to
the abovementioned solder tabs. Specimens were then held in tension at 5 N for 30
minutes, to allow the strain gages to equilibrate. Following this hold period, the gages
were electronically balanced to a strain of 0 %.
Tension-tension fatigue loading, with a sufficiently high load ratio (R = 0.25) was
employed in all experiments to avoid specimen bending. In a previous study on the
same material [44], a pronounced rate effect was evident in the indentation and tensile
response of nc Ni. However, ufc Ni did not exhibit a similarly strong rate effect. It was
therefore necessary to sample a broad range of loading frequencies to ascertain the
strain rate dependence, or lack thereof, of the cyclic deformation response. Samples
were tested to failure at a fatigue frequency of 0.2 Hz and 20 Hz (sinusoidal waveform)
at room temperature.
Each test was conducted under a constant range of applied loads. Both the 0.2
Hz and 20 Hz loading conditions required several cycles (30 or less) to achieve a truly
constant load amplitude. Load, displacement, and strain data was acquired at 0.5
kHz and 5 kHz for the 0.2 Hz and 20 Hz tests, respectively.
Figure 2-11 depicts the testing facilities described in Sections 2.3.1 through 2.3.4.
All experiments were performed at room temperature in a laboratory atmosphere.
54
(a)
(b)
(c)
Figure 2-11: (a) Testing facility for fatigue crack growth studies on thin metallic foils.
Changes in crack length are monitored in-situ with a telescopic CCD camera module.
(b) Clevis used to pin load compact tension specimens of ufc Al-7.5Mg as well as mc
and ufc Ti. Crack growth is monitored optically using a traveling microscope. (c)
Tabletop servohydraulic machine utilized in all cyclic deformation studies. Data is
acquired from strain gages on either side of the specimen.
55
56
Chapter 3
Total Fatigue Life and Fatigue
Crack Growth
3.1
Introduction
It is well established that the resistance to fatigue crack initiation and propagation
in most metals and alloys is significantly influenced by grain size (e.g., [27]). On
the basis of experimental results obtained in mc metals with grain sizes typically
above 1 µm, it is widely recognized that an increase in grain size generally results
in a reduction in the fatigue endurance limit. Here, with all other structural factors
approximately held fixed, the endurance limit of initially smooth-surfaced specimens
generally scales with the strength of the material, which increases with decreasing
grain size. On the other hand, a coarse grain structure can lead to an increase in
the fatigue crack growth threshold stress intensity factor range and a decrease in the
rate of crack growth owing to such mechanisms as periodic deflections in the path of
the fatigue crack at grain boundaries during crystallographic fracture [42], especially
in the near-threshold regime of fatigue crack growth (e.g., [43]). The relevance of
such broad trends extracted from conventional mc alloys to ufc and nc metals is
largely unknown at this time. The fatigue behavior of ufc metals produced by severe
plastic deformation using equal channel angular pressing has been studied [68–70].
Here, cyclic softening and deterioration in low cycle fatigue response have been found
with grain refinement, despite an improvement in the fatigue endurance limit seen
57
in stress-life tests. However, conclusive general trends could not be extracted from
such observations in that mc metals with severe initial cold work are also known to
exhibit cyclic softening [71]. Comprehensive knowledge of the fatigue properties of
nc and ufc metals and alloys is critical to the overall assessment of their usefulness
in service applications involving structural components. Inadequate fatigue behavior
would likely overshadow several potentially attractive characteristics [2–5, 10] of finegrain materials (i.e. enhanced strength, hardness, wear and corrosion resistance).
The difficulty associated with characterizing the fatigue properties of fully dense
nc materials of relatively uniform purity and grain size stems from current limitations
in the production of samples with sufficient dimensions for ‘valid’ fatigue testing. The
thickness of laboratory specimens produced for exploratory studies is often limited to
a few hundred micrometers or less, which severely complicates conventional fatigue
testing and analysis. While the mechanical behavior of several nc metals and alloys
has been successfully characterized under monotonic loading conditions [1], detailed
and systematic studies regarding the resistance of nc materials to fatigue damage have
only been reported through preliminary findings [54] of the work described below.
The present study was initiated to investigate the effects of cyclic loading on the
fatigue resistance of fully dense nc metals. The stress-life (S-N) fatigue response and
the fatigue crack growth resistance of nc electrodeposited pure Ni were compared
with a similarly produced ufc pure Ni, as well as mc pure Ni. A particular objective
of the present experimental work was to investigate whether grain refinement in the
ufc and nc regimes results in (a) an enhancement in the fatigue endurance limit and
(b) an increase in the rates of fatigue crack propagation. For the latter effect, additional crack growth experiments were also conducted in a cryomilled ufc Al-Mg alloy
and an equal channel angular pressed (ECAP) Grade 2 pure Ti, for which sizeable
quantities of bulk specimens were available so that conventional fatigue testing could
be employed.
58
800
nc Ni
ufc Ni
mc Ni
Stress Range (MPa)
700
600
500
400
300
200
100
4
10
10
5
10
6
10
7
No. of Cycles to Failure
Figure 3-1: A comparison of the S-N fatigue response showing the stress range versus
number of cycles to failure for nc, ufc and mc pure Ni [54].
3.2
3.2.1
Results
Model Material System: Pure Ni
Total Fatigue Life
The experimental method used to investigate the total fatigue life behavior of pure
Ni is described in Section 2.3.1. The effect of grain size on the resistance to stresscontrolled fatigue is plotted in Figure 3-1 in terms of the stress-life (S-N) diagram.
It is seen that the nc Ni, with an average grain size of approximately 30 nm, has a
slightly greater resistance to stress-controlled fatigue loading than the ufc Ni, with an
average grain size of approximately 300 nm. This trend is observed both in the stress
range at a given number of cycles to failure and in the endurance limit. In addition,
the range of endurance limit values observed for mc pure Ni [72] is significantly below
those for nc and ufc pure Ni. The results shown in Figure 3-1 thus clearly illustrate
that grain refinement leads to an enhancement in the resistance to S-N fatigue.
59
Fatigue Crack Propagation
The experimental method used to extract fatigue crack growth trends from pure mc,
ufc, and nc Ni foils is detailed in Section 2.3.1. The variation in fatigue crack growth
rate with respect to ∆K for pure Ni at load ratios of R = 0.1, R = 0.3, and R =
0.7 is plotted in Figure 3-2. In order to enforce the assumptions inherent to linear
elastic fracture mechanics (LEFM), all data was truncated such that the remaining
uncracked ligament was at least twenty times larger than the crack tip plastic zone
size. It is evident from Figure 3-2 that the resistance to fatigue crack growth is
substantially lower in the nc Ni, relative to the ufc Ni, at all levels of applied loading
over a wide range of load ratios. Due to the relatively limited strength of the mc
Ni, however, valid fatigue crack growth experiments using ∆K as the characterizing
parameter were not possible under the abovementioned requirements.
To circumvent the above plasticity issues, a preliminary set of data was collected
relating the variation in crack length to the number of fatigue cycles in mc, ufc, and
nc Ni (Figure 3-3). Each material experienced identical initial loading conditions of
√
∆K = 9.5 MPa m, R = 0.3, and a cyclic frequency of 10 Hz at room temperature.
Figure 3-3 clearly illustrates that the crack growth rate in nc Ni is significantly higher
than that in ufc Ni. Among the three materials, mc Ni showed the slowest fatigue
crack growth rate (four to seven times smaller than that of ufc Ni) at a given value
of ∆K.
The extent of crack path deflection in mc, ufc, and nc Ni fatigue specimens,
subjected to similar initial loading conditions, is given in Figure 3-4. Under smallscale yielding conditions, the crack tip opening displacement can be expressed as:
δmax = dn
2
Kmax
,
σy E
(3.1)
where δmax is the maximum opening displacement at the tip of the crack, dn is a
constant which is strongly influenced by the strain hardening exponent, n, σy is the
yield strength, and E is the Young’s modulus. dn typically varies between 0.3 and 0.8
as n is increased from 3 to 13 [73]. Assuming a value of dn = 0.8, the maximum crack
60
61
10
10
10
-7
-6
-5
2
(a)
3
ufc Ni
nc Ni
4
10
10
10
10
-7
-6
-5
-4
2
(c)
5 6 7 8 910
1/2
∆K (MPa m )
3
nc Ni
ufc Ni
R = 0.1
4
20
-7
-6
-5
-4
2
3
ufc Ni
nc Ni
R = 0.7
(b)
5 6 7 8 910
1/2
∆K (MPa m )
10
10
10
10
5 6 7 8 910
1/2
∆K (MPa m )
20
4
R = 0.3
20
Figure 3-2: Variation of the fatigue crack growth rate, da/dN, as a function of ∆K for pure electrodeposited ufc, and nc Ni at
load ratios (a) R = 0.1, (b) R = 0.3, and (c) R = 0.7, at a fatigue frequency of 10 Hz at room temperature.
da/dN (mm/cycle)
-4
da/dN (mm/cycle)
10
da/dN (mm/cycle)
Variation In Crack Length (mm)
5
nc Ni
ufc Ni
mc Ni
4
3
2
1
0
0
20
40
60
80
100
120
140
Fatigue Cycles (In Thousands)
Figure 3-3: Variation in crack length as a function of the number of√imposed fatigue
cycles for mc, ufc, and nc Ni subjected to an initial ∆K of 9.5 MPa m, load ratio R
= 0.3, and cyclic frequency of 10 Hz at room temperature.
62
tip opening displacements calculated for the samples in Figures 3-4a through 3-4c are
3.6 µm, 0.60 µm, and 0.63 µm, respectively. The height of the corresponding surface
asperities in the mc and ufc Ni is approximately 10 µm and 5.2 µm, respectively.
Because the fracture surface asperities are significantly larger than the respective
maximum crack tip opening displacements in both the mc and ufc Ni specimens,
crack closure is expected to influence the fatigue crack growth rate in these materials.
Conversely, the maximum measurable surface asperity height of the nc Ni (Figure
3-4f) was well below the corresponding δmax . In addition, there was no substantial
crack deflection observed in the nc Ni, effectively rendering crack closure irrelevant
in this material.
To further explore the validity and generality of the above fatigue crack growth
trends, additional ufc materials fabricated via cryomilling (ufc Al-7.5Mg) and equal
channel angular pressing (ufc pure Ti), for which larger bulk specimens could be
procured, were examined.
3.2.2
Cryomilled ufc Al-7.5Mg
Full details of the processing, structure, and properties of the Al-Mg alloy investigated, as well as the fatigue crack growth experimental method, are given in Sections
2.2.2 and 2.3.2. Because the supersaturated Al alloy could only be fabricated via cryomilling, which ultimately results in a very fine grain structure, a direct comparison
to mc Al-7.5Mg could not be made. However, Al-5083, containing 4.0 - 4.9% Mg [74],
is a close mc counterpart often used for comparison purposes [58].
Figure 3-5 illustrates the fatigue behavior of the ufc Al-Mg alloy investigated,
from threshold to final failure. Also shown in this figure, for comparison purposes,
are the corresponding fatigue crack growth characteristics at R = 0.33 of a commercial
5083 Al-Mg alloy [75, 76]. Although the processing conditions for these two materials
are different, it is evident from Figure 3-5 that consistent with expectations, grain
refinement from the mc to the ufc regime results in a noticeable reduction in ∆Kth
and a significant increase in the rate of fatigue crack growth.
63
Figure 3-4:√Scanning electron
micrographs√of mc, ufc, and nc Ni subjected to sinusoidal fatigue loading at initial ∆K values
√
of 10 MPa m, 6.2 MPa m, and 8.5 MPa m respectively. A cyclic frequency of 10 Hz and load ratio, R = 0.3 were used in
all cases. Crack path tortuosity clearly decreases with decreasing grain size. Images (d) through (f) are higher magnification
images of (a) through (c), respectively, and the magnification of (f) is 10 times that of (d) and (e).
64
The stress intensity factor range for catastrophic failure in the Al-7.5Mg alloy,
which is representative of the fracture toughness and static-mode failure mechanisms,
is also several times smaller than that in the 5083 aluminum alloy. A scanning electron
fractograph of the ufc Al-Mg fatigue fracture surface, at a growth rate in the upper
end of the Paris regime, is shown in Figure 3-6. Here, ductile transgranular fracture
is mixed with growth around cracked inclusion particles, which were introduced into
the microstructure by the cryomilling process. As previously mentioned, ductile FCC
powders tend to agglomerate during the process of mechanical attrition. The liquid
nitrogen medium, as well as the stearic acid introduced during the milling procedure
[57], actively controlled the cold welding between particles, but could not prevent it
entirely. These agglomerated particles were capable of surviving the compaction and
extrusion processes and their presence is believed to contribute to the lowering of the
fracture toughness and of the ∆K values at which catastrophic fracture is instigated
during fatigue crack growth in the ufc Al-Mg alloy.
Two of the Al-7.5Mg compact tension specimens were loaded to failure at a rate
√
of 1.0 N/s. The critical stress intensity factors at fracture were 6.59 MPa m and
√
6.72 MPa m, respectively. Although the fracture surfaces in the catastrophic failure
regimes (Figures 3-7a-b) reveal that failure occurred in a ductile fashion, the toughness
of the cryomilled ufc Al-Mg alloy is still considerably lower than that of its closest
mc counterpart, Al-5083.
3.2.3
Equal Channel Angular Pressed Pure Ti
The fatigue crack growth response of pure mc and ECAP ufc Ti was also fully characterized from threshold to final failure. The material system and experimental protocol
are fully described in Sections 2.2.3 and 2.3.3. Figure 3-8 depicts the effects of grain
size on the variation of da/dN as a function of ∆K at load ratios of R = 0.1 and
R = 0.3. Here, grain refinement from the mc to the ufc regime leads to a reduction
in ∆Kth by a factor of 2.5. The rate of fatigue crack propagation is more than an
order of magnitude higher in the ufc Ti, over a wide range of applied loading, further
65
da/dN (mm/cycle)
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
Increasing R
ufc Al-7.5Mg
mc Al-5083
1
10
∆K (MPa m )
1/2
Figure 3-5: Variation of fatigue crack growth rate, da/dN, as a function of the stress
intensity factor range, ∆K, for ufc cryomilled Al-7.5Mg at R = 0.1 - 0.5 and fatigue
frequency of 10 Hz at room temperature. Also shown are the corresponding crack
growth data for a commercial mc 5083 aluminum alloy at R = 0.33 [54].
Figure 3-6: Scanning electron fractograph showing the fatigue fracture features of the
Al-7.5Mg alloy. Transgranular crack growth is accompanied by cracking of inclusion
particles (indicated with arrows) introduced during the mechanical alloying process.
66
2 µm
2 µm
(a)
(b)
Figure 3-7: Scanning electron fractograph illustrating the catastrophic fracture surfaces of two separate ufc Al-7.5Mg compact tension specimens. A ductile dimpled
failure was observed in both cases. The measured toughness was considerably lower
than that in mc Al-5083, however.
validating the trends captured in electrodeposited Ni.
Subsequent to the fatigue characterization, four monotonic tests were performed,
where two compact tension specimens of mc and ufc Ti were loaded to failure in
displacement control at a rate of 5 x 10−3 mm/sec. The values of the stress intensity
√
factor corresponding to the onset of fracture in the mc Ti were 63.32 MPa m and
√
62.04 MPa m. The ufc Ti specimens exhibited a substantially higher resistance to
√
fracture, with corresponding critical stress intensity factors of 101.61 MPa m and
√
106.16 MPa m.
3.3
Discussion
The primary mechanism responsible for the accelerated fatigue crack growth rate observed with decreasing grain size is the reduction in crack path deflection with grain
refinement. Microstructural size scales can play a dominant role in crack morphology as well as the mode of fracture, especially near the threshold regime. Periodic
deflections in the fatigue crack at grain boundaries during crystallographic fracture
can lead to a relatively tortuous crack path in coarser grain materials. In addition,
67
da/dN (mm/cycle)
10
-3
10
-4
10
-5
10
-6
10
-7
10
-8
ufc Ti
mc Ti
ufc Ti
mc Ti
R = 0.1
R = 0.1
R = 0.3
R = 0.3
1
10
20
∆K (MPa m )
1/2
Figure 3-8: Variation in fatigue crack growth rate as a function of ∆K for commercially pure mc Ti and ECAP ufc Ti at a fatigue frequency of 10 Hz at room
temperature.
68
intergranular fracture can predominate as the grain size approaches the nc regime,
as there is an abundance of essentially undeflected grain boundary paths oriented
normal to the loading axis for the crack to follow.
3.3.1
Theoretical Background: Model for Crack Deflection
Induced Closure
The significance of fatigue crack closure under cyclic tensile loading conditions was
first recognized by Elber [77, 78]. Various other types of crack closure mechanisms
were later characterized by Ritchie, Suresh, Moss, and Zamiski [79–83]. Of particular
importance to this investigation is the crack deflection induced closure mechanism, a
model for which was developed in [83]. Under pure mode I global loading, any crack
path deviation toward the tensile axis leads to mixed mode I and mode II loading
conditions locally at the tip of the crack. When a fatigue crack propagating in the
pure mode I plane kinks to an inclined angle, θ (Figure 3-9) the local mode I and
mode II stress intensity factor ranges, ∆k1 and ∆k2 , can be expressed as:
¶
µ
¶
θ
3θ
3
θ
3θ
3cos + cos
∆KI −
sin + sin
∆KII
2
2
4
2
2
µ
¶
µ
¶
1
θ
3θ
1
θ
3θ
∆k2 =
sin + sin
∆KI +
cos + 3cos
∆KII
4
2
2
4
2
2
1
∆k1 =
4
µ
(3.2)
(3.3)
where ∆KI and ∆KII represent the global mode I and mode II stress intensity factor
ranges, and the bracketed coefficients are dimensionless factors determined by [84, 85].
Under pure mode I far field cyclic loading conditions, the second term in each equation
vanishes, and ∆k1 and ∆k2 can be reduced by triple angle formulas to
µ
¶
3θ
∆k1 = cos
∆KI
2
µ
¶
θ 2θ
∆k2 = sin cos
∆KI
2
2
(3.4)
(3.5)
The local effective stress intensity factor range at the tip of the crack is then given
by the geometric average of ∆k1 and ∆k2 ,
69
∆KI
∆kI
∆kII
θ
Figure 3-9: Schematic illustration of a kinked crack and the relevant terminology.
µ
∆kef f =
2θ
cos
2
¶
∆KI
(3.6)
Equation 3.6 clearly demonstrates that deflection alone, without the effect of crack
closure, reduces the driving force for crack propagation.
The idealized case of a periodically deflected crack is represented in Figure 310 [83]. Here, the repeat unit is composed of a nominally straight crack of length
S, oriented perpendicular to the global mode I loading axis, and a kinked crack, of
length D, inclined at an angle, θ. Taking the weighted average of the effective stress
intensity factor range for the kinked crack, given in Equation 3.6, and the straight
crack,
Ã
∆kef f =
!
¡ ¢
D cos2 2θ + S
∆KI
D+S
(3.7)
Equation 3.7 describes the effective stress intensity factor for an ideally elastic
periodically deflected crack, where the fracture surfaces come in complete contact at
zero load only. However, crack tip plasticity induced residual stresses (among other
factors [83]) typically result in a relative sliding displacement between crack faces. The
surfaces of the crack therefore do not generally mate perfectly during the unloading
70
D
uI
∆δ
θ
θ
uII
θ
∆δ∗
S
(a)
(b)
Figure 3-10: Schematic illustration depicting a segment of a periodically deflected
crack subjected to global mode I fatigue loading (a) in its fully opened state at the
peak fatigue load and (b) at the first point of contact upon unloading.
phase of the fatigue cycle, which leads to some level of premature crack closure (Figure
3-10b). The mismatch between fracture surfaces, χ, at the onset of contact during
unloading is characterized by the ratio of in-plane and normal displacements of the
crack faces,
χ=
uII
uI
(3.8)
The value of ∆kef f is further reduced by this fracture surface mismatch. The
cyclic crack tip opening displacement (Figure 3-10) can be expressed as
∆δ = ∆δ ∗ + uI
(3.9)
and from the geometry of the crack,
∆δ ∗ = uII tanθ
(3.10)
Noting that the stress intensity factor varies with the square root of the crack tip
opening displacement, the strength of the closure effect is given by
∆Kcl
=
∆KI
r
∆δ ∗
∆δ
r
=
s
uII tan θ
=
uII tan θ + uI
χ tan θ
χ tan θ + 1
(3.11)
In addition, the closure effect can be incorporated into Equation 3.7 as follows
71
Ã
∆keff =
!
¡ ¢
D cos2 2θ + S
(∆KI − ∆Kcl )
D+S
(3.12)
and the ratio of ∆KI to ∆keff is therefore
∆KI
=
∆keff
Ã
s
!−1 Ã
!−1
¡ ¢
D cos2 2θ + S
χ tan θ
1−
D+S
χ tan θ + 1
(3.13)
Furthermore, the effective rate of fatigue crack propagation (measured along the
Mode I direction) is apparently reduced for a periodically deflected crack, relative
to an undeflected crack. From Figure 3-11, the total length of the deflected crack
repeat unit, a, is the sum of the inclined length, D, and the undeflected length, S.
Experimentally, crack length is generally measured along the Mode I direction (aL ),
which is simply D cos θ + S. aL can therefore be expressed as:
µ
aL =
If
¡ da ¢
dN L
D cos θ + S
D+S
¶
a
(3.14)
represents the growth rate of a linear undeflected crack, the effective crack
growth rate of a periodically deflected crack is therefore:
µ
3.3.2
da
dN
µ
¶
=
ef f
D cos θ + S
D+S
¶µ
da
dN
¶
(3.15)
L
Grain Size Effects on Crack Path and Morphology
Equations 3.13 and 3.15 can be used to predict the rate of crack growth as a function
of ∆K for tortuous crack paths, assuming the linear undeflected crack growth rate
is known. As mentioned above, the character of the nc Ni fatigue cracks can be
approximated as perfectly undeflected (Figures 3-4c and 3-4f). Therefore, the crack
growth rate of the ufc Ni can be estimated by assuming the rate of crack growth in the
¡ da ¢
nc Ni is tantamount to the linear growth rate, dN
. The segmental crack lengths
L
of the ufc Ni are then measured to determine values for D, S, and θ. The mismatch
72
aL
a
θ
D
S
Figure 3-11: Schematic illustration of the relevant segment lengths for the repeat unit
of a periodically deflected crack.
parameter, χ (Equation 3.8), is subsequently varied to gage the level of crack closure
under each loading condition.
Figure 3-12 depicts the crack growth trends predicted from the nc Ni data, superimposed on the data from Figure 3-2. A reference curve for an ideally elastic
periodically deflected crack (χ = 0) is plotted in each case. The level of crack closure,
represented by the strength of the mismatch parameter, χ, varies inversely with load
ratio. This is attributed to the increase in fracture surface separation with increasing
load ratio. The relatively low values of χ indicate that crack deflection, rather than
closure, is more dominant in reducing the effective driving force for crack propagation
in this system. Deviation from the predicted crack growth curves at elevated levels of
∆K is expected since the crack tip opening displacement, and therefore the level of
crack closure, are not constant, but are rather dependent upon the applied loading.
In addition, elevated stress levels are accompanied by increased crack tip plasticity.
When the plastic zone size encompasses many grains, multiple slip dominates, resulting in a more planar Stage II [41] crack growth. The experimental crack growth data
is therefore expected to approach that for a linear undeflected crack at elevated levels
of applied loading, even in coarser grain materials. This was, in fact, observed in the
73
electrodeposited Ni system (i.e. Figure 3-12).
Figure 3-13 displays a series of electron micrographs taken in the fatigued regions
of mc, ufc, and nc Ni, under similar loading conditions. Each individual montage
depicts fatigue fracture features in a given region, with images increasing in magnification in a clockwise fashion. The crack grew from left to right in each case. The
general decrease in fracture surface feature size at finer grain sizes further indicates
that the level of crack path tortuosity in the nc Ni is significantly below that in the ufc
or mc Ni. This reduction in deflection leads to a higher effective stress intensity factor
(Equation 3.6) and a resultant increase in the fatigue crack growth rate. Reducing the
fracture surface feature size can also act to diminish the level of crack closure. The
smaller the asperities, the less likely they are to come into contact during tensiontension fatigue loading. A decrease in the level of crack closure also contributes to
the observed increase in fatigue crack growth rate, as evidenced by Equation 3.12.
In addition to the trend of increasing fatigue crack path tortuosity with increasing
grain size, post failure analysis revealed evidence signifying a potential dependence
of the level of intergranular crack growth on the average grain size. Typically, grain
boundaries are less resistant to crack propagation than the grain interior. In the limit
of exceedingly fine grain materials, there is an abundance of relatively straight grain
boundary paths that exist normal to the imposed loading axis. These paths become
progressively more tortuous as the grain size increases, resulting in more pronounced
transgranular crack propagation. The mode of crack growth is therefore also expected
to influence da/dN.
Transgranular fatigue crack growth is apparent in the mc and ufc Ni (Figures 313a-b). However, the images in Figure 3-13c illustrate a nc Ni fracture surface feature
size on the order of a few grain diameters. It should be noted that the highest magnification image in this figure was approaching the resolution limits of the electron
microscope. Additional images of the nc Ni fatigue fracture surfaces were therefore
taken on a field emission gun scanning electron microscope (FEGSEM) with enhanced
resolution capabilities (Figure 3-14). These figures provide further evidence of crack
74
75
10
10
10
-7
-6
-5
2
3
4
5
10
10
10
10
1/2
-7
-6
-5
-4
2
6 7 8 9 10
χ = 0.08
∆K (MPa m )
χ=0
nc Ni
ufc Ni
3
χ=0
nc Ni
ufc Ni
R = 0.1
4
2
6 7 8 9 10
10
-7
-6
-5
-4
1/2
∆K (MPa m )
5
χ = 0.04
20
(a)
10
10
10
R = 0.7
3
6 7 8 9 10
1/2
∆K (MPa m )
5
(c)
20
4
χ = 0 χ = 0.06
nc Ni
ufc Ni
R = 0.3
20
(b)
Figure 3-12: Fatigue crack growth trends, depicted as broken lines, predicted from the crack deflection/closure model described
in Section 3.3.1, superimposed on the data from Figure 3-2. The nc Ni growth rate is assumed tantamount to the linear crack
growth rate in Equation 3.15.
da/dN (mm/cycle)
-4
da/dN (mm/cycle)
10
da/dN (mm/cycle)
(a)
mc Ni
(b)
ufc Ni
(c)
nc Ni
Figure 3-13: Scanning electron micrographs of the fatigue fracture surface features of
(a) mc Ni, (b) ufc Ni, and (c) nc Ni. Each
√ sample was subjected to similar loading
conditions, with an initial ∆K = 7 MPa m, load ratio R = 0.3, and a cyclic frequency
of 10 Hz at room temperature. The direction of crack propagation is left to right in
each image. White outlines represent regions examined at higher magnification, with
increasingly magnified views arranged in a clockwise fashion.
76
1 µm
200 nm
(a)
(b)
Figure 3-14: Field emission gun scanning electron micrographs
of the fatigue fracture
√
features of nc Ni subjected to an initial ∆K = 7 MPa m, load ratio R = 0.3, and a
cyclic frequency of 10 Hz at room temperature. Clusters of features measuring ∼ 60
nm in size (or one to two grain diameters) are indicated with arrows in (b).
growth along grain boundaries. Clusters of features measuring ∼ 60 nm are apparent
in Figure 3-14b. Such features could result from an intergranular fatigue crack propagating over two or more grains, whose boundaries are aligned perpendicular to the
tensile axis. This potential increase in the level of intergranular fracture could also
contribute to the decrease in resistance to crack propagation observed in the nc Ni.
The same crack deflection analysis from Section 3.3.1 was applied to the mc and
ufc ECAP Ti system described in Sections 2.2.3 and 3.2.3. Figure 3-15 illustrates the
level of crack path tortuosity in the mc and ufc Ti, under similar loading conditions.
As was the case for the nc electrodeposited Ni, the ufc Ti exhibits a comparatively
straight crack path, relative to its mc counterpart. The reduction in effective driving
force for crack propagation in the mc material is again assumed to result from a
combination of crack deflection and closure. This can also be substantiated by the
sensitivity to the load ratio of the two materials. While the ufc Ti exhibits a relative
insensitivity to R (Figure 3-8), the mc Ti shows a clear shift in the entire da/dN vs.
∆K curve as R is decreased from 0.3 to 0.1, indicating deflection and closure are more
prevalent in the coarser grain material.
77
mc Ti
(a)
ufc Ti
(b)
Figure 3-15: Illustration of the crack path
√ tortuosity in (a) commercially pure mc
Ti subjected to an initial ∆K of 6.5 MPa
√ m, and the lack thereof in (b) ufc ECAP
Ti subjected to an initial ∆K of 5 MPa m. Each sample was loaded with a fatigue
frequency of 10 Hz and load ratio of R = 0.3 at room temperature.
Assuming the fatigue crack in the ufc Ti does not deviate from the pure mode I
growth plane, the model described in Equations 3.13 and 3.15 can again be applied
to assess the effect of crack deflection and crack closure in the mc Ti. Figure 3-16
illustrates the upper and lower bounds of the mismatch parameter, χ, for R = 0.1
and R = 0.3. In the near-threshold regime where closure is expected to strongly
influence the rate of crack propagation, a value of χ = 0.5 most accurately captures
the observed behavior. At sufficiently high levels of applied loading, large crack tip
opening displacements and Stage II crack growth dominate, significantly reducing the
extent of crack deflection and closure in the mc Ti. Accordingly, its crack growth rate
approaches that of the ufc Ti at elevated ∆K levels. These trends are in complete
agreement with those observed in the model electrodeposited Ni system.
78
10
-3
da/dN (mm/cycle)
ufc Ti
mc Ti
10
-4
10
-5
10
-6
10
-7
R = 0.1
χ = 0.05
10
χ = 0.5
-8
1
10
∆K (MPa m )
1/2
(a)
10
-3
da/dN (mm/cycle)
ufc Ti
mc Ti
10
-4
10
-5
10
-6
10
-7
10
R = 0.3
χ = 0.05
-8
χ = 0.5
1
10
∆K (MPa m )
1/2
(b)
Figure 3-16: Fatigue crack growth rate predictions, based on the deflection/closure
model defined in Section 3.3.1, for commercially pure mc Ti at load ratios of (a) R =
0.1 and (b) R = 0.3. The crack growth rate data for the ufc ECAP Ti is assumed to
correspond to the linear undeflected growth rate in Equation 3.15.
79
3.3.3
Effects of Particle Reinforcement on Fatigue Crack Growth
In an attempt to increase the level of crack path tortuosity in a nc material, obstacles
in the form of 1 µm diameter SiC particles were introduced in an electrodeposited nc
Co metal matrix. Comparisons between the crack growth rate in pure nc Co, and that
containing 10 vol.% SiC were then made. Figure 3-17 illustrates the particle size and
spatial distribution in the nc Co matrix. Particle reinforcement in electrodeposited
Ni was not studied due to the extreme loss of ductility at similar volume fractions of
SiC.
The same sample geometry and preparation technique described in Section 2.3.1
were used to investigate the resistance to subcritical fatigue fracture in pure and SiC
reinforced nc Co. Single-edge-notch tension specimens were loaded with a sinusoidal
waveform at a cyclic frequency of 10 Hz and a load ratio of R = 0.3 at room temperature. Figure 3-18 indicates that the crack growth rate is relatively unaffected by
the addition of 10 vol.% reinforcing SiC particles to the nc Co matrix. Although the
effect on the resistance to crack growth is negligible, a considerable improvement in
the tribological response (described in Section 4.3.4) was observed in the reinforced
Co, with respect to its pure counterpart. The potential therefore exists to enhance
the resistance to contact damage through particle reinforcement, without sacrificing
the resistance to fatigue crack growth.
3.4
Conclusions
In this chapter, the effects of grain size on total life and fatigue crack growth resistance
of nc, ufc, and mc materials were systematically investigated. A deflection/closure
model was employed to rationalize the observed crack propagation behavior. The key
results of this study can be summarized as follows:
§ Grain refinement in the nc and ufc regimes has been shown to have a substantial
effect on total life under stress-controlled fatigue and on fatigue crack growth.
Specifically, fully dense nc and ufc Ni produced by electrodeposition exhibit
80
50 µm
15 µm
(a)
(b)
Figure 3-17: SiC particle size and spatial distribution in an electrodeposited nc Co
metal matrix (a) in cross-section and (b) in plane.
-3
10
da/dN (mm/cycle)
Pure nc Co
SiC Reinforced nc Co
-4
10
-5
10
-6
10
-7
10
1
1/2
∆K (MPa m )
10
Figure 3-18: Variation in fatigue crack growth rate as a function of ∆K for nc electrodeposited pure and SiC (10 vol.%) reinforced Co at a fatigue frequency of 10 Hz
and load ratio R = 0.3 at room temperature.
81
substantially higher resistance to stress-controlled fatigue compared to conventional mc Ni. However, fatigue crack growth results obtained in this study also
appear to indicate that grain refinement in the nc regime can have a deleterious effect on the resistance to subcritical fatigue fracture. These trends seen
in this study are thus consistent with expectations of the role of grain size in
influencing fatigue crack initiation and stable crack growth (i.e. [27]).
§ A crack deflection/closure model [83] was used to justify the decrease in fatigue
crack growth rate, da/dN, in coarser grain materials. Crack path tortuosity
was observed to increase significantly with increasing grain size, from the nc
to the mc regime. A resultant reduction in the effective stress intensity factor
range due to deflection and deflection induced closure accounts for the observed
lowering of the crack growth rate.
§ Experimental results obtained for a cryomilled ufc Al-7.5Mg alloy and a ufc
ECAP pure Ti also corroborate the above interpretations of the effects of grain
size on fatigue crack growth. The level of crack path tortuosity was again observed to increase dramatically with increasing grain size in the pure Ti system.
While a direct comparison to mc Al-7.5Mg could not be made, crack deflection
in the ufc Al alloy was comparable to that in other ufc materials investigated.
§ The above results indicate that grain size, rather than material strength, dominates the mechanical fatigue response, assuming all other structural factors are
held fixed. Over the range of materials investigated, the grain size was found
to dictate the level of crack path tortuosity, which was shown to significantly
influence the driving force for crack propagation. The relative insensitivity of
the crack growth rate to SiC reinforcement confirms this hypothesis, as the reinforced nc Co maintained a considerably higher strength than the pure nc Co,
with no apparent affect on da/dN.
§ Valid fracture experiments using a linear elastic fracture mechanics framework
in the available nc, ufc, and mc Ni were not possible due to excessive crack tip
82
plasticity. At the onset of fracture, the plastic zone was comparable in size to
the remaining uncracked ligament length in all three materials.
§ Fracture experiments performed in the ufc Al-7.5Mg alloy showed a marked decrease in toughness, relative to its closest mc counterpart, Al-5083. This was attributed to the presence of inclusion particles introduced during the cryomilling
process. On the other hand, ufc ECAP pure Ti exhibited a substantially higher
resistance to fracture, relative to the pure mc Ti from which it was fabricated.
83
84
Chapter 4
Early Stage Contact and Contact
Fatigue of Nanocrystalline
Materials
4.1
Introduction
The usefulness of nc materials in structural applications will likely depend directly
upon their mechanical and contact fatigue behavior. Currently, however, there is
a relative paucity of experimental data pertaining to these properties within the
nc grain size regime. This study was initiated to probe the sliding contact fatigue
behavior of several nc and ufc materials, with direct comparisons made to their mc
counterparts, wherever appropriate. An instrumented microindenter with a spherical
sapphire tip was used to introduce repeated unidirectional sliding contact. Indenter
modifications facilitated in-situ monitoring of the friction coefficient throughout the
experiment. The efficacy of such low load experimentation resides in the fact that
abrasion typically results from the repeated scratching of a surface by particulate
matter under low amplitudes of applied loading.
Several previous studies have been initiated to characterize abrasion and wear
properties of mc materials [86–90], however the complexity of the process has, in
general, lead only to empirical results without associated fundamental trends. While
there is no simple relationship between properties such as wear performance and
hardness (for example), it has been proposed that scratch testing provides a more
85
accurate means of characterizing a single abrasive event [91–94]. Repeated scratch
testing, where a single region of the surface is exposed to multiple insults, is extremely
useful in terms of monitoring damage evolution [95, 96], and has previously been
employed to study the wear behavior of plasma sprayed coatings and hard metals
[97–99].
While there are several material properties used to characterize the tribological
response of a material, the friction coefficient is often considered to be of critical importance. It is therefore useful to explicitly monitor the evolution of friction between
the substrate and counterface material during sliding contact fatigue. The objective
of this study was to determine the effects of grain size on friction and damage evolution. Because sliding contact entails significant compression and shear at asperity
contacts, large plastic strains are expected, even at low applied loads. Plastic deformation, and the associated energy dissipation, can therefore contribute significantly
to the level of friction during sliding. As a result, an attempt was made to isolate the
effects of grain size reduction from the associated increase in strength on the observed
friction evolution.
4.2
Experimental Details
Figure 4-1 illustrates the instrumented microindenter used in all sliding contact fatigue
experiments. Indentation occurs horizontally, with the indenter tip affixed to the
bottom of a rigid pendulum. Applying an electric current to the coil at the top of
the figure attracts the upper end of the pendulum toward the permanent magnet,
resulting in a forward displacement of the indenter tip toward the sample. This
displacement can be measured with extreme precision by monitoring the capacitance,
and therefore the spacing, between the capacitor plates seen at the bottom of Figure
4-1. The position of the left plate is fixed, while the other is free to move with
the indenter. Force transducers were mounted on either side of the tip to monitor
tangential loads generated during scratch experiments, and a spherical sapphire tip
(1/16-inch diameter) was used in each test. Tips were replaced after every experiment
86
to avoid material transfer between samples.
The scratch testing protocol can be described as follows. First, individual samples were mounted to a 1-inch diameter Al-7075-T651 cylinder using a thin layer
of cyanoacrylate glue (superglue). Specimens were subsequently polished to a 0.25
µm finish, and thoroughly cleaned in ethanol. Initial contact was made between the
specimen and the indenter tip, after which a prescribed normal load was applied as
the sample stage began to displace at a constant rate of 25 µm/sec. The normal
load was ramped to its maximum value over the first 50 µm of stage motion, and
remained constant thereafter. A 500 µm scratch at the maximum normal load was
introduced, followed by a 15 µm tip retraction from the surface. The sample stage
was subsequently replaced to its initial position, and the scratch was repeated in this
unidirectional fashion, up to 98 times. Normal and tangential loads were acquired
throughout the entire length of the scratch.
4.3
4.3.1
Results
Electrodeposited Pure Ni
The above scratch tests were performed on the pure nc, ufc, and mc Ni described in
Section 2.2.1. Figure 4-2 illustrates the early stage evolution of friction at a normal
indentation load of 1.25 N, as a function of the number of unidirectional scratch
passes. A ‘steady state’ friction coefficient was reached after approximately 40 - 60
passes in all three materials. The figure clearly illustrates a lowering of the steady
state friction with grain refinement, over the first 98 passes.
Figure 4-3 displays the damage evolution following 10 and 98 repeated scratches
in nc, ufc, and mc Ni, at a normal load of 1.25 N. In each case, the accumulated
debris within the nc Ni wear path was considerably less than that in the ufc or mc
Ni, after an equivalent number of passes. As expected, the width of the scratch path
diminishes with decreasing grain size, as the hardness increases. In all three grain
size regimes, there is an apparent ‘ploughing’ of material to the end of the wear path,
87
Permanent
magnet
Coil
Pendulum arm
Capacitor plates
Sample
Indenter tip
Sample
Strain gages
Figure 4-1: Instrumented microindenter used for all repeated sliding contact fatigue
experiments. A modification of the indenter tip (see the inset magnified view) facilitated the monitoring of tangential loads during scratch experiments.
88
89
Average Friction Coefficient
0
0.05
0.1
0.15
0.2
0.25
0
0.05
0.1
0.15
0.2
0
0
10
nc Ni
ufc Ni
mc Ni
2
nc Ni
ufc Ni
mc Ni
6
30
Pass Number
20
Pass Number
4
40
8
50
10
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0
0.05
0.1
0.15
0.2
0.25
0
0
20
nc Ni
ufc Ni
mc Ni
5
nc Ni
ufc Ni
mc Ni
15
60
Pass Number
40
Pass Number
10
80
20
100
25
Figure 4-2: Early stage friction evolution as a result of repeated unidirectional scratching of nc, ufc, and mc pure Ni, at a
normal load of 1.25 N. An apparent improvement in the ‘steady state’ friction coefficient with grain refinement was observed.
Average Friction Coefficient
0.25
Average Friction Coefficient
Average Friction Coefficient
where the indenter tip retracts from the surface.
In addition to characterizing the friction and damage evolution, focused ion beam
(FIB) microscopy was also performed following the scratch tests in nc, ufc, and mc
Ni. Figure 4-4 clearly illustrates regions of coarsened grains within the wear paths of
nc and ufc Ni, after only a limited number of passes. A similar change in grain size
was difficult to detect in mc Ni, as the entire width of the scratch path was composed
initially of only a few grains.
4.3.2
Equal Channel Angular Pressed Cu
In addition to the scratch tests performed on pure Ni, a separate set of experiments
designed to isolate the effects of material strength (from those due solely to grain refinement) were performed on an ECAP Cu system. Here, two Cu samples of 99.999%
purity were subjected to 5 ECAP cycles, with one subsequently annealed at 473 K
for 1 hour. The annealing process resulted in only minor levels of grain growth. Measurements via dark-field TEM revealed average grain sizes of 340 ± 20 nm and 400 ±
20 nm for the as-received and annealed ECAP Cu, respectively [100]. Compression
testing uncovered dramatically different flow behavior between the two materials,
however. The 0.2% offset yield strengths were measured at 340 MPa and 110 MPa
in the as-received and annealed conditions, respectively. The strain hardening was
minimal in the as-received Cu, however substantial hardening was observed in the
annealed material.
Samples of the as-received and annealed ECAP Cu were subjected to a similar
scratch testing protocol to that described above. A normal load of 1.0 N was imposed through a 1/16-inch diameter spherical sapphire tip, with varying numbers of
unidirectional passes (500 µm in length) in both the as-received and annealed ECAP
specimens. Figure 4-5 illustrates the evolution of friction as a function of the number of contact fatigue cycles. Consistent with the above pure Ni results, the lower
strength annealed ECAP Cu initially exhibits a higher friction coefficient relative
to its as-received counterpart, under the same scratch conditions. However, these
90
nc Ni
ufc Ni
mc Ni
(a)
(b)
(c)
nc Ni
ufc Ni
mc Ni
(d)
(e)
(f)
Figure 4-3: SEM images of the scratch paths produced in nc, ufc, and mc Ni at a
normal load of 1.25 N after (a-c) 10 passes and (d-f) 98 passes. Debris accumulation
within the boundaries of the wear region exhibits a positive grain size sensitivity.
91
2 µm
1 µm
(a)
(b)
1 µm
2 µm
(c)
(d)
1 µm
(e)
Figure 4-4: FIB images of scratches produced in nc Ni at a normal load of 1.25 N after
(a) 1 pass, (b) 10 passes, and (c) 98 passes. Similar FIB images for ufc Ni subjected
to (d) 50 passes and (e) 98 passes, at a normal load of 1.25 N. Local increases in grain
size were observed with an increasing number of sliding contact fatigue cycles.
92
0.22
Friction Coefficient
0.2
0.18
0.16
0.14
0.12
As-received ECAP Cu
Annealed ECAP Cu
0.1
0
20
40
60
80
100
Pass Number
Figure 4-5: Friction evolution during unidirectional sliding contact fatigue of ECAP
pure Cu in its as-received and annealed (473 K for 1 hour) conditions.
coefficients converge after approximately 90 passes.
As expected, the breadth of the wear path in the plastically softer annealed ECAP
Cu is somewhat larger than that in the as-received material, under identical loading
conditions (Figure 4-6). A noticeably higher level of deformation at the periphery of
the scratch in the annealed material is also apparent. In an attempt to gauge the
level of hardness (and to a first approximation, the local strength) inside and outside
the damaged regions, both samples were subjected to instrumented nanoindentation
with a normal load of 7 x 10−3 N. Figure 4-7 illustrates the variation in hardness
between the as-received and annealed samples both far from and within the confines
of the scratch paths. While the hardness of the annealed ECAP Cu is noticeably
below that of the as-received material outside the damaged region, there appears to
be no significant variation between the two materials within the scratch.
93
Annealed
ECAP Cu
As-received
ECAP Cu
(a)
(b)
Figure 4-6: Damage introduced following 98 passes of repeated unidirectional sliding
contact between sapphire and (a) annealed ECAP pure Cu and (b) as-received ECAP
pure Cu.
4.3.3
Equal Channel Angular Pressed Ti
Additional contact fatigue experiments were conducted on the mc and ufc ECAP pure
Ti system described in Section 2.2.3. In this case, there was a relatively large grain
size variation between the mc and ufc Ti, with a somewhat limited strength variation.
Scratches 500 µm in length were introduced in both specimens with a normal load of
1.25 N. Figure 4-8 illustrates the early stage friction evolution as a function of pass
number for the ufc and mc pure Ti. The mc material exhibits a very slight increase
in friction coefficient, with respect to the ufc Ti. The difference between the two
is minimal, however, relative to that observed between mc and nc electrodeposited
Ni. A significantly higher amount of wear debris was found within and around the
scratches introduced in the mc and ufc Ti, relative to all other materials examined
(Figure 4-9).
4.3.4
SiC Reinforced Electrodeposited nc Co
The electrodeposited pure and SiC (10 vol. %) reinforced nc Co described in Section
3.3.3 were also subjected to sliding contact fatigue at a normal load of 1.25 N and total
94
2.2
Annealed ECAP Cu
As-received ECAP Cu
Hardness (GPa)
2
1.8
1.6
1.4
Scratch
Region
1.2
1
0
2
4
6
8
10
12
14
16
Indent Number
(a)
Annealed
ECAP Cu
As-received
ECAP Cu
#1
# 15
#1
# 15
(b)
#1
# 15
#1
# 15
(c)
Figure 4-7: (a) Hardness variation as a function of position across the damaged and
undamaged regions of (b) annealed and (c) as-received ECAP Cu. Each row of indents
contains 15 measurements, labeled ‘1’ through ‘15’ for reference in (a).
95
Friction Coefficient
0.54
0.52
0.5
0.48
0.46
0.44
0.42
0.4
0
2
10
4
6
30
Pass Number
20
Pass Number
8
40
ufc Ti
mc Ti
ufc Ti
mc Ti
10
50
0.6
0.55
0.5
0.45
0.4
0.35
0.52
0.5
0.48
0.46
0.44
0.42
0.4
0.38
0
0
5
20
10
15
60
Pass Number
40
Pass Number
20
80
ufc Ti
mc Ti
ufc Ti
mc Ti
25
100
96
0.38
0.6
0.55
0.5
0.45
0.4
0.35
0
Friction Coefficient
Friction Coefficient
Figure 4-8: Early stage friction evolution as a result of repeated unidirectional scratching of ufc ECAP and mc pure Ti with a
1/16-inch diameter sapphire spherical indenter at a normal load of 1.25 N.
Friction Coefficient
mc Ti
ufc Ti
(a)
(b)
Figure 4-9: Wear debris produced after 98 passes of unidirectional sliding contact
between a 1/16-inch diameter sapphire spherical indenter and (a) mc pure Ti and (b)
ufc ECAP pure Ti, at a normal load of 1.25 N.
scratch length of 500 µm. Figure 4-10 illustrates the effects of particle reinforcement
on friction evolution. Here, the nc Co/SiC system consistently displays a lower friction
coefficient than its pure nc counterpart. Additionally, Figure 4-11 illustrates the
relatively limited surface damage introduced in the SiC reinforced nc Co, relative to
that observed in the pure material under identical loading conditions.
4.4
Discussion
For surface coatings and other tribological applications, a higher scratch resistance
and reduced friction coefficient are typically desired. It is apparent from the results
obtained in pure Ni that a reduction in grain size can result in a diminishing coefficient
of friction. It was necessary, however, to determine whether this effect was grain size
or strength dominated, as the strength typically increases with grain refinement.
The results obtained in the ECAP Cu system, where material strength was varied
at a relatively constant grain size, indicate that strength reduction has a deleterious
effect on both the scratch resistance and friction coefficient. The steady state friction
coefficients of the annealed and as-received material are comparable, apparently due
97
0.2
0.18
0.16
0.14
5
10
20
20
0.2
0.18
0.16
0.14
0.1
0.12
60
0
80
10
100
Pure nc Co
SiC Reinforced nc Co
Friction Coefficient
Pass Number
40
25
Pure nc Co
SiC Reinforced nc Co
15
Pass Number
0.2
0.18
0.16
0.14
0.12
0.1
0
20
40
50
Pure nc Co
SiC Reinforced nc Co
30
Pass Number
98
0.12
0.1
0
Friction Coefficient
Figure 4-10: Friction evolution during unidirectional sliding contact fatigue of electrodeposited pure and SiC (10 vol.%) reinforced
nc Co.
Friction Coefficient
200 µm
200 µm
(a)
(b)
Figure 4-11: Damage accumulation following 98 passes of unidirectional sliding contact fatigue at a normal load of 1.25 N in (a) electrodeposited pure nc Co and (b)
SiC (10 vol.%) reinforced electrodeposited nc Co.
to the equivalence in hardness (and to a first approximation local strength) within
the confines of the damaged regions. The large plastic strains associated with sliding
contact are known to produce a positive hardness gradient in Cu, where a higher local
hardness exists at the surface, within the damaged region [101]. This observation was
confirmed in the current experiments. The above results indicate that strength, rather
than grain size, dominates the contact fatigue response.
In addition, the yield strength variation between pure mc and ufc ECAP Ti was
substantially smaller (by a factor of 3.7) than that between the pure mc and nc Ni
investigated. The steady state friction coefficients observed in the former (Figure 4-8)
were only moderately different, even with a grain size variation of nearly two orders
of magnitude. This relative lack of disparity supports the above contention that
strength dominates the friction response. The level of wear debris produced during
abrasion events is also assumed to be strength dominated, considering its apparent
insensitivity to the large variation in grain size between mc and ufc Ti. The amount
of debris observed in the nc Ni, however, was substantially less than that in the ufc or
mc Ni, under equivalent loading conditions. Again, the strength variation between mc
99
and nc Ni is much larger than that between mc and ufc Ti. It is therefore reasonable
to assume that damage accumulation, in terms of material removal and wear debris,
is also dominated by material strength, rather than grain size.
A separate study has previously shown that tungsten alloying additions can significantly improve the hardness and scratch resistance of nc Ni [102]. Here, an electrodeposited nc Ni-W alloy (13 at.% W) displayed a 14% increase in hardness, relative
to the strongest pure nc Ni. This increase was attributed almost entirely to grain
refinement, rather than solid solution strengthening. The average grain size of the
Ni-W alloy was reportedly 8 ± 2 nm, whereas to date, the lowest achievable grain
size in pure nc Ni has been approximately 20 nm. Additionally, the depth of penetration during ‘nano-scratch’ experiments, where the load was continuously ramped
to a maximum of 10 mN over a total scratch length of 5 µm, was reduced in the nc
Ni-W, relative to pure nc Ni. No friction measurements were reported, however.
Scratch tests performed at a normal load of 1.25 N on the same nc Ni-W examined
in [102] indicate a relative insensitivity of the friction coefficient to alloying content
(Figure 4-12). The nc Ni-W and pure nc Ni display a similar friction response over
the full range of imposed contact fatigue cycles. This insensitivity to alloying is in
agreement with a similar observation for a mc Pb-Sn alloy in contact with a steel
sphere, where the friction coefficient was relatively invariant over a wide range of
compositions, from pure Pb to pure Sn [101].
In addition to the effects of alloying, the dependence of friction and damage evolution on particle reinforcement was also investigated. Figure 4-10 clearly demonstrates
the beneficial effect of SiC particle additions, in terms of the early stage friction evolution response. The severity of surface damage was also consistently lower in the reinforced nc Co, relative to its pure nc counterpart. As previously mentioned in Section
3.3.3, the resistance to fatigue crack growth is seemingly unaffected by the addition
of 10 vol.% SiC (1 µm diameter particles) to the nc Co metal matrix. Therefore,
an apparent improvement in the resistance to tribological damage can be attained
through particle reinforcement in the nc Co, without sacrificing its resistance to sub-
100
101
10
15
20
25
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0
Pass Number
20
nc Ni
nc NiW
ufc Ni
mc Ni
60
Pass Number
40
0
5
0
0
0.05
0.1
0.15
0.2
0.25
0.05
0.1
0.15
0.2
nc Ni
nc NiW
ufc Ni
mc Ni
Friction Coefficient
0
80
10
20
30
Pass Number
100
nc Ni
nc NiW
ufc Ni
mc Ni
40
50
Figure 4-12: Alloying effects on the friction evolution of nc Ni. Only minor variations in the friction coefficient were observed
between pure and tungsten alloyed nc Ni.
Friction Coefficient
0.25
Friction Coefficient
critical fatigue fracture. Additional experiments on alternate material systems, with
varying levels of particle reinforcement, would be necessary to verify the generality
of this trend.
Finally, it is of critical importance to recognize that the grain size within the
scratch region of the nc and ufc Ni is unstable, as evidenced by the images in Figure
4-4. These results are in agreement with similar findings in the same material subjected to cyclic indentation, where grain growth was observed within and around the
indented region [103]. Possible mechanisms for this instability include grain boundary migration and/or grain rotation. Because surface grains have varying crystallographic orientations, neighboring grains typically will not experience identical levels
of deformation. Those oriented preferentially for extensive plastic deformation may
experience a different degree of slip plane rotation, relative to grains that are not similarly oriented. Once rotation crystallographically aligns two neighboring grains, the
boundary they previously shared will vanish, and the two will coalesce. Because low
angle grain boundaries have been observed in the current electrodeposited Ni, this
mechanism appears more reasonable than pure grain boundary migration at room
temperature, due to the lack of long range diffusion required in the former. The increase in temperature associated with the above scratch tests is assumed minimal, as
the scratch velocity and time between subsequent passes (25 µm/sec and 7 minutes,
respectively) allow sufficient time for heat dissipation. It is, however, possible to produce a local rise in temperature in severely deformed regions, making it somewhat
difficult to rule out temperature induced grain boundary migration entirely.
Regardless of the mechanism, this observed instability is of considerable practical
interest for tribological applications. An unstable grain structure may result in variable surface properties, as the deformed material progresses from the nc to the ufc or
even mc regime. Considerable attention must therefore be devoted to stabilizing the
grain size under contact loading conditions.
102
4.5
Conclusions
The early stage sliding contact fatigue response of several nc, ufc, and mc material
systems has been investigated. The effects of grain size, material strength, and alloying additions on friction evolution were characterized, the results of which can be
summarized as follows:
§ The steady state friction coefficient of nc electrodeposited fully dense pure Ni,
subjected to repeated unidirectional sliding contact with a spherical sapphire
indenter tip, was significantly below that of fully dense ufc and mc pure Ni.
The grain size variation between mc and nc Ni spanned more than two orders
magnitude, from 10 µm to 30 nm, respectively, while the strength varied from
180 MPa to 930 MPa.
§ The mc and ufc ECAP pure Ti exhibited a similar, but considerably less pronounced trend in friction evolution. Here, the friction coefficient of ufc Ti was
only slightly below that of mc Ti, even with a grain size variation of approximately two orders of magnitude, from 250 nm to 23 µm. The disparity in
strength between the mc and ufc Ti was considerably reduced, however, relative to that between mc and nc Ni.
§ Pure ECAP Cu was examined in its as-received and annealed (473 K for 1
hour) states. The heat treatment resulted in a substantial reduction in 0.2%
offset yield strength (by a factor of three), without a significant increase in grain
size. Sliding contact fatigue results indicate the plastically softer Cu initially
maintained a higher friction coefficient, although the two materials eventually
converged to the same steady state value. Instrumented indentation performed
inside the wear paths of both materials revealed the hardness (and to a first
approximation, the local strength) of the as-received and annealed Cu were
identical after 98 scratch passes.
§ On the basis of the above results, it was concluded that the contact fatigue
behavior was dominated by material strength rather than grain size, over the
103
range of materials investigated. In addition, alloying effects appeared minimal
in terms of their influence on the friction coefficient for the nc Ni-W alloy studied. The reported increase in hardness and scratch resistance associated with
the reduction in grain size attainable through tungsten additions [102] therefore presents an attractive method of improving the tribological properties of
pure nc Ni. Similarly, the addition of SiC particles to a nc Co metal matrix
resulted in a pronounced reduction in friction evolution and damage accumulation with respect to the pure nc Co, without sacrificing fatigue crack growth
resistance. Although additional material systems must be studied to confirm
the generality of these trends, alloying and particle reinforcement should be
considered in conjunction with (or in place of) grain refinement to further improve the tribological response. Given that both friction and damage evolution
were dominated by material strength, it appears that traditional strengthening
mechanisms, rather than grain refinement to the nc regime, could provide a
more viable (economical) means of improving tribological resistance.
§ The observed instability in surface grain structure of the nc and ufc Ni is of
critical importance in terms of the practical applicability of these materials.
This instability was assumed to result from stress induced grain rotation as
well as limited grain boundary migration. Because surface grains are not, in
general, identically aligned crystallographically, certain grains are more favorably oriented for deformation and rotation. Since electrodeposited nc Ni has
been observed to contain low angle grain boundaries, long range diffusion would
not be required for neighboring grains to rotate and coalesce. Such a mechanism
requires much less energy at room temperature than that required for pure grain
boundary migration to a similar grain size. Both phenomena can, however, be
operating simultaneously. Regardless of the mechanism, considerable attention
must be devoted to stabilizing the grain size under contact loading conditions.
104
Chapter 5
Cyclic Deformation Response of
Nanocrystalline Materials
5.1
Introduction
The mechanisms responsible for monotonic deformation in nc materials remain widely
under debate. The number of systematic experimental studies probing the deformation behavior of metals and alloys with an average grain size less than 100 nm is
currently limited. A significant constraint, which restricts the viable material processing routes for such studies, is the need to maintain the total range of grain sizes
well below 100 nm, to prevent several interspersed ‘large grains’ from controlling the
deformation response. Furthermore, laboratory specimens must be fully dense and
highly pure for an accurate characterization of the deformation behavior.
Previous studies on the mechanical properties of nc metals have been performed
[11–16]. The yield strength, σy , and hardness are generally found to increase with decreasing average grain size, down to at least 20 nm. On the other hand, the strain to
failure typically decreases with grain refinement to the nc regime, purportedly due to
local plastic instability events [14, 18–20]. ‘Inverse hardening’ has been reported for
reductions in grain size below ∼ 10 nm in several materials, where strength decreases
with further grain refinement [21–24]. It is assumed that deformation is accommodated by grain boundary sliding in this regime [25, 26]; however, no experimental
evidence has been obtained to substantiate this claim.
105
Several atomistic computational simulations [26, 104–108] have been developed to
probe the monotonic deformation behavior of nc materials, typically at a grain size
below 20 nm. The main findings of these studies can be summarized as follows:
• Below a critical grain size (typically 10 nm), grain boundary sliding becomes
the dominant mode of deformation, as dislocation activity becomes severely
limited.
• Partial dislocations are commonly emitted from grain boundaries or triple junctions, leaving a faulted region in their wake.
• Upon increasing the structural order within the grain boundary region (so called
‘annealing without grain growth’), a measurable decrease in the extent of plasticity under uniaxial tension is observed. Here, as grain boundaries approach a
more equilibrium state, the material is correspondingly strengthened [104].
It should be noted, however, that the intensive computational power required to
run atomistic simulations necessitates the use of extremely high strain rates, which
would not be experienced under typical service conditions. Damage evolution and
creep mechanisms are therefore not currently captured in such models. The mechanisms of deformation at extremely high strain rates may also be different from those
operating under typical loading conditions.
Currently, to the author’s knowledge, there are no experimental data in the open
literature relating to the cyclic deformation behavior of nc materials. Several authors
[68–70, 109] have previously studied the fatigue and cyclic deformation behavior of
ufc materials produced via severe plastic deformation techniques. In general, they
observed cyclic softening and deterioration in low cycle fatigue response, despite an
improvement in the fatigue endurance limit, with decreasing grain size. However,
materials initially subjected to elevated levels of cold work exhibit extremely high
dislocation densities, and are known to cyclically soften as a result of dislocation
realignment to lower energy configurations [71]. It therefore becomes difficult to
isolate the effects of grain size on the deformation behavior of these materials.
106
The present study was initiated in an attempt to characterize the cyclic deformation response of a fully dense, pure, nc material, with extremely low initial dislocation
density, whose average and total range of grain sizes are well below 100 nm. The
material system chosen for this investigation was the electrodeposited pure Ni fully
described in Section 2.2.1. The objectives of this study were to determine:
(i) the extent to which the nc and ufc material cyclically softened or hardened, and
(ii) whether the fatigue response of the electrodeposited Ni exhibited a similar strain
rate dependence to that observed under monotonic tension and indentation
loading [44].
5.2
5.2.1
Results
Cyclic Deformation Behavior of Electrodeposited Pure
Ni
The experimental method used to probe the cyclic deformation behavior of nc and
ufc electrodeposited pure Ni is fully detailed in Section 2.3.4. The nc Ni had a
columnar grain structure with an aspect ratio of 7-10, whereas the ufc material was
nearly equiaxed. The nc and ufc Ni were found to have relatively defect-free initial
structures, with average grain sizes of 20-40 nm and 300 nm, respectively. The total
range of grain sizes in the nc Ni was well below 100 nm, however the grain size
distribution in the ufc Ni was somewhat less narrow. Because the level of strain
experienced by mc Ni during typical loading conditions surpassed the maximum level
for which the strain gages were rated, its deformation behavior could not be assessed
in this study. Its relatively high ductility resulted in strain gage failure prior to the
completion of the first loading cycle.
Since all experiments were conducted under load control, the strain amplitude
response was used as an indicator of the cyclic deformation behavior. In general, a
material that cyclically hardens under a constant range of imposed cyclic loads will
exhibit a decreasing strain amplitude with increasing numbers of cycles. Conversely,
107
a material that cyclically softens will show a continual rise in strain amplitude, with
increasing fatigue cycles.
Cyclic Deformation Response: nc Ni
Figure 5-1 depicts the experimentally measured strain amplitude as a function of
cycle number for electrodeposited nc Ni specimens subjected to a constant range
of applied loading, with peak stresses of 800 MPa, 850 MPa, and 1000 MPa. It
is evident that cyclic hardening occurs over a broad range of loading frequencies in
the nc Ni, as the strain amplitude continually decreases throughout the duration of
each experiment. The apparent strain rate sensitivity on the rate of hardening, as
evidenced by the difference in slope between the 0.2 Hz and 20 Hz curves during the
initial 30 - 50 cycles, is an artifact of the experimental facilities. On average, the 20
Hz experiments produced an initial 1.9% overshoot in maximum stress during the first
cycle. An average 6% overshoot in initial stress amplitude was also observed at that
testing frequency. Both parameters settled to their respective nominal values within
the first 50 cycles in each case, and remained constant throughout the balance of the
experiment. This initial reduction in strain amplitude accounts for the discontinuous
change in slope between the first 50 cycles, and the remaining cycles to failure observed
in the 20 Hz tests. At a fatigue frequency of 0.2 Hz, the errors in initial maximum
stress and stress amplitude were negligible (much less than 1%).
In order to account for the above abberation in initial imposed loading, the results
in Figure 5-1 are replotted in Figure 5-2, with the strain amplitude normalized by
the applied stress amplitude. This eliminates the effect of initial stress amplitude
variations. From the figure, it is clear that the normalized rate of hardening is approximately constant throughout the duration of each experiment, and there appears
to be no significant strain rate effect over the range of frequencies examined.
Figure 5-3, which represents the width of the stress-strain hysteresis loop as a
function of cycle number, substantiates the above contention that nc Ni cyclically
hardens. Moreover, a strain rate effect was observed on the hysteresis loop width, as
108
109
(a)
0.185 0
10
0.19
0.195
0.2
0.205
10
1
2
10
3
0.235 0
10
0.24
0.245
0.25
0.255
0.26
0.265
0.27
0.275
4
10
10
5
101
Cycle Number
102
103
10
104
1
Cycle Number
2
10
Max Stress = 850 MPa
0.2 Hz
0.2 Hz
20 Hz
20 Hz
(b)
0.21 0
10
0.215
0.22
0.225
0.23
0.235
0.24
Max Stress = 1000 MPa
(c)
Cycle Number
10
0.2 Hz
0.2 Hz
20 Hz
20 Hz
10
3
10
0.2 Hz
0.2 Hz
20 Hz
20 Hz
4
Figure 5-1: Strain amplitude as a function of cycle number for electrodeposited nc Ni under a constant range of applied loading,
with peak stresses of (a) 800 MPa, (b) 850 MPa, and (c) 1000 MPa. A load ratio of R = 0.25 was used in all experiments.
Strain Amplitude (%)
0.21
Max Stress = 800 MPa
Strain Amplitude (%)
0.215
Strain Amplitude (%)
Normalized Strain Amplitude (x 10 %/MPa)
6.8
6.7
6.6
6.5
6.4
102
103
Max Stress = 800 MPa
101
-4
(a)
6.3 0
10
7.4
7.2
7
6.8
6.6
6.4
6.2 0
10
104
0.2 Hz
0.2 Hz
20 Hz
20 Hz
105
Normalized Strain Amplitude (x 10 %/MPa)
-4
7.4
7.3
7.2
7.1
7
6.9
6.8
6.7
Cycle Number
102
Max Stress = 850 MPa
101
104
0.2 Hz
0.2 Hz
20 Hz
20 Hz
(b)
103
6.6 0
10
Cycle Number
102
Max Stress = 1000 MPa
(c)
101
103
0.2 Hz
0.2 Hz
20 Hz
20 Hz
104
110
Cycle Number
Normalized Strain Amplitude (x 10 %/MPa)
Figure 5-2: Strain amplitude response from Figure 5-1, normalized by the applied stress amplitude. A constant rate of hardening
is observed throughout the duration of each test, over a wide range of cyclic frequencies.
-4
evidenced by the offset between the 0.2 Hz and 20 Hz data. The level of accumulated
strain under the low frequency testing conditions was also noticeably higher than that
in the 20 Hz experiments (Figure 5-4).
Cyclic Deformation Response: ufc Ni
For the electrodeposited ufc Ni specimens tested at a frequency of 20 Hz, the maximum stress during the first fatigue cycle was 1.2% above the nominal target value.
However, the initial stress amplitude was 5% below the anticipated value, on average.
At a frequency of 0.2 Hz, the target maximum stress was achieved with an average
error of less than 1%. There was, however, an overshoot in average stress amplitude
of 3.82%. Again, plotting the strain amplitude (normalized by the stress amplitude)
against the number of fatigue cycles, Figure 5-5 clearly shows that ufc Ni also exhibits
cyclic hardening. The mid-width of the stress-strain hysteresis loop continually decreased throughout the test, further substantiating the evidence of cyclic hardening.
No obvious rate dependence of the strain accumulation could be extracted from the
ufc Ni, as the initial stress levels in the 0.2 Hz and 20 Hz tests led to noticeably
different values of strain in the first cycle. The relevant data concerning the mid-loop
width of the stress-strain hysteresis and the strain accumulation sustained by the ufc
Ni are presented in Figures A-1 and A-2, respectively in Appendix A.
5.2.2
Rate Dependence on Total Fatigue Life
The specimens used to investigate the cyclic deformation response of electrodeposited
pure Ni were cycled to failure at their respective loading frequencies (0.2 Hz or 20
Hz). The stress-life behavior as a function of strain rate for the nc and ufc Ni is
depicted in Figure 5-6. A clear shift to longer fatigue lives is evident as the frequency
is increased from 0.2 Hz to 20 Hz. In addition, the nc Ni exhibits a higher resistance
to stress controlled fatigue, relative to the ufc Ni, in agreement with the results in
Section 3.2.1.
111
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
10
(a)
1
10
2
Max Stress = 800MPa
10
0.03
0.025
0.02
0.015
0.01
0.005
0
0
10
10
3
0.2 Hz
0.2 Hz
20 Hz
20 Hz
10
4
Hysteresis Loop Width (%)
1
2
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
3
1
4
2
Cycle Number
10
Max Stress = 850MPa
10
10
0.2 Hz
0.2 Hz
20 Hz
20 Hz
(b)
10
0.002
0
10
Cycle Number
10
Max Stress = 1000 MPa
(c)
10
10
3
0.2 Hz
0.2 Hz
20 Hz
20 Hz
10
4
112
Cycle Number
Hysteresis Loop Width (%)
Figure 5-3: Stress-strain hysteresis loop width as a function of the number of fatigue cycles at R = 0.25 for nc Ni, at peak
stresses of (a) 800 MPa, (b) 850 MPa, and (c) 1000 MPa. Values reported were extracted from the center of the hysteresis loop.
Widths measured at 30% above and below center displayed the same trends.
Hysteresis Loop Width (%)
113
0.6 0
10
0.65
0.7
0.75
10
1
0.2 Hz
0.2 Hz
20 Hz
20 Hz
2
10
3
0.85 0
10
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Cycle Number
10
10
0.2 Hz
0.2 Hz
20 Hz
20 Hz
4
10
1
10
5
2
Cycle Number
10
10
0.7 0
10
0.75
0.8
0.85
0.9
Max Stress =
1000 MPa
(a)
Max Stress = 800 MPa
0.95
3
1
10
(c)
10
0.2 Hz
0.2 Hz
20 Hz
20 Hz
4
2
Cycle Number
10
10
3
Max Stress = 850 MPa
10
(b)
4
Figure 5-4: Maximum sample strain as a function of cycle number at R = 0.25 for nc Ni, at peak stresses of (a) 800 MPa,
(b) 850 MPa, and (c) 1000 MPa. In all cases, lower frequency testing resulted in a measurably higher amount of accumulated
strain.
Maximum Strain (%)
0.8
Maximum Strain (%)
Maximum Strain (%)
-4
6.8
6.6
6.4
6.2
6
5.8
(a)
5.6
0
10
1
10
2
10
3
10
Max Stress = 475 MPa
10
-4
6.6
6.4
6.2
6
5.8
5.6
5.4
5.2 0
10
4
(c)
10
0.2 Hz
20 Hz
5
6
-4
101
102
6.6
6.4
6.2
6
5.8
5.6
0
10
103
Max Stress = 550 MPa
10
Normalized Strain Amplitude (x 10 %/MPa)
Cycle Number
2
10
3
10
Cycle Number
10
Max Stress = 500 MPa
1
105
0.2 Hz
20 Hz
10
(b)
104
4
5
0.2 Hz
20 Hz
10
10
6
114
Cycle Number
Normalized Strain Amplitude (x 10 %/MPa)
Figure 5-5: Strain amplitude as a function of cycle number for electrodeposited ufc Ni under a constant range of applied loading,
with peak stresses of (a) 475 MPa, (b) 500 MPa, and (c) 550 MPa. A load ratio of R = 0.25 was used in all experiments.
Normalized Strain Amplitude (x 10 %/MPa)
1100
nc Ni: ν = 0.2 Hz
nc Ni: ν = 20 Hz
ufc Ni:ν = 0.2 Hz
ufc Ni:ν = 20 Hz
Maximum Stress (MPa)
1000
900
800
700
600
500
400
300
3
10
10
4
10
5
10
6
Number of Cycles To Failure
Figure 5-6: Stress-life diagram depicting the variation in number of cycles to failure
with maximum applied stress for electrodeposited nc and ufc pure Ni at a load ratio
of R = 0.25. A clear beneficial effect, in terms of total life, with increasing fatigue
frequency (i.e. strain rate) is apparent.
115
5.2.3
Failure Analysis
Figure 5-7 illustrates the differences in failure mode under monotonic and cyclic loading conditions. Clearly, monotonic loading results in considerable local plasticity, as
evidenced by the dimpled rupture fracture surfaces (Figures 5-7a - b). Fatigue loading, however, eliminates all evidence of ductile fracture, regardless of the imposed
cyclic frequency (Figures 5-7c - f).
5.3
Discussion
Figures 5-2 and 5-3 summarize the first conclusive evidence of cyclic hardening in
a nc material. A decreasing strain amplitude with an increasing number of fatigue
cycles (under a constant range of imposed cyclic stresses), coupled with a continuously
narrowing cyclic stress-strain hysteresis loop, constitutes the characteristic behavior
of a cyclically hardening material. In addition, the observed strain rate effect on the
stress-strain hysteresis behavior is in agreement with a previous study conducted on
the same material [44]. Here, a positive strain rate sensitivity was observed for the
yield and tensile strengths during monotonic tensile testing of nc Ni. For a given
applied stress, a higher strain rate therefore leads to a somewhat lower strain level.
As a result, a narrower hysteresis loop is expected at higher loading frequencies, which
is the case in Figure 5-3.
While the above data and fractography clearly demonstrate cyclic hardening in
nc and ufc electrodeposited Ni, the underlying mechanism for such behavior cannot
be determined from this data alone. The shift to a lower number of cycles to failure with decreasing fatigue frequency (Figure 5-6) could potentially result from an
environmental effect. Here, the potential exists for an increased level of diffusion in
the 0.2 Hz experiments, relative to the 20 Hz tests, as the total time spent at elevated stress levels is significantly higher in the former. Fatigue cracks would therefore
remain open for longer periods of time, resulting in prolonged exposure of fresh surfaces to the environment. This could lead to enhanced levels of embrittlement, with
116
1 µm
2 µm
(a)
(b)
1 µm
2 µm
(c)
(d)
4 µm
1 µm
(e)
(f)
Figure 5-7: SEM images illustrating the fracture surfaces after (a-b) monotonic tensile
testing, (c-d) fatigue testing with a sinusoidal waveform at a cyclic frequency of 0.2
Hz, load ratio R = 0.25, and maximum stress of 850 MPa at room temperature, and
(e-f) fatigue testing with a sinusoidal waveform at a cyclic frequency of 20 Hz, load
ratio R = 0.25, and maximum stress of 850 MPa at room temperature.
117
a concomitant reduction in fatigue life. Attempts were therefore made to separate
potential environmental effects from possible structural effects.
First, a nc Ni sample was loaded monotonically to failure with an exceedingly
slow strain rate (3.5 x 10−7 sec−1 ). The time spent at relatively elevated stress levels
was similar in length to the slowest fatigue tests (0.2 Hz), and much longer than
the 20 Hz experiments. The positive strain rate sensitivity of the yield and tensile
strengths are in line with that observed in a previous study on the same material
(Figure 5-8) [44]. If an environmental embrittling process were activated after long
exposures to high stress levels, such a test would be expected to result in a more
brittle fracture than those observed in Figures 5-7a - b, where the imposed strain rate
was orders of magnitude higher. In fact, no apparent differences in fracture surface
morphology were observed over the entire range of loading rates examined. Figure
5-9 shows the same characteristic dimpled rupture following an imposed strain rate of
3.5 x 10−7 sec−1 as that seen for samples loaded at rates ranging from 3 x 10−1 sec−1
to 3 x 10−4 sec−1 [44]. In addition to the observed local ductility, the strain at
failure was approximately equivalent under the slow and fast strain rate conditions
(²fail = 3.63% at 3.5 x 10−7 sec−1 and ²fail = 3.73% at 3 x 10−1 sec−1 ). Based on the
above information, it is therefore concluded that environmental embrittlement is not
instigated solely by extensive exposure to elevated stress levels in nc Ni.
In a previous study examining the effects of environment on the mode of fracture
in mc Ni [110], tensile specimens were cathodically precharged with hydrogen at room
temperature. Intergranular failure across the entire gage section (4.5 mm x 0.2 mm)
was found to occur only after 16 hours of charging. Specimens subjected to shorter
charging periods exhibited a mixture of ductile and intergranular fracture. The strain
to failure in specimens free of hydrogen was more than an order of magnitude higher
than those exposed to 16 hours of precharging. These results imply that Ni is not
particularly susceptible to hydrogen embrittlement in a laboratory air environment,
as a relatively extended period of hydrogen charging was required before intergranular
fracture became the dominant failure mode.
118
1800
Stress (MPa)
1500
1200
Increasing
Strain Rate
900
600
ε = 3.5 x 10-7 s-1
ε = 3 x 10-4 s-1
ε = 1.8 x 10-2 s-1
ε = 3 x 10-1 s-1
300
0
0.0
1.0
2.0
3.0
4.0
5.0
Strain (%)
Figure 5-8: Stress versus strain response for electrodeposited pure nc Ni as a function
of strain rate.
(a)
(b)
Figure 5-9: Fracture surface images of a nc Ni sample loaded to failure monotonically
at a strain rate of 3.5 x 10−7 sec−1 . A ductile (dimpled) failure mode prevailed, and
no apparent regions of brittle fracture were observed.
119
Still, the clear shift in number of cycles to failure with increasing cyclic frequency
(Figure 5-6) indicates a strain rate dependence on the stress-controlled fatigue response of nc and ufc Ni. As previously mentioned, strain accumulation in the nc Ni,
as well as the maximum strain at failure, are consistently lower under the 20 Hz condition, as depicted in Figure 5-4. Here, dislocation dominated deformation, rather
than grain boundary sliding, is expected at higher strain rates, as grain boundary
sliding involves short range diffusion and atomic shuffling. Such processes require
sufficient amounts of time at high stress levels to occur. It is apparent that a lower
strain rate leads to higher levels of plastic deformation, throughout the duration of
the experiment. This increased level of time-dependent deformation (creep) likely
contributed to the lowering of the total fatigue life at slower cyclic frequencies.
To substantiate the above creep-fatigue interaction, several constant-load experiments were performed, in an attempt to ascertain the room temperature creep behavior of electrodeposited nc Ni. The deformation response of specimens loaded at
900 MPa, 1100 MPa, and 1300 MPa was recorded as a function of time. Figure
5-10 clearly shows the relatively large creep strains accumulated over elapsed times
comparable to those required for catastrophic failure under the 0.2 Hz fatigue loading
conditions. Considering these creep strains comprise a substantial fraction of the total
strain to failure in the nc Ni, it is reasonable to assume the strain rate sensitivity of
the total fatigue life can be attributed to a creep-fatigue interaction, which is clearly
exacerbated at lower cyclic frequencies.
In addition, the deformation and failure mechanisms for nc Ni proposed by Kumar,
et al. [11] suggest that grain boundary sliding leads to void formation along grain
boundaries and at triple junctions. Subsequently, void growth leads to a relaxation of
constraint. The monocrystalline ligaments separating such voids continue to deform
under the applied loading, until they fail in a chisel-point fashion. The potential
suppression of grain boundary sliding at a cyclic frequency of 20 Hz could hinder void
formation, resulting in delayed crack initiation, and therefore final failure. This could
also explain the apparent beneficial effect of an increase in strain rate on the stress
controlled fatigue response.
120
2
σ = 900 MPa
σ = 1100 MPa
σ = 1300 MPa
Creep Strain (%)
ε = 7.2 x 10-8 s-1
1.5
1
ε = 2.5 x 10-8 s-1
ε = 7.0 x 10-9 s-1
0.5
0
0
10
20
30
40
50
Time (hr)
Figure 5-10: Creep strain accumulated in electrodeposited pure nc Ni as a function of
time at 900 MPa, 1100 MPa, and 1300 MPa. Steady state creep rates are indicated
on the figure.
In terms of the hardening behavior, there are several potential mechanisms that
could act alone, or in concert, to produce the observed effect. They include enhanced
dislocation interaction with an increasing number of stacking faults (produced during cycling), environmental effects, and/or strengthening due to a defect source exhaustion mechanism detailed below. The effects of environment on total fatigue life
(described above) and the hardening behavior must be separated, as the latter assumes diffusion through the grain interior, while the former could result from grain
boundary diffusion alone.
Atomistic simulations have shown stacking faults produced in monotonically loaded
nc Ni as a result of Shockley partial dislocation emission from grain boundaries and
triple junctions, and their subsequent absorption at opposing boundaries [105]. Stacking faults were observed in simulations of pure Ni with grain sizes as low as 12 nm.
For reference, the average grain size of the Ni used in the current cyclic deformation
experiments was ∼ 30 nm. Interaction between the faulted material and mobile dis121
locations could result in the observed hardening behavior. As previously mentioned,
however, caution must be exercised when comparing experimental and atomistic computational results. The strain rates required in such simulations are not realistic, and
could result in a response that would not typically be observed under normal operating conditions.
To confirm or refute the above mechanism, ex-situ TEM images were taken of
nc Ni specimens cyclically loaded to failure at frequencies of 0.2 Hz and 20 Hz.
TEM samples were extracted from several regions well within the gage section of the
failed specimens (i.e. far from the fillet). Figure 5-11 illustrates a general lack of
faulted material and dislocation debris following the imposed cyclic loads. Clearly,
dislocations can be reabsorbed by the grain boundaries subsequent to fatigue failure,
however some level of residual debris would be expected if this mechanism were active.
While the interaction between stacking faults and mobile dislocations could partially
contribute to the overall hardening behavior, the lack of evidence suggests it is not
the dominant hardening mechanism.
In addition, Figure 5-11 shows no evidence of mechanical fatigue induced grain
growth, in contrast to the behavior observed under contact fatigue loading conditions. As previously mentioned, strengthening and hardening mechanisms that are
operable in ufc and mc metals may not necessarily be so in nc metals, as the grain
size approaches the characteristic defect spacing. Had grain growth occurred, the
fundamental hardening mechanism would likely have shifted to a more conventional
means prior to final failure. Based on the images in Figure 5-11, however, mechanical fatigue induced grain growth can be ruled out as a contributing factor to the
hardening behavior.
For environmentally assisted hardening to occur, the embrittling agent is assumed
to originate from the internal hydrogen residing within the electrodeposited Ni, or externally from the laboratory air environment. As the internal level of hydrogen seems
not to affect the locally high level of plasticity under monotonic loading (i.e. Figures
5-7 and 5-8), it is precluded from further consideration. The potential embrittling
122
(a)
(b)
Figure 5-11: TEM images depicting the relative lack of dislocation debris and faulted
material in samples cycled to failure at (a) 0.2 Hz and (b) 20 Hz. TEM samples were
extracted from the gage length of failed specimens, far from the fillet.
source would therefore likely result from the decomposition of water vapor (humidity). The initiation of a fatigue crack provides fresh metal surfaces that can act as a
catalyst for this reaction. Grain boundary diffusion would then be expected, considering the excessive boundary volume in nc materials. However, for an environmental
species to affect the hardening behavior (i.e. Figure 5-2) it must diffuse into the bulk
as well, where it can instigate solid solution strengthening, and possibly migrate to
dislocation cores. The ratio of grain boundary diffusivity to lattice diffusivity is typically greater than ∼ 60 however [111], rendering boundaries the dominant diffusion
path. Hardening contributions from environmental interactions are therefore likely
to be minimal as well.
To further rule out environmental embrittling effects on the hardening behavior,
a series of interrupted fatigue tests were performed at a maximum stress of 850
MPa and a load ratio of R = 0.25. Here, samples of nc Ni were cycled to some
fraction of their anticipated total fatigue life (Nf = 10, 000 cycles at σmax = 850
MPa), after which they were unloaded completely, and then loaded monotonically
123
100
1000
5000
7500
Cycles
Figure 5-12: Electrodeposited pure nc Ni specimens loaded in fatigue to 100, 1000,
5000, and 7500 cycles (e.g. 1 %, 10 %, 50 %, and 75 % of their total fatigue lives,
respectively), unloaded, and then reloaded monotonically to failure.
to failure. Figure 5-12 shows a transition from a macroscopically ductile fracture
(with failure occurring at ∼ 45o to the tensile axis) to a more brittle type of failure
(fracture occurs perpendicular to the tensile axis) after approximately 5,000 fatigue
cycles. Fracture surface examination (Figure 5-13) also reveals a transition in dimple
morphology. Here, specimens subjected to 100 or 1000 fatigue cycles exhibit an
elongated dimple failure mode, whereas those subjected to 7500 cycles display a much
shallower, symmetric dimple morphology. No evidence of progressive embrittling
from the periphery of the sample was observed, as might be expected if the outside
environment were the source of hardening. Samples apparently hardened throughout
the entire gage section with increasing numbers of fatigue cycles, further indicating
that environmental effects are, in fact, minimal.
Finally, defect source exhaustion is a hardening mechanism for which there is
computational and experimental evidence. Previously, it has been shown that an
124
100 cycles
1000 cycles
5000 cycles
7500 cycles
Figure 5-13: Fracture surface examination of the samples depicted in Figure 5-12,
illustrating the change in dimple morphology with increasing numbers of fatigue cycles. A transition from an elongated dimple morphology (indicating extensive shear
deformation) to a more symmetric dimpled failure mode (indicating a hardened state)
is apparent with increasing numbers of fatigue cycles.
125
intermediate anneal of nc materials (annealing without grain growth) can result in an
increased level of structural order within the grain boundary region, thereby bringing
boundaries closer to their equilibrium state. Consequently, a decrease in the level
of plasticity under uniaxial tension is observed, effectively increasing the strength
of the material. A reduction in the internal strain, typically developed during the
fabrication process, is reported to cause the increased level of strength subsequent to
the anneal. As mentioned, this trend was observed both computationally [104] and
experimentally [112, 113].
On a similar basis, it is proposed here that cyclic hardening could occur due
to an exhaustion of dislocation sources (e.g. grain boundary defects). Based on
experimental and computational results [11, 105], there appears to be no shortage of
dislocation activity under monotonic loading conditions. The observed dislocations
are typically emitted from, and absorbed at, opposing grain boundaries. Figure 514 schematically illustrates a hypothetical grain containing several boundary defects,
which require different stress levels to activate dislocation emission.
It is possible for a single boundary defect to emit multiple dislocations. However,
boundaries are not continuous sources of dislocations like, for example, a FrankReid source. After the emission of one or more dislocations from a boundary defect,
the imperfection is removed, eliminating that site as a source of dislocations. The
dislocations absorbed at opposing boundaries may require the same, higher, or lower
stress levels to be ‘re-activated.’
Because the current fatigue tests are conducted at a constant range of applied
stresses, it is possible that defect sources (boundary defects) are in fact exhausted,
resulting in the observed hardening behavior. Taking Figure 5-14 as an example,
assuming a stress of 800 MPa is sufficient to activate dislocation emission at sites ‘1’
and ‘2’ only, one can ignore sites ‘3’ through ‘5’ during stress controlled fatigue cycling
with σmax = 800 MPa. After several cycles of dislocation emission from sites 1 and
2, these boundary defects will have ‘healed,’ exhausting them as dislocation sources.
If the stress required to re-activate dislocations absorbed at opposing boundaries is
126
4
3
2
5
1
Figure 5-14: Schematic illustration of an imperfect grain boundary with several peripheral defects. It is assumed that sites ‘1’ through ‘5’ act independently, requiring
different stress levels for dislocation emission from each site.
higher than 800 MPa, the material will effectively begin to harden. This theory
is substantiated by the experimentally and computationally observed strengthening
upon ‘annealing without grain growth,’ as described above [104, 112, 113]. Materials
subjected to an intermediate anneal are observed to have boundaries that are ‘closer
to a more equilibrium structure.’ Such a material would have fewer boundary defects,
which would explain the observed increase in strength.
5.4
Conclusions
The cyclic deformation behavior of electrodeposited, fully dense, pure nc and ufc Ni
has been characterized. Electro-discharge machined ‘dog-bone’ type specimens were
cyclically loaded to failure over a wide range of applied stresses and frequencies. A
summary of the pertinent results is given below.
§ The first assessment of the cyclic deformation behavior of a nc material is reported above. It was found that electrodeposited nc and ufc pure Ni cycli127
cally harden over a wide range of fatigue loading conditions. Under a constant
range of applied stresses, a continuous decrease in strain amplitude and cyclic
stress-strain hysteresis loop width with increasing numbers of fatigue cycles was
observed.
§ Several potential hardening mechanisms were described, including environmental effects, enhanced dislocation interaction with increasing numbers of stacking
faults (produced during cycling), and strengthening due to a ‘defect source
exhaustion’ phenomenon.
The latter was proposed due to supporting evi-
dence from experimental and computational observations [104, 112, 113]. Postmortem TEM images did not reveal an increased level of dislocation debris or
stacking faults in samples cycled to failure at 0.2 Hz or 20 Hz. However, this can
be at least partially attributed to the re-absorption of defects at grain boundaries upon unloading. Experiments carefully designed to isolate the effects of
environmental embrittlement showed no apparent environmental contribution
to the failure process during monotonic or cyclic loading, over a wide range of
strain rates.
§ An apparent strain rate effect on the total life under stress-controlled fatigue
was also observed, with higher testing frequencies consistently leading to an
increase in the number of cycles to failure. Here, the accumulated strain was
inversely proportional to cyclic frequency, which likely contributed to the lowering of the fatigue life at a frequency of 0.2 Hz, relative to that at 20 Hz, as a
result of a creep-fatigue interaction. Creep tests conducted on the nc Ni confirmed the relatively substantial room temperature creep strains accumulated at
stress levels comparable to those imposed during the fatigue investigations. In
addition, elevated strain rates are assumed to reduce the level of grain boundary
sliding, as the associated short range diffusion and atomic shuffling processes
become progressively more difficult with increasing loading rates. Dislocation
dominated deformation is assumed to prevail at increased cyclic frequencies,
resulting in a reduction in the level of void formation that accompanies grain
128
boundary sliding. Damage initiation would therefore be delayed at higher cyclic
frequencies, resulting in a longer total fatigue life.
129
130
Chapter 6
Concluding Remarks and
Suggested Future Work
6.1
Conclusions
The fatigue response of nanocrystalline materials, with average and total range of
grain sizes well below 100 nm, has herein been characterized for the first time using
appropriate experimental, analytical, and computational tools. The key contributions
of this thesis can be summarized as follows:
1. Grain refinement to the nc and ufc regimes has been found to substantially
affect the total life under stress-controlled fatigue. Electrodeposited nc and ufc
Ni exhibited a significantly higher resistance to S-N fatigue, relative to their mc
Ni counterpart. As the crack propagation rate is considerably higher in the finer
grain material, it was concluded that grain refinement to the nc regime enhances
the resistance to the initiation of a dominant fatigue flaw. Assuming fatigue
cracks initiate to a length comparable in size to the average grain dimension,
the initial propagation rate under stress-controlled fatigue is presumably lower
in the nc material than the ufc or mc materials, consuming more fatigue cycles
in the generation of an ‘engineering-size’ crack.
2. In addition to the above total life trends, grain refinement to the nc and ufc
regimes was found to have a significant effect on the resistance to subcritical
fatigue fracture. Specifically, a higher rate of fatigue crack growth was observed
131
in a fully dense electrodeposited pure nc Ni, relative to that in a similarly produced ufc Ni, as well as conventional mc Ni, under identical loading conditions.
Crack growth trends extracted from a cryomilled Al-7.5Mg alloy and an equal
channel angular pressed pure Ti are consistent with those obtained in the above
‘model material system.’ In each case, grain refinement resulted in a substantial
reduction in fatigue crack path tortuosity, with an attendant rise in the effective
stress intensity factor range locally at the crack tip. A crack deflection/closure
model [83] was therefore employed to justify the decrease in crack growth rate
consistently observed in coarser grain materials.
3. The contact fatigue properties of nc materials subjected to repeated unidirectional sliding were also investigated. Specifically, friction evolution and damage
accumulation were monitored as a function of the number of sliding contact
fatigue cycles imposed at the surface of a variety of nc, ufc, and mc material
systems. Critical experiments designed to isolate the effects of grain size and
material strength established that the latter dominated friction and damage
evolution, over the range of materials and grain sizes examined. The effects of
alloying and particle reinforcement were also characterized. Both had a propensity to improve the tribological behavior. A grain size instability was observed
in nc and ufc electrodeposited pure Ni after a limited number of contact fatigue
cycles, where significantly coarser grains were observed within the confines of
the damaged regions. This instability has clear practical implications, as an
initially nc surface coating (for example) could progress locally to the ufc or mc
grain size regime in regions where abrasive contact is prevalent.
4. The above results clearly illustrate that the mechanical fatigue response is dominated by the grain size of the material, while the contact fatigue behavior is
controlled by its strength. While the grain size dictated the level of fatigue
crack path tortuosity, and therefore the effective stress intensity at the crack
tip, the strength controlled both the friction and damage evolution under contact fatigue loading.
132
5. The first evidence of cyclic hardening in an nc material was reported, based
on fatigue experiments conducted in electrodeposited nc and ufc pure Ni. The
strain amplitude response to constant ranges of imposed cyclic loads was monitored over two largely different cyclic frequencies. A continuous reduction in
strain amplitude, as well as stress-strain hysteresis loop width, was observed
with increasing numbers of fatigue cycles, indicating cyclic hardening in both
the nc and ufc Ni. A strain rate effect was observed on the number of cycles to
failure in both material systems, with higher frequencies resulting in prolonged
fatigue lives. Potential mechanisms responsible for the above behavior were discussed, and a combination of a defect source exhaustion hardening mechanism
and a potential creep-fatigue interaction was proposed.
6.2
Future Work
Although the results presented here pertain only to a limited set of nc metals and
experimental conditions, it is interesting to speculate about possible implications for
potential applications. It appears from the results obtained here and from those found
for severely deformed ufc metals [68–70] that grain refinement into the nanoscale
regime offers the possibility of enhanced resistance to high cycle fatigue, such as
that characterized by the stress-life approach. Such an approach to tailor surfaces
with nc grains may offer enhanced resistance to fatigue crack initiation under low
amplitudes of cyclic stresses. Possible microstructural designs (see, for example, [114])
involving graded transitions from a nanostructured surface grain morphology to a
relatively coarser grain interior may also provide gradual transitions from a surface
layer resistant to high-cycle fatigue to a core which is more resistant to fatigue damage
and crack growth.
Such was the motivation for a preliminary study on the fatigue behavior of an
electrodeposited pure Ni possessing a through-thickness grain size gradient. Initial
experiments were conducted on two separate foils 300 µm and 450 µm in thickness,
each with a stepwise gradient in grain size. Both materials were composed of three lay133
100 µm
Figure 6-1: Cross-sectional view of a three-layer electrodeposited plastically graded
pure Ni specimen. From top to bottom, the layers are composed of mc, ufc, and nc
grains, respectively, with a concomitant increase in hardness through the thickness.
ers of approximately equal thickness, with the first, second, and third layers residing
in the nc, ufc, and mc regimes, respectively. A representative (etched) cross-section of
the 450 µm specimen is depicted in Figure 6-1. The indentation and fatigue response
of these materials is characterized in Appendix B. While the response of elastically
graded materials, with no associated gradation in plastic properties, has been studied
previously [114–119], the behavior of materials with grain size induced plasticity gradients has been relatively unexplored. In addition to more detailed experimentation,
extensive computational modeling of grain size induced plasticity gradients could
provide useful information regarding the indentation and contact fatigue response
of such materials. The applicability of materials tailored with nc grains at the surface, and coarser grains within, could then be assessed by recourse to computational
simulations.
Additional efforts should also be directed toward characterizing the influence of
alloying on the resistance to subcritical fatigue fracture and stress-controlled fatigue
in the nc regime. The model material system chosen for this study was of ultra134
high purity in order to isolate grain size effects on the fatigue response. While the
enhanced strength of pure nc materials may justify their use in structural applications,
alloying could provide additional advantages, as evidenced by the increased resistance
to tribological damage in the Ni-W investigated. Alloy additions may also act to
stabilize the grain size in contact fatigue and higher temperature applications, as a
result of a ‘solute drag’ mechanism, which effectively impedes grain growth.
135
136
Appendix A
Cyclic Deformation Response of
ufc Ni
137
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0
10
(a)
1
10
2
10
3
10
Max Stress = 475 MPa
10
0.025
0.02
0.015
0.01
0.005
0
0
10
4
(c)
5
10
0.2 Hz
20 Hz
10
10
1
6
10
2
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0
10
10
3
Max Stress = 550 MPa
Hysteresis Loop Width (%)
Cycle Number
4
5
2
10
3
10
Cycle Number
10
Max Stress = 500 MPa
1
10
0.2 Hz
20 Hz
10
(b)
10
4
5
10
0.2 Hz
20 Hz
10
6
138
Cycle Number
Hysteresis Loop Width (%)
Figure A-1: Average stress-strain hysteresis loop width as a function of the number of fatigue cycles at R = 0.25 for electrodeposited ufc Ni at peak stresses of (a) 475 MPa, (b) 500 MPa, and (c) 550 MPa. Values are reported for mid-loop width,
measured directly at the center of the hysteresis loop. Widths measured at 30% above and below center displayed an identical
trend.
Hysteresis Loop Width (%)
139
0.85
0
10
0.9
0.95
1
(a)
10
1
2
10
3
10
1
100
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
4
10
5
10
0.2 Hz
20 Hz
6
(c)
101
103
0.75
0
10
0.8
0.85
0.9
0.95
Cycle Number
102
Max Stress = 550 MPa
Cycle Number
10
Max Stress = 475 MPa
1
104
1
2
10
3
10
Cycle Number
10
105
0.2 Hz
20 Hz
10
(b)
Max Stress = 500 MPa
4
10
5
10
0.2 Hz
20 Hz
6
Figure A-2: Maximum sample strain as a function of cycle number at R = 0.25 for electrodeposited ufc Ni at peak stresses of
(a) 475 MPa, (b) 500 MPa, and (c) 550 MPa. No conclusive rate effect on the strain accumulation with fatigue cycling was
observed.
Maximum Strain (%)
1.05
Maximum Strain (%)
Maximum Strain (%)
140
Appendix B
Fatigue Response of Functionally
Graded Electrodeposited Pure Ni
An example involving microstructural design to enhance fatigue behavior
B.1
Introduction
The introduction of spatial gradients in material composition, microstructure, and
mechanical properties is by no means a novel concept. Gradients in mechanical properties are commonly observed in nature. Gears used for the transmission of large loads
are generally carburized or nitrided to produce a hard, wear resistant outer ‘case,’
while maintaining a tough, impact resistant core. The applications for functionally
graded materials (FGMs) are, in fact, quite numerous; however, their limitations
must be recognized. Recently, high temperature applications for FGMs have been
investigated in the aerospace and fuel cell industries, with somewhat discouraging
results. It has become clear that diffusion-induced changes in composition and structure may preclude the use of FGMs at high temperature [114, 115]. As a result,
focus has been shifted toward lower temperature applications to capitalize on the enhanced contact damage resistance exhibited by FGMs. Examples include coatings for
magnetic storage media, dental implants, and articulating surfaces in hip and knee
prostheses [115].
The indentation response of elastically graded materials has been characterized
141
previously. Giannakopoulos et al. have used computational indentation techniques
to study solids with variations in Young’s modulus, E, as a function of depth beneath
the indented surface, z [116, 117]. Two types of modulus variations were incorporated into their study: (a) a simple power law, E = Eo z k , where −1 < k < +1 is a
non-dimensional exponent and Eo has dimensions of stress × length−k and (b) an exponential law, E = Eo0 eβz , where Eo0 is the modulus at the surface, β < 0 corresponds
to a hardened surface, and β > 0 corresponds to a soft surface.
For the case of an exponentially varying modulus, computational results indicated
a stiffer indentation response for β > 0, due to a redistribution of stress beneath the
indented surface. Maximum values of tensile stress, which are responsible for the
nucleation of surface damage, are ‘spread’ toward the interior (where larger loads
can be sustained), thereby enhancing contact damage resistance. The opposite is
true for materials graded with an exponentially decreasing modulus as a function
of depth (β < 0). Here, tensile stresses tend to diffuse toward the surface. For
the power law modulus variation, the indentation response of the graded material
tends to stiffen with increasing load, whereas the homogenous material (zero modulus
gradient) maintains a constant elastic contact stiffness [116, 117].
The superior damage resistance of elastically graded surfaces was also demonstrated through a series of experiments [118]. A sample of dense, fine-grain alumina
was infiltrated by an aluminosilicate glass, creating a power law variation in modulus
from 72 GPa at the surface, to 375 GPa at a depth of approximately 2 mm. Samples
of monolithic alumina, monolithic aluminosilicate glass, and the graded composite of
the two were mounted individually to the stage of a tension-torsion servohydraulic
testing machine and loaded normally with a spherical indenter. A tangential load
was then introduced via controlled rotation of the stage. Sliding velocities were kept
below 0.3 mm/s, and the length of the sliding track was at least 1.5 mm. Because
the off-center distance of the sample on the stage (82.5 mm) was much greater than
the sliding distance, the arc produced could be approximated as a straight line.
For each material described above, a critical normal load, Pcr , necessary to cause
142
surface cracking was identified. As expected, the dense alumina exhibited a much
higher resistance to cracking (Pcr = 1600 N) than the aluminosilicate glass (Pcr = 800
N). However, the graded alumina-glass composite far outperformed its homogeneous
constituents, with a critical load of Pcr = 2200 N. In addition, the graded composite
sustained much less surface damage than the alumina or the glass, both of which
exhibited severe herringbone cracks at their respective surfaces. No such cracks were
detected on the graded composite, rather a more graceful microcracking pattern was
observed.
While the indentation and tribological response of elastically graded materials has
been characterized, similar studies on grain size variation-induced plasticity gradients
have not been performed to the author’s knowledge. Such was the motivation for this
preliminary study involving an electrodeposited pure Ni with a through-thickness
grain size gradation.
B.2
Material and Experimental Methods
Two electrodeposited pure Ni foils were produced with stepwise grain size gradients.
The first was composed of three ∼ 100 µm thick layers of mc, ufc, and nc Ni. The
second had a similar stepwise gradient, with a layer thickness of ∼ 150 µm. Figure
6-1 illustrates a representative etched cross-sectional view of the latter. Without
etching, the interfaces between layers are indiscernible, as evidenced in Figure B-1,
where cross-sectional indentation has been performed at a maximum load of 1.0 N
across the three layers.
Prior to characterizing its fatigue response, additional indentation experiments
were conducted on both the nc and mc faces of the plastically graded material, to a
maximum load of 1 N, 5 N, 10 N, and 15 N, using a Berkovich indenter tip. Because
the depth of penetration was relatively limited, samples were polished to remove ∼ 50
µm of material from the top and bottom layer of each sample, thereby more readily
revealing the effects of the intermediate ufc layer.
Additional ‘dog-bone’ type specimens were electro-discharge machined to examine
143
100 µm
Figure B-1: Cross-sectional indentation across the grain size gradient of an electrodeposited pure Ni, illustrating the variation in hardness from the mc top layer, to the
ufc and nc layers beneath. All indents were performed to a maximum load of 1 N.
the effects of grain size variations on fatigue behavior. A single thumbnail notch,
aligned perpendicular to the tensile axis, was introduced in one of the surface layers
(mc or nc) at the center of the gage length of each sample. The notch depth was
50 µm, or approximately one-half the layer thickness. Samples were subsequently
subjected to fatigue loading at room temperature, with a sinusoidal waveform at a
frequency of 10 Hz and load ratio R = 0.25. A comparison was then made between
the number of cycles to failure in specimens notched on the nc face and those notched
on the mc face.
B.3
Results and Discussion
The electrodeposited grain-size-gradient pure Ni had a significantly stiffer indentation
response at the nc face, relative to the mc face (Figure B-2). For comparison purposes,
the deformation induced at a maximum load of 15 N is illustrated in Figure B-3. It
is clear that the resistance to penetration and contact damage increases from the mc
to the nc layer.
144
1.2
16
nc Ni Face
mc Ni Face
1
nc Ni Face
mc Ni Face
14
Load (N)
Load (N)
12
0.8
0.6
0.4
10
8
6
4
0.2
2
0
0
0
1
2
3
4
5
0
5
10
Depth (µm)
Depth (µm)
(a)
(b)
15
20
Figure B-2: Load versus depth response of the mc and nc faces of a grain size graded
electrodeposited pure Ni at a maximum load of (a) 1 N and (b) 15 N.
mc face
nc face
(a)
(b)
Figure B-3: Load-controlled indentation of the (a) mc face and (b) nc face of an electrodeposited pure Ni foil, with a through thickness grain size gradient. The maximum
indentation load was 15 N in each case.
145
The effect of a negative grain size gradient, where the average grain size decreases
with increasing depth beneath the surface, appears stronger than that of a positive
gradient, where grains become coarser with increasing depth. Figure B-4a illustrates
four load versus depth (P − h) curves, depicting the effects of a negative grain size
gradient. First, a relatively low load indentation experiment was conducted on the
mc face (polished to half its original thickness) of the graded Ni sample. As the depth
of penetration (∼ 4.3 µm) was less than 10% of the total layer thickness, the effect of
the ufc Ni layer below was assumed negligible. The loading portion of the indentation
curve was then fit via Kick’s Law, which can be written as
P = Ch2
(B.1)
where C represents the loading curvature. This fit was subsequently extrapolated to
much higher loads, where it was compared with experimental data from an indentation
test conducted on the mc face at a maximum load of 15 N. Figure B-4a illustrates
that a negative grain size gradient effectively stiffens the indentation response with
increasing depth. Here, a 15 N indentation into the mc surface layer displayed a
substantially stiffer response than that predicted from the Kick’s Law fit, as well
as that for pure mc Ni with no grain size gradient. While the reverse appears to
hold for a positive grain size gradient (Figure B-4b), the magnitude of the effect is
considerably smaller than that in Figure B-4a.
The beneficial effect of a negative grain size gradient, in terms of a stiffening
indentation response with increasing depth, was expected considering the hardness
and load carrying capacity of the material increases from the mc to the nc face.
Although a similarly strong effect of a positive grain size gradient was not detected,
additional indentations to larger depths of penetration would be required to more
adequately reveal the interaction between the nc and ufc layers in this system. The
load capacity of the available microindenter prevented such experiments.
After quantifying the indentation response, the fatigue behavior of the graded Ni
was characterized. An attempt was made to control the site of crack initiation by
146
16
mc Ni Face (1 N)
Kick's Law Fit
mc Ni Face (15 N)
mc Ni (no gradient)
14
Load (N)
12
10
8
6
4
2
0
0
5
10
15
20
25
Depth (µm)
(a)
16
nc Ni Face (1 N)
Kick's Law Fit
nc Ni Face (15 N)
nc Ni (no gradient)
14
Load (N)
12
10
8
6
4
2
0
0
2
4
6
8
10
12
14
Depth (µm)
(b)
Figure B-4: Effect of (a) a negative grain size gradient and (b) a positive grain size
gradient on the load versus depth response of an electrodeposited pure Ni.
147
introducing a precise thumbnail notch to either the mc or nc face of each specimen.
Due to the limited quantity of material, it was not possible to conduct multiple repeat
experiments at a single stress level. However, over the range of applied stresses
investigated, samples notched on the nc face achieved anywhere from 7% to 70%
longer fatigue lives, relative to those notched on the mc side, under identical loading
conditions (Figure B-5).
Clearly, additional experiments are required to confirm the validity of the above
trend. However, the initial findings of this study reinforce the hypothesis that grain
refinement to the nc regime enhances the resistance to crack initiation. Furthermore,
the beneficial effects of a nc surface layer, in terms of the resistance to penetration
and contact damage (Figure B-3), has been demonstrated. Additional efforts to
characterize the fatigue response of materials with alternate grain size gradients (e.g.
linear, power law, or exponential, rather than stepwise), therefore seems prudent at
this time.
B.4
Conclusions
The indentation and low-cycle fatigue response of electrodeposited pure Ni, with a
stepwise through-thickness grain size gradient, was investigated. A clear increase in
resistance to penetration and contact damage was observed at the nc surface layer,
relative to the mc surface. In addition, a beneficial effect of a negative grain size
gradient, where grain refinement occurs with increasing depth, was observed. Here,
a negative gradient resulted in a stiffer indentation response, relative to that in pure
Ni with a similar (but invariant) grain size throughout the thickness.
The total life under stress-controlled fatigue for tensile specimens notched in either the nc or mc surface layer was also investigated. An apparent increase in total
life was observed in samples notched on the nc surface, relative to those notched on
the mc side. This observation reinforces the previously described trend of enhanced
resistance to fatigue crack initiation with grain refinement to the nc regime (Section
3.2.1). Clearly, additional experiments are required to confirm the validity and gen148
Maximum Stress (MPa)
800
Notch on nc Side
Notch on mc Side
700
600
500
400
300
R = 0.25
200
3
10
10
4
10
5
10
6
10
7
Number of Cycles to Failure
Figure B-5: A comparison of the total fatigue life, as a function of maximum applied
stress at a constant load ratio of R = 0.25, for electrodeposited pure Ni with a
through-thickness grain size gradient. A single controlled notch was introduced (to
a depth of 50 µm) on either the mc or nc face of electro-discharge machined tensile
specimens.
149
erality of this behavior. However, preliminary results obtained in this investigation
provide further incentive to investigate the effects of similar microstructural designs
for potential applications involving grain size gradients.
150
Bibliography
[1] Kumar KS, Van Swygenhoven H, and Suresh S, Acta Mater. 2003; 51:5743-5774.
[2] Gleiter H, Acta mater. 2000; 48:1-29.
[3] Artz E, Acta Mater. 1998; 46(16):5611-5626.
[4] Gleiter H, Nanost. Mater. 1992; 1:1-19.
[5] Hahn H, Nanost. Mater. 1993; 2:251-265.
[6] Suryanarayana C, Inter. Mater. Rev. 1995; 40:41.
[7] Jeong DH, Gonzalez F, Palumbo G, Aust KT, Erb U, Scripta Mater. 2001;
44:493.
[8] McFadden SX, Mishra RS, Valiev RZ, Zhilyaev AP, Mukherjee AK, Nature
1999; 398:684.
[9] Lu L, Sui ML, Lu K, Science 2000; 287:1463-1466.
[10] Kim YW and Bidwell LR, “High-Strength Powder Metallurgy Aluminum Alloys”, Eds. Kiczak MJ and Hildeman GJ, 1982; 107-124.
[11] Kumar KS, Suresh S, Chisholm MF, Horton JA, and Wang P, Acta Mater.
2003; 51:387-405.
[12] Nieman GW, Weertman JR, and Siegel RW, J. Mater. Res. 1991; 6:1012.
[13] Sanders PG, Eastman JA, and Weertman JR, Acta Mater 1997; 45:4019.
151
[14] Ebrahimi F, Bourne GR, Kelly MS, and Matthews TE, Nanost. Mater. 1999;
11:343.
[15] Legros M, Elliot BR, Rittner MN, Weertman JR, and Hemkar KJ, Philos. Mag.
A 2000; 80:1017.
[16] Lu L, Li SX, and Lu K, Scripta Mater. 2001; 45:1163.
[17] Meyers MA and Chawla KK, Mechanical Behavior of Materials, 1999; PrenticeHall.
[18] Dalla Torre F, Van Swygenhoven H, and Victoria M, Acta Mater. 2002; 50:3957.
[19] Ebrahimi F, Zhai Q, and Kong D, Scripta Mater. 1998; 39:315.
[20] Ma E, Scripta Mater. 2003; 49:663.
[21] Chokshi AH, Rosen A, Karch J, and Gleiter H, Scripta Metall. 1989; 23:1679.
[22] Masumura RA, Hazzledine PM, and Pande CS, Acta Mater. 1998; 46:4527.
[23] Schuh C, Nieh TG, and Yamasaki T, Scripta Mater. 2002; 46:735.
[24] Schuh C, Nieh TG, and Iwasaki H, Acta Mater. 2003; 51:431.
[25] Hahn H, Mondal P, and Padmanabhan KA, Nanost. Mater. 1997; 9:603.
[26] Hasnaoui A, Van Swygenhoven H, and Derlet PM, Phs. Rev. B 2002; 66:184112.
[27] Suresh S, Fatigue of Materials, 2nd Ed., Cambridge University Press, 1998.
[28] Mughrabi H, Ackermann F, and Herz K, In Fatigue Mechanisms, Special Technical Publication 675, Philadelphia: ASTM 1979; 69-105.
[29] Wood WA, Phil. Mag. 1958; 3:692-699.
[30] Kennedy AJ, Processes of Creep and Fatigue in Metals 1963; New York: Wiley.
152
[31] Lin TH and Lin SR, Micromechanics Theory of Fatigue Crack Initiation Applied to Time-Dependent Fatigue. In Fatigue Mechanisms, Special Technical
Publication 675, Philadelphia: ASTM 1979; 707-728.
[32] Essmann U, Gösele U, and Mughrabi H, Phil. Mag. A 1981; 44:405-426.
[33] Ma BT and Laird C, Acta Metall. 1989; 37:325-336.
[34] Ma BT and Laird C, Acta Metall. 1989; 37:337-348.
[35] Katagiri K, Omura A, Koyanagi K, Awatani J, Shiraishi T, and Kaneshiro H,
Metall. Trans. 1977; 8A:1769-1773.
[36] Hunsche A and Neumann P, Acta Metall. 1986; 34:207-217.
[37] Winter AT, Pederson OB, and Rasmussen KV, Acta Metall. 1981; 29:735-748.
[38] Pohl K, Mayr P, and Macherauch E, Scripta Metall. 1980; 14:1167-1169.
[39] Paris PC, Gomez MP, and Anderson WP, The Trend In Engineering 1961; 13:
9-14.
[40] Paris PC and Erdogan F, J. Basic Eng. 1963; 85:528-534.
[41] Forsyth PJE, A Two Stage Process of Fatigue Crack Growth. In Crack Propagation: Proceedings of Cranfield Symposium 1962; 76-94.
[42] Suresh S, Metall. Trans. 1985; 16A:249-260.
[43] Vasudevan AK, Sadananda K, and Rajan K, Int. J. Fatigue 1997; 19:S151-S159.
[44] Schwaiger R, Moser B, Dao M, Chollacoop N, and Suresh S, Acta Mater. 2003;
51:5159.
[45] Cullity BD, Elements of X-Ray Diffraction, 2nd Edition, Addison-Wesley Publishing Co., 1978.
[46] Elsherik AM and Erb U, Mater. Sci. 1995; 30:5743.
153
[47] Koch CC, Nanost. Mater. 1997; 9:13-22.
[48] Fecht HJ, Nanost. Mater. 1995; 6:33-42.
[49] Inoue A, Mater. Sci. Eng. 1994; A179/A180:57.
[50] Gleiter H, Prog. Mater. Sci. 1989; 33:223-315.
[51] Lu K, Mat. Sci. Eng. 1996; R16:161-221.
[52] Wang Y, Jiang S, Wang M, Wang S, Xiao TD, and Strutt PR, Wear 2000;
237:176-185.
[53] Valiev RZ, Islamgaliev RK, and Alexandrov IV, Prog. Mat. Sci. 2000; 45:103189.
[54] Hanlon T, Kwon YN, and Suresh S, Scripta Mater. 2003; 49:675-680.
[55] Suryanarayana C, Prog. Mater. Sci. 2001; 46:1-184.
[56] Shen TD and Koch CC, Mater. Sci. Forum 1995; 179-181:17-24.
[57] Zhou F, Rodriguez R, and Lavernia EJ, Mater. Sci. Forum 2002; 386-388:409414.
[58] Han BQ, Lee Z, Nutt SR, Lavernia EJ, and Mohamed FA, Metall. Mater. Trans.
A 2003; 34(3):603-613.
[59] Segal VM, Mater. Sci. Eng. 1995; A197:157-164.
[60] ASTM. B 265-02, “Standard Specification for Titanium and Titanium Alloy
Strip, Sheet, and Plate,” 2002.
[61] Stolyarov VV, Zhu YT, Alexandrov IV, Lowe TC and Valiev RZ, Mater. Sci.
Eng. 2001; A299:59-67.
[62] Bloom JM, Int. J. Frac. 1967; 3:235-242.
[63] Harris DO, Trans. ASME, J. Basic Eng. 1969; 89:49-54.
154
[64] Bowie OL and Freese CE, Eng. Frac. Mech. 1981; 14:519-526.
[65] Marchand N, Parks DM, and Pelloux RM, Int. J. Frac. 1986; 31:53-65.
[66] Suresh S, Eng. Frac. Mech. 1983; 18:577-593.
[67] Christman T and Suresh S, Eng. Frac. Mech. 1986; 23:953-964.
[68] Agnew SR and Weertman JR, Mater. Sci. Eng. 1998; A244:145-153.
[69] Agnew SR, Vinogradov AY, Hashimoto S, and Weertman JR, J. Electronic
Mater. 1999; 28:1038-1044.
[70] Mughrabi H and Höppel HW, Mater. Res. Soc. Symp. Proc. 2001; 634:B2.1.1B2.1.12.
[71] Feltner CE and Laird C, Acta Metall. 1967; 15:1621-1642.
[72] Forrest PG, Fatigue of Metals, Pergamon Press, New York 1962.
[73] Shih CF, J. Mech. Phys. Solids 1981; 29:305-326.
[74] ASTM. B 209-02a, “Standard Specification for Aluminum and Aluminum-Alloy
Sheet and Plate,” 2002.
[75] Ohta A, Suzuki N, and Mawari T, Int. J. Fatigue 1992; 14(4):224-226.
[76] Campbell JE, Gerberich WW, and Underwood JH, Eds. Application of Fracture
Mechanics for Selection of Metallic Structural Materials, American Society for
Metals, Metals Park OH, 1982; 193-203.
[77] Elber W, Eng. Frac. Mech. 1970; 2:37-45.
[78] Elber W, Damage Tolerance in Aircraft Structures, Special Technical Publication 486, Philadelphia: American Society for Testing and Materials, 1971;
230-242.
[79] Ritchie RO, Suresh S, and Moss CM, J. Eng. Mater. and Tech. 1980; 102:293299.
155
[80] Suresh S, Zamiski GF, and Ritchie RO, Metall. Trans. 1981; 12A:1435-1443.
[81] Suresh S and Ritchie RO, Fatigue Crack Growth Threshold Concepts (eds.
Davidson DL & Suresh S) Warrendale: The Metallurgical Society of the American Institute of Mining, Mineral and Petroleum Engineers, 1984; 227-261.
[82] Suresh S, Metall. Trans. 1983; 14A:2375-2385.
[83] Suresh S, Metall. Trans. 1985; 16A:249-260.
[84] Bilby BA, Cardew GE, and Howard IC, Fracture 1977 (ed. Taplin DMR) 1977;
3:197-200.
[85] Cotterell B and Rice JR, Int. J. Frac. 1980; 16:155-169.
[86] Larsen-Basse J, Powder Metall. 1973; 16:1-32.
[87] Larsen-Basse J, Shishido CM, Tanouye PA, Wear 1974; 19:270-275.
[88] Feld H and Walter P, Powder Metall. Int. 1975; 7:188-190.
[89] Wayne S, Baldoni J, and Buljian S, Tribol. Trans. 1990; 33:611-617.
[90] O’Quigly DGF, Luyckx S, and James MN, Int. J. Refrac. Hard Mater. 1997;
15:73-79.
[91] Bull SJ, Rickerby DS, Matthews A, Leyland A, Pace AR, and Valli J, Surf.
Coat. Technol. 1988; 36:503.
[92] Bull SJ, Wear 1999; 233-235:412-423.
[93] Axen N, Kahlman L, and Hutchings IM, Tribol. Int. 1997; 30(7):467-474.
[94] Lee SK, Tandon R, Readey MJ, Lawn BR, J. Am. Ceram. Soc. 2000; 83:14281432.
[95] Bennett S, Matthews A, Perry AJ, Valli J, Bull SJ, and Sproul WD, Tribologia
1994; 13:16-28.
156
[96] Bull, SJ, Rickerby DS, Thin Solid Films 1989; 181:545.
[97] Xie Y and Hawthorne HM, Wear 1999; 225-229:90-103.
[98] Xie Y and Hawthorne HM, Wear 1999; 233-235:293-305.
[99] Gee MG, Wear 2001; 250:264-281.
[100] Chokshi AH, Mater. Sci. Forum 2003; 426-433:4393-4398.
[101] Wang XJ and Rigney DA, Wear 1995; 181-183:290-301.
[102] Schuh CA, Nieh TG, and Iwasaki H, Acta Mater. 2003; 51:431-443.
[103] Schwaiger R and Suresh S, 2003; unpublished results.
[104] Hasnaoui A, Van Swygenhoven H, and Derlet PM, Acta Mater. 2002; 50:3927.
[105] Van Swygenhoven H, Spaczer M, and Caro A, Acta Mater. 1999; 47:3117.
[106] Van Swygenhoven H, Spaczer M, Caro A, and Farkas D, Phs. Rev. B 1999;
60:22.
[107] Schiotz J, Di Tolla FD, and Jacobsen KW, Nature 1998; 391:561.
[108] Yamakov V, Wolf D, Salazar M, Phillpot SR, and Gleiter H, Acta Mater. 2001;
49:2713.
[109] Vinogradov A and Hashimoto S, Advanced Eng. Mater. 2003; 5:351.
[110] Yao J and Meguid SA, Int. J. Hydrogen Energy, 1997; 22:1021-1026.
[111] Tsuru T and Latanision RM, Scripta Metall. 1982; 16:575.
[112] Volpp T, Goering E, Kuschke WM, and Artz E, Nanost. Mater. 1997; 8:855.
[113] Weertman JR and Sanders PG, Solid State Phenom. 1994; 35-36:249.
[114] Suresh S and Mortensen A, Fundamentals of Functionally Graded Materials,
The Institute of Materials, London, UK, 1998.
157
[115] Suresh S, Science 2001; 292:2447-2451.
[116] Giannakopoulos AE and Suresh S, Int. J. Solids Structures 1997; 34(19):23572392.
[117] Giannakopoulos AE and Suresh S, Int. J. Solids Structures 1997; 34(19):23932428.
[118] Suresh S, Olsson M, Giannakopoulos AE, Padture NP, and Jitcharoen J, Acta.
Mater. 1999; 47(14):3915-3926.
[119] Jitcharoen J, Padture NP, Giannakopoulos AE, and Suresh S, J. Am. Ceram.
Soc. 1998; 81(9):2301-2308.
158