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Ph.D degree in

This is to certify that the
dissertation entitled

INDENTATION AND TRIBOLOGICAL BEHAVIOR OF NITI ALLOYS
AND STUDY OF lNSTRUMENTED SPHERICAL INDENTATION

presented by

WANGYANG NI

has been accepted towards fulﬁllment
of the requirements for the

Materials Science

   

   

/ , {ma

Date

MSU is an Afﬁn'native Action/Equal Opportunity IHSUTUI‘I'OH

   

L R
Michigan State

 

University

PLACE IN RETURN BOX to remove this checkou I from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

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INDENTATION AND TRIB OLOGICAL BEHAVIOR OF NITI ALLOYS AND
STUDY OF IN STRUME NTED SPHERICAL INDENTATION

By

Wangyang Ni

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemical Engineering and Materials Science

2004

 

ABSTRACT

INDENTATION AND TRIBOLOGICAL BEHAVIOR OF NITI ALLOYS AND
STUDY OF IN STRUMEN TED SPHERICAL INDENTATION

By
Wangyang Ni

In this work, micrOSCOpic shape memory (8 NE) and superelastic (SE) effects in

martensitic and austenitic NiTi alloys were probed by instrumented indentauon

. . . chank’a‘

techmques. Both pyramidal and spherical indenters were used to study the In6
. . - - don W35
response of the NITI alloys. It was found that deformation due to indent?l
recoverable by the shape memory or superelastic effect and that the magnitude of indent
recovery can be rationalized using the concept of the representative strain and maXimum
strain. Instrumented indentation techniques, especially using spherical ind
enters, are
shown to be useful in quantifying shape memory and superelastic effects at flu-Cm“ and
nanometer length scales.

Novel tribological applications of superelastic NiTi thin ﬁhns suggested by these
results Were also studied. A novel composite coating, with a superelastic NiTi interlayer
“Ween soﬁ aluminum substrate and hard CrN coating, was studied using instrumented

indentat:ion, scratch, and pin-on-disk wear tests. It was found that a superelastic NiTi

mteﬂaYer can dramatically improve hard-coating adhesion and wear resistance' The

improved coating performance is attributed to the large elastic recovery ratio and strain

tolerance of the superelastic NiTi interlayer-

It was demonstrated that spherical indentation is very useful in the

Characterization of the mechanical properties of NiTi shape memory alloys. To further

understand the spherical indentation process, a general study of spherical indentation in

elastic-plastic materials was carried out. Two previously unknown relationships between

hardness, reduced modulus, indentation depth, indenter radius, and work of indentation

were found. Based on these relationships a novel energy-based method for determining
- . ' \
contact area, reduced modulus, and hardness of materi als from instrumented spheﬂca

. . . . of
indentation measurements was proposed. This method also provrdes a new wa‘]

calibrating the effective radius of imperfectly shaped spherical indenters,

T my Parents and Wife with Great Appreciation
0

iv

ACKNOWLEDGEMENTS

I am deeply grateful to Prof. David. S. Grummon at Michigan State University

and Dr. Yang-Tse Cheng at GM R&D Center for their excellent advising and continuing

support during my dissertation work.

Sincere appreciation is expressed to my other guidance committee member,

Martin A. Crimp, James, P. Lucas, and David Tomanek, for their important comments

and valuable suggestions.

I would like to thank Anita. M. Weiner, Michael J. Lukitsch, Michael p. Ba‘ogh’
Leonid C. Lev, Yue Qi, Louis. G. Hector, T. Wes Capehart, Thomas A. Perry, Cameron
J, Dash, Charls H. Olk, Jihui Yang, Mark W. Verbrugge at GM R&D Center, and Xu
Ding, Chee Kuang Kok, Thomas LaGrange, Ken Geelhoood, Fu Guo, Haiping Gong,

Liang Zeng at Michigan State University for the help and valuable discussions.

I would like to thank the Materials and Processes Laboratory at GM R&D Center

for the financial support and summer internships to conduct this study.

Final 1y, 1 would like to thank my wife, Lei Wang, for her support and patience

during the preparation of this work.

TABLE or CONTENTS

LIST OF TABLES ..............................................................................
LIST OF FIGURES ............................................................................
INTRODUCTION .............................................................................
CHAPERT 1: LITERUATURE REVIEW ..................................................

1-1 NiTi Shape memory alloys .............................................................
1.1.1 Shape memory and superelastic effects .........................................
11-2 Sliding wear and indentation behavior of NiTi alloys ........................
1.1.3 Processing and characterization of NiTi thin ﬁlms .............................

1.2 Tribological coatings ......................................................................
1.2.1 Hard coating materials ...............................................................
1.2.2 Characterization of tribological coatings .........................................

1.2.2.1 Residual stresses..............................-
1.2.2.2 Adhesion strength ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
1.2.2.3 Hardness .......................................................................
1.2.2.4 Friction and wear ..............................................................
123’ Tribological coating With interlayers ..............................................

1.3 Instrumented indentation experiments ...........................

1.3.1 Instrumented Berkovich indentation experiments. . . . . .. ....................
1.3.1.1 Oliver-Phan’s method for hardness and mod ''''''''''''' ’
1'3'1'2 Piling-up and sinking-in ......................... Hill's. .measurementm, . .
1.3.1.3 Scaling relationships....................................:: .................. .
1.3.1.4 Correlation between indentation and uniaxial tensile expenmems . .

1.3.2 Instrumented spherical indentation experiments .................... . . .
13-2-1 Analyzing methods ............................................................. '
1.3.2.2 Representative strain for spherical indentation experiments” .

CHAPTER 2: ON THE STUDY OF MICROSCOPIC SHAPE MEMORY
EFFECT, SUPERELASTIC EFFECT AND WEAR BEHAVIOR OF NITI
ALLOYS .....................................................................................

2.1 Introduction .................... ' .........................................................
2.2 Instrumented indentation experiments ...............................................
2.2.1 Sample preparation and experimental methods ................................
2.2.2 Results and discussion .............................................................
2.2.2.1 Transformation temperatures and structures .............................
2.2.2.2 Shape memory effect of indents ..............................................
2.2.2.2.1Berkovich and Vickers indents ....

vi

ix

35

35
37
37
38
38
39
4O

40

2.2.2.2.2 Spherical indents ...........................................................
2.2.2.3 Superelasticity under indentation ............................................ 42

2.2.2.3.] Berkovich indentation .................................................... 43

2.2.2.3.2 Spherical indentation .................................................... 43

2.2.3 Representative strain and strain distribution under indenters. . . . . . . . . 45

2.3 Dry sliding wear behavior of NiTi alloys ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 47
2.3.1 Sample preparation and experimental methods ............................ 47
2.3.2 Results and discussion ......................................................... 48
2.5 Conclusions .............................................................................. 50
CHAPTER 3: IMPROVE THE ADHESION AND WEAR RESISTANCE OF
CHROMIUM NITRIDE COATING ON ALUMINUM SUBSTRATE USING A 52
SUPERELASTIC INTERLAYER ...........................................................
3.1Introduction...................... ........................................................ ii
3.2 Sample preparation and experimental methods ..................................... 56
3.3 Results and discussion. - .. .. ............................................................. 56

3.3.1 Structure characterization ........................................................

3.3.2 Mechanical properties .............................................................. 57
3.3.2.1 Indentation test- - ................................................................ 57
3.3.2.2 Adhesion test .................................................................... 59
3.3.2.3 Dry sliding wear test ........................................................... 61

3.4 Conclusions .............................................................................. 65
CHAPTER 4: lNSTRUMENTED SPHERICAL INDENTATION ..................... 67

4.1 Introduction ............................................................... 67

4.2 Dimensional analySis . ..... 68
4.2.1 Dimensional analysis of loading ................................................. - 69
4.2.2 Dimensional analysis of unloading .............................................. 71
4.2.3 Scaling relationships from dimensional analysis ..............................

4.3 Finite element analysis ................................................................. 71
4.3.1 Piling-up/sinking-in in spherical indentation... . .. . 773
4.3.2 Relationship between hf/hTm and (W,- Wu)/W, ................................... 76
4.3.3 Relationship between H/E and (W,- Wu)/W, ..................................... 77

4.4 Experimental application of the energy-based method ............................ 79
4.4.1 Sample preparation and experimental methods ................................ 79
4.4.2 An experimental proof of the relationship between hf/hmax and

(W,- Wu)/Wi ........................................................................... 80

4.4.3 A novel method for indenter shape function calibration ...................... 80
4.4.4 Hardness and Young’s modulus measurement by the energy-based

method ................................................................................ 81

4.5 Constraint factors for spherical indentation experiments .......................... 84

4.6 Conclusions .............................................................................. 87

CHAPTER 5: SUMMARY AND FUTURE WORK ..................................... 88

vii

APPENDIX: FUNDAMENTALS OF DIMENSIONAL ANALYSIS AND H
THEOREM .................................................................................... 92

REFERENCES ................................................................................. 163

viii

LIST OF TABLES

Table 1.1.1 Crystal Structure and lattice parameters ofNiTi alloys....................
Table 1.2.1 Properties of metallic hard materials ..........................................
Table 1.2.2 Properties of covalent hard materials .........................................
Table 1.2.3 Properties of ionic hard materials .............................................

gable 2.1 Phase transformation temperatures and Structures of specimen BH and
S ...........................................................................

tenitic

Table 2.2 Mechanical PrOpertieS of martensitic (specimen BH), aus
entation test..

(specimen BS), and amorphous NiTi thin ﬁlm obtained from nanoind

Table 3.1 Description of specimens .........................................................

Table 3.2 Composition and phase transformation temperatures of NiTi thin ﬁlms...

Table 3.3 Nanoindentation properties of aluminum substrate, interlayer materials

(81, S2 and Cr) and CrN hard coating ................................

Table 3.4 A comparison of the mechan' 1 ' , _ ,
and P01yisoprene ........................... 1.0.3. propertl 68 .C.’ {between SuPerelastic NiTi

Table 4.1 Mechanical properties of the tested materials. .

Table 4.2 Relationship between Poisson’s ratio and constraint factor for elastic

contact with a rigid spherical indenter ............................

ix

.....
.0.
OOOOOOOOOOOOOOOOOOOOOO
O.

95
96
97

98

99

99
l 00

100

101

102

102

LIST OF FIGURES

Figure 1.1.1 DSC test shows characteristic phase transformation temperatures of

NiTi shape memory alloy ..................................................................... 103

Figure 1.1.2 A schematic representation of the shape memory effect of Ni Ti

alloy ............................................................................................. 103
104

Figure 1.1.3 A schematic representation of superelasticity of NiTi alloy ..............

Figure 1.1.4 Representative stress-strain curves of shape memory and superelastic
NiTi alloys ....................................................................................... 104

Figure 1.1.5 Phase diagram of binary NiTi alloy .......................................... 105
Figure 1.1.6 NiTi shape memory alloy: dependence of martensite start
temperature on composition ....................................... 105
Figure 1.1.7 A comparison of wear rates between TiSONi47Fe3 and SAE 52100
steel .............................................................................................. 106
Figure 1.1.8 A schematic representation of sputtering process .......................... 106
Figure 1.2.1 Residual stresses in thin films cause bending of the specimen ,,,,,,,,,,, ‘07
Figure 1.2.2 Schematic representation of coating failure mode '
. _ . . s in th
in profile and plan View: spalling failure (a); buckling failure (b)- chjgsicriatgglmu:
(c); conformal cracking (d), and tensile cracking (e). . .. . . . . . . . . . . . ,. .. g 108
Figure 1.3.1 A schematic illustration of the load-displacement curve of
instrumented indentation test and the graphical interpretation of contact depth 109
Figure 1.3.2 Illustration of conical indentation experiment ............................ 109
Figure 1.3.3 Degree of piling-up and sinking-in, mm, as a function of the ratio of
yield stress to Young’s modulus, Y/E, and work hardening exponent, n, in conical
indentation experiments .................................................................... 110
Figure 1.3.4 The top-point, instead of the cross point, defines the contact
perimeter when piling-up occurs ........................................................ 1 10
Figure 1.3.5 A relationship between the ratio of irreversible work to total work
Win/Wt. and ratio of residual depth to maximum indentation depth, h/hm, in conieal
indentation experiments ............................................................ 1 ll

Figure 1.3.6 A relationship between the ratio of residual indentation depth to
maximum indentation depth, h/hm, and ratio of harness to reduced modulus, H/E',
in conical indentation experiments . ......................................................... 112

Figure 1.3.7 Different combination of Y/E and n can lead to the same load-
displacement curve in conical indentation experiments: Highly elastic materials
(a), and high plastic materials (b) ............................................................. 113

Figure 1.3.8 Relationship between representative strain ~ hardness and true strain
~ true stress. Curve A, mild steel. Curve B, annealed copper. O x hardness 114
measurement. —— stress-strain curve. (Pm stands for the hardness in this ﬁgure). .

Figure 1.3.9 A schematic illustration of the evolution of plastic zone during

spherical indentation process: elastic (a), elastic-plastic (b), and fully-plastic (c). . .. 115

Figure 2-1 DSC curves ofspecimen BH (a) and BS (b) ................................. 116

Figure 2.2 XRD patterns of specimen BH and BS ........................................ 117

Figure 2.3 A schematic illustration of thermally activated recovery 0f indent on
shape memory alloy (specimen BH) ......................................................... 117

Figure 2.4 Change of residual indentation depth was observed for Berkovich
indent (a) and Vickers indent (b) on a NiTi shape memory alloy (specimen BH)

aﬁer heating above to austenite ﬁnish temperature. 118

Figure 2.5 Relationship between recovery ratio and residual indentation depth for
Berkovich and Vickers indents on a NiTi shape memory alloy (samme BH) ........ . 119

Figure 2.6 Geometry of the spherical indenters measured by SEM: R=213.4pm
(a), and R=106.7p.m (b) ....................................................................... 120
Figure 2.7 Spherical indents on a NiTi shape memory alloy (specimen BH):
before heating (a), after heating (b), 3D proﬁle of indent before heating (c), 3D
proﬁle of indent after heating ((1), and recovery ratio as a function of residual
indentation depth (6) ........................................................................... 121
Figure 2.8 Cross-section proﬁle of the spherical indents on specimen BH shows

that no piling-up occurs ....................................................................... 122

Figure 2.9 A schematic illustration of indentation sinking-in for spherical
indentation experiments ....................................................................... 122

xi

Figure 2.10 Relationship between thermally activated recovery ratio and
representative strain, and the relatlonship between the true stress and true strain of
a NiTi shape memory alloy (specimen BH). The recovery ratio starts to decrease
when the representative strain exceeds the critical strain in the stress-strain curve... 123
Figure 2.1 1 A schematic representation of the elastic recovery of indents after

removal of the load ............................................................................ 124

Figure 2.12 Berkovich indentation of a superelastic NiTi alloy (specimen BS) and
copper: load-displacement curves (a), and depth (squares) and work (triangles)

recovery ratios upon unloading at various depths (1;). Filled symbols for NiTi and
unﬁlled symbols for copper .................................................................. 125

Figure 2.13 Comparison between spherical indentation on a superelastic NiTi

alloy (specimen BS) and copper (R=213.4pm) (a), and relationship between the

depth recovery ratio and representative strain, and the relationship between the

true stress and true strain of a superelastic NiTi alloy (specimen BS) (b). The. .

recovery ratio starts to decrease when the representative strain exceeds the critical 126

strain in the stress-strain curve ...............................................................

Figure 2.14 XRD shows indentation induced austenite ——) martensite

transformation in specimen BS: non-indented area (a) and inside the indent (b). . 127
Figure 2.15 Finite element modeling of strain distribution under sharp indenter (a)
and spherical indenter (b). The white region right under the conical indenter has a
minimum strain larger than the maximum strain under the Spherical indenter.
Regions with the same color have a plastic strain of the same value in (a) and (b), , _ 128
Figure 2.16 A schematic ﬁgure of the target for the deposition of amorphous NiTi
ﬁlm ................................................................
............................... 129
Figure 2.17 XRD of amorphous NiTi thin ﬁlm .......................................... 130
Figure 2.18 Load-displacement curves of martensitic (specimen BH), austenitic
(specimen BS) and amorphous NiTi ......................................................... 130
Figure 2.19 Dry sliding wear rate of martensitic (specimen BH), austenitic
(Specimen BS) and amorphous NiTi ......................................................... 131
Figure 2.20 XRD spectra show wear-induced austenite —+ martensite
transformation in specimen BS: outside the wear track (a) and inside the wear
track (b) .......................................................................................... 131
F igure 3.1 A schematic illustration of the structure of sputtering equipment for
deposrtion NiTi thin ﬁlms ................................................................... 132

xii

Figure 3.2 DSC curves of post-annealed NiTi thin films show that, at room
temperature, specimen 81 is austenitic (a), while specimen $2 is martensitic (b). . 133

Figure 3.3 XRD patterns of post-annealed NiTi thin ﬁlms: S 1 (a), and 82 (b) ....... 134

Figure 3.4 XRD pattern of Sam thick CrN coating on aluminum substrate
(specimen CrNS-Al) ........................................................................... 134

Figure 3.5 Berkovich indentation test on various materials; load-displacement 35
curves (a) and the relationship between HIE and depth recovery ratio (b) ............ 1
Figure 3.6 Berkovich indentation tests at various depths: composite hardness (a), 136
and depth recovery ratio (b) ..................................................................
Figure 3.7 SEM images of the end of scratches on (3er -A1 (a), CrNS-Al (b), t h
CrN-S 1 -Al (c), CrN-SZ—Al (d), and CrN-Cr-Al (e). The arrow indicates the scra c 137
direction .........................................................................................

Figure 3.8 A schematic illustration of the stress-strain curves of superelastic NiTi

(a) and elastomeric polymer (b) .............................................................. 140

Figure 3.9 Friction coefﬁcient and durability of coatings obtained by pin-on—disk

test: specimen Cer-A land CrN-SZ-Al (a), and specimen CrN-Cr-Al, CrNS-Al
and CrN-Sl-Al ................................................................................ . 14‘

Figure 3.10 Friction coefﬁcient of specimen CrN-Sl-Al and CrN-Cr-Al measured
by scratch test using progressive load up to 2N ............................................ 142

Figure 3.11 Illustration of a spherical indenter sliding on a material; without
elastic recovery in wear track (a) and with elastic recovery in the wear track (b)..- . 143

Figure 3.12 Illustration of a spherical indenter sliding on a material: piling-up (a)

and Sinking-in (b) .............................................................................. 144

Figure 3.13 Extent of material piling-up around a scratch made by a progressive

load up to 6N: 3D proﬁle of CrN-Cr-Al (a), 3D proﬁle of CrN-Sl-Al (b), cross-

section proﬁle of CrN-Cr-Al (c), and cross section proﬁle of CrN-Sl-Al (d). Note

that dash lines in (a) an (b) indicate the locations for cross section proﬁle ............ 145

Figure 3.14 Wear rate of the specimens. Note that the Y-axis is in logarithm scale, 146

Figure 4.1 Schematic illustration of indentation load-displacement curve and
deﬁnition of the irreversible work, W,- W“, and reversible work, Wu .................... 147

xiii

Figure 4.2 Finite element modeling: overall mesh and contact counterparts (a),
and magniﬁed image ofthe top-1e ﬂ part Of the overall mesh (b) ........................ 148

Figure 4.3 A schematic illustration of indentation piling-up for spherical
indentation experiment ........................................................................ 149

Figure 4.4 Extent of piling-up (Ir/hm?” and sinking-in (ho/hqu) as a function
of hmax/R (a—c), Y/E (d), and strain-hardening exponent n (e), in spherical .
indentation simulations. Note that (a), (b) and (c) represent materials with strain-
hardening exponent n=0.1, 0.3 and 0.5, respectively, ((1) represents material With
n=0.1, hmax/R=0.05, 0.2 and 0.4, (e) represents materials with Y/E=0.05,

hm/R=0.05, 0.2 and 0.4. PU stands for piling-up and SI stands for sinking—in ....... 150
Figure 4.5 Calculated load-displacement curves ofa material with Y/E=0.025, 152
v=0.2, and n=0.5 at various indentation depths ............................................

Figure 4.6 Finite element result shows that, for all the materials studied, a linear 153

relationship exists between h, Mm and (W,-W..)/W, .....................................

Figure 4.7 For each ﬁxed Irma/R, a linear relationship exists between H/E* and
(W,- W.t)/W, for spherical indentation in elastic-plastic solids with work-hardening... 154

Figure 4.8 A linear relationship between In (hm/R) and ln(—B) .......................... 154

Figure 4.9 Spherical indentation experiments show that a linear relationship exists
between h f /h,,m and (W,- Wu)/W,. The ﬁnite element results are also shown in this

ﬁgure ............................................................................................ . 155

Figure 4.10 Experimental load-displacement curves for Spherical indentation in a
c0pper sample ................................................................................. .

156
Figure 4.11 Effective indenter radius, Rey], as a function of indentation depth, hm
for an imperfect spherical diamond indenter ............................................... 157
Figure 4.12 Experimental load-displacement curves obtained from instrumented
spherical indentation experiments in aluminum (a), tungsten (b), and ﬁised silica
(c) ................................................................................................ 158
Figure 4.13 Measured composite reduced modulus (a) and hardness (b) USng the
energy-based method together with indenter Shape calibration. The error bar
indicates the standard deviation of the measured values ................................. 159

xiv

Figure 4.14 Rel ' '
indentation in elitOinShlp between hardl‘less and tru
material with Y/E=(()3 $22621? ) 2]” ﬁaterial with Y/lgfgrggs for Spherical
. ‘ a = - . e ' ~ - 2 :
representative strain of the same Valuehorizontal aXis represerlitsoti and (c)
.................. 3 Strain or

Figure 4.15 Con tr ‘ . 160
a, images: {2; an... mm .. .. .
(b) and (c) .......... ' ' me that the Scale folrﬁerem Indentation depths:
.................................... X-axis is different in (a),
...................................... 161

XV

 

 

 

II~1TRODUCTION

NiTi alloys are well known (or the Shape memory and superelastic effects. Six-1Ce

their first discovery in 1960’s, NiTi a“oys have been extensively studied. Recent yﬁﬁr

s
have seen an increasing interest in the application of sputtered NiTi thin ﬁlms, as thlr
actuators and as tribological coating materials, which calls for a new method to
characterize shape memory and superelastic effects at the microscopic scale. The
approach taken in this study has been instrumented indentation experiments. Two types
of recovery effects have been observed for indents in NiTi: one is the isothermal strain
recovery upon unloading due to superelasticity, and the other is the strain recovery on
heating due to the shape memory effect. Inﬂuences of indenter geometry and indentation
depth on the recovery effects were studied. It was found that instrumented indentation
experiments, especially using spherical indenters, are useful to quantitatively characterize
the shape memory and superelastic effects at the microscopic scale. In addition, the
maximum recoverable strain can be measured in spherical indentation experiments.

In this study, the wear behavior of martensitic, austenitic and amorphous NiTi
were compared by dry sliding wear tests. It is found that superelastic NiTi is less wear
resistant than amorphous NiTi, although the former has a higher elastic recovery ratio. To

make superelastic NiTi a good wear resistant material, ploughing during sliding should
be Prevented. This can be achieved by depositing a hard coating on the top of the NiTi.

Base on the above observations, a novel composite tribological coating, using

S“lllerelastic NiTi as an interlayer material between hard CrN coating and soft aluminum

Substrate, was developed. The indentation, adhesion, friction, and wear behavior were

 

Studied. It is found that the Sapere lastic NiTi interlaYBI‘ can dramatically [mirror/6 the
adhesion, decrease the friction coef'f-lcient and increase wear resistance due to its 131‘ go
Strain tolerance and elastic recovery effect.
To further understand the spherical indentation process, dimensional and fillit
e
element analysis were conducted to StUdy spherical indentation in elastic-plastic so 1 ids
with work hardening. Scaling relationships between hardness, reduced modluus’
indentation depth, indenter radius, and work of indentation were studied. Based on the
scaling relationships revealed by ﬁnite element modeling, an energy-based analysis
method for instrumented spherical indentation measurements was pr0posed. This method
applies for both piling-up and sinking-in of the materials around the indenter. It also
provides a way of calibrating the effective radius of imperfectly shaped spherical
indenters. The validity of this new method was tested by instrumented spherical
indentation experiments on copper, aluminum, tungsten, and fused silica. Finally,
constraint factors, deﬁned as the ratio of indentation hardness to uniaxial true stress, for
different stage of spherical indentation were studied using ﬁnite element analysis. The
feasibility of using constraint factor to derive stress-strain curves was studied.

The main body of this dissertation is organized into four chapters. Chapter 1
reviews the literature on topics related to this dissertation work. Chapters 2-4 provide
detailed descriptions of the sample preparation, experimental methods, experimental

1‘ esults, discussion, and conclusions of the dissertation work in three self-contained parts:
Chal3ter 2 reports on the study of microscopic shape memory effect, superelastic effect
and wear behavior of NiTi alloys. Chapter 3 describes experiments on improving the

adhesion and wear resistance of chromium nitride coating on an aluminum substrate

 

, , . . , C .
using superelastic NiTi interlayer hapter 4 details on the study of instrumented
, . . ina .
Spherical indentation experiments. 1;— "y, Chapter 5 provrdes a general conclusions anQ

Comments on possible directions fol’ futul‘e research,

 

CHAPTER 1
LITE; RATURE REVIEW

This chapter will introduce NiTi shape memory and superelastic alloys and t1) .
11)
ﬁlms, provide background on issues related to tribological coatings, and review previous

work on and study of instrumented indentation experiments.

1.1 N ITI SHAPE MEMORY ALLOYS

1.1 - 1 Shape Memory and Superelastic Effects
NiTi alloys are well known for the shape memory effect (SME) and
superelasticity (SE). Since the discovery of the shape memory effect in NiTi alloys in
1960’s, [1-3] they have become increasingly important materials with wide applications.
[4—6] NiTi alloys have a low temperature phase (the martensite), an intermediate phase
(R-phase), and a high temperature phase (the austenite). The crystal structure and lattice
parameters of these phases are shown in Table 1.1.1. [7-9] A schematic of the differential
scanning calorimetry (DSC) response of NiTi is shown in Figure 1.1.1. [10] When
temperature increases NiTi transforms from martensite into austenite; when temperature
decreases the austenite phase transforms into martensite phase. Sometimes, during the
Cooling, there exists a R—phase before martensite is formed. The formation of martensite

and austenite is characterized by a start and ﬁnish temperature.

 

Both shape memory and Sup erelaSn-C Effects are closely related to [115 maﬂgﬂsi tic
transformation. The martensitic trar’ Sfonnation is a difﬁisionless phase transformation in
Solids, in which atoms move collecti Vely, and often by a shear-like mechanism.

When NiTi is deformed in the martensitic phase, it recovers to its original sh§pe
by reverse transformation upon heating to above the austenite ﬁnish temperature, Af. T1718
effect is called the shape memory effect. The deformation may be in tensiOn,
compression, or bending, [11] as long as the strain is below some critical value. The
mechanism of shape memory is illustrated in Figure 1.1.2. [5] When a single crystal
parent phase, the austenite, is cooled to a temperature below the martensite ﬁnish
temperature, M]; martensite is formed in a self-accommodating way by internal twining,
as shown in Figure 1.1.2(a) and (b). In this process, the shape of the specimen does not
change because the phase transformation occurs in a self-accommodating manner. When
an external stress is applied, the twin' boundaries moves so as to accommodate the applied
stress, as shown in Figure 1.1.2(c) and 1.1.2(d), and if the stress is high enough it will
become a single variant of martensite under stress. When the deformed specimen in

Figure 1.1.2(d) is heated to a temperature above austenite start temperature, As, the
reverse phase transformation occurs. The shape recovery begins at A, and the original
shape is regained at austenite ﬁnish temperature, A], as shown in Figure 1.1.2(c). Once
the Shape has recovered at Af, there is no change in shape when the specimen is cooled to
below Alf. In the above explanation, it is assumed that the deformation proceeds solely by
tWin boundary movement and the transformation is crystallographically reversible. If
either of the conditions is not satisﬁed, complete shape memory effect can not be

obtained .

 

When NiTi is deformed at a temperature slightly above the 3115,6711? 6, ﬁnish
ternPeirature, it recovers to its origi ﬁal Shape When the load is removed. This effect is
Called superelasticity, and it is relata‘j t0 the transformation of stress-induced martens i \e
For the austenite —-> martensite transformation in NiTi alloy, there is a coupling efﬁ§c

t
between the transformation temperature and applied stress. If a stress is appl 1‘ $0,
martensite can form above the normal martensite start temperature, M3, and martensite So
formed is termed stress-induced-martensite (SIM), which has been observed by iii-Sm,
TEM experiment. [12] Stress-induced-martensite is reversible upon unloading. The
transformation mechanism is schematically shown in Figure 1.1.3. The stress needed to

produce SIM obeys a uniaxial version of the Clausius-Clapeyron equation

d 0' AH

mM,—_T%’

 

UJJ)

where AH is the transformation latent heat; T is the temperature; a- is the applied stress;
MS is the martensite start temperature, and so is the transformation strain resolved along
the direction of the applied stress. The formation of stress-induced martensite may
compete with the plastic deformation of austenite phase. If the dislocation movement is
activated before stress-induced-martensite is formed surperelasticity can be inhibited.
Representative stress-strain curves of NiTi alloys are shown in Figure 1.1.4.
When the test temperature is below the martensite ﬁnish temperature, Mf, a residual strain
is left after the removal of the load, as shown in Figure 1.1.4(a). The residual deformation
is recoverable by heating to above A]. The initial plateau arises from the stress—induced
grOWth 0f some martensite variants at the expense of others. When the test temperature is
Slightly higher than A], Figure 1.1.4(b), it is possible for little or no residual deformation

‘0 be leﬁ after removal of the load. It has been demonstrated by tensile tests that the

recoverable strain

history. \l 3\

transformation g'h
. . 5110
”SS ‘5 m gh to i "
nitiate dislocation

etc when the 8‘
ti ca]
Strain def

med by th
6 end of the stress pl t
a can.

exceeds the 6“ mediated slip 311'
' p

incompl
begins when the strain
1
uch 14 g1]
e1- than A];

e!!! i . .
gum I. .
IS

When the work t
e the formation 0
ation bacomes irreversible, and no 12

S ape mem0ry effect

tress;
activated befor f 5 Induced marte '
nsrte can begin and
no Stress

plateau is observed. The deform

elasticity will be observed.
e ordered intermetalli

gram, Figure 1.1.5, this compound exists as a

or super
c compounds based on near eqw'atom'
lC

NiTi alloys at
ording to the phase dia

compositions. Ace
ature. The NiTi single phase

own to room temper region becomes very

3K, and the alloys often contain precipitates of a second

stable phase d
narrow at temperatures below 92

phase.
e transformation temperatures are strongly

ows that the phas
martensite start temp

Figure 1.1.6 sh
erature, Ms, decreases

mposition. [4] The

hen Ni content increase “/0 to 51 at.%.

endent on co
m 100°C to -lOO°C w
and transformation hyst

on can stabilize the stres

dep
s from 49at.

dram atically
eresis are also dependent on

ation temperatures
s—induced

Phase transform
[14—16] Deformati

ature. [17} Precise comp

in alloys.

l and mechanical history.
osition control

the therrna

transformation temper

marten si te and increase the
and care ful heat treatment are therefore required in the processing of N

 

 

 

 

‘.‘.2 S‘o‘dc‘“gw eat and ‘ndentation BebaV‘Q‘ Q‘ N“ i A“
Oys

. ' ' 1
Good wear reSistance 0f N‘T‘ 3 103’s “333%.“ reoortedb
‘J a “uni
be!“ of
expe '
“meats

alloys
, alt
[Tough they haVe 10
We;- hardne
SS.

tudied the Slid'm

631'
Claymn “9‘ S Stance of Ti43 INi47 9F
' ' e3.6 Usjn -
g pm

‘OH-I‘ing

sliding wear test, where a Ti4siNi4‘L9F—63‘5 Pin slides against D55
94 steel
' The Wear
rate

was obtained by measuring the W612” 1083 Of the pin. It was reveal d
ear rate

e16 is lower than that of K44 pearlitic steel. Clayton S
uggested that th
e

of TusiNimsF

good wear resistance of ThaiNimgFeM, was due to the hardening 0f the all (1
0y uring the

sliding wear process. Singh and Alpas [20} investigated the dry sliding wear resi t

S ance of
TisoNi47F63 alloy against a SAE 52100 steel under a wide range of load and sliding speed
shows that the intermetallic TisoNi47Fe3 has 2-5% as much wear

conditions. Figure 1.1.7
as SAE 52100 steel during dry sliding wear, although TisoNimFeg has a lower bulk
hardness (300kg/mm2) in comparison to that of the SAE 52100 bearing steel
(900kg/mm2). [20] Microhardness measurement on the worn surface of TisoNi47Fe3 alloy
at surface hardness can reach up to 400kg/mm2, an increase of about 30%

shove/ed th
may not be the

relati V6 to the bulk hardness. Nevertheless, surface hardening of NiTi
main factor responsible for the good wear resistance of NiTi since even the hardness of
the worn surface is lower than the bulk hardness of 52100 steel.
Li [21} investigated the wear behavior of Ni5i,5Ti alloy subject to 1.5 and 24.5 hour
aging at 500°C and found that the 1.5 hours aging leads to better wear resistance. Li [21]
precipitation hardening of the NiMTin precipitate. The

attﬁbUted the difference to the

8

—__

   

 

 

 

 

precipitates gradually lose the Coherence with the matrix with increasing aging time,
which causes a decrease in hardness. The change of transformation temperature due to
different aging and its inﬂuence on wear behavior were not reported. It is possible that
the transformation temperature of Nisi .5Ti485 increases with aging time since precipitation
of nickel rich NiMTin will decrease the nickel content in matrix, and the stress-stain
relationship and wear behavior will change accordingly. The wear resistance of a shape
memory Ni50_3Ti with a superelastic Ni51,5Ti4g,5 was compared. Li [21] found that the
wear resistance of the superelastic Ni51,5Ti43,5 is superior to that of shape memory
Ni50.3Ti49.7. [21] Similiarly, Lin [22] found that the austenitic NisrTi49 alloy exhibits better
wear resistance than the martensitic NisoTiso alloy in the dry sliding wear against a SUI-2
Cr-steel ball. Liang et. al. [23] compared the wear behavior of superelastic and shape
memory NiTi and argue that the wear resistance of NiTi is mainly dependent on the
recoverable strain limit, i.e. the sum of the pseudoelastic strain (also termed as
superelastic strain) and pseudoplastic strain limit, where the pseudoelastic strain is the
recoverable strain aﬁer unloading and the pseudoplastic strain is the recoverable strain on
heating. Liang [23] argued that, in essence, wear is fracture at small scale, which is
nucleated at locations where the dislocation density increases obviously. In wear of a
superelastic alloy, deformation occurs at contacts by transformation of austenite to
martensite. It will recover immediately by reverse transformation on unloading. Stress-
;nduced martensite has been found in the sliding wear tracks of otherwise austenitic NiTi,
Which indicates that stress-induced martensite does occur under this complex loading
angﬁion. [22] For shape memory NiTi, psuedoplastic deformation occurs, and it will

remain even after the load is removed, but permanent defects, such as dislocation, can not

N

be created because the deformation is only through the reorientation 0f the self-
accommodating martensite. In addition, as demonstrated by ﬁnite element modeling
between two spherical asperities, [24, 25] the low stress-plateau related to shape memory
and superelastic NiTi makes the materials deform easily, which can increase asperity
contact area and consequently decrease contact stresses. Both superelasticity and shape
memory effect are responsible for the good wear resistance of the NiTi alloy. The better
wear resistance exhibited by the superelastic NiTi might be due to its higher hardness.
Under the same applied load it is more difﬁcult to generate dislocations in superelastic
NiTi than in shape memory NiTi, since the former is stronger. Furthermore, for
superelastic NiTi, there is no accumulative deformation under the cyclic wear test loading
since the deformation is recoverable when the load is removed. However, for shape
memory NiTi, the deformation is cumulative since the deformation is irreversible when
the load is removed. An extra deformation is generated in each loading cycle, which will
deteriorate the shape memory ability and wear resistance. The cyclic loading condition
exists when NiTi alloys serve as the disk in pin-on-disk wear test. Theses investigations
demonstrate that NiTi alloys, especially the superelstic NiTi, are promising as novel
tribological materials. However, there has been no reported research on the tribological
application of NiTi thin ﬁlms.
Because the loading conditions in wear tests are very similar to those in indentation
exp eriments, efforts have been conducted to correlate the wear resistance of NiTi alloys
Witlz their indentation behavior. [26-28] Mechanical properties, such as hardness,
mg§u\“s, work recovery ratio and depth recovery ratio, can be obtained by instrumented

indentation experiments. [2 8—3 1] A detailed description of the indentation experiment and

10

analysis methods used to calculate hardness, Young’s modulus, work recovery ram), and
depth recovery ratio will be presented in section 1.3. It was reported that superelastic
Ni5iTi alloy exhibits an energy recovery ratio as high as 47%, in contrast to the 304
stainless steel which has an energy recovery ratio of 11%. [28, 32] The energy recovery
ratio is deﬁned as the ratio of elastic work to total work in the indentation experiment,
and the depth recovery ratio is deﬁned as the ratio of reversible indentation depth to total
indentation depth. The high recovery ratio of NisiTi alloy was attributed to the reversible
stress-induced martensite transformation under the indenter, which has been veriﬁed by
TEM observation. [29]

The shape memory effect under indentation loading has been studied as well using
Rockwell indenter. [26] Recovery of the Rockwell indents upon heating were observed in
NiTi alloy. It was found that the ratio of indentation depth after heating to indentation
depth before heating is a ﬁmction of the amount of martensite present. It was suggested
that, for NiTi alloys, the deformation under indenters can be divided into three types: [26,
29] (i) elastic deformation, which includes both linear elasticity and superelasticity
arising from the stress-induced martensitic transformation (ii) pseudoplastic deformation
arising from the reorientation of martensite variants, and (iii) unrecoverable deformation

due to generation of permanent defects, such as dislocations. The contribution of each
type to the total deformation may depend on the indenter geometry and applied load.
Ha wever, no systematic study on shape memory effect and superelasticity using
instrumented indentation techniques has been reported, which take into account of

\rxngntation load and indenter geometry.

11

1.1.3 Processing and Characterization of N iTi Thin Films

The microstructure and mechanical behavior of NiTi thin ﬁlms have been
extensively studied since 1990. [7, 33-45] NiTi thin ﬁlms are interesting because they
have the potential to be high performance actuating materials for photolithographically
micromachined systems. NiTi shape memory alloys have the largest actuation force and
displacement among many actuator materials. [7, 46-49]

NiTi thin ﬁlms have been successfully processed by the sputtering method. A
schematic representation of the sputtering process is shown in Figure 1.1.8. A glow
discharge is generated ﬁrst and the working gas is ionized. The working species is
accelerated toward the target due to the potential difference between the target and
plasma, which cause the atoms come off the target and ﬁnally deposit on the substrate.

It has been generally found that Ti content in sputtered NiTi thin ﬁlms is lower
than that in target. [7] This composition shift may arise from differential sputtering yield,
[7] difference in angular ﬂux distribution, [50-52] or by differential lateral drift caused by
ﬂux thermalization. [53, 54] It has been shown that the polar angular distribution of Ti is
wider than that of Ni during sputtering. [50] This means that TizNi ratio is larger at low
angle from the target surface and is smaller at normal direction of the target surface. The

effect of angular distribution on ﬁlm composition is more pronounced at larger distance
from the target.

Thermalization of the deposition ﬂux is caused by collision of the deposited

species with the working species. The thermalization is controlled by the parameter of

P xd, where P is the working pressure and d is the working distance. [53] More sputtered

atoms are diverted by the collision with the working gas species when de value

12

 

rel

go<

tre;

 

relax

Theh

TEN];

 

 

increaseS- The diversion of the deposited species depends on their mass. A concentration
shift occurs due to the mass difference in the deposition flux, and it will affect the
transformation temperature and mechanical properties of the thin ﬁlms.

The as-deposited NiTi thin ﬁlms are amorphous if the substrate temperature is
kept low. Crystalline NiTi thin ﬁlms can be obtained by subsequent annealing after
deposition. It was reported that the crystallization temperature of Nl439Tl5H thin ﬁlm is
about 500°C. [55]

Careful control of the annealing temperature and time is required to make shape
memory and superelastic NiTi ﬁlms since the transformation temperatures are closely
related to the annealing method. Two types of annealing methods have been used to make
good crystalline ﬁlms: (i) two-step annealing method: the as-deposited ﬁlm is solution
treated at 973 K followed by aging at temperatures from 573K to 773K; [56] (ii) one-step
annealing method: the as-deposited ﬁlm is annealed at a temperature between
crystallization temperature and 973K. [57]

The effect of annealing on Ni-rich thin ﬁlm is very similar to that on bulk
materials. [44, 56] Lenticular Ti3Ni4 precipitates are formed during annealing. Ti3Ni4 has
a rhombohedral structure, which belongs to the space group R3. The orientation

relationship between Ti 3Ni4 and the matrix is:
(0001) Ti3Ni4| I (111) matrix
[010] Ti3Ni4H [ 5 i3] matrix
The habit plane of the Ti3Ni4 precipitates is (111) of the matrix. [5] The precipitation of

FYBR'U decreases the nickel content in the matrix and causes an increase in the mastensite

13

start temperature. [7] In addition, precipitation hardening by Ti3Ni4 increases the yield
stress of the ﬁlm, which can improve strain recoverability in the ﬁlm.

Crystalline Ti-rich thin ﬁlms contrast the Ti-rich bulk NiTi alloy in that the
former is more ductile than the latter. The improved ductility in thin ﬁlms arises from the
suppression of the coarse grain boundary precipitates, which has been observed in Ti-rich
bulk material. [47] In Ti-rich ﬁlms, evolution of microstructure during annealing follows
the following sequence: GP—zones —9 GP zones and TizNi precipitates within the grain —+
spherical TizNi precipitates unifome distributed within the grain —> TizNi precipitates
along the grain boundaries. [44, 58, 59] The T izNi precipitates within grains are not in an
equilibrium state. When annealed for longer times or at higher temperatures, equilibrium
TizNi precipitates form along grain boundaries. [7] The precipitates within in the grain
can increase the resistance to plastic deformation, which improves the shape memory
effect and superelasticity. [60]

It has been reported that the elongation of NisoTiso, Ni4g,3Ti5L7 and Ni51.5Ti4g,5
ﬁlms are 40%, 20% and 8% respectively. [43] Both Ni-rich and Ti-rich thin ﬁlms in

crystalline form have good ductility and can be used as engineering materials.

14

1.2 TRIBOLOGICAL COATINGS

The surface is arguably the most important part of an engineering material, where
many components fail due to wear. The task of tribology and surface engineering is to
design surfaces to reduce wear 1058, while keeping the desirable properties (usually
toughness) of the bulk solid materials. The early 1980’s saw the development of
technologies in surface engineering, such as ion implantation, physical vapor deposition
(PVD) and chemical vapor deposition (CVD). A variety of coatings have been developed
to protect substrate materials in speciﬁc working environments. In the following sections,
properties of hard coating materials, and characterization and design aspects of

tribological coatings, are discussed.

1.2.1 Hard Coating Materials

Hard coatings can be produced by a number of techniques, which can be divided into
two broad categories — ﬁlm deposition and surface modiﬁcation. Among the deposition
methods, PVD and CVD are the most widely used techniques for producing hard
coatings. Depending on the chemical bonding character, hard coatings can be divided into
three groups, i.e.,

(i) Metallic hard materials (transition metal borides, carbides, and nitrides),
(ii) Covalent hard materials (borides, carbides and nitrides of A1, Si, and B as well as

diamond)

(iii) Ionic hard materials (oxides of A1, Zr, Ti and Be).

15

Tables 1.2.1-123, list the typical Propenies of these three groups Ofmatenals, [61] A11
show high hardness, high Young’s rnc’dlllus and high melting point. Irnportant parameters
in designing tribological coatings include: [62]

(i) Young’s modulus and Poisson’s ratio of the coating and substrate
(ii) Strength of the coating and coating-substrate interface

(iii) Thickness of the coating

(iv) Roughness of the mating surfaces

(v) Surface adsorbtion and reaction

All these parameters inﬂuence the mechanical performance of the materials, such as

residual stress, fracture, adhesion, friction and wear. These will be discussed in detail in

the section followed.

1.2.2 Characterization of Tribological Coatings

1.2.2.1 Residual Stresses

Residual stresses in the coating are critical to coating performance and reliability.
Residual stresses of thin ﬁlms on substrates are produced by processes which would
cause the dimension of the ﬁlm to change if it were not attached to the substrate. Residual
stresses include thermal stresses and intrinsic stresses. Thermal stresses are generated by
the difference in the thermal expansion coefﬁcient between the ﬁlm and substrate. The

dependence of thermal stress in a planar ﬁlm, 0' , on temperature change, dT , is given
by: [63]

E
d" Aa ’ (1.2.1)

 

16

where Aa is the difference between the thermal expanSion coefﬁCient; E/ and U/ are

the Young’s modulus and Poisson’s ratio of the ﬁlm, respectively. Thermal stresses are
often dominant when high temperature deposition is adopted or when high temperature
annealing occurs during subsequent processing.

Intrinsic stresses are developed during the growth of the ﬁlm. The magnitude of
intrinsic stress is dependent on the relative kinetics of various processes that contribute to
stress generation. Factors that inﬂuence intrinsic stress include grain growth, excess
vacancy annihilation, phase transformation, and epitaxy. The presence of a biaxial stress
in thin ﬁlm on a substrate will cause elastic bending of the substrate. Tensile stresses in
the coating cause the specimen bend toward the coating, while compressive stresses in
the coating causes the specimen bend toward the substrate, as shown in Figure 1.2.1. [64] .
If the ﬁlm thickness is less than one percent of the substrate thickness, the average stress,

0', in thin ﬁlm can be calculated from the radius of curvature of the substrate using: [63]

E t2
0' = 5 3 , (1.2.2)

 

where R is the curvature of the substrate; E,, v, and t, are Young’s Modulus, Poisson’s

ratio and thickness of the substrate, respectively; tfis the thickness of the ﬁlm.

1.2.2.2 Adhesion Strength

Interfacial adhesion strength is a measure of the resistance of coatings to
debonding or spalling. Interfacial adhesion can be measured by indentation tests, scratch
tests, bending tests, or bulge and blister tests. [65-68] The scratch test has been widely

accepted as a comparative measurement of the adhesion strength of hard coatings on

17

metal substrates because it is reliable’ SimPle to use, and requires no 51350131 specimen
preparation. In the scratch adhesiOI1 test, a diamond indenter is drawn over the coated
surface under constant or increasing normal load until a critical load is reached at which
coating failure, occurs. Adhesion is generally quantiﬁed using this critical load to failure
in a scratch test. [69, 70] Acoustic emission and change in the slope of the time-
dependent tangential force curve in the progressive-loading scratch test, as well as
microscopic observation of the scratch scars, can all be used to determine the critical
load. [71-73] During the scratch adhesion test, a compressive stress ﬁeld is induced ahead
of the indenter. When the mean compressive stress exceeds a critical value, the coating
detaches from the substrate to lower the elastic energy stored in the coating. The material
behind the indenter is subject to a tensile stress, and the material under contact is bent to
form the scratch track. The scratch ridge, which is the edge of a scratch along scratching
direction, is also subject to bending deformation. [74, 75] A range of non-adhesive failure
modes may occur before or along with adhesive failure during scratch test. Two types of
major failure produced by scratch tests are: cracking in the through-thickness direction
and adhesive failure, as shown in Figure 1.2.2. [76] Sometimes, there are two distinct
transition points in the output of the friction force, indicating two “critical loads”. The
lower value corresponds to the onset of through-thickness cracking around the indenter,

while the higher value is associated with coating penetration and detachment. [77-79]
1.2.2.3 Hardness

Hardness has long been regarded as a primary parameter deﬁning wear resistance.

According to the Archard’s wear equation for abrasive wear test, the volume loss, AV , is

18

linearly preponional to the applied normal load, L , and inVerser Proportional to

hardness, H , [80] i.e.,

L
AVoc—. 1.2.3
H ( )

Therefore, many scientiﬁc researches have focused on the development of super-hard
(H>4OGPa) wear resistant materials. [81]

One of the most effective methods to increase hardness is to decrease the grain
size. In metal and alloy ﬁlms, small grain size causes hardening of materials in agreement
with the Hall-Fetch relation

H = H0 + kd’m, (1.2.4)
where H is the hardness; H0 is an intrinsic material parameter; d is the grain diameter and
k is a constant related to both shear modulus and the critical shear stress for dislocation
movement. The Hall-Petch relation has been found to be valid for grain sizes larger than
10mm. For grain sizes smaller than 10nm, grain boundary sliding plays an important role
in determining the mechanical properties. [81] The deposited thin ﬁlms usually have
grain sizes smaller than 1pm. The density of the ﬁlm and defects also inﬂuence the

hardness. Usually, voids and vacancies decrease the coating hardness.

1.2.2.4 Friction and Wear

Friction and wear properties of tribological coatings are often evaluated by
sliding wear tests. The normal load and tangential force are measured during sliding wear

test. The ﬁiction coefﬁcient, ,u , is deﬁned as the ratio of the tangential force, F; , to the

nonnal force, F" :

19

”= may

:Mm

where the tangential force, F ), arises from two sources: an adhesion force, F; , developed
at the contact area between the two contact surfaces, and a deformation force, Fd , needed

to plough into the material, i.e., [80, 82]

E=ﬁ+ﬁ mam

The adhesion is given by

F=Ar man

a

where A is the true contact area between the two surfaces, and r is the shear stress of the
junction formed at the contact area. A low friction coefﬁcient is usually desirable for
most tribological coatings.

Wear of tribological coatings can be categorized into two types: wear dominated
by coating detachment, i.e. fracture in the coating/substrate interface, and wear caused by
gradual removal of the coating materia1.[73, 83] Wear of the ﬁrst type can be decreased
by improving interfacial adhesion; while wear of the second type can usually be reduced
by increasing hardness or decreasing the friction coefﬁcient of the coating material.

As discussed in section 1.2.2.3, hardness is the major factor determining the wear
resistance of materials. However, recent studies showed that there exists cases where the
Archard’s equation does not apply, i.e. materials with lower hardness could have better
wear resistance. [24, 84] It was suggested that the ratio of elasticity plays an important
role in determining wear resistance as well. [26, 27, 84] For instance, some polymers,

particularly elastomers, have low hardness and Young’s modus and they can provides

excellent wear resistance. The elasticity can be easily characterized by the instrumented

20

indentation experiments using the {ﬁne 0f hardness t0 modulus, E, or the ratio ofﬁnal

hf

 

1ndentatlon depth to maxrmum 1ndentatlon depth, . Note that 7:: rs drmensronless

max

and it is termed as “elastic strain to failure”. [84] H /E can be used to characterize the

elastic strain under contact. An almost linear relationship between the ratio of hardness to

h
reduced modulus, %, and f has been reported. [85, 86] It needs to be pointed out

max

that no experiments existed that unambiguously demonstrated the effect of H / E without

altering other attributes, such as the chemical composition at the surface that could also

affect wear, because in most previous studies different materials systems were used to

test the effect of H / E . To clearly demonstrate the effect of H / E on wear resistance, the

surface chemistry and surface hardness have to be the same.

1.2.3 Tribological Coating with Interlayers

Hard ceramic coatings are often deposited on the soft metallic substrates to
protect the soft metal from wear loss. Typically, the Young’s modulus of ceramic
coatings is 3~4 times higher than that of metal substrates. The coefﬁcient of thermal
expansion for ceramics is often much smaller that that of metals. Ceramic coatings on
metal substrates sometimes have a strong tendency to fail by cracking or delamination
due to the large mismatch of mechanical and thermal properties. In addition, if the
substrate is not hard enough to carry the load, plastic deformation will take place in the
substrate under contact. For a softer substrate, cracks occur in the coating both within the

contact area and outside at the substrate material piling-up area. [76] One way to increase

21

the load supporting ability is to depOSit thicker coatings. However, the Perfom‘lance of a
coating may not improve with increasing coating thickness because the deposited
coatings typically have columnar structure. Any crack normal to the surface will be large
in thick coating, and may exceed the critical crack length for fracture, whereas in the thin
coating this may not be the case. Furthermore, the interfacial thermal stress is
proportional to the coating thickness. A large interfacial shear stress often leads to large
thermal strain and premature failure of the coatings.

To improve the load supporting ability, adhesion, and wear resistance, composite
coatings with various interlayer materials, such as Ni, Ti, Cr and Mo, have been
developed. [71, 72, 87-89] With proper choice of interlayer materials and thickness,
improved friction, wear and adhesion behavior have been achieved. It has been claimed
that interlayers can provide beneﬁtsiby arresting crack propagation, a problem which can
otherwise increase with thickness. [90] It is desirable to produce tribological coatings
where the interlayer provides good adhesion to the substrate and the outer layer provides

high harness, low friction and good stability.

22

1.3 lNSTRUMENTED INDENTATION EXPERIMENTS

Traditional Vickers hardness measurement requires imaging of the indents to
calculate the contact area and hardness. Large errors are introduced in the measurement
of indentation size. In addition, it is very difﬁcult to image indents of sub-micron scale.
With the instrumented indentation technique, hardness can be calculated directly from the
load-displacement curves. Instrumented indentation experiments, also termed
nanoindentation or depth-sensing indentation experiments, have been widely used in
probing mechanical properties at sub-micrometer scale. During an instrumented
indentation test, both the applied load and indenter displacement are recorded, and
mechanical properties, such as hardness and reduced modulus, are measured. A
schematic load-displacement curve from a loading-unloading cycle of the instrumented
indentation test is shown in Figure 1.3.1. [91] A variety type of indenters, such as
Vickers, Berkovich, Knoop and spherical indenter, were used in indentation tests. [92]
Recently, Berkovich indentation and spherical indenters have been widely used for
indentation measurement. [91][119] In the following sections, issues related to

instrumented Berkovich and spherical indentation experiments will be discussed.

1.3.1 Instrumented Berkovich Indentation Experiments
1.3.1.1 Oliver-Pharr’s Method for Hardness and Modulus Measurement

A Berkovich diamond indenter, which has a triangular pyramid shape, can be
easily manufactured since three facets always intersect at one point. It has the same area-
to-depth ratio as the traditional Vickers indenter. Berkovich indentation experiments have

found wide application in measuring hardness and Young’s modulus of bulk materials

23

 
   

‘1‘“ 1q...

 
  

.ugvn-

'1
-.

,.g:., n

_,~h-v—ﬁ—I‘I'?1“hih$l.‘f".“"liv -. a... 1,. 5:... p. -“... .d.‘.-.o-‘ ‘ in" 5"
:‘ 5"‘OV{$!‘ 1 ‘ '

 

 

and thin ﬁlms. [93‘95] A detarled description 01" Berkovich indentation eXpen'mc/zt the
analySiS method for measuring hardness and modIllus is presented in this section.
' d as
The hardness, H’ 15 equal to the average Pressure under the indenter, calculate

the applied load, Fmaxr divided by the ContaCt area, Ac, between the indenter and the

sample:

A” - (1.3.1)

For aprefect BerkoViCh indenter, the relationship between contact area, Ac and contact

depth, 17c, i 3 given by the area function: [91]

Ac :: 24.5’7: °
(1.3.2)

contact de th .
Accurate determination Of contact area and P are On ti

c£11 in nanoindentation
measurement.
. t ro osed that the Contac ed
Doerner and le [96] to ﬁrs p p t ePth can be calemat

‘ the i ' ’ .

This method was later modiﬁed by Oliver and th’ [91] and who’s method is now

widely accepted to determine contact depth, contact area, hardness, and

modulus -

at a

conical indentation process can be used ‘° S‘mula‘e the Berkovich indentation ”we
8

because the conical indenter, like the BerkOViCh indenter, has the same depth-area
relationship had geometric singularity at the liP- The BCYkOViCh indenter is equivalent to a
c—‘mical indenter with a half-angle of 703°, as shown in Figure 1.3.2. [97] For a conical

in denter, the contact depth, he, is given by:

24

  

  
  

Y-JH" tong}:-
.' ‘obot
‘ol’hlogbqn- .

. -... ma.W-“-mns4ulliﬂﬁ|t\4us ‘_‘." i
, .
.‘v . , ,

 

 

hr : [Imax — 0.72% (1.3.3)
S ,

where hm is the diSP‘acemem at the maXimum load' Fm.“ and Sis the initial unloa‘d‘“g

stiffﬂeSS, respectively. [91} Based on a large nuInber of experimental observations, Ohver

and Pharr suggested that the contact depth for Berkovi ch indentation is Sﬁghﬂy different
from equation (1,3,3) and is given by: l: 91, 98]
F
h :hmax ‘0.75-—ﬂ.
c 5 (1.3.4)
A comparj 5 contact depth for Berkovich indentation .
son of th expenment and conical
i"dentition expen-mmt is shown in Figure 131-
Accurate detemination of the initlal an loading Sti
fﬁless

is crucial in
. , t the un -
nmomdentation analySIS - It was observed tha loading Cu

e Obeys a power—law
relationship: \91 3

F, =K(h“hf)m’

(l 3.5)
where F“ is the force during unloading;

h is the indenter diSpIac .
ement dunng unloading,
and hf is the residual indentation depth aﬁer unloading. The

cQl'lstants K anq I” can b
. . 6
determined by a lﬁast Square ﬁtting of the relationshlp betwee11 F and ( h \ 5

. . f) Initial
unloading stiffness, S, is then found by analytlcally dlfferentiating equation 1

.3. 5
. . and
evaluating the denvative at the peak load:
-_ dFu
’ dh

[7“:qu

S

 

(1.3.6)

25

 

‘2 37‘“ $9.9ﬁ9" ’

  
 

   
 
  
 

      
 

. . -,
. ,~.-.D .- V
.-...n-1~\...‘..-nu..;;.-,.n:-\6¢1.' - '

tyvn'rhhﬁ-“H‘HY’”

 

,.,,.-~- _ .. e17-.---.~.~a;~--910§

 

 

 

 

dF
S = 2,7] : 2E. Ac , ([37)
[3:qu 7Z-
The reduced modulus, E *, is given by:
1 ___ (1 —-USZ) (I 2
E‘ f i, “L? (1.3.8)

I

where E: and Vs are Young S mOdUhls and POiSSOD’S ratio for the specimen, respectively.
3

E; and 14‘ are Young,S modulus and Poisson’s ratio for the indenter respectiv l
a e y,

Diamond 1‘ s the most popular indenter material because of its hi .
gh Stlffness
and hardness.
The Young’s modulus and Poisson’s ratio of the (:11 anond indent
, . . er are 1141GPa and
0'07’ respectively. For a rigid indenter With inﬁnite modulus, t e
TedUCed modulus is

expressed as:

1 __ (1 ~03)
E' Es 3.3.9)

 

Equation 0.3.7) was ﬁrst derived by Sneddon for elastic

c ' '
OI‘ltact between a “gld’
axisymmetric punch of an arbitrary smooth proﬁle and an elastiQ 1) If It
a -space- applies to

both conical and Sphelical indenteI’S- Recently, Cheng and Cheng [86 1001
’ bro

Ved that

this equation holds true for elastic-plastic solids with or without ork har
w de .

. . . ”In
ragldual stress. The measured initial unloading stiffness can thus be used to c 1 g and
a Cu!

. ate t
reduced mOduluS 1f the comma area can be accurately determined he
Practically, no Berkovich tip is PerfeCtly Sharp at ‘he end The tip roundin f
' g e fECt
i 5 taken into accoum by the indenter Shape function calibration, For a rounded Be k
r ovich

ti), as a good approximation, the shape function is given by: [91 1

2 1/2
A, = 24-5hc +Cihc +C2hc (1.3.10)

26

3%‘!‘?"""‘ -O‘ -‘-.l. gs:iu‘.n“|i§‘l§§ T?”~'P',"f"""?‘"‘.)"""""“" " "“‘
.. , .. . . . .\-'v‘~"~‘¢;|,-A.Wtr.¢*

 
   

~.h-u}n--t“‘
.

 

 

The constants Cl’ C2 can be Obtained by a least SQUare ﬁtting of the relationship “Mean

t (16 B ' _ n ’s
the contact area and Contac 1: th' Y 1“dentmg a material with a known Y0“ g
an be cal 11 . m can
modUhlS, the contact area c C lated 118mg equation 1.3.7. The ComaCt dep

be determined using equation 134' Most 0ﬁen, fused silica is used as the calibration
material. The Young’s modulus and POISson’s ratio of fused silica are 726%, and 0.17,

respeCtiVCIy. [101]

1.3. liPiIing41p and Sinking-in

EX tensive ﬁnite element modeling 0f come a] l.ndentationi l .
n e ast1c

98 10 'perfecuy
P‘aStiC [102-104] and elastic-plastic [85, 86’ 97’ ’ 5, 106] 301i

h Was is h can be large has been conducted.
\ln r
d that, the contact depth ( c) than the .

th c dentation depth at the
. e 0
maximum load (hmax), i.e- piling-UP occurS, or “met depth

e
can be smaller than th
' - ' ' ' -in
1ndentation depth at the maximum load, ”3' Slnkmg OCC 111‘s.

For a conic2A ideentef with some speCIﬁC angle, the degree of piling—up and

. . _ , ' ' ld stress to Youn ’

smklng-m is dependent on the fat“) 0f yie g s
. - modulus, Y/G, and the

work hardening eXPOnem, n, as shown in F1gurel.3.3. [97, 107

. - - as Ic
materials (large Y/E and n) sinking-m occurs and the Oliver-P118“ method can b
6 ”86d t
0

determine the Contact depth- However, for materials with low Y/E and n mater-1'31
’ Pilin -

up occurs. It is Claimed that, 35 a simple practical rule, when the ratio of resid
ual

h
indentation depth 10 maximum indentation depth, 714

max

"51638 them 0.7, the Oliver-Pintrr
method provides a reasonable estimate 0f the com“ area' HOWever, when 111-— > 0.7

"BX

me O\\\i er-Pharr method underestimat es the coma“ area due to material Filmer“? AS is

27

“.1..-

, -,.~.~-u
-r...-o~.
o‘u’
\l‘.-Il.t"h‘
'0‘
“ Vutv- O ‘

 

  
 
 
 
 
 
 

.l‘\'-,ba‘ax"'

 

 

obViO“S in equation (1’3'4)’ the coma“ depth (he) is always smaller than the indentation
depth at maximum ‘Oad (I'M) Wh 6“ Oliver‘Pharr’s method is used. [107] Materia‘ Piling‘
“? has been observed in Berkovich indents on aluminum. The projeaed contact areas
measured by AFM were up to 50% greater than those calculated using the Oliver-Phal-
method [109] To accurately determine the contact area in the case of piling-up, we {med
to measure the Pmﬁle 0f the residual indents aﬁe’ "Illoading using surface proﬁlometer.

The “tap point” shown in Figure 1.3.4 can be used to deﬁne the contact perimeter. [110]

1'3-1-3 Sealing Relationships

. - ' ve be
Some interesting 30311118 relationshlps ha en reported ~

. ‘17 Con' ' entation
ﬁnite ical 1nd

' . . . and 616
eXDenment using dimensmnal analys‘s ment

Odellng The scaling

. - ' work to
relationships between the ratio of irrever51ble total work WP
’ X , ratio 0{ r

W

(0!

esidua‘

h
. __f_ ' f hard
de t ‘ m ind ' n depth, ’ ratio 0 “338 t
p h to maximu entatlo hm 0 reduced mo (1111118, _. ,

E

have been reported- 1:01. a conical indenter with an arbitrary angle a single
’ 0”NO-one

. . . Wp hf as shown in Fi u
relationship ex1tS between ,— and T ’ g re 1 ~35.

m

10
tot [105, 6’ II

1] 7721's

h
. . , . L
relatlonsl'np IS approximately Imear for hm > 04 and the expression iS given by:

 

W hf h;
P = — for >
(1+7th 7 hm (14, (1.3.11)

(0!

Where 7 = O -27. This general relationship is independent of material pmperties and

iwdenter angle. For a conical indenter of given half-included angle, 9, an approximately

7.8

 
   

’-1&~I11?0i?“."° '? ,- "_..’.y,u_y§g‘\n_l§'l§€?_’_"4_~'!""’99,?!"3.3.f"“‘-‘""‘ y. ‘-4§._ “v . .. ("-‘W'l'." ‘1“. }Q- .9...

 

' \/ v

 

, - - xistS between 4 ﬂ
1111621I relationship e 11 and Ei , as Shown in Figure 1.3.6. [85, 106’ 112]

m

The relationship is given by:

h H
f "" -- \
7’1 RE. , (1.3.12)
where
11:1.5tan6 +0327 for 60° 0
( ) $9380 . (1.3.13)

e.g. 45°,

For ‘7 conical indenter With sharp angle, the l inear relationship betw hf
een K and
h

1.1/Eat remains valid aItbough the angular dependence 0 f A no longer 1
app ies.

n Indentation and Uniaxial Tensile 13‘

1.3.1.4 Correlation betwee
periments

n, 8r, for conical] in

' ' trai
\t is suggested the representative 5 2
elltation is givenby K9 ’

113]:

gr = 0.2 tan9 ,
(1.3.14)

where, 6, is the half included angle of the conical indenter .
. Berkowch and V' k
. _ _ . . IC CI‘S
indenter e u1v meal Indenter Wlth 703°
S are ‘1 ale!“ ‘0 a °° half-included

angle me

representative strain f0!“ Berkovich and Vickers indentation is approxi mat i
e y
equal
to

0.08. Tabor claimed that the signiﬁcance 0f representative Strain is that hardn
688 (H)

equals 2. 8 times the true stress (0;) at the representative strain, i e [92]

H = 2.80, .
(1.3.15)

Where O-r is the truc 311688 at 0.08 true strain in an uniaxial tensile test

29

 

 

usa-_- - 9- - ‘, 9.—---~.~.-\‘-§Jnl

   

a-aquy- ‘*.“.‘~"Y1¥!Hu§"'"""9" w v-a

 

 

I
\

 

b"§~“ 'Q;|Iag*'.l'

  

  
   

 

n has been reported that equation (1.3.15) applies only to highly plastic W’WIS‘
' - is
For highly-elastic the rat10 Of hardness to ﬂow stress (termed as the conS‘?ralnt factor)

. . t'
aller than 28 [he constraint factors decrease from 2 8 to 1,7 for highly 9‘35 1c
Sm o o .

materials to highly-613““; materials, respectively. [86, 112]

Recently that6 have been arguments about the value of the representative 81min,

By mapping the strain distribution of the SUbsurface under the indents, Chaudhn‘ [114]

suggested that the representative straitl ranges ﬁ'0m 0.25 to 0.36. However, using ﬁnite

Blame”! Calculation, Mata 6" 31' [115] suggeSted that the representative strain should be

close to 0- 1 _

Efforts have been made to explore the POSS‘bll lty of delivl‘

g the true stress-strain

- arnidal in .
re\ationShips using instrumented conical 0r PYT dentatlon

"Petiments. [105, 1 16’

ml \thas been found that different combina‘mns of View str

_ ‘ lacement cune i
expone-m can lead to the same load (115‘) n a Sham in dentatiO“ teS‘a as

shown in Figure 1.3.7 . Therefore, the Stress'suam relationship may not be uniquely

. - ment curve of conical Or . -
determtned from load-diam:e pyramidal1 Indentation

experirn ents. [105]

13,2 Instrumented Spherical Indentation Experiments
1.3.2.1 Analyzing Methods

Since its inception by Brinell 3130‘“ 100 hundred years ago, spherical ind entation
techniques have been widely used to measure hardness of materials. [92, 118-121] In the

spherical indentation test, a hard Spherical indenter is pressed into a ﬂat surface under a

30

 
 

ifill?“”‘r"'—OD‘. I‘ucon..ao-u~.nh~‘,raﬂr$‘4N"!T“3.3-1"”!‘5IYH‘h”‘?" ‘-“4l.va:.-. .,_.....-.-‘-,-4I'~ﬂ"!" H ‘2‘?!” 7"""':1'

 
 
    

 

, v
._‘,n’ -'

normal load making impreSSl on- Hardness and reduced modUIus can also be 316351” ed in
instrumented spherical indentauon tes‘ “Sing equations 1 3.1 and 1.3.7.
In Spherical inden‘a‘mn expeniments, as in Berkovich indentation expeﬁmen‘sa

t of hardness and

ation 0f the contact area is Crucial to the measuremen

accurate determin
' ' tat‘
reduced modulus. III spherical inden 10“, the circle delimiting contact between the

indenter and the indentation is usually not in the plane of the original surface but may be

abo we or below it. The piling-up or sinking-in makes it difﬁcult to determine the Conta t
c

‘1er and area under indenters. TWO types 0f methods, i.e., Nor-bury Sam 1’ th (1
‘ ue 8 me O

and 0113/6 I-Ph arr’ 5 method, have been used to detetjnine the Cont t
ac area in spherical

indentation exp eﬁmeﬂts-

the indent proﬁle aﬁer unloading using a "1‘

lcr OS d
Cope Norbury an

- ' tween the c0nt ’

Samuel “22} found that the relatlonShIP be ac‘ rad ~

“’3, a and the radius 3"

here c i
, w S a constant dependent only on the

By imaging
. - ’ . 2202/61 92
the ongtna\ surface, 0 satisﬁes C
work hardening exponent, n,

5(2 - )1)
2(4 + n) '

2

2 a

6:7:
a

(1.3.16)

Hill et. al. [123] analyZCd the Brinell indentation and Claimed that Nobury an
<1 s
amUejs’

observation are valid- Equation 1.3.16 has been widely used in Spherical inden
tati

to determine Contact area and material properties. [124-128] Evidently

on test

aCCOrding to
equation 1.3 - 16, the piling—Up and sinking-in depends on the Work hardening exp
Onent

only, and it is independent of indentation depth and other mater—1'31 pr0perties Howe
. Vet,
recent finite element analysis shows that the extent of piling'uP/Sinking-in is a function f
0

‘15 applied load and material properties, such as yield stress, in addition to the work

\mdeximxg exponent. [129, 1 3 0]

31

-_.'.

     

h ".u. .e 4,?

 
  

“ﬂaunts;74N1I?1"!f”?1¥1‘.'JI-tn’”“‘4" “ v-u-«t—w 1;": “MW“W'“ ""' "h'

 

 

‘.* _‘.’ b4” 5‘ '

0‘ _ ’ method 9 1 '
“'5‘ PM” 5 [ 1 '8 ano‘her method that has been used to date/7121113
the

Contact area in Spherical “‘den‘a‘ion teSts, For sph ' 1 ' d t t‘ xperiments
enca m en aion e ’

. - by a simple
contact area, Ac, 18 gtve“ geometry ‘
COnSIderation: [ 13 1]

Ac = ”(ZRhc _hf), (1.3.17)

where R is the indenter radius. The contact depth h is given by CQuation l 3 3
obviously, in the oliver-Pharr method, Contact depth h is assumed to b 1 th
3 C, 8 335 an the

maximum indention depth, hmax. Therefore, the Oliver-Phan- method 1-
app ies only When

SIIIkIIIg-in occurs. It underestimates the contact area when Piling
‘up occu
I'S.

herical Indentation Ex
Peri».
e

1.3.2.2 Representative Strain for SP
hts

ch inde -
ntatlon ‘

1
that the angle between

Spherical indentation differs from Berkovr
extent

dunng indenter pene

the indenter and specimen surface changes

05 the strain under the indenter. Tabor [132’ 133] demonsnated th
that there was 3 d6? -

sensitive representative strain, 5,, that could be associated W‘
1th - - '
Sphencal Indentation

eliverirnent, expressed as:

g =o.2i"—=o.2f’—,
r D R
(1.3.18)

where a and d are the contaCt radius and diameter, respectively R and D at

and diameter of the indenter, respectively. Tabor [92, 132, 1 3;] also Showe the radius
ed

some metals, the hardness, H, is about 2.8 times the true stress, 0- for a Stra. that, for

the representative strain, i.e., the constraint factor, CF , is: m equal to

H
CF=—: 2.8 when 8r = 5‘.
(1.3.19)

r

32

where 8‘ is the true strain and 8r iS the representative strain given by equation 1.3.18.
Figure 1.3.8 shows the relationship between the representative strain ~ hardness and true
stress~ true strain for spherical indentation in metals. [132] The correlation between
spherical indentation experiments and uniaxial tensile data indicates that, using the
concept of representative strain and constraint factor, spherical indentation experiments
may possibly be used to measure the true stress-strain relationship. Compared with the
tensile test, the spherical indentation experiment has the advantages in that it is non-
destructive and can be conducted at small scale.

Francis [134] argued that spherical indentation in elastic/plastic materials evolves
in three distinct stages —— elastic, elastic-plastic, and fully-plastic, as shown in Figure
1.3.9. [125] The deformation is purely elastic when H/Y<1.I, where H is the hardness
and Y is the yield stress of the undefonned material. In the purely-elastic indentation
range, the material around and underneath the indenter deforms elastically. The analytical

solution to elastic indentation is given by the Hertzian equation: [113]

 

1/3
a = [3:21]?) , when a<<R, (1.3.20)

where a is the contact radius, Fm is the applied indentation load, R is the indenter

radius, and E ' is the reduced modulus. When H/Y reaches 1.1, plastic deformation starts
at a point below the center of the contact region. This occurs at a depth dependent on the
strain hardening of the material, but is always close to 0.5a below the bottom of the
indentation impression. In the elastic-plastic range, the plastic zone is surrounded by

elastically strained material. When H/o; z 2.8, fully plastic deformation is established and

H/O'r remain approximately constant with increasing indentation depth. In the fully-plastic

33

 

indentation range, the plastic 20116 r 6aChes out to the surface and all the material around
the indenter deforms plastically.

It has been found that the constraint factor increases when the indentation evolves
from the elastic to the fully-plastic stage. Constraint factors from 1.1 to 3 have been used
in deriving true stress-strain relationship using spherical indentation experiments,
depending on the stages of the indentation experiments. [135-140] However, so far, there

has been no systematic study of the limitation of using the constraint factor to derive the

stress-strain relationship.

34

CHAPTER 2

ON THE STUDY OF MICROSCOPIC SHAPE MEMORY EFFECT,

SUPERELASTIC EFFECT AND WEAR BEHAVIOR OF NITI ALLOY

2.1 INTRODUCTION

NiTi alloys are well-known for the shape memory and superelastic effect. Since
the ﬁrst discovery of shape memory effect in NiTi in 1960’s, [1-3] there have been
extensive research efforts on both the fundamental understanding and industrial
applications of NiTi alloys. Recent years have seen an increasing interest in using NiTi
alloys for small-scale applications, including shape memory thin ﬁlms for MEMs devices
and, in this study, wear resistant surfaces. For example, shape memory alloys exhibit
desirable wear properties under cavitation erosion [141-143] and dry sliding wear
conditions. [20, 22, 23, 26-28] However, there exist few studies on the indentation
behavior of NiTi alloys. [26, 29, 32] The indentation behavior of NiTi is interesting
because (i) the indentation experiments may be used to characterize the shape memory

and superelastic effect at small scale, which will be especially useful for characterization

of N iTi ﬁlms on substrates, and (ii) the loading condition in wear tests is very similar to

that in indentation experiments. The indentation study of NiTi alloys can help us
understand the wear behavior of NiTi alloys.

This chapter ﬁrst presents a systematic study of shape memory and superelastic

effect using instrumented indentation experiments to answer the following questions: (i)

how does the indenter geometry inﬂuences the shape memory and superelastic effect (ii)

35

what are the effects of indenter radius and indentation depth on the mechanical response
of shape memory materials? In addressing these questions, a set of quantitative
characterization methods using micro and nanoindentation techniques have been
developed. Speciﬁcally, spherical and Berkovich and Vickers pyramidal indenters were
used to determine the mechanical response of NiTi alloys over a wide range of
indentation depths. The magnitude of the shape memory effect was quantitatively
characterized by the thermal-induced depth recovery ratio of the residual indentation
depth. The magnitude of the superelasticity was quantitatively characterized by the depth
and work recovery ratios obtained from the load-displacement curves. It is found that (i)
the magnitude of the shape memory and superelastic effects can be rationalized using the
concept of the representative strain and maximum plastic strain, and (ii) instrumented
indentation techniques, especially the spherical indentation experiments, are useful in
quantifying shape memory and superelastic effects at micrometer and nanometer length
scales.

In order to look into the possibility of using NiTi as a novel tribological material,
dry sliding wear behavior of martensitic, austenitic and amorphous NiTi was studied
under different loads using pin-on-disk wear test. It was found that the wear resistance of

Ni Ti alloys increases in the order of martensitic, austenitic, and amorphous. The
austenitic NiTi is less wear resistant than amorphous material although the former has a
higl'ler elastic recovery ratio. To make superelastic NiTi wear resistant, the surface

Ploughing needs to be prevented.

36

2.1\NSTRUMENTED INDENTATION EXPERIMENTS
2.2.1 Sample Preparation and Experimental Methods
Melt-solidiﬁed NiTi shape memory (specimen BH) and superelastic (specimen
BS) alloys were obtained from Shape Memory Application, Inc. (San Jose, California) in
the form of 0.75mm and 0.43mm thick ﬂat annealed sheets, respectively. The nominal
composition of sample BH and BS is 50.8 at.% Ni, balance Ti, with oxygen and carbon
levels below 0.17 at.% and 0.22 at.%, respectively. Characteristic phase transformation
temperatures were measured using a TA Instrument 2929 Modulated Differential
Scanning Calirometry at a heating and cooling rate of 5 K/min. Regular X-ray diffraction
(XRD) measurements were carried out on a Siemens D500 diffractometer using Cu—Ka
radiation at 40 kV voltage and 30mA current. Microfocus XRD was carried out on a
Simens D5000 diffractometer using a spot radius of 50 um and Cu-Ka radiation at 40 kV
voltage and 30 mA current.
Samples were mechanically polished, ﬁnishing with a 0.25 pm diameter diamond
paste, to give an average surface roughness of less than 50nm. Berkovich indentation
experiments were conducted using a Nano Indenter XP from MTS System Inc.. A
Berkovich diamond indenter was used to make indentation with residual depths ranging
from 500 to 1000 nm. The tip radius of the rounded Berkovich indenter is less than 150
nm- Instrumented Vickers and spherical indentation experiments were conducted using a
CSEM Hardness Tester from CSEM Instruments. A Vickers diamond indenter was used
for I‘esidual depths ranging from 1000 to 6000 nm. Spherical diamond indenters with
radii 213.4 and 106.7 urn, measured by scanning electron microscope (SEM) imaging,

were used for instrumented spherical indentation experiments on the CSEM indenter.

37

Both the applied load and indenter diSplacement were recorded during the entire loading
and unloading cycle of instrumented indentation experiments. The indentation
experiments were conducted at room temperature (25 0C).

To characterize the shape memory effect of specimen BH, 3-D proﬁle of the
spherical and Vickers indents were measured using a WYKO RST-Plus optical
proﬁlometer, while the proﬁles of Berkovich indents were measured by a tapping mode
atomic force microscope (AFM) from Digital Instruments. After topographical
characterization of indents, the samples were heated in air to 150 °C for 10 minutes to
transform martensite phase into austenite phase and cooled back to ambient temperature.
Proﬁles of the same indents were measured by the methods described above after
thermal-induced recovery.

Tensile tests of specimen BH and BS were conducted using a United Testing
System tensile tester. The gauge length was set at 20 mm and the displacement rate was
lmm/min. Displacement of specimens during tensile test was monitored by a laser optical

extensometer. The tensile experiments were conducted at room temperature (25 OC).

2.2-2 Results and Discussion
2.2-2.1 Transformation Temperatures and Structures
Transformation temperatures of specimen BH and BS were measured by
differential scanning calirometry (DSC) tests, as shown in Figure 2.1. From DSC
measurements, the rhombohedral “R-phase,” martensite, and austenite start and ﬁnish
temperatures (R3, Rf, M,, Mf, A, and Af, respectively) were determined and are

summarized in Table 2.1. The martensite ﬁnish temperature of specimen BH is slightly

38

above fOOm temperature (RT), WhiCh indicates that it is martensitic at room telhperature.
1n speCimen BH, the transformation enthalpies for austenite—+R~phase, R—
phaseemartensite, and martensite—>austenite transition are 3.9, 11.3 and 23.1 J/g,
respectively. In specimen BS, A, < RT < Af and Rf< RT < R,, which indicates that BS
sample is a mixture of B2 and R-phase at room temperature. The transformation
enthalpies for austenite—>R-phase, and R-phase—>austenite transition are 3.4 and 4.4 J/g,
respectively. X-ray diffraction patterns, Figure 2.2, shows that sample BH consists of

B19’ monoclinic martensite and BS consists a mainly of B2 austenite and a small amount

of R-phase.

2.2.2.2 Shape Memory Effect of Indents

The shape memory effect arises from the recovery of strain during transformation
of a deformed martensite to austenite upon heating. In this study, recovery effect of
indents was determined from surface proﬁle measurements by deﬁning a thermal-induced

recovery ratio, 5 , as

 

a: f f, (2.1)

where h f is the residual indentation depth recorded immediately after unloading and h}

is the ﬁnal indentation depth after the completion of thermal-induced recovery. A

schematic illustration of the thermal-induced recovery of the indent is shown in Figure

2.3.

39

2.2.2.2.1 Berkovich and Vickers Indents

Figures 2.4(a-b) show the proﬁle of the Berkovich and Vickers’ indents on
specimen BH (shape memory NiTi) before and after heating. The thermal-induced
recovery ratio of Berkovich and Vickers indents is plotted in Figure 2.5. The recovery

ratio of both Berkovich and Vickers indents on specimen BH is about 0.34 and is depth

independent from 500 to 6000 nm.

2.2.2.2.2 Spherical Indents

The geometries of the spherical indenters with radius of 213.4 and 106.7 um are

shown in Figure 2.6(a) and (b), respectively. The tip radius was measured by SEM
imaging. For specimen BH, a spherical indenter with 213.4um radius (Figure 2.6(a)) was
used. Optical micrographs of spherical indents on specimen BH before and after heating,
Figure 2.7(a) and (b), show the recovery of indents. To quantitatively characterize the
recovery effect, 3D proﬁles of indents were measured using a WYKO optical
proﬁlometer. Figure 2.7 (c) and (d) shows the 3D proﬁle of an indent made at 8 N before
and after heating, respectively. Residual indentation depths of the indent before and after
heating were obtained from 3D proﬁle of the indents, and the thermal-induced recovery
ratio was calculated using equation (2.1). The relationship between the thermal-induced
reCOVery ratio and the residual indentation depth is presented in Figure 2.7 (e). It is
e"ident that shallow indents disappeared completely after heating, while deep indents
recovered almost completely. The magnitude of recovery is a function of indentation

depth for a given spherical indenter radius.

40

The concept of representative strain is invoked to present the depth-dependence of
recovery ratio for spherical indentation in shape memory alloys. For a spherical indenter
of radius R , the representative strain, 6, , associated with the indentation experiment is
given by: [92]

a, = 0.2a/R , (2.2)
where a and R are the contact radius and indenter radius, respectively. The
representative strain is dimensionless. Cross-section proﬁles of the spherical indents
produced at 10 N and 25 N load are illustrated in Figure 2.8, which shows that no
material piling-up occurs even at the maximum applied load of 25 N. A schematic
illustration of the indentation sinking-in and meaning of the symbols are shown in Figure

2.9. The c0ntact depth, hc, can be calculated ﬁ'om load-displacement curves using the

Oliver-Pharr method, [91] since no material piling-up occurs in this study. Speciﬁcally,

the contact depth is obtained from:

h = hm — 075(an /S), (2.3)

C

where hm is the penetration depth at the maximum load, Fmax, and S is the initial

unloading stiffness calculated from the unloading curve. The contact radius is determined

ﬁ-om the geometry and is given by:

a = ,/2h,R —hf , (2.4)

The relationship between the representative strain and thermo-activated recovery ratio is
Plotted in Fig. 2.10. It is evident that the recovery ratio is constant and close to 1 when

the representative strain is lower than a maximum recoverable representative strain of

41

about 0.047. The thermally induced recovery ratio starts to decreases with increasing
representative strain when the representative strain exceeds a critical value.

The true stress-strain curve from tensile test for the same NiTi shape memory
alloy is also shown in Fig. 2.10. It exhibits the well-known behavior that includes, with
increasing strain, initial elastic deformation, twinning deformation, and, ﬁnally,
additional elastic deformation plus plastic deformation due to dislocation activitiy.[5] The
twinning deformation corresponds to the plateau region in the stress-strain curve, while
dislocation slip starts at the end of the stress plateau. The strain at the end of the stress
plateau is regarded as the critical strain for complete recovery. For specimen BH, a
critical strain of about 0.047 corresponds to the maximtun recoverable strain upon
heating in the uniaxial tensile experiment. Fig. 2.10 also shows that the maximum
recoverable representative strain from spherical indentation coincides with the critical
strain in a tensile experiment. This observation suggests that spherical indentation can be
used to probe the maximum recoverable strain for the shape memory effect, especially for

sample conﬁgurations where tensile measurements become impractical.

2.2.2.3 Superelasticity under Indentation

In this study, the indentation-induced superelastic effect was characterized by the
depth- and work-recovery ratio measured directly from indentation load-displacement
curves. A schematic representation of the elastic recovery due to removal of the load is

shown in Figure 2.11. The depth recovery ratio is deﬁned as:

-———-, (2.5)

42

where hmax is the indenter displacement at maximum indentation load, h f, is the

residual indentation depth at which the load becomes zero during unloading. The work

recovery ratio, 77“,, is deﬁned as:

 

 

hmax
[Path
_ Wu _ "I
77“” _ m _ h... (2.6)
[Pdh
0

where W, is the total work done during loading and Wu is the reversible work during

unloading.

2.2.2.3.] Berkovich Indentation

Figure 2.12(a) shows the load-displacement curves of Berkovich indentations in
specimen BS (superelastic NiTi) and annealed copper. Copper was chosen as the
comparison material because it represents metals having elastic-plastic behavior. Figure
2.12(b) shows the depth and work recovery ratio of Berkovich indentation at various
depths. Evidently, 77,, and 7],, for specimen BS are about 0.45, which is signiﬁcantly
larger than the value of 0.08 measured for copper. Both the depth and work recovery

ratios are depth independent.

2. 2.2.3.2 Spherical Indentation
Load-displacement curves for spherical indentation (R=213.4um) on specimen
BS and copper are shown in Figure 2.13(a). It is evident that the specimen BS displays a

much greater recovery ratio than that of copper. The depth recovery ratio and

43

representative strain, together with the true stress-strain curve of specimen BS, are shown
in Figure 2.13(b). By comparing the recovery ratios from two radii of 106.7 and 213.4um
in Figure 2.13, it is evident that the depth recovery ratio indeed scales with the
representative strain and is independent of the tip radius. Contrasting with Berkovich
indentations, the magnitude of both the depth and work recovery ratios is signiﬁcantly
greater under spherical indentation conditions compared to the Berkovich indents. The
recovery is nearly complete when the representative strain is less than a maximum
recoverable representative strain of about 0.05.

To explore the mechanism of the high recovery ratio, a microfocus XRD
experiment on a Rockwell C indent made in specimen BS was carried out to study
indentation-induced phase transformation behavior. Figure 2.14 (a) and (b) shows the
XRD spectra of the non-indented area, and the area inside the indent, respectively. The
(002) diffraction peak of martensite phase appears in the indented area, which indicates
that the austenite —> martensite phase transformation was induced by the applied
indentation load. Superelasticiy can therefore occur under the indentation loading
conditions. As we know from the uniaxial tensile test that this transformation is
associated with a large reversible strain. The appearance of martensite in the indented
area also indicates that part of the indentation-induced martensite is highly strained and
can’t transform back to the austenite phase when the load is removed, which corresponds
to the irreversible part in the load-displacement curves.

The plateau in the true stress-strain curve of the superelastic NiTi alloy (specimen

BS) results from a stress-induced-martensite phase transformation. For specimen BS, a

Critical strain of about 0.05 corresponds to the maximum recoverable strain below which

44

a completely reversible phase transformation from martensite to austenite can occur upon
unloading in the tensile experiment. Figure 2.13(b) shows that the maximum recoverable
representative strain from spherical indentation coincides with the critical strain in the
tensile experiment. Dislocation slip is initiated when the strain is greater than the critical
strain. Accordingly, the depth recovery ratio decreases with increasing representative
strain once the representative strain exceeds the critical strain of 0.05. This observation
suggests that spherical indentation can be used to probe the maximum recoverable strain

by the superelastic effect.

2.3.3 Representative Strain and Strain Distribution under Indenters

For ideally sharp pyramidal or conical indenters, the representative strain is
determined by the face angles. Since no length scale is involved in describing the
indenter geometry, the representative strain is independent of indentation depth. For
Berkovich and Vickers indentations in elastic-plastic solids the representative strain is
approximately 0.08 for all indentation depths. [113] Hence, it is reasonable to expect that,
for ideal Vickers anduBerkovich indenter, both the shape memory and superelastic
recovery ratios should be independent of indentation depth, provided that there is no
other length scale involved in describing the indenter geometry. However, for real
Berkovich and Vickers indenters, which will have some degree of tip blunting, recovery
ratio is expected to be close to that of spherical indentations when the indentation depth is
small (i.e., comparable to the'tip radius of the Berkovich and Vickers indenters). Tip
blunting needs to be taken into account when doing shallow indentation measurement

using Berkovich or Vickers indenter. The constant recovery ratio observed in this study

45

indicates that the effect of tip blunting is insigniﬁcant when the indentation depth is
greater than 500nm, which is consistent with the fact that the tip radius of the Berkovich
indenter is about 150nm.

For spherical indentation in elastic-plastic solids, the representative strain
produced is not constant but varies with contact radius according to 0.2a/ R. [91, 92,
133] Since the contact radius increases with increasing indentation load, so does the
representative strain. For specimens BH and BS, shape memory and superelastic effects
under uniaxial tension or compression exist only up to a maximum recoverable strain of
0.05. We can therefore expect that, in spherical indentation experiments, the recovery
ratio decreases with indentation depth when the representative strain exceeds the
recoverable strain limit.

In is instructive to note that the recovery ratios are much larger for spherical
indentation than that for pyramidal indentation at the same representative strain of 0.08.
This difference may be related to the magnitude and the spatial distribution of the
maximum stress and strain for the two indenter geometries. Indeed, using ﬁnite element
analysis, Mata et al. [115] showed that the plastic strain level attained directly underneath
sharp indenter tips can be as high as 2.5 for elastic-plastic solids. The maximum plastic
strain for sharp indenters in annealed copper is less than 0.1 under spherical indentation
[144] when the a/ R value is less than 0.3, which is about the maximum 0 /R in this
study.

In this work, ﬁnite element modeling was used to study the strain distribution

under sharp and spherical indenters at a representative strain of 0.08. A detailed

description of the mesh and boundary condition for the ﬁnite element modeling will be

46

presented in Chapter 4. The stress-strain response of specimen BH obtained from tensile
tests was used to determine the relevant constitutive parameters for ﬁnite element
modeling. Figure 2.15(a) shows the strain distribution under a conical indenter with
70.3° half-angle, in which the representative strain is 0.08. Figure. 2.15(b) shows the
strain distribution under a spherical indenter with representative strain of 0.08. It is found
that the maximum plastic strain under conical indenter (half angle = 70.3°) is 0.79; while
it is 0.18 for spherical indentation at the representative strain of 0.08. The blank region
under the conical indenter indicates the region with a strain larger than 0.18. Thus, a
sufﬁciently large volume of material directly under the pyramidal indenter is so highly
strained that signiﬁcant deformation occurs by dislocation motion, which deteriorates the
shape memory and superelastic effect. It appears that the strain under the spherical
indenter is largely accommodated by martensite twinning in the shape memory NiTi alloy
or by stress-induced martensite transformation in the superelastic NiTi alloy, leading to

large shape memory and superelastic effects, respectively.

2.3 DRY SLIDING WEAR BEHAVIOR OF NITI ALLOYS
2.3.1 Sample Preparation and Experimental Methods
Dry sliding wear behavior of NiTi alloys with different structures, i.e., martensite
(specimen BH), austenite (BS) and amorphous NiTi thin ﬁlm, was studied. The surface
ﬁnish of specimen BH and BS for the wear test was the same as in the indentation test
(see section 2.3.1). An amorphous TiNi thin ﬁlm was deposited on a surface-oxidized
(100) silicon substrate by DC magnetron sputtering. The target material was Ni51Ti49

angmented with pure Ti inserts, as shown in Figure 2.16. The base pressure achieved was

47

better than 6x10'6Pa. Argon with purity of 99.99% was used as the working gas and the
working pressure is 0.533Pa. The working distance between the target and the substrate
was 64mm. The substrate temperature was measure by a K-type thermocouple placed in
contact with the backside of the substrate. The substrate temperature was maintained at
300°C by a built-in substrate heater in the chamber. The target was pre-sputtered for 30
minutes before deposition to obtain stable output ﬂux. The thickness of the amorphous
ﬁlm, measured by scanning electron microscope, was 4pm.

The Berkovich indentation test was carried out at a maximum load of 36mN and the
testing method was the same as described in section 2.3.1. Pin-on-disk dry sliding wear
tests were performed using an Implant Science ISC-200 Tribometer. Wear tests were
conducted in air at room temperature with a sliding velocity of 0.045m/s. The applied
load ranged from 0.245N to 4.9N. The pins were made of 52100 steel and were 3.175
mm in diameter. Young’s modulus and Poisson’s ratio of the pin were 210GPa and 0.3,
respectively. The cross-section area of the wear track after 200 revolutions was measured
using a Wyko RST Plus Optical surface proﬁlometer and wear rate was calculated

accordingly.

2.3.2 Results and Discussion

A XRD 0-20 scan of the as-deposited NiTi thin ﬁlm is shown in Figure 2.17. A
broad diffuse peak around 42" indicates the short-range ordered structure of amorphous
NiTi. Differential scanning calirometry (DCS) test shows a crystallization temperature of

453°C for the amorphous ﬁlm.

48

Figure 2.18 shows the load-displacement curves of specimenw BH, BS and
amorphous thin ﬁlm from nanoindentation test with a Berkovich tip. Mechanical
properties, such as hardness, Young’s modulus and depth recovery ratio, were obtained
from the nanoindentation test and listed in Table 2.2. Sample BS, which consists mainly
of austenite, shows a higher hardness, Young’s modulus, and ratio of reversible work to
total work than martensitic NiTi (specimen BH). The hardnesses of specimens BH and
BS were 2.5 and 4.4GPa, respectively. The amorphous NiTi thin ﬁlm has the highest
hardness at 7.9GPa, although its work recovery ratio is lower than that of specimen BS.

Wear loss vs load of specimens BH, BS, and amorphous NiTi thin ﬁlm are plotted
in Figure 2.19. It is not surprising that specimen BS has a better wear resistance than
specimen BH because specimen BS, has a higher hardness and a larger ratio of reversible
work to total work than that of specimen BH. The amorphous NiTi thin ﬁlm displayed
the best wear resistance due to its high hardness.

Figure 2.20 (a) and (b) show microfocus XRD collected outside the and inside the
wear track, respectively, of specimen BS. As in the indentation test, the martensite (002)
peak appears after the wear test, which indicates that martensite was stress-induced
during the test. Specimen BS, despite its superelasticity and high elastic recovery ratio,
does not provide better wear resistance than an amorphous thin ﬁlm. It is believed that
ploughing of materials during sliding wear deteriorates the recoverability of superelastic

NiTi.

49

2.5 CONCLUSIONS
Microscopic shape memory and superelastic effects exist under indentation

loading conditions (e. g., spherical and pyramidal indentations). The magnitude of
indentation recovery for martensitic and austenitic NiTi alloys has been studied. It can be
conclude that:

(1) Both the shape memory and superelastic recovery ratios are independent of depth
under Berkovich and Vickers indenters,

(2) The recovery ratio of spherical indents depends on the representative strain. It remains
constant when the representative strain is below the critical strain for maximum recovery.
The recovery ratio decreases with increasing representative strain when it exceeds the
critical strain for maximum recovery.

(3) At the representative strain of 0.08, the recovery ratios are lower for sharp indenters
than that for spherical indenters, which is attributed to the different strain. level under the
indenter. The maximum plastic strain under Berkovich indenter is much higher than that
under the spherical indenter.

(4) Instrumented indentation, especially instrumented spherical indentation, offers a new
method for studying shape memory and superelasticity at micrometer and nanometer
length scales.

(5) Indentation-induced and wear-induced martensite is formed during indentation and
wear test, respectively.
(6) Dry sliding wear resistance of martensitic, austenitic and amorphous NiTi are

Compared. The wear resistance of the austenitic NiTi is not as good as the amorphous

50

NiTi although the former has a h‘gher recovery ratio. To use SUperelastic
N177 as
a

tribological material, the surface ploughing needs to be prevented-

(7) The austenitic NiTi sample 38 used in this Study is not perfected for sun
erelaStic'

. a It

because the sample consrsts of b0th austemte and R-phase at the test tern y
eramIe. A

higher recoverability and better Wear 1' eSlStance would be expected in

. . austenitic NiTi
with martensite start temperature slightly higher than test temperature

51

 

 

CHAPTER 3

IMPROVE THE ADHESION AND WEAR RESISTANCE OF CHROMIUM

NITRIDE COATING 0N ALU MINUM SUBSTRATE USING A SUPEREL

INTERLAYER

ASTIC

3.1 INTRODUCTION

Various hard coatings have been deveIOped to protect soﬁ SUbstrates from I
wear OSS.
- and cod adhesion are crit' - ar
[61, 145] Both high hardness g rca1 In making good we

resistant coatings. One approach to increase the load-carryin g ability is to grow a thicke‘

coating so that the applied load will be distributed mostly in the hard h However, '1
p ase.

is usually the case that the hard coating and soft substrate exhibits (I, - mismatch of
arnatrc

’ f 'ent of thermal ex ansion. This .
Young s modulus and CDC ﬁCI P can lead to large (CSlduai
stresses, especially when high temperature processing is involved- The ,

Inter e
, . . . . . - f 310121 Shear
stresses increase wrth increasmg coating thickness and cause the fa, lure in ‘12
§

at the interface. Therefore, an interlayer, which has a 800d mechanical coiling 0,
match with both the hard coating and the substrate, is oﬁeﬂ ngn to ,- (715017178 1
”Drop
6
the

adhesion, [72, 146]

Hardness has traditionally been regarded as a primary Parameter controllin
8 wear

resistance_ However, recent studies suggested that the ratio of hardness to Inodulus H
. ’ E ,

also plays an important role in determining wear resistance. It was found that high E is

beneﬁci a] to wear resistance. [84] In addition, ﬁnite element modeling of the indentation

52

H , .
experiments shows that - 15 proportional to the work or depth I'ecoVe’IY ratio [106
' 1

Therefore, it will be desirable to make tribological coatings having high haI‘dn
683 and
depth recovery ratio.
This chapter focuses on the novel tribOIOglcal application Of superelastic N' ,
t' 1T1 ﬁlfns
' terials between hard 003 mg and soﬂ substrates. The p _
as mterlayer ma . “rpose of this Study
' 1 ar resistant material by taki ng advantage of .
Is to develop a nove we the hlgh hardness of
the surface coating and high depth recovery ratio 0f the superelastic NiTi interlayer.
. - - - ' ar test were cond
Indentation, scratch, and pin on disk we 11°th to Study the hardness,
adhesion, and wear behaviors of this novel layered composite material. TribOlOgical
- ' interla er materials and differ . was
behavmr of samples With other y Cut coating 1:111 ckﬂess
u erelastic NiTi interla er ' 10"
compared. It was found that the S P y caI1 dramatieany \mp

adhesion and wear resistance of hard coatings on soﬁ substrates.

3.2 SAMPLE PREPARATION AND EXPERIMENTAL METHODS

Austenitic NiTi, martensitic NiTi and pure Cr ﬁlms were used as (1)

materials between a CrN hard coating and an aluminum substrate. Desclib [bier/dyer
ti
. O
SPeCimens are shown in Table 3.1. Substrate material was 6061—T6 ah. i oftbe
12
plate

20mmX20mmx3mm in size. The aluminum plate was p°1i5h6d through 0'25um diam
diamond paste and subsequently ultrasonically cleaned in acetone and methanol_ N::
thin ﬁlms were deposited on both aluminum and silicon (100) substrate by DC magnetron
sputtering, the latter for use in DSC and XRD experiments. A schematic Structure Of the
DC magtletron sputtering equipment for NiTi thin ﬁlm deposition is Show}1 in Figure 3.1.

The base pressure achieved was better than 2.7x10'5 Pa. An austenitic NiTi thin ﬁlm was

53

d posited from NinTi target; While martenSitic NiTi thin ﬁlm was depQSited from
c .

N' Ti target The target was lore-sputtered for 30 minutes before sputter deI’OSition t
148 - 0

btain stable plasma Working pressure was set at 0.33Pa and working distanCe betwe
o - En

the target and substrate was 64111111 SUbStrate temperature was controlled by a built -
.11.)

0f 9 . ° ‘ used for
substrate heater in the chamber. Argon 9 99/0 punty was the generation of

Plasma. NiTi ﬁlm was (161)095th at a substrate temperature 0f 300°C fOr 60 minutes at a
deposition rate of 1.1mn/s. The ﬁlms were annealed at 550°C for 50 minutes right aﬁer
deposition to crystallize the ﬁlms. ThickneSS 0f the ﬁlm was determined by measuring
the step of the masked area using a WYKO surface proﬁlometer, The NiTi c0ated 6061'

T6 aluminum was then transferred to a TEER unbalanced magnetron sputtering sys‘em,

ting
Sﬁconds. A C‘“ 003

was made by depositing from two pure chromium targets of 99.99

The specimens were sputter-cleaned in argon atmosphere for 60

. e“.
. _ (“Hog
9%) punty 111 3

containing argon environment. The base pressure 0f the system Was 8x 10.4 Y3 and the
Pressure during the deposition was 0.13Pa. The working gas was a Proprietary .
”Ware of

k»
. - - S
CrN ﬁlms were deposited at 4 Amps With 150V bras applied to the substrate. 465667”.

99.99% pure argon and 99.99% pure nitrogen- The nitrogen gas ﬂow rate

Composition of the NiTi ﬁlm was measured by Wet Chemical

. . . ' - aly .

Speciﬁcally, samples were dissolved wrth mtnc and hydroﬂuoric acrd and "1e 81.9,
' - ' al emission microsco

were made by Inductively coupled plasma OPP“ py (ICP/AES)_

Characteristic phase transformation temperatures of NITI thin ﬁlm were determined “Sing

a TA In went DSC 2929 Modulated differential seaming calorimeter (DSC). The
s

temper-at e ranged from -50°C to 200°C under a controlled heating/cgoling rate of
hr

54

 

 

 

58

“'6

the

8pc
me

WET

5K/min X-ray diffraction (XRD) measurements were carried 01.1 t on a Siemens D500

d'fﬁactorneter using Cu-KO. radiation at 40 kV V01tage and 30mA C urren t.
1

1‘ 3&0) Of
easured using the Nano XP instrument from MTS with a Berkovich d'
were In

Indentation properties (Gaga hardness, YOUng’s modulus and the recove

1am0nd
indenter and a spherical diamond indenter With nominal radius of 10mm. The applied

indentation loads ranged from SmN t0 ZOOmN to test the 11160113111021] properties at Various

indentation depths.
Adhesion strength 0f the coatings was evaluated by scratCh tests using a CSEM

micro-scratch tester. A progressive load from 0 to 6N was applied to scratch all the
samples The spherical scratch indenter had a tip radius of 21 3‘411111. The scratch scars

. ' “ate
were observed using a Hitachi S4000 scanning electron microsQQpe (SEM) to eva

the adhesion.
pin—on-disk dry sliding wear tests were carried OUt 01) an Implamt SCiCIlCC

tribometer (Model ISO-200), using a tungsten carbide ball of 3. l 7 3mm in di at d
I] 61' (m er

an unlubricated condition. The applied load was 1N and the sliding Speed w

' 0. .
tests varied between 3000 and 101,000 cycles, depending on the vvea,~ 0801/81!)
ate

specimens. The friction coefﬁcient was recorded during the wear test. Tb

. rate
measured with a Wyko optical surface proﬁlorneter. Indentation, Scratch, and w was
tests

were all conducted at room temperature (25°C)-

55

 

 

pn

De

3.3 RESULTS AND DISCUSSION

3. 3.1 Structure Characterization

The NiTi ﬁlm dePOSited from the Ni49-3Ti502 target was found to be Ni I‘iC Ch
With a
composition near Ni51 3Ti43.2 (Specimen $1) The ﬁlm deposited from the N
target
(spec‘men 321.1: 1’
s

apparent that about 1. 5~ 2 at. % of titanlum was lost during the Sputteri

was found to be slightly Ti-rich With a composition near Ni 49.51150~ 5

ng process

The as deposited NiTi thin ﬁlm Was amorphous and it Was subSeunnﬂy arm 1 d
ea c

to CD'staIIize it. From DSC measurements the rhombohedral “R‘Phase” ,martensite, and

austenite start and ﬁnish temperatures (Rs: Rﬁ Ms, Alf: As and A; respectively) were

determined. DSC curves of specimen SI and 82 are shown in Figure 3 2(a) and (b),
respectively. The composition and phase transformation temperat e of the two wpes of

NiTi films are listed in Table 3.2. For specimen Sl , A: is 1°C C in the

O
and A f is 15
heating cycle; R. is 8°C and Rf lS —4°C in the cooling cycle Therefore specimen S]
should be austenitic at room temperature Specimen 32 has a much higher tr
"sﬁnnation
temperature than that of specimen 81. The martensite ﬁnish temperatureo ofS
indicates that it should be martensitic at room temperature. 6010161] S2
XRD of specimen SI and 32, shown in Figure 33, Conﬁr,228

predictions. Specimen 81 shows a (110) diffraction peak from the aUStenite Db above

132 strueture. The (122) diffraction peak of Ni4Ti3 also appears, which Was

precipitation process during annealing The (020) (111) (002) and (021) diffracuon
peaks frOm NiTi martensite phase which has a monoclinic structure, ,appear 1n specimen

$2.

56

CrN coating was dePOSited on the top of SPeCimen SI, 82 , the Cr int

erlayor and
base aluminum substrate, in 33011 Case after Sputter cleaning for 60 seconds

‘ A" XRD
pattern of the specimen with 59111 thiCk CrN Coating on aluminum SUbStrate (

SpeClmen

CrNS-Al) is shown in Figure 3 '4- The Weak peaks at 29:37.1°, 43.50 and 75 5°
. at

indexed as (111), (200) and (311) diffraction OfCI‘N, respectively.

3.3.2 Mechanical Properties

3. 3. 2.1 Indentation Test

Indentation properties of the coatings and substrate, such as hardness Young’s

modulus and recovery ratio, were obtained by instrumented ~

- t,
llIdentation expenme“

) . . - m
Hardness, H, and reduced Young S modulus, E , were detenmn d from the macaw“

We. 90

load and initial unloading slope of the unloading curve using Olivﬁtxpharf 5 me

The depth recovery ratio, 17h, is deﬁned as the ratio of

QCover-able indentation
depth to indenter displacement at maximum load:

= hmax - hf
77h hm ’
where hm, is the indenter displacement at maximum load While 12, is (3'1)
6
I' .
indentation depth after unloading. Hardness, H/E* and 77h represent the esldual
engtb an

. d

elasticity of the matenals.

Load-displacement curves of Berkovich indentation tests on an 6061

‘T6
aluminum substrate, 4 pm thick auetenitic NiTi ﬁlm on a Si substrate (Specimen 81), 4

Hm thick martensitec NiTi ﬁlm on a Si substrate (specimen 32), 4 pm thick Cr on a Si

substrate and 5pm thick CrN coating on a 6061-T6 aluminum substratQ are shown in

57

 

Figure 3.5(a). The indentation depths were less than 10 Percent c) fthe film thickn
. CSS to

minimize the influence of substr ates on coating prOperty measurements. From th I
e Dada

displacement curve of a BerkoVi Ch indentation t€St both hardness and Young ’8 m

, OdUIuS

can be calculated using Oliver/Phil” 5 method, [91] as discussed in seen-0n 1
.3.1. 1

Mechanical properties obtained from the nanoindentation test are listed in Tab]
5 3.

3- The

larger
than those of the aluminum substrate (0946? a, 77.6GPa). There ex't 1
18 S a arge

hardness and Young’s modulus of the CF N coating (23GPa, 257Gpa) are m h
uc

mechanical mismatch between the CfN hard coating and aluminmn substrate H ver
. 0W6 7

the Young’s modulus of specimen SI (9501’?!) and specimen 82 (89 3GPa) are not very
different from that of the aluminum SUbStl'ate (77.6GP a).

For the interlayer and substrate materials, the hardness day of

. or
creases in the

Cr, 81, 82 and Al, while the depth recovery ratio decreases in “1% gonna“ Sl,

order of SP

Cr, specimen 82, and aluminum. The depth recovery ratio Of supe l tic “.1.“ ﬁlm
re as

(specimen 81) is higher than that of martensitic NiTi ﬁlm (Special S
en

2) w ' '
consistent with the observation of bulk NiTi alloys in section 2. 1 - 4. Ff 2 IIICII IS
gut e

that there exists an approximately linear relationship between the depth Fe ‘50) SIIOWS
Q

' H - 6’3»
77;, , and the ratio of hardness to reduced modulus, —E—. Clearly, Figure 3'5(b r302),
Sbo‘vs
, th
the depth recovery ratio depends on both hardness and Young s modqus 01“ at
e teSt
ed

materials, A material with low hardness may have high depth recovery ratio if it h
as a

small Young’s modulus. As is observed that the austenitic ﬁlm (specimen St

Hz4-7GPa, E=95GPa) has a larger depth recovery ratio than that Qf the Cr mm

( H=6-‘7(3pa, E=318.4GPa) although the former has a lower hardnﬁss, A Similar

58

- H
. . recov tlo an _
relationship between the depth ery fa d E' has been I 6190116" by Cheng (1

Cheng based on the ﬁnite elemfﬂ’lt Calculation. [147]

For all the CrN coated composite coatings, the composite hardnesS and
depth

recovery ratio were also calculated from the indentation load-displac ement curves (1
an the

results are shown in Figure 3.6. It was found that the composite hardness and w k
01'

recovery ratio are strongly dependent on mterlay er matenals, coating thiCkness and

indentation depth. The Sum CrN coated aluminum (specimen CrN5- A1) shows much

higher composite hardness and, accordingly, better 103d“can’)’ing ability than the 1pm

CrN coated aluminum (specimen Cer-Al)- The Specimen with austenite NiTi interlayer

(specimen CrN-Sl—Al) has a larger work recovery ratio the the specimen with

‘ ' ’ —Cr-
martensitic NiTi interlayer (spec1mens CrN-SZ—Al) and Cr Interlayer (specimee CrN

Al), although specimen CrN-Cr-Al has larger composite hardness-

' ' N-S 1 -Al arises ii»
The large recovery ratio of specrmen Cr 01)] the su . .
Perelastlc NiTi

interlayer. A large recovery ratio of sharp and spherical indents On austenjt ‘
1 O
and indentation-induced martensite transformation were noted in Sect,- NIT; alloy
Q

2.3

reversible strain can be up to as large as several percent in unraxral tenSiIQ . The

b test-
induced phase transformation under indenter has also been 0 served using 81,688‘

Te
. . . . M
suPeI‘ 81 asticity occurs under the indentatlon loading conditlon. [29] and

3.3.2.2 Adhesion Test

The interfacial adhesion strength of the CrN coated specimens was compared
qualitati Vely by observing the scratches using SEM imaging. SEM imaggS of the end of

the Scratches are shown in Figure 3.7. Flakes of delaminated CrN coating at the scratch

59

end are observed on 513601.an Cer-Al, CfNS'Al and CTN-SZ-Al. 1')
e coating

fth

Cracks caused by bending are also observed inside the scratCh Scar on Sp e Cim

delamination occurs as a result 0f the compressive stress ﬁeld ahead 0 ,
e Indenter.

en CrN.Sz_

A1. As shown in Figure 3.7 (a) and (b), increasing the thickness of the CrN hard .
coating

on Improvmg interfacial adhesion. Nevertheless

has little beneﬁcial effect
no

delamination occurs at the end of the scratches on specimens With Cr interlayer and
superelastic NiTi interlayer, as shown in Figure 3. 7( d) and (e). Specimens with austenitic
Ni Ti and Cr interlayerS, i.e., specimens CrN-SI-AI and CrN-Cr—Al, Show better adhesion
despite the fact that they have lower composite hardness than that of CrNS- A1,
Specimen with austenitic interlayer (CrN-S 1 -Al) shows much better adheSion
than specimen with martensitic NiTi interlayer (CrN—SZ-Al) does, although there is little

chemistry difference between the interlayer materials. The differen t inter fac ial adhesion

strength must be due to the different mechanical prOpem’eS of the austenitic and

martensiticNiTi. AS is known that martensitic NiTi is highly Plastic and a reg ‘d 1
1 ”3 strai
. . . . .n
is left when the applied stress exceeds llS elastic llmll of less than Q

Neverthe\ess, the austenitic NiTi is superelastic and its deformation is rép

81311)] e. NO

residual deformation is left when the load is removed, and the reversible Strain
C
e as

large as Several percent. The improved adhesion may be attributed to the large ev er ‘1)
31 1e

strain 0 f the superelastic NiTi.

The stress-strain curve of the superelastic NiTi alloy bears some Similan‘ties to
that Of elastomeric polymer adhesiveS, as shown in Figure 3-8- l5, 148] A detailed
compari son of the mechanical properties of superelastic NiTi and a typical elastomeric

Downer (e.g., polyisomene) is listed in Table 3.4. Obviously. both of them have large

60

 

 

elastic strain without permanent deformation, and a hysteresis associated

with the
loading-unloading cycle. [5, 1 48] However, the elastic modulus and Strength f
0 the
superelastic NiTi alloy are several orders 0f magnitude greater than that of the l
po .Vmel‘ic

- - ' ' tes that the superelastic NiTi '
adheswes, which 1ndlca material may act as a hi
811 Strength

metallic adhesive for bonding ceramic coatings to ductile substrates, This study
demonstrates that the superelastic NiTi indeed functions as good bonding materi a1.
Furthermore, it is speculated that Other materials with large reversible strain can
potentially be good bonding material 8.

A chromium interlayer can provide 800d adhesion between CrN and aluminum
substrate as well. However, as will bee seen in the next section, the wear resistance of the

composite coating with Cr interlayer is not as good as the Composite coating “nth

superelastic NiTi interlayer.

3.3.2.3 Dry Sliding Wear test

The durability, friction coefﬁcient and wear rate of the Suite of We
were measured by pin-on-disk wear tests. Figures 3.9 (a) and (b) shows U;

c
I . ange
friction coefﬁcient during pin-on—dlsk test. Flgures 39(3) Sh0W8 that speCiIDen C Of

Al and Cer-Al fail aﬁer 1100 and 3000 cycles, respectively, which is indicated by a
sudden increase in the friction coefﬁcient. The worn surface was observed using WYKO
surface proﬁlometel’ and SEM microscopy. It was found that thﬁ CTN hard Coating has
been Cut through, exposing aluminum substrate. The poor adhesion of the single CrN

00‘“ng with aluminum substrate and martensitic NiTi interlayer leads to premature

failure of the coating- The Sum CrN coated aluminum (SPCCimen CTNS‘AI) shows much

6l

 

longer lifetime (the test was halted before failure) than the 1pm CrN COated alumi
(specimen Cer-AD' BY increaSing the thickness of the CrN hard coating, the dUrab:1m
can be increased dramatically due to the increased hardness and load~canying abn-tlty
Durability of the coating can also be improved using Cr or superelastic interlayer 1 y.
shown in Figure 3.9(b). , as
Interestingly, the composite coating with SUperelastic interlaYer (Specimen CrN-
S l-Al) shows a lower friction coefﬁ Cient than that With the Cr interlayer (Specimen CrN.
Cr—Al) in both sliding wear test (Figure 3.9) and scratch test (Figure 3.10), although they
have the same surface chemistry and specimen CTN-Cr-Al has a higher hardness. The

friction coefficient, ,u, is deﬁned as the ratio or the tangential force F to the normall
7 t ,

force, 15;:
,, z a
F, (32)
u no elastic recovery occurs inside the wear track formed by the Sliding ind
Figure 3.\\\a), the tangential force should balance with two types of forces: enter,
force, Fa , developed at the contact area between the two Contac t 511113068 adbeSI-on
defonnation force, F d , needed to plough into the material, i.e.,[80, 82] ’ and a
E = F, + Fd (3.3)
The adhesion force is given by
F = AT (34)

where A is the true contact area between the two surfaces and r is the shear stress of the
junction formed at the COntact area. In this study, the junction shear stress should be the

‘ ' ' ses with
same Slnce they have the same Surface coating. The contact area increa

62

 

 

decreasing hardness. Therefore, specimen with superelastic interlayer (CrN 3
~ 1

-Al)
should have a largel’ Contact area and adhesion force than Specimen with Cr int 1
er ayer

(CrN-Sl- A1) since the former- has a lower hardness. For the conﬁguration shown '
m
FigUre 3.11(a), the deformation force, Fd , was found to be dependent on the true contact

true contact area, the m '
area. [149] The larger the ore material needs to be PIOUgh ed into,
' e- A low h - .
and the larger the deformation forc afdness wnl lead to high deformation force.
Therefore, materials with low hardness should Show larger tangential force and friction
coefﬁcient if elastic recovery effect is DOt considered, This is contradictory to what was
observed in this study.
If the elastic recovery inside the wear track is taken into account Figure 3 -1100,
. ' t ' . in the
the tangential force should balance With an ex ra DUShlng force, Fp, which acts
same direction as the tmgential force,

E=e+e-c as)

The change of the tangential force due to the elastic recovery will depend o

11 .
. the TC’latIVe
contribution from the pushing force and adhesmn force. The friction 00%

. . . 10161” W 11
decrease if the contribution from pushing force 13 dominant. The extent 0 11
. e elasti C
recovery is directly proportional to the depth recovery ratio measured by indentat
10

tests.

In addition, materials in front of the indenter either pile up (Figure 3.12(a)) or sink
in (Figure 112(1)» when the indenter is forced into materials. A larger deformation fOrce
is required when piling-up occurs, while a smaller deformation force is needed when
sinking‘ in happens. Finite element simulation of the indentation experiments shows that,
H
E

' ' und the
for highly elastic material (high __ or large depth recovery ratio), material aro

I.

63

 

 

indenter tends to sink—in. However, for highly plastic material (low 1

E‘ 01‘ 8

recovery ratio), material arou nd the indenter tends to pileup. [97] Th
erefore it '
2 IS

expected that, compared ‘0 Spedme“ With supe‘e‘aS‘ic interlayer (CrN~SI A1)
- ' , Specimen
with Cr interlayer (CTN‘Cr'Al) tends to Pile up since the latter has a sm 11
a or depth
test, WYKO

surface proﬁlometer was used to measm'e the proﬁles of the scratch
68 on specimen CrN-

recovery ratiO- T0 StUdy the 8}“th Of pilingup/Sinki11g-in during sliding

S 1 -Al and CrN-Cr-Al, as shown in Figure 3'13- A5 eJ‘ercted, less material piles up along
the edge and at the end of the scratch in specimen CrN.31 -A1 than that in specimen CrN-
Cr—AI.

Therefore, friction coefﬁcient is a function of hardness, elastic recovery, and
material ijjng-up/sinl<ing-in. However, there exists no them.y linking thC friction
coefﬁcient with these parameters. A better understanding of the ﬁiction Coefﬁcient
requires extensiV e runneric modeling of the sliding process. This Study demonstrates

that,

friction coefficient of tribological coatings can be TCdUCCd "Sing an interla e ‘
. ’ With high
H/E (or \arge depth recovery ratio).

The wear loss of all the composite coatings was Shown in Pigta-

e 3.14

specimen Cer-Al and CrN-SZ-Al, the wear loss was measured after failur . For
e 01‘ the

coating- For specimen CrN-Sl—Al, CrN-Cr-Al, and CrNS-Al, the wear loss was

meaSured
when the wear tracks were about 0.5 micrometer deep. Note that the aluminum SUbstrateS
0f Specimen Cer-Al and CrN-SZ—Al were exposed and the wear “SS d°es “°t truly
represent the abrasive loss of the CrN coating itself. Specimen CrN-Sl-Al shows a lower

wear 1035, 540 an/N, than that of CrN-Cr-A], 2200 nmz/N. The superelastic NiTi

interlayer can effectively improve the wear resistance of the composite coating. Spec1men

64

 

CrNS-Al has the lowest wear rate of 340 nmz/N. The wear resistance of CTNS
‘Al is only

slightly better than that of CrN-Sl-Al at the applied load of 1N despite th
e fact that

specimen CrNS-Al has a much higher hardness. At higher teSting load th
’ e Composite

. - ' ' terl ayer (specimen C N-
coatrng wrth superelastic 1“ r Sl-Al) may have b
_ - Btter perfon‘nance
than that of CrNS-Al due to its Improved adhesion.
It is instructive to note that Specimen CrN~S1- - ,
A1 15 more wear‘fesrstant than
specimen CrN-Cr-Al although the former has a loner hardness This Observat‘ .

' 1011 IS
contradiCtOFY t0 the ClaSSical “Chad’s law for abrasive wear, [80] which states that the
wear loss is inversely proportional to the hardness. Leyland and Matthews [84] suggested
that, in addition to hardness, H/E may play an important role in determining the Wﬁat
resistance. It has been found that H/E is proportional to the depth recovery ratio. [106] A
large fraction of the deformation under indenter is elastic for materials with high H/E (or

large depth recovery fatiO), WhiCh Win mt contribute to the Weat loss. This is the ﬁrst

unambiguous experiment demonstrating the effect of H/E (or depth recove
17 ratio)
01)

wear 1038 Which rules out the surface chemistry effect since the Sufface coat ‘
’ I

. g w
the sme, This study demonstrates that both high hardness and large ”/0 aSkept

. - . (or d
TCCOVery ratiO) are desirable in making wear resrstant coatings. ept};

3.4 CO mcLUSlONS
It was found that the composite hardness and elastic recovery ratio are Strongly

dependent on coating thickness and indentation depth. The hardness 0f composites
increase:s with increasing hard coating thickness. However, increasing hard coating

thiCkness has little beneﬁcial effect on interfacial adhesion strength. By using prOper

65

 

 

_ lastic NiTi the interfacial adh ~
. 1 such as Cr or supere , es
interlayer materla , 0n can be

’ roved As compared to CI’ interlayer, the superelastic NiTi interlayer Can e
imp -

cc 0

coating. The ratio of
hardness to Young’s modulus or depth recovery ratio, in addition to hardness, needs to be

taken into account in the design of tribological coatings.

66

 

CHAPTER 4

lNSTRUMENTED SPHERICAL INDENTATION EXPERIMENTS

4.1 INTRODUCTION
Since the inception by Brinell about 1 00 hundred years ago Spherical i d
’ n entation

experiments have become one of the standard methods for measuring h f
ardness 0

materials. [92, 118, 119] Recent years have seen an increasing interest in instrumented
spherical indentation techniques for measuring the IneChanical PIOperties of materials
across multiple length scales. BY analyzing the load-displacmnent curves, several

researchers have suggested methods 0f obtaining hardness, elasﬁc modulus guess-Strain

' ' ° 1 stresses from instrument , . tion
relationships, and resmua ed Sph e ncal mdenta

proposed methods depend on the estimation of the contact area under th 1,
e 5P en'cal

indenter, which is difﬁcult, especially when the surface around the in den
°’ cX/zib'
Its

“piling-up,” \97, 107, 152]

In this work, by extending a recently developed scaling approach [86
, 106] to

Spherical indentation in elastic-plastic solids with work-hardening, two Drew
Ously

unknown relationships between hardness, reduced modulus, indentation depth, in dearer

radius, and work of indentation were revealed. Together with a well-known relationship
[91, 100] between reduced modulus, initial unloading slepe, and contact area, an energy-

based rtlethod W35 Proposed to determine the contact area, reduced modulus, and

hardness of materials in instrumented spherical indentation experiments. The preposed

67

 

 

method also provides a new way 0f calibrating the effective radius of imperfe
Qt Spherical

indenters. The validity 0f the energy-based method is tested by instru e t
I“ n ed 8 .
Phencal

indentation experiments on copper, aluminum, tungsten, and fused Sili
Ca' These 1]
_ - . . . ewl
found relationships also prOVlde ﬁeSh ms‘ghts ““0 Contact Problems th t y
a are ubi .
qurtous

in many science and engmeenng areas’ “1““de friction wear
3 ,

as W8“ as maCI‘O- and

nano-scale mechanical formm g processes,

Tabor [92] showed that, for some metals hardn e .
, ss IS about 2 8 times rh
' 6 true

stress, for a strain equal to the representative strain associated with Spherical indentation.
Thereafter, ratio 0f hardness to true stress ranging {Tom 1.1 to 2.8, when indentation
process evolves from elastic to fuIIY-Plastic, has been used to derive true stress-strain
relationships using spherical indentation eXperiments. [135-1 3 9] In this studYa ﬁnite
element calculation was used to study the constraint factors for Spherical indentation on

elastic-plastic materials at various depths.

4.2 DIMENSIONAL ANALYSIS

A three dimensional, rigid, spherical indenter of radius R ind entin

11:0 e .
plastic materials with strain-hardening is consndered in this study. The Stress 1&8th
s ai" (o: )
CUTVCS of the solid under uniaxial tension are taken as: [153]
0::EE ,forsSY/E
(4.1)

0' :: K8" , for sZY/E
Where E is the Young’s modulus, Y is the initial yield stress, K iS the strength coefﬁcient,

and n is the strain-hardening exponent. To ensure continuity of stress and strain at the

initial Yield stress, we note K = Y( E / y)" , Consequently, either the set of (E, Y, K) or set

68

of (E, Y, n) is sufﬁcient to describe the stress- strain relationship. W 6 use the Sc, f/[ y
0 ; a

n) in the latter analysis. The friction COEl‘ﬁCient at the contact surface between the

indenter and the solid is assumed to be zero.

Sections 4.2.1 to 4-2-3 focus on the dimensional analysis of Spherical indentation
in elaStiC'Plastic materials with work hardening. The purpose of the dimensional anaIYSiS
is to ﬁnd the essential relationships between dimensionless parameters. For those who are

not familiar with the dimensional analYSis, please see the appendix “Fundamentals 0f

Dimensional Analysis and I] Theorem” for details.

4-2-1 Dimensional Analysis of Loading

Both the applied load and indenter displacement were recorded during a loading

and unloading cycle in an instrumented indentation test- Elastic recovery occurs when the

load is 1,ernoved. A representative load-displacement curve and associated depth and

work recovery are shown in Figure 4.1. In the spherical indentation 1'
Process, or an

isotrOpic elastic-P138510 solid fOlIOWing a pOWer-law strain-harde .
mag Pu

dependent variables, force (F), and contact depth (he), must be ﬁ‘nctI-On 16’, the two
in depe n dent governing parameters. The functions are given by; S of all of the
F=f,_(E,v,Y,n,h,R)
hr = g(E,v,Y,n,h,R). (4.2)
where V is the Poisson’s ratio and h is the indentation depth. Among the (4.3)

. six goVernin
parameters’ E, v, Y, n, I; and R, E and R have independent dimensions D‘ g
. 1m

ensions of the
remaining goveming and governed Parameters are given by:

69

[Y] -—= [E]
[vl= [E]°[R]°
M = [E 10 [R10 (4.4)
lhl = [R]
[F] = [EllRlz
th= [R]
By applying the II theorem in dimensional analysis [ 1 54], equation 4.2 and 4.3 become:

Y h 4.5
F: ERZ naif’v’n’fj = ERZHa[H1,v,n,%) ( )

Y h ' 4.6
hr ZRHﬂ[E,V,n,72-): R Hﬂ(nl,v,n’ 1;?) ( )

where U1 5 Y/E is a dimensionless function. The tOtal work during loading is given by:

hﬁ‘m‘ zhnnx h 3

W, 2 deh =ER llla 1,v,n,\ dh =ER 17 I,

0 R T HID V ,2 max
0 9 ’.

1?

where H, is a dimensionless function , (47)
Such
Y i _ i that
R% {(E’V’n’RJ—H“[Y/E’V’n’R)'

 

4.2, 2 Dimensional Analysis Of Unloading

Unloading occurs after the Indenter reaches the maximum indentation dept/1

Therefore, duﬁng unloading, the force (Pu) and residual indentation depth (if) are also

dependent on hmax, and they are given by:

Fa ‘ f"(E,V,Y,n,h,R,hmax) (4-8)

hf 5 gu (E, V,Y,n, R,hmax) (4.9)

BY applying the II theorem in dimenSiOHaI analysis [ 1 54], equation 4.8 and 4.9 become:

F“ =ERZI'17[HI,V’ ”,1 5.1 (4.10)
A” R
hf =RHI(H,,v,n,@) (4.11)
. R

The rev <31.3'1ble work during unloading is given by:

hm hm
Wu = [Fudh 2": ERZ IH,( “mini 1’
hf hf R

’7 (”1

 

: ERB “#[HL V, n, hmax)
R

 

(4.12)
where ﬂy is a dimensionless function
Such
Y h h hmax that
a —-' ’_ = Y/E9 a- a '
REFIP(E’V’" R] n7[ V," R R J

4 2 3 Scaling Relationships from Dimensional Analysis

The ratio of irreversible work to the total work for a Complete 10
ading-

uﬂlOading
cycle is written as:

71

 

”max '

 

hrnax hmax
ER2 [11(11! ’ V’n’GJ * ERZ np[HL V,n, y,___

R a
=1L/171,V,/67$E‘]

(4.13)

 

 

W, — ERZI—It n‘,v,n,£"3}_)
R

- . . ' f
The ratio of residual depth to total depth can be obtained by dwidmg both SldCS 0

equation (4.11) by hmax,

_ __,—— V "lax .— H uniax] (4.14)

km

At the maximum indentation load, hardness, H, IS given by:

F Fm FmX (4.15)
H: Ac =71'612_7£‘2Rh _/22
depth 3‘ “l6

' ' I e a ontact
where Ac is the contact area, a IS the contact radius- The fore nd c

maximum indentation depth, h=hmm, are glven by;

 

 

Y h
—_ 2 __ ﬂux _ 2 b
me —- ER I—IaEE)V,n, R )— ER Ha[nlavyn, Ex) (4.16)

 

 

 

Y hmax 1,
h‘\h=hmax = Rnp(-E‘,V,n, R 3: RHﬁO—L ,V,n, %)
(4.17)
By combining equation (4.15) (4.16) and (4.17), the hardness can be express
as;
hmax
15R2 [1"[HI’V’H’T] E
/,/——/-~/—f h =-Ho[n,,v,,, hm
H 7’ hm 2 2 n V ’1 max 7: ’\ (4
¢{2R2np ntavon,T -R Hp l’ ’ ’ R R '18)
C onsequentIY9
"‘ 2 hmax
ﬂzﬂswno U‘,V,n9 )znw(nl’v n hmax
E. E n’ R ’ ’ T (4.19)

72

 

According to equation (4-13) (4.14) and (4.19), it is evident that ’ \

are

[If ’2..—

”tax

and E7 are all dependent on the dlmenSionless parameters, Y/E, V, n, and ﬁmr/A’. It is

therefore interesting to StUdY the relationship between the dimensionless parameter

VIC-”7“ [If

W ’2’“,

’ max

and "E- B)’ applying the dimensional analysis to the spherical

indentation experiments, the number 0f independent variables has been reduced from Six

(i.e., E, V, Y, 71,}! and R ) to four (Y/E’ V: II, and hmmt/R).

4-3 FINITE ELEMENT ANALYSIS

Since there is no analytical solution for Sp her-i cal indentation in elasllc‘i)‘asnc

materials, a ﬁnite element analysis was used to Study the Problem. In this work, an

extensive ﬁnite element computation was carried out

“Sing ABAQUS [155] to explore
. h W, _ W.
the rel ationshlp between —h 'f ’ W , and “Eli“. . The radius

l

 

01‘ th - - .
e ng'd lIldenter was
lum. Young’s modulus was ZOOGPa and Poisson’s ratio was 0 2 Th
. . e Sl‘l—a .
1

CXponeIlt, n , was chosen to be 0.1, 0.3, and 05, respectively, which rcpt ~ ardenjng
Gse
1]
from heavily worked to fully annealed state. For each Strain‘hardenin ts materiajs
. eXp
differeﬂt Y/E values were used, namely, 0.002, 0005, 0.01, 0025 omen
. ’ and 0.1

resent materials from soﬁ metals to hard ceramics, For each Com . . which
rep Ination O

f n
Y / E computations were carried out for several values of /, n allow‘ a11d
3 n x 3
mg the evaluatio
n

. hum
of the scaling ﬁmctions for a range 0f \x— values from 0.05 to 0.5.

73

 

The rateindependent incremental theo ' - -
’ ry of plast1c1ty 1n ABAQUS
was used in

the ﬁnite element 031C1113ti°ns° In p articular, the plasticity theory uses the V0,, Mises’
yield surface model with associated plastic flow rule. Because of the axisymmetry ofthe
problem, a tvVo-dirnensional mesh was used, as shown in Figures 4,2(a) and (b). Note that
Figure 42(1)) shows the magniﬁed region 0f the top_1cﬁ corner in Figure 4.2(a), which
will be in contact with the indentef- The Smallest element in the contact region is 2531171'
As for the boundary Conditions, the baton? edge Was ﬁxed in directions 1 and 2, and the
axis or symmetry (leﬁ edge in Figure 4.2(a)) was ﬁxed in direction 1. The true contaCt
area, At, along the curved contact surface was calcu lated by the AB AQUS program“ The
contact depth, he, was calculated using equation:

11, = A, /27rR (410)

Loach-lsptacernent curves were obtamed from the ﬁnite element calculationS- Residual

in dentatioﬂ depth, hp and maximum load, Fm“ , were obtained ﬁ‘o the load
In -

displacement curves for each given hm. The total work, W’al‘ld
1' eVersrb 1
e work, W,

are obtained by integrating the loading and unloading curves, respe

4.3.1 Piling—up/Sinking-in in Spherical Indentation

During the spherical indentation process, materials around th
e inde
the].

gure 4.3) 01‘ Sink- in (Figure 2. 9). In this Study, the ratio of co rmaJ'pjle-

maximum indentation depth, h Him, , is used to eValuate the e)“ ept tth
em of
Pilin

up (F1

h cfhmax>1) and sinking-in (h/hmmd). The calculated VaIUes of 12 / g-up
c h

"Rx for variOUS
materials at different indentation depths are shown in Figure 4 4 (a) (e) I
1 18 clear that
in

general, I), //1 depends on hmax / R, ,n, and Y/E for Spherica] In den
tatlon 1n elastic

74

‘

¢

 

plastic solids with strain-hardening. For materials with small values of 175 and” or

indentation With large hmM/R, piling—up (ho/hmax>1) tends to occur, While waking-in
(ho/hmax<1) teTlds to occur for materials With large Y / E and n or at small indentation
depth. These observations can be underStood by the fact that sinking-in always occurs for
Hertzian elastic contacts while piling’up occurs for rigid-plastic contacts. [92] Thus, the

ratio of “elastic component” to “Plasnc Component” of deformation decreases Wlih
. . I: . _ . - -
increasmg ‘23- and decreasmg values of Y/E and n for spherical indentation 1n elasuc

plastic Solids with work-hardening.

. . - - _ . - ° endent
It is Instructive to note that the extent of p111 ng-Up and sinking-m is rude?

of dept}l for conical and pyramidal indentation in the same class of solids. This ep

. . ° with
1ndependence is the consequence of the absence of a length parameter associated
ideany sharp conical and pyramidal indenters. It is also instructive to compare the present

numerical results with some early experimental Work by Norbury and Samuel S [122] Who

believed that piling-up and sinking-iii depended on work-hardenir1g e
1: Uncut only Th '
- 611'

on was based primarily on indentation in metals (i.e., 3111a

observ ati 11 Values

n values from 0.0 to 0.5) where the effect of n is dominant, In gen 1’ / E With
Bra],

. . 0
degree of piling-up and sinking-1n depends on Y/ E , n , and km N? Wh. Wet/er, the

dete ination of contact area under load difﬁcult using convenn'OnaI m es the
[m e

f “owing analysis, we show that it is possible to circumvent this dimCUIty the
0 of

eStima .

. . I t

act area usmg an energy-based method derived ﬁ'om a Scaling relatj mg
0nshi

cont

H/E' and (WFWLWWV

P between

75

 

 

 

4.3.2 Relationship between hf/hmax and (Wt-WJ/W.
The representative load-diSplacement curves, obtained by finite element
calculations, of a material with Y / E = 0-025 , v = 0.2 , and n = 0.5 at various depths are

ShOWn in Figure 4.5. By analyzing the load-displacement curves of all materials

. ' W _ h . . W11 in
simulated, We observed a relationShlp betWeen (WWII and TL, which 15 sho

X
I ma

 

Figure 46. This relationship can, from a least-square ﬁt, be written as
hr _ W, -W,, (4.21)
h W '

max t

' ratio
Equation (421) shows that the degree of permanent deformation, measured by the

h . , .0
of residual depth to maximum indenter displacement, hi, , 18 Simply related to the tan
max

W _
of irreversible work to total work, Jul.“ The measurement of one leads to the

W

1

measurement of the other. in practice, however, the detemﬁnation of the work can be

made more accurately than the measurement of residual indentation depth, hf , since the

form er is from the integration of loading-displacement curves While the latter is from the
estimation of a Single point on the unloading curve, Furthennore, this relationship is
“universal,” because it does not depend on the details of the mechanical behavior of
solids, such as E , Y, and n , Nor does the relationship depend on the indenter radius, R,
or indentation depth, )1 . This new relationship is analogous to a relationship P’thOusly
established for conical and Pyramidal indentation in elastic-plastic SOlids with Strain-

hardening. [105, 106] Together, they demonstrate that a simple linkage exists between

76

the work of indentation and deformation that is independent of the details ofmaten'als

properties and indenter geometry-

4.3.3 Relationship between H/E a: and "VI" WJ/W,

‘ - W: " Wu rical
An approximately linear relationship between 2:1 and f for Sphe

!

. . / R , this
indentation in elastic-plastic solids 15 r evealed 1n Figure 4.7. For each ﬁxed hmax

relationship can be expressed as

 

" W 4.22
W, E *
where B is found to depend on ma" only (see, Figure 4.8), i.e.,
—O.62
B = -1.687[-}1"3x—] . (4.23)
R

Combining equations (4.22) and (4.23), it is obtained that

H hmax 0.62 PI,“
E; = 0.592%?) (W, J (424)

H .
Thus, the ratio of hardness to reduced modulus, N—E'“ , can be obtained by determining

 

h W . . 0 ° H W
[ﬂax U h "\ U
T and if. Recently, an approx1mately linear relations 1p between 5* and Wwas

obtained for conical and pyramidal indentation in ela~"ttl'C-Plastic solids with Stn'an—

hardening. [85, 106, 1 1 6] The “"0 quantities were f°und ‘0 be pmp‘m‘m‘al ‘0 each Other

with the proportionality factor a function of the indenter angle in conical indentation

77

modeling and experiments- Equation (4.24) shows that, for the ﬁrst time, a szmz'laf

relationship exists for spherical indentation in elastic-plastic solids.

. Fm
By Combining equation (4°24) wlth the definition of hardness H =—-—- and a

C

. - . o , S ,
well known relationship between redUCed modulus, E , initlal unloading stiffness

and contact area, Ac: [91, 100]

13* = [’5 S (4.25)

Zt/Z’

 

it was obtained that:

A = 1.90:5me ‘ (4,26)

 

 

 

 

h 0.62 w]
0.46 2 ﬂex— "
. 573 i R j i
E _

 

 

 

_ i, (4.27)
me
h 1.24 W 2 52
= .276 --—“‘“" “ ——--,
H. t.) m,“ (.28)
Since F , in; Wu and S can all be measured directly from load‘displacement
max R 2 W! 9

curves, contact area, reduCEd modulus, and hardness can in principle be Obtained from
equations 4.26, 4.27, and 4.28, respective” This new mum“ is ”“6" the “energy based
method” for spherical indentation analysis since the elastic energy (Wu) and total energy
(W,), are used to determine the mechanical properties. The main advantage ofthe energy.

based method is that it applies to both piling-up and Sinking-in while the commonly used

78

th ' ' - ' ' .
me ods cannot be used when plhng Up occurs. While this method ,5 based 0,, the
31131 ysis of rigid spherical indentation in elastic-plastic solids with strain—hardening, it is
1160655?in to test its robustness through experiments under realistic and oﬁen imPeI'ﬂ‘E’Ct

conditions: Such as non-sphericit)’ and non-I‘igidity of spherical indentCI'S-

4.4 EXPERIMENTAL APPLICATION OF THE ENE RGY-BASED METHOD

4. 4. 1 Sample Preparation and Experimattal Methods
Indenter XP

Spherical indentation experiments were conducted using a Nano

from MTS with a rounded conical diamond indenter. The included cone angle was 90

and the nominal tip radius was 10pm. The load range was between 10 and 300mN. At

least ﬁve. indentations were made at each load to generate average values and standard

deviations reported in this work. The indentation eXperiantS Were conducted using load
control with a constant loading rate. Unloading was initiated immediately after the load
reached the prescribed maximum load at the end of each loading cycle without a holding
period. All indentations were conducted at room temperature. The mechanical properties

of all the tested materials, i.e., pure copper, 6061“T6 aluminum, pure tungSten and fused

silica, are shown in Table I. [101, 156’ 157] The composite reduced modulus, E. is given

by

 

 

1 .
—.‘ “-3 + ,
E E E.- (4.29)

where E3 and vS are the Young’s modulus and Poisson’s ratio of the Sam 1
P 3,

respectively. E; and V.- are the Young’s modulus and Poisson,s ratio of the indent
er,

respectively, Speciﬁcally, E; =114lGPa and V.- = 0.07 for the diamond indenter Th
- e

79

{1153“ Silica sample was obtained from MTS as the standard calibration material Copper,

aluminum, and tungsten samples were mechanically polished, ﬁnishing with 0.25”!“

diameter diamond paste. The average surface roughness, measured using a Wyco optical

profilometer, was 20, 49, and 23 “m for the polished copper, aluminum, and tungsten

samples, respectively.

44-2 An Experimental Proof of the Relationship between h f/ hm; and (W :- WJ/W '

h _ .
f and WW’, W") for copper, aluminum, “mgSten’

 

The relationship between

max t
evident

and fused silica is shown in Figure 4.9, together with ﬁnite element results. It IS

M, which is consistent with the ﬁnite

 

h . -
that f is approxrmately proportional to
rmx t

element analysis. The agreement suggests that this relationship is insensitive to the ﬁnite

elasticity of the diamond indenter and imperfections in the diamond indenter geomCU'Y-
However, the imperfection in the spherical shape of the diamond indenter can be shown,
in section 4.5.4, to cause problems for direct applications 0f equations 4.26 - 4,28, In

section 4.5.3, a novel method for obtaining an effective radius for imperfect spherical

inden ters will be established to circumvent these problems.

4. 4.3 A Novel Method for Indenter Shape Function Calibration

For indenter shape calibration, instrumented spherical indentation experim e ts
n
were conducted on copper for depth ranging between 150nm and l850nm, The values 1‘
or

S , F and Wu /W‘ were obtained from load-displacement Curves Shown .
1n

niax ’ hmax’

80

 

Figure 4.10‘ Equation 4.27 was then used to calculate the effective tip radius, 1%], 3’

Various depths, assuming a Constant composite reduced modulus fbr copper,

EC; = 127.2 GPa. The relationship between Ref, and hm is shown in Figure 4.11.
Ideally, for a perfect spherical indenter, the effective tip radius Should be independent of
the indentation depth. However, in this Work, the effective tip radius was found to be a
ﬁmction of indentation depth due to its imperfect geometry. An increase of more than
50% in effective tip radius over the depth was observed. A power—law ﬁt was used to
interpolate the effective indenter radius. This indenter “shape function” is given by (see,

Figure 4.ll)

Re” = 19 1 56km,”2755 for 150nm< h max <1850nm. (4.30)

,

The manufacturing Of a Perfect spherical diamond indenter becomes challenging
as the tip radius becomes smaller. In addition, the worn surface of a used indenter can
cause the non-sphericity. Therefore, a regular calibration of the indenter shape is critical
for accurate measurement. The method described above can be used to calibrate the shape
function of any non-perfect Spherical indenter. The proposed method is efﬁcient and it

requires no extra investment in capital equipment.

4.4.4 Hardness and Young ’s Modulus Measurement by the Energy-based Method
Using the same diamond indenter, spherical indentation experiments were then
conducted on 6061-T6 aluminum, tungsten, and fused silica with indentation depth from
18011111 to 1650nm. The load-displacement curves are shown in Figure 4.12(a)-(c). The
composite reduced modulus (E‘) for aluminum, tungsten, and I”l-lsed Silica, calculated

using equation 4.27, together with the shape function equation 4.30, at Various depths is

81

pIOtted In Figure 413(3) AS expected, the measured COmPOSitB T educed modulus values
are apprmiirnately depth independent. The measured composite reduced modulus of
aluminum ranges from 74.3 to 78-6GP3- The composite reduced modulus of tungsten
ranges lion-1 296 to 316.8GP3- Compared With the calculated composite reduced modulus
of aluminum and tungsten in Table I, the difference is within 8%, which suggests that the
propcsed energy-based method together with indenter shape calibration is applicable to
materials With a wide range of elastic modulus values. The measured composite reduced
modulus of fused silica is between 58.2 and 60,4GPa. The difference between the
noted that the

calculated and measured value for fused silica is within 16%. It should be

fused silica data also exhibit the largest deviation in the correlation between hf Mm and

(Wi-WQ/W‘ (see, Figure 4.9). These differences may be caused by indentation-induced
microcracking for brittle materials such as fused silica. It also suggests that the
relationship between h I I hm and (W,- WJ/W, may be used to help screen materials for
which the new method is applicable. Speciﬁcally, the energy-based method Consists Of
the following steps:

(1) Using equations 4, 27 and 4.29 to determine the effective indenter rad" R
1115
2 eﬂ' ,

as a ﬁmction of indentation displacement, hm , by indenting a mate . 1
Fla with a

known, depth independent Young’s modulus and Poisson’s ratio Thi h
‘ S S ape
function is an interpolation function over the indentation depth of inte
rest and

is not necessary of the form given by equation 4.30.

(2) Checking the applicability 0f the energy-based method b .
y Plotting h, ”I"...

X

and (Wt-WKJ/m’ A necessary condition is that the correlation ex'
ists for

materials of interest.

82

 

 

 

(3) Evaluating the reduced modulus for materials of interest using eq Hat/bus 4.27
and 4.29 together With the shape function determined in step (1 ).
The 1' ObUStness of this method is seen from the evaluation of the reduced modulus values
for several I‘naterials using an imperfect Spherical indenter with a varying effective radius
of about 5()0/0- The method does not depend on assumptions about piling-up and sinking-
in of materi als around the spherical indenters.

Finally, hardness values for ﬁlsed silica, W, A], and Cu are obtained using
equation 4-28 together with the indenter shape function equation 4.30. The results are
shown in Figure 4.13(b). While these values are within the range of reported hardness for
the Cu, Al, and W, detailed comparison is complicated because of several factors.

Speciﬁcally, (i) most of the literature data were obtained using Berkovich indenters
where a pronounced indentation size effect was reported for these materials. [158-160]
Strain- gadient plasticity is believed to be one of the primary mechanisms responsible for
the increase in hardness with decreasing indentation depth.[161] (ii) The indentation size
effect is different under spherical indenters, where the hardness is not expected to show
depth dependence but is expected to depend on the radius of Spherical ind enters. [162]
(iii) Hardness increases with indentation depth for spherical indentation in eIaStiC-plastic
solids with work hardening- [92] With an imperfect spherical indenter, SUch as the one

used in this work, it is possible that the tW0 effects, work hardening and Strain grad'
‘ lent

plasticity, cancel each other because 0f increasing Rex; With depth, resulting in a Sligh 1
t)’

decreasing hardness for C11, Al, and W With depth (866’ Figure 4'13 (bl) Whil
' e the
imperfection in spherieity can be remedied for mOdUIUS measurements using a h
S ape

function (e.g., Equation 4.30), hardness is indenter shape dependent It is the f
‘ re ore

83

 

 

desirable to use as perfect a spherical shape as possible for hardness measurements ”5mg

spheﬁcﬂ indenters.

4,5 CONSTRAINT FACTORS FOR SPHERICAL INDENTATION

EXPERIMENTS

- - - atio of
For spherical indentation, the Constraint factor, CF, IS deﬁned as the r
' in, i'e',
hardness, H , to true stress, 0 , when the representative strain equals the true stra

H 4.31

. . . . ' in iven
where s is the true strain in unlaXlal tensﬂe test, and g, is the representatwe stra g

by
a (4.32)

where a is the contact radius. Given the constraint f316101”, the true stress-strain
relationship can be determined by the hardness-representative Strain relationship. In this
work, the constraint factors for elastic indentation, elastic-Plastic indentation and fully-
plastic indentation were Studied using ﬁnite element calculations,

The relationship between true stress-strain and hardness-representative strain
curves for sphericaI indentation on 613860, 50ft elastic-plastic and hard eIaStiC-plastic
materials are Shown in Figure 414(3) (b) and (c), respectively, The horizontal axis
represents true strain or representative strain 0f the same value, Figure 4.14 (3) Shows
that, for the contact between a rigid indenter and an elastic material with E=200K, psoz

the constraint factor is close to 2.21- The analytical solution for the contact between a

84

 

 

 

 

rigid indenter and an elastic ﬂat surface has been solved by Hertz. Speciﬁcall y, for elastic

contact, the contact radius, a , is given by [113]

3F U3
(1 =(7’12:_R] , when a<<R. (4.33)

 

 

F . . .
Note that we also have H = m“; , E =1 E 2 and 0' = 55:0,ZE, By combining
Ira —u R

these three equations and equations 4.31, 4.32, and 4 -33 together, the constraint factor for
elastic contact with a rigid indenter is obtained, i.e. ,

CF = E 20 (4.34)

0' : 37r(l - V2 ) O
For elastic contact wi th a rigid indenter, the constraint factor is dependent on Poisson’s
ratio only. Specifically, constraint factors increase from 2.12 to 2.83 when Poisson’s ratio
increases from 0 to 0.5, as shown in Table 4.2. For v=O.2, equation 4.34 gives a
constraint factor of 2.21 , which is consistent with the ﬁnite element result. Figure 4.14(b)
shows relationships between hardness and true stress for spherical indentation on a soft
material with Y/E=0.002 and n=0.3, which represents typical metallic materials. It shows
that the constraint factor is close to 2.8 for all the indentation tests from hmax/R=0.02 to
hmm/R=O.5 . The ﬁnite element results are consistent with Tabor’s observation of Spherical
indentation on metals. [129] Figure 4.14(c) shoWS the relationship between hardness and
true stress for spherical indentation on hard materials with Y/E=0-025 and ":03. The
constraint {actor is less than 2,8 for all the indentation tests from hmx/R =0.02 to Ana/R

=05 \ d“ increases With increasing indentation depth.
an

F1, gufe 4.15 shows the constraint factors for all materials tested at different
121013712“? ‘01’ depth- The horizontal axis, E'a/O'R, includes information of both material
‘11!

85

properties (Ei/O') and the indentation test (a/R). It shows that the constraint factor reaches

0

E a . . . . . .
2.8 when TRzAtO, Wthh Indicates the beginning of full-plasticny in indentation

experiments. The constraint factor remains about 2.8 with increasing indentation depth

once full-plasticity is reached- For soﬁ materials (low Y/E and n), full-plasticity can be
easily achieved. For exatnple, for materials with Y/E=0.002, n=0.3, £1=41 when
0R

hmax/R =0.02. For hard materials (high Y/E and 72), there is a large elastic-plastic transition

to 2.8 with increasing indentation

 

range, and constraint factor increases from 2
372'(1- V )

depth. Full-plasticity and the constraint factor of 2.8 can’t be reached even at large

indentation depth. For example, for materials with Y/E=0.025 and n=O.3 ___,—E a = 19 when
’ O'R

rim/R =05.
In conclusion, the constraint factor for spherical indentation processes is

20
31(1- V2)

 

dependent on material properties and indentation depth. It changes from to

2.8 when indentation evolves from elastic to fully-plastic. Caution must be taken when
using spherical indentation to derive stress-strain relationship of hard materials, such as
ceramics or materials with large work hardening eXponent, because there exists a large
elastic-plastic transition range for those materials. For soﬁ materials, a constraint factor

of 2.§ (“33! be used to derive true stress-strain relationship approximately. However, as

%

,7;ch {”61“ due to the indentation size effect.
5

ed in section 2.3.5, indenter radius plays an important role in the hardness
1’

86

4.6 CONCLUSIONS

 

The extent of piling-up/sinking—in and the relationships between E}: W’ ” ,

 

and have been investigated using dimensional analysis and ﬁnite element

max
calculations. For spherical indentation in elastic-plastic materials, there is an equivalence

I: W —W h
f u max ‘ '
between II\ and —‘————~. For a fixed —— , a 11 near relationship exists between

max I R E*

z ,, . . h
and W and the proportionality depends on $011”. Using the above

I

 

relationships, together with the initial unloading stiﬂiiess, an energy-based method has
been proposed to derive the contact area, reduced modulus and hardness of materials
from instrumented spherical indentation experiments. This new method can also be used
to calibrate the effective tip radius of an imperfect spherical indenter. The validity 0f the
new method was studied by instrumented indentation experiments on copper, aluminum,
tungsten, and fused silica. Constraint factor for Spherical indentation experiment has been

studied using ﬁnite element calculations as well. The constraint factor changes from

20

W to 2.8 when indentation evolves from elastic to fully-plastic. For soft

material, the fully-plastic indentation can be easily reached; however, for hard material
there exists a large elastic-plastic transition region. Caution must be taken when using

con8\\,&\“‘ factor to derive stress-strain relationships.

87

CHAPTER 5
SUMMARY AND FUTURE WORK

This study, for the ﬁrst time, presented a systematic study of the shape memory

and super elastic effect of NiTi alloys at the micrometer scale using instrumented
indentation experiments. It was found that the shape memory and superelastic effects
exists under indentation loading conditions and the recoverability depends on both the
indenter geometry and indentation depth. For Berkovich and Vickers indentation
experiments, the recovery ratio is a constant at all indentation depths. For spherical
indentation experiments, the recovery ratio decreases with increasing indentation depth
and scales with the representative strain. For both shape memory and superelastic NiTi
alloys, the maximum strain for complete recovery can be measured by the instrumented
spherical indentation experiments. Instrumented indentation techniques can be used to
quantitatively characterize the shape memory and superelastic effect at small size scale,

such as thin ﬁlms on substrates and welded joints.

The thermally—induced recovery of the indents on the shape memory alloy
indicates that the shape memory thin ﬁlms may be used as a self-healing coating, in
which the damage caused at low temperature can be healed at high temperature. It also
indicates that a shape memory alloy can be used as a material that can change Strrface
rou%ess according to the environmental temperature.

Motivated by the high elasticity of the superelastic NiTi and its potential

app/1&9. ’0” 35 a novel tribological material, the wear behavior of the superelastic NiTi
4:711

88

was studied. It was found that the wear rate of superelastic NiTi is larger than that of the
amorphous NiTi. Ploughing during sliding test deteriorates the recoverability of the
superelastic NiTi, which can be prevented by deploying a hard layer on the top of
superelastic NiTi.
Based on the above indentation and wear experiments on superelastic NiTi, a
novel layered composite coating was produced. This composite coating is made of a
superelastic NiTi interlayer deposited between a metallic Substrate and a hard ceramic
coating. The superel astic interlayer provides high elasticity while the hard coating
prevents ploughing. It was found that the composite coating with superelastic interlayer
has good interfacial adhesion, low friction coefficient, and good wear resistance. This
experimental observati on suggests that (i) superelastic NiTi can be used a high Strength
“metallic adhesive”, and (ii) increasing the interlayer elasticity can decrease the friction
coefficient and improve wear resistance. Thus, elasticity, in addition to hardness, plays an
important role in determining the friction and Wear behavior of the tribologi cal materials.
This observation will be useful in the design of better tribological coatings. Future study
of this novel composite coating should include the quantitative measurement of the
adhesion strength and optimization of the interlayer thickness.
To further explore the spherical indentation eXperiments, a general study of the

spherical indentation in elastic-plastic materials Was conducted. Using dimensional

analysis and ﬁnite element modeling, new scaling relationships between

 

the
d'm s arameter —7, —-"‘9-"-, , ’ ” were revealed fo the ﬁrst '
I §IZSI'OﬂleS p E R hm” I 1‘ trme.

5an ﬂ these relationships and a well-known relationship between reduced modulus,

initial [Wading slope, and contact area, a novel energy-based method for analyzing

89

spherical indentation experiment was proposed. The rObustness Of the new energy-based
method Was verified by spherical indentation experiments in materials with a wide range
of Young’s moduli and Poisson’s ratios. The pr0posed energy-based analysis method also
provides an efﬁcient and low—cost approach for indenter shape function calibration.

The constraint factor for spherical indentation process was studied using finite

20

element calculation. It was found that the constraint factor changes from 2)
37r(l—v

t0

 

2.8 when indentation evolves from elastic to fully-plastic. For highly—plastic materials, a
constraint factor of 2.8 may be used to derive the true stress-strain relationship
approximately. However, for highly-elastic materials, there exists a large elastic-plastic
transition range within which the constraint factor is a ﬁmction of indentation depth and
material properties. The constraint factor of 2.8 can not be used to derive stress-strain
relationship of highly-elastic materials. Future study will focus on how to obtain the
stress-strain relationship using the information ﬁ-om the whole indentation load-

displacement curve.

90

APPENDIX

91

APPENDIX

FUNDAMENTALS OF DIMENSIONAL ANALYSIS AND H THEOREM

PhYSical properties are expressed as a number associate with some unit. The
choice of unit for the measured properties is arbitrary. For example, we can choose either
meter (m) or millimeter (mm) as the unit when we measure the length. Whatever the unit

is chosen, the length should be the same. Therefore, for physical property it , the

measured number should increase by a factor of X when the unit decreases by a factor of
X. We say that the dimension of physical property x, denoted by [x] , equals the factor X.
The PhySiCal units can be divided into to types: the fundamental units and the
derived units. For instance, once the units for length and time are chosen as the

fundamental units, the unit for velocity becomes a derived one. The dimension of

velocity can be expressed in the form of the dimension of length and time

-I
[Vl=[1][t] - (A1 )
It has been proved that the dimension of any physical property is always a power.law
monomial, For the length-mass-time unit system, the dimenSion of any phySiCaI property

2 can be expressed as
[Z] = [1]“ [fl/3 [le (A2)
whe‘\ m It] and [m] are the dimensions of length, time and mass, respectively, a, 5
e ,

31]”, cal number associated with z,

92

A group of physical prOperties z,,zz,...,zi is dimensionally independent if the

relationship

[2'1“l [22]"2 ...[zn]"" :1 (A3)

exists only when a1: a2 = ...= a = O.

n

A physical law speciﬁes the relationship between a governed variable, 2, and a

group of governing variables, 2, , 2;, ,. . ., z" , in the mathematical form of

z = f(z,,zz,...,zn) (A4)
Among the n governing variables, let z]...z'. be dimensionally independent. Therefore, the

dimension relationship can be express as
[21421]“l [22 T12 ".[Zila’ (A5)

[z,+,.]=[z. 1““ [221“]: [1, J- =1,2...,n_i (A6)

According to equation (A5) and (A6), the following physical quantities should be

 

dimensionless
2
II = ———-——-—
21‘" 2:" ...zf' (A7)
[1,: a a”! a- ’ -=1,2,...,n— .
1 z1 "22-”...21.” J J (A8)

Then, the equation A4 can be transformed into new form
H : f(zl’“'zi’nl’°”’nn—i) (A9)
Not§ at when the unit system for the physical property z,,...,z,. changes from one to
‘11

3,101 the number of physical prOperties 2],...,Z,- Changes accordingly, Nevertheless,

\gq’;

93

the number for [I should remain unchanged since it is dimensionless. Therefore, z,,...,z.

I

should not appear in equation A9 and the equation for II should be
l'I = f(l'I,,...,Iln_,.) (A10)

It is obvious that, by transforming equation A4 into A10, the governing variables change
from n dimensional variable to n—i dimensionless variables. This is known as the H
theorem. The foundation of the H theorem is that the physical law should not be
dependent on the arbitrarily chosen unit system. The dimensional analysis can help us
ﬁnd the essential relationships between physical properties.

A detailed description the dimensional analysis and II theorem can be found in
the work by Barenblatt [154] and Cheng. [163] In addition, Cheng and Cheng [85, 86,
103, 106, 147] pioneered the study of instrumented indentation using the dimensional

analysis.

94

 

 

Table 1.1.1 Crystal Structure and lattice parameters of NiTi alloys.

 

 

 

 

Phases Crystal system Lattice Parameters Space group
martensite monoclinic a=0.2898nm, b=0.4108nm, P2l/m [9]
c=0.4646nm,[3=97.78 [8]
R-phase trigonal a=0.3012nm, a=89.53° [7] P3 [9]
austenite cubic a=0.3012nm [8] pmg m [9]

 

95

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 1.2.1 Properties of metallic hard materials. [61] ‘5
Materials Density Melting Hardness Young’s Resistivity CTE
(g/cm3) Point (HV) modulus (pﬂxm) (10“K")
(°C) (GPa)
TB; 4.5 3225 3000 560 7 7.8
TiC 4.93 3067 2800 470 52 8.0-8.6
TiN 5.4 2950 2100 590 25 9.4
ZrBz 6.1 1 3245 2300 540 6 5.9
ZrC 6.63 3445 2560 400 42 7.0-7.4
ZrN 7.32 2982 1600 510 21 7.2
VB; 5.05 2747 2150 510 13 7.6
VC 5.41 2648 2900 430 59 7.3
VN 6.11 2177 1560 460 85 9.2
Nsz 6.98 3036 2600 630 12 8.0
NbC 7.78 3613 1800 580 19 7.2
NbN 8.43 2204 1400 480 58 10.1
TaBz 12.58 3037 2100 680 14 8.2
TaC 14.48 3985 1550 560 15 7.1
CrBz 5.58 2188 2250 540 18 10.5
Cr3C2 6.68 1810 2150 400 75 11.7
CrN 6.12 1050 1100 400 640 2.3
M0285 7.45 2140 2350 670 18 8.6
M02C 9.18 2517 1660 540 57 7.8-9.3
W285 13.03 2365 2700 770 19 7.8
WC 15.72 2776 2350 720 17 3.8-3.9
LaB6 4.73 2770 2530 400 15 6.4

 

96

 

 

Table 1.2.2 Properties of covalent hard materials. [61]

 

 

 

 

 

 

 

 

 

 

Materials Density Melting Hardness Young’s Resistivity CTE
(g/cm3) Point (HV) modulus (uQ.cm) (10'6K'1)
(°C) (GPa)
B4C 2.52 2450 3000~4000 441 0.5x106 4.5(5.6)
BN(cubic) 3.48 2730 ~5000 660 1018 /
C(diamond) 3.52 3800 ~8000 910 1020 1.0
B 2.34 2100 2700 490 10‘2 8.3
A11312 2.58 2150 2600 430 2x1012 /
SiC 3.22 2760 2600 480 105 5.3
Sin, 2.43 1900 2300 330 107 5.4
Si3N4 3.19 1900 1720 210 10“r 2.5
AlN 3.26 2250 1230 350 10IS 5.7

 

97

Table 1.2.3 Properties of ionic hard materials. [61]

 

 

 

 

 

 

 

 

 

Materials Density Melting Hardness Young’s Resistivity CTE
(g/cm”) Point (HV) modulus (pacm) (1 O‘K' 1)
(°C) (GPa)
A1203 3.98 2047 2100 400 1020 8.4
AlTiOs 3.68 1894 / 13 1016 0.8
Tio2 4.25 1867 1100 205 / 9.0
Zro2 5.76 2677 1200 190 1016 11(7.6)
Hfo2 10.2 2900 780 / / 6.5
T1102 10.0 3300 950 240 10"5 9.3
BeO 3.03 2550 1500 390 1023 9.0
MgO 3.77 2827 750 320 1012 13.0

 

98

Table 2.1 Phase transformation temperatures and structures of specimen BH and BS.

 

SPCCimen As (°C) Ar(°C) Rs(°C) Rr (°C) Ms (°C) Mr (°C) Structure

 

BH 72 94 63 56 47 27 819’

 

BS 3 46 44 4.0 / / B2 + R-phase

 

Table 2.2 Mechanical Properties of martensitic (specimen BH), austenitic (specimen
BS), and amorphous NiTi thin ﬁlm obtained from nanoindentation test.

 

 

 

 

Specimen Hardness (GPa) E (GPa) ETGPa) H/E' m.

BH 2.5 43.6 46.9 0.0553 0.33
BS 4.4 64.3 67.9 0.0648 0.47
Amorphous TiNi 7.9 158.0 153.6 0.0514 0.32

 

99

Table 3.1 Description of specimens

 

 

 

 

Specimen Cer-AI CrNS-Al CrN-Sl-Al CrN-SZ-Al CrN-Cr-Al
CrN 1 5 1 1 1
thickness (pm)

lnterlayer No No N151.8at%- Ti Ni49.5at%-Ti Cr
material

lnterlayer / / 4 4 4
thickness (pm)

 

Table 3.2 Composition and phase transformation temperatures of NiTi thin ﬁlms.

 

Specimen Film Target A, A; R, R; M, M;
composition composition (°C) (°C) (°C) (°C) (°C) (°C)
S1 N151.83t%- Ti Ni49.8at%-Ti 1 15 8 -4 / /
SZ Ni49.5at% -Ti Ni48.0at%-Ti 67 96 / / 62 28

100

 

 

 

Table 3.3 Nanoindentation properties of aluminum substrate, interlayer materials (S1, S2
and Cr) and CrN hard coating.

 

Material Al 81 (Ni51.8at°/o- Ti) SZ (Ni49.5at%-Ti) Cr CrN

 

 

 

H (GPa) 0.94 4.7 2.4 6.7 22.6
E (GPa) 77.6 95.0 89.3 318.4 252.6
m, 0.067 0.33 0.23 0.16 0.64

 

Table 3.4 A comparison of the mechanical properties of between superelastic NiTi and
polyisoprene.

 

 

 

Materials Young’s modulus Tensile strength Elongation Recoverable
(GPa) (GPa) strain
Superelastic NiTi 75 754-960 15.5% 5~8%
Polyisoprene. 0.002~0.1 0.01 100~800% 100~800%

 

Note: Polyisoprene is a thennoset elastomeric polymer.

101

 

Table 4.1 Mechanical properties of the tested materials.

 

 

 

 

 

Materials Young’s Poisson’s Composite Reduced Reference
modulus ratio modulus
E (GPa) v E* (GPa)
Copper 126 0.345 127.2 [156]
6061 -T6 [157]
Aluminum 70.4 0.347 74.8
Tungsten 409.8 0.28 320.4 [157]
Fused 72 0.17 69.6 [101]
silica

 

Table 4.2 Relationship between Poisson’s ratio and constraint factor for elastic contact
with a rigid spherical indenter.

 

Poisson’s ratio 0 0.1 0.2 0.3 0.4 0.5
Constraintfactor 2.12 2.14 2.21 2.33 2.53 2.83

 

 

102

 

2.0 -

 

 

 

1.5 —
R—>M A")R
§ 1.0 ~
5 O
3 0.5 ] cooling
ﬂ:
1'?
I 0.0 .
M—)A
-0.5 e . ’ V
heating
'1.0 I l l I l I
0 20 40 60 80 100 120

Temperature (°C)

Figure 1.1.1 DSC test shows characteristic phase transformation temperatures of NiTi
shape memory alloy.

 

(a)

 

Figure 1.1.2 A schematic representation of the shape memory effect of NiTi alloy. [5]

103

 

     

 

 

   

 

loading 'llll'lllll
, l
‘ —————
"""""'
unloading llllulllll
austenite Stress-induced martensite

Figure 1.1.3 A schematic representation of superelasticity of NiTi alloy.

 

 

 

 

 

 

 

600 — (c) Below M,
b ”or (a)
.. 8
50° 3 100
W I
a 400- l (b) o /' .
2 200 7 0 4 Strum c
5’ 300 b /" / / /
g ,8; 100 %
E5 200 m /
' ‘t o 4 Strain c
100 &\°‘.
w
«9“
00 2 4 Strain :7.

 

Figure 1.1.4 Representative stress-strain curves of shape memory and superelastic NiTi
alloys. [4]

104

 

Figu

C011

18W

g-n

1310 °C

1304
TiNi

  

1118 °C

Temperature (0 C)

...1

0 10 20 30 40 so on 70 so 90 100
Ti Ni
Atomic Percent Nickel

Figure 1.1.5 Phase diagram of binary NiTi alloy.

200 n n l l

 

 

 

j
o
150 e O —
o
100 ‘ J
.3 r . . .
" O Q I
o O
‘5 soi- o. -
E I I f ‘ I
8 "a.
E» 0 F as '
U o
_ 0 Wang et al. A
.50 AIHarrison et al. T
OlHanlon et al. g
400 _ I|Purdy at al. ‘ _
, O
450 1 l l J_ 1

 

47 48 49 50 '51 52 53
Nickel atomic (96)

Figure 1.1.6 NiTi shape memory alloy: dependence of martensite strart temperature on
composition. [4]

105

 

V V'vvvv' v v V'VV'Y' V V WV

10—2 E' O Ti50Ni47F¢3 1
E O SAE 52100 i

103 r
10" r

10'5 r

A AA“.

 

 

 

10*;- 1:

1
AL #4 AAAAAA. A A AAAAAA

100 101 102 103

 

Figure 1.1.7 A comparison of wear rates between Ti50Ni47Fe3 and SAE 52100 steel.
[20]

  
 

.... working gas

    

 

0

 

power
supply

 

 

 

1:-

 

vacuum
vacuum chamber

pumps

 

 

 

Figure 1.1.8 A schematic representation of sputtering process.

106

ﬁlm

 

substrate

tensile stress

ﬁlm

    

compressive stress
substrate

Figure 1.2.1 Residual stresses in thin ﬁlms cause bending of the specimen. [64]

107

 

prC
COI

 

 

spalling failure , . / spall ed
" coating

 

buckling failure

Q7“? )Dﬁ

prev10us
(b) failures

spallation or buckling
Qﬁeﬁaus failures

embedded by stylus
(c) bending causes

WM cracking
—>o - <—

(d)
compresswe ', ,, ,,
Fotensilea "’ {(1, “(i
\\

l ll‘ii («g

 

Mbuc ing failures
embedded coating

 

 

 

.ll

Tensile failure

(6)

Figure 1.2.2 Schematic representation of coating failure modes in the scratch test in
proﬁle and plan view: spalling failure (a); buckling failure (b); chipping failure (c);
conformal cracking (d), and tensile cracking (e). [76]

108

LOAD, P

   

 

 

‘l'- i ,,
hemmed/y \hm

I'Ic FOR 8-0.72
DISPLACEMENT , h

Figure 1.3.1 A schematic illustration of the load-displacement curve of instrumented
indentation test and the graphical interpretation of contact depth. [91]

 

  
 

deformed
surface

Figure 1.3.2 Illustration of conical indentation experiment. [97]

109

 

 

1.4 ————— _-
1.3

1.2 go

1.1 2 00

1.0 0.7% .
0.9 DOS

0
a».
0.8 . 5

6 . l

0.7 i ° ' 3 ° i

0.6 e . . . l
0.00 0.02 0.04 0.06 0.08 0.10

Y/ E

Figure 1.3.3 Degree of piling-up and sinking-in, ho/h, as a function of the ratio of yield
stress to Young’s modulus, Y/E, and work hardening exponent, n, in conical indentation
experiments. [97]

 

ODQO
:33:
uuuu
9999
mweo

 

 

 

hc/h

 

D

OD<10_
o

0810

 

 

residual indent CTOSS point
proﬁle (solid line)

 

o_riginal surface to oint

(dotted line)

 

 

 

 

 

 

Figure 1.3.4 The top-point, instead of the cross point, deﬁnes the contact perimeter when
piling-up occurs. [110]

110

 

F igu
and 1
expe

9 n

80. 0.5

80. 0.1

80. 0.0

70.3, 0.5

70.3, 0.1

70.3, 0.0

60, 0.5

60. 0.1

45. 0.5

45. 0.0

60. 0.0

Linear Function

----- Lawn and Home
0 Mencik and Swain

 

 

 

I+OXXI>OO

tot

I30

 

 

 

 

 

 

 

 

Figure 1.3.5 A relationship between the ratio of irreversible work to total work, Wp/W,,
and ratio of residual depth to maximum indentation depth, hf/hm, in conical indentation
experiments. [106]

111

 

1.20

 

Finite element results:
n=0.5( 0 ), n=0.1 (A ), and n-o.0 ( .1 )
Solid line: linear functions

 

 

 

 

 

 

 

 

1 '00 Dash line: Lawn and Howcs for 0 = 70.3°
Experimental data of Menéik and Swain: -
0.80 ‘ o
\ / 45°
h f 0.60 - . 60°

 

 

 

m A ° 0
0.40 ~ ‘ \ <>A °
703° \ °
80° / ‘ °

 

 

 

 

 

 

 

 

 

 

0.20 7
' x
6
o
0.00 ’ ‘ L
0.00 0.05 0.10 0.15 0.20

H
t
E
Figure 1.3.6 A relationship between the ratio of residual indentation depth to maximum

indentation depth, h/hm, and ratio of harness to reduced modulus, H/E‘, in conical
indentation experiments. [106]

 

112

 

 

100

 

 

 
   

 

 

 

 

 

   

 

 

 

 

   
 

 

 

 

 

 

 

+E=200, Y-19, n=0.0
80 - n 13:200. Y=18, n=0.l
A o E=200,Y-15,n=0.3
E 60 ' o E=200,Y-12, n=0.5
I: 40
20
O l
0.00 0.20 0.40 0.60
(a) h (1m!)
40
+E=200, Y=2.36, n-0.0
30 a E=200,Y=2.00,n-0.1
Z o E=200,Y=1.24,n=0.3
g 20 --
La.
10
0
0.00 0.20 0.40 0.60
(b) h (“I“)

Figure 1.3.7 Different combination of Y/E and n can lead to the same load-displacement
curve in conical indentation experiments: Highly elastic materials (a), and high plastic

materials (b). [105]

113

 

 

 

200 4
x 2.8Y
L A o 1
A ’ l‘
”a
go 100 .-
M b
v .-
946 .
' B ‘ 2.8Y
[
5 10 15
I l l

 

I I

0.1 0.2 0.3 0.4 0.5 0:6 0.7 0.8 0.9 1.0

d/D

Figure 1.3.8 Relationship between representative strain ~ hardness and true strain ~ true
stress. Curve A, mild steel. Curve B, annealed copper. O x hardness measurement. ——
stress—strain curve. (Pm stands for the hardness in this ﬁgure.) [132]

114

Elastic Elastic-plastic Fully plastic

     
 

 

 

  

Elastic /‘
stress Contained
contour plastic zone Uncontained
plastic zone
0)) (C)

Figure 1.3.9 A schematic illustration of the evolution of plastic zone during spherical
indentation process: elastic (a), elastic-plastic (b), and fully-plastic (c). [125]

115

 

_x
O

 

 

 

 

 

 

 

 

 

 

 

 

A 5 -. 3" R cooling
D) 7 s ‘—
E E f MS Rf A
a O i As A’ l
~09; _5 j -———>
‘5 Z heating
9’ i
I -10 ~:
3 (a)
-151 +.4 wwwwwwwe
-50 0 50 100 150 200
Temperature ( °C )
1.5 r
1.2 “E as cooling
5. 06 E Rf R,
8 '
c 0.3
a _E A
i3 0 E As ‘ ,
-0.3 ‘EK—A—J” heating (b)
‘0.6 : 1 l l l i l i ‘ 1 f ‘ 1 L ‘ i 1 1 1 1 i 1 1 1 L1
-50 0 50 100 150 200

Temperature (°C)

Figure 2.1 DSC curves of specimen BH (3) and BS (b).

116

2000

 

 

 

 

 

 

 

 

 

 

 

 

1600 ~
2
g 1200 a
a?
3 800 -
2
E
400 -
0 l l I 1 i l
35 49
Figure 2.2 XRD patterns of specimen BH and BS.
Fmax
2‘
LE,
'0
to
o
..J
h l
: f heating hf
L
1‘ !
hmax

Displacement (nm)

Figure 2.3 A schematic illustration of thermally activated recovery of indent on shape
memory alloy (specimen BH).

117

 
 

 

    

3 after heating

Height (pm)

Vickers (b)
-8h"":~ur""+""r

40 60 80 1 00 120 140

Lateral position (um)

 

 

 

Figure 2.4 Change of residual indentation depth was observed for Berkovich indent (a)
and Vickers indent (b) on a NiTi shape memory alloy (specimen BH) after heating to
above austenite ﬁnish temperature.

118

 

 

 

 

 

 

 

1.0 .
:51) 0.8 “E OBerkovlch
g : DVlckers
E‘ 0.6 7E
9 O4 5
8 ' Ee—ﬁe—j G a m-
g 0.2 -E

LllLlthllllllLl
l l l

0 2000 4000 6000 8000
Residual indentation depth (nm)

 

 

 

9
0

Figure 2.5 Relationship between recovery ratio and residual indentation depth for
Berkovich and Vickers indents on a NiTi shape memory alloy (sample BH).

119

100 pm

100 1....

 

Figure 2.6 Geometry of the spherical indenters measured by SEM: R=213.4um (a) and
R=106.7um (b).

120

200 pm

  
 

 

 

 

 

 

 

 

 

um
0:
-25§
500‘-
100
‘5 o 100 20° 300
1.2 :
O 1%. o o
'5 : ° 0
E 0.8 “E ’
5 0.6 —E
> :
8 0.4 ~E
G’ t
0‘ 0.2 -5 (e)
OZ‘ 41111191 1
0 3000 6000 9000 12000

Resudual indentation depth (nm)

Figure 2.7 Spherical indents on a NiTi shape memory alloy (specimen BH): before
heating (a), aﬁer heating (b), 3D proﬁle of indent before heating (0), 3D proﬁle of indent
after heating ((1), and recovery ratio as a function of residual indentation depth (6).
Figures (c) and (d) are in color.

121

 

Illl

IrllllllrrlTll

 

Residual depth (pm)
1.

— 25N
—10N

 

 

 

 

 

l
0 CD 05
L 1
ITTfrrTrrl

 

11111L1111111L1L11_Llll_1_1_11111
if T l l l

50 100 150 200 250 300
Lateral position (pm)

0

Figure 2.8 Cross-section proﬁle of the spherical indents on specimen BH shows that no
piling-up occurs.

deformed surface

original surface

 

 

 

 

 

Figure 2.9 A schematic illustration of indentation sinking-in for spherical indentation
experiments.

122

 

True strain

 

 

1.2 t _ 1500
Q 1 1*— O 0 O o L 1200£
o-l : O .1
i! 0.8 “E O i 900 if
5 0.6 —E —’§ 8
(>3 : :r 600 3;;
u 0.4 2: I —
é’ : ' i 300 9
0-2 “E I slip starts 1 .3
O 1 1 1 % 1 1 1 1T 1 1 1 % 1 1 1 % 1 1 1 _, 0

 

 

0 0.02 0.04 0.06 0.08 0.1

0.2aIR
0 Recovery ratio — Stress-strain

 

 

 

 

Figure 2.10 Relationship between thermally activated recovery ratio and representative
strain, and the relationship between the true stress and true strain of a NiTi shape memory
alloy (specimen BH). The recovery ratio starts to decrease when the representative strain
exceeds the critical strain in the stress-strain curve.

123

 

 

Fmax

\

  

unloadin 1

hf Displacement (nm) hm"

Figure 2.11 A schematic representation of the elastic recovery of indents after removal of
the load.

124

 

 

 

 

 

250 _
7 Superelastic NiTi
200 ~
E 150 —
R
o 100 —
.1
50 - f /
-/// (a)
O “ 1 I 1 l
0 500 1000 1500 2000 2500
Displacement (nm)
0.6
: Superelastic NiTi

' Ital

. 9 9
-b 01
111111111141

recovery ratio
9 o
N 00

(b)

11111111

 

 

 

0‘1 Copper Q E! D Q E!
O I I i l I I I I I I I T T 1 W I T I I I I I
0 500 1 000 1 500 2000 2500

Displacement (nm)

Figure 2.12 Berkovich indentation of a superelastic NiTi alloy (specimen BS) and
copper: load-displacement curves (a), and depth (squares) and work (triangles) recovery
ratios upon unloading at various depths (b). Filled symbols for NiTi and unﬁlled symbols
for copper.

125

 

30000 1

N

01

O

O

O
1

Load (mN)
a
o
O
o

   
     

(a)

 

 

 

 

 

 

 

 

0 _— 1 1 r
O 4000 8000 12000 16000
Displacement (nm)
True strain
12 _...+1...41....1....1....1..ﬁ.q1800
1 — i 1500 ’~
.9 : 4—4 M A —§§ g
E 0.8 ~; :- 1200 .5,
: “ m
E‘ 015~; i 900 g;
o i 1 3 13
o 0.4 4 -- 600
g ; —-§slip starts 5 g
0.2 1 | (b) 300 I-
0 ‘1111111111111411111L1‘:0
0.00 0.02 0.04 0.06 0.08 0.10 0.12
0.2aIR
o R=213.4mlcromoter A R=106.7micromoter ———axlalstross~strain

 

 

 

Figure 2.13 Load-displacement curves of spherical indentation on a superelastic NiTi
alloy (specimen BS) and copper (R=213.4um) (a), and relationship between the depth
recovery ratio and representative strain, and the relationship between the true stress and
true strain of the superelastic NiTi alloy determined in a tensile test (b). The recovery
ratio starts to decrease when the representative strain exceeds the critical strain in the
stress-strain curve.

126

 

 

 

(110)A

 

 

 

 

 

 

 

 

if
e :3
a <3.
2
a (b)
E v “7 -—._
(a)
30 35 40 45 50 55

20

Figure 2.14 XRD shows indentation induced austenite —-) martensite transformation in
specimen BS: non-indented area (a) and inside the indent (b).

127

0.78812
0.1 766
0.1692

, 0.1619
Strain larger 0.1545

0.1472
than 0.1766 0.1398
0.1324
0.1251
0.1 1 77
0.1 1 04
0.1030
0.09566
0.08830
0.08094
0.07358
0.06622
0.05887
0.051 51
0.044 15
0.03679
0.02943
0.02207
0.01472
0.007358
0

 

 

 

I'I 0.1766
[I 0.1693
[1 0.1545
[,1 0.1472
1:; 0.1398
El 0.1325
'7‘ 0.1251
0.1177
.: 0.1104
0.1030
0.09567
0.08831
0.08095
0.07359
0.06623
I 0.05887
. Li! 0.05151
0.04415
0.03679
0.02944
0.02208
0.01472
1 0.007359
:51 0

 

 

 

 

Figure 2.15 Finite element modeling of strain distribution under sharp indenter (a) and
spherical indenter (b). The white region right under the conical indenter has a minimum
strain larger than the maximum strain under the spherical indenter. Regions with the same
color have a plastic strain of the same value in (a) and (b). Images in this ﬁgure are in
color.

128

Ti49at.%-Ni

/ ’ """" 24,.
, / /\

76.2mm {I “'75 ‘

9/

\‘7-%'6.35mm

 

Figure 2.16 A schematic ﬁgure of the target for the deposition of amorphous NiTi ﬁlm.

129

1000

 

 

 

 

8001
’15
Q
Q 6001
.3.“
2 4001
.8
s
2001
01.1.11.1111r1Tﬁr1111111r
38 40 42 44 46 48

20

Figure 2.17 XRD of amorphous NiTi thin ﬁlm.

 

 

 

 

 

50 p
1
40 13 amorphous BS BH
’2‘ .
E 30
1:
3 20 1
.1
10 ~;
0h 111 111*11‘1L
0 200 400 600 800 1000
Displacement (nm)

Figure 2.18 Load-displacement curves of martensitic (specimen BH), austenitic
(specimen BS) and amorphous NiTi.

130

.4"
o

 

9"
o

   

 

—e—BS

   

Wear loss (pmz)
N
o

 

 

 

 

 

 

1.0 -B—BH
—-£s—amorphous
0.0 F 1 1 1 1 1 1 4 e 1 1
0 1 2 3 4 5 6
Load (N)

Figure 2.19 Dry sliding wear rate of martensitic (specimen BH), austenitic (specimen
BS) and amorphous NiTi.

 

 

 

 

<
a
12‘ E
E
8 6.7
a 8
g v
a (b)
.E .
(a)
35 40 45 50
20

Figure 2.20 XRD spectra show wear-induced austenite —) martensite transformation in
specimen BS: outside the wear track (a) and inside the wear track (b).

131

  

i r111—

 

 

 

 

 

I Hi—vacuum

 

 

 

 

 

 

\\\\K 3 .\\\"\\ \‘ -.\"~ \\\\\\\\' \\j‘ ,\ .\\‘ \

   

 

 

 

 

 

 

  
 

 

 

 

 

 

  
   
  
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 
  

 

 

 

chamber
Ti Internal
sublimation ,, b31970!“
/ lamp
85 % Ti- Wafer
Mo furnace
1 Working
gas inlet
lll‘ ~11
Sublimation
power pump Inlet valve Rough pump
Micrometer
gas control Argon gas
1 valve cylinder
/ Wafer
~10mm
thermocouple
Wafer furnace

 

 

 

 

 

Figure 3.1 A schematic illustration of the structure of sputtering equipment for
deposition NiTi thin ﬁlms.

132

 

 

A
l

cooﬁng

M
—.’ V
heaﬁng

9
U1
1

lIllerlel

.6
01 0
W4

Heat ﬂow (ng)

S1(Ni51.8at.'/o-Ti) (a)

1 1111111111141111111

 

[L11

 

 

~50 -20 10 40 70 100
Temperature (°C)

 

 

 

 

 

 

 

 

3
E
g: 2 l: cooling
C
l <—
3 1 : 7’1
o L.
E 0 3:
:1; : 7 ——>
I -1 if heating
; SZ(Ni49.5at.%-Ti) (b)
_2b4111pm111lL111L1111111111

-50 O 50 100 1 50 200
Temperature (°C)

Figure 3.2 DSC curves of post-annealed NiTi thin ﬁlms show that, at room temperature,
specimen 81 is austenitic (a), while specimen S2 is martensitic (b).

133

 

 

     
    

 

 

 

2 z
2 2 a g :3
a; 8 :2 o 9, 8
a. sz 3 i g V
(M49.Sat%-Ti) "
95 (b)
.2 N m
m E,
2 a '2
c 2 8?
'— 31 v 51'
M51.3at°/.-Ti "
( ) (a)
I I Y I I T ﬁr r f T l
35 40 45 5O

29

Figure 3.3 XRD patterns of post-annealed NiTi thin ﬁlms: 81 (a), and 82 (b).

1800

 

1 500

l

A
to N
O O
O O
l

     
 

 

200)CrN

(111)CrN

Intensity (CPS)

 

30 4O 5O

(311)CrN

 

60 70 80 90
29

Figure 3.4 XRD pattern of Sum thick CrN coating on aluminum substrate (specimen

CrNS-Al).

134

 

Load (mN)

 

 

 

 

 

 

 

 

(a)
0 200 400 600 800
Displacement (nm)

0.8 _
.2 r
E 06 a:
2' ' :
2 :
8 0.4 f
2 C
.: ~ :3
... 0.2 a
3 (b)
0

01, l“ I
O 0.02 0.04 0.06 0.08 0.1 0.12

HIE"

Figure 3.5 Berkovich indentation test on various materials: load-displacement curves (a)
and the relationship between H/E and depth recovery ratio (b).

135

00
O

 

 

+ CrN1 -Al
—9— CrN-SZ-AI
—¢— CrN-S1 -AI
—8— CrN-Cr-Al
—-x—- CrN5-AI

25 +

   
 
  

 

 

 

f liTY‘l’TjTYTYYlIY'YY

(a)

 

Hardness (GPa)
o 01 8 a B

 

 

i
p
'l)
)-

       

1 L4_L 1 L Lu J l
l l I

 

 

 

 
 

 

 

  

 

 

 

 

O 500 1000 1 500 2000
Displacement (nm)
1
o : +CrN1-AI
=3 0.8 —~ —e—CrN-SZ-Al
E I +CrN-S1-Al
E‘ : +CrN-Cr-AI
¢ 0.6 a: +CrN5-Al
3 .
0 C
e 0.4 -;
'5 r
o. i
8 0.2 ~~
_ (b)
0 A . 1 * i * 1 * ‘ I T ‘ ‘ '
O 500 1 000 1 500 2000

Displacement (nm)

Figure 3.6 Berkovich indentation tests at various depths: composite hardness (a), and
depth recovery ratio (b).

136

 

 

137

 

 

138

 

Figure 3.7 SEM images of the end of scratches on Cer-Al (a), CrNS-Al (b), CrN-Sl-Al
(c), CrN-SZ-Al (d), and CrN-Cr-Al (e). The arrow indicates the scratch direction.

139

Superelastic N iTi

(a)

stress

(b)

 

Elastomeric polymer

__,_._...—-—-SS

, 33 b
strain

 

 

Figure. 3.8 A schematic illustration of the stress-strain curves of superelastic NiTi (a)
and elastomeric polymer (b).

140

 

 
   
    

 

 

 

 

  

 

 

 

 

1.2 ,
E 1%
33 :
g 0.8 -:
g CrN-SZ-AI
o 0.6 ‘:
g :
'3 0.4 -
“7 0.2 j CrN1-AI (a)
0:....,-...,....,....
0 1 000 2000 3000 4000
Cycles
1 .
g 0.8 CrN-Cr-Al
I§ :
i=8 0.6 a;
0 CrN5-Al
: 0.4
.2
‘6
°: 0.2
u. CrN-S1-Al (b)
0.111*:L+11:1'11:1‘11
0 20000 40000 60000 80000
Cycles

Figure 3.9 Friction coefﬁcient and durability of coatings obtained by pin-on-disk test:
specimen Cer-A land CrN-SZ-Al (a), and specimen CrN-Cr—Al, CrNS-Al and CrN-Sl-
A1.

141

 

0.3

0.2

CrN-Cr-AI

 

Friction coefficient

 

 

 

O 5 1O 1 5 20 25
Penetration depth (p m)

Figure 3. 10 Friction coefﬁcient of specimen CrN—Sl—Al and CrN-Cr-Al measured by
scratch test using progressive load up to 2N.

142

 

----1

 

 

 

 

 

 

 

Elastic recovery

0))

 

 

 

Fig. 3.11 Illustration of a spherical indenter sliding on a material: without elastic
recovery in wear track (a) and with elastic recovery in the wear track (b).

143

   
 
 
 

piling-up
Fl

deformed surface

   

riginal surface

 

(a)

 

 

 
  
  

sinking-in

1:11

original surface

I

hc deformed surface

____—__—-

   

(b)

 

 

 

Fig. 3.12 Illustration of a spherical indenter sliding on a material: piling-up (a) and
sinking-in (b).

 

 

A

 

Height (pm)
c':
01

 

 

 

CrN-Cr-Al
(c)
0 50 100 150 200
Lateral position(um)
0.5

 

O

in.“

 

Height (pm)
6
0|

I
_l

[NAM Av/\'\ I\
V

" V

CrN-S1-Al

W

(d)

 

 

 

L.
o:
c: .

l
T

50 1 00

1 50 200

Lateral positionmm)

Figure 3.13 Extent of material piling-up around a scratch made by a progressive load up
to 6N: 3D proﬁle of CrN-Cr-Al (a), 3D proﬁle of CrN-Sl-Al (b), cross-section proﬁle of
CrN-Cr—Al (c), and cross section proﬁle of CrN-Sl-Al (d). Note that dash lines in (a) an
(b) indicate the locations for cross section profile. Figures (a) and (b) are in color.

145

 

  
  

2

   

-..////////////////

  

CrN--S

 

 

 

 

_____________
qqqqqq

00000000
++++++++

logarithm scale.

rate of the specimens. Note that the Y-axis is in

146

 

Load (F)
_\____.___ _ ----

2

 

\

__\_

 

 

 

Displacement (h) hf hmax

Figure 4.1 Schematic illustration of indentation load-displacement curve and deﬁnition
of the irreversible work, W,- W“, and reversible work, W...

147

25pm

 

25pm

2pm J
V'l

 

 

Figure 4.2 Finite element modeling: overall mesh and contact counterparts (a), and
magniﬁed image of the top-left part of the overall mesh (b).

148

feformed surface

 

original surface

 

 

 

 

Figure 4.3 A schematic illustration of indentation piling-up for spherical indentation
experiment.

149

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.5
. oY/E=0.002
. . . a a PU
0 Cl 0 D ‘ T
B a 9 . . A oY/E=0.005
: 1 t A ' x x x 7"
A X
E 1 x x * . i AY/E=O.O1
‘0 . ’ SI
5 . O O 0
0-5 ‘i ' ' xY/E=0.025
FM (3) . YIE=0.1
0 L 1 L ? L4 4 l L
0 0.2 0.4 0.6
hmle
1.5
” OY/E=0.002
1 P ; - oY/E=0.005
é f g 3 a g § § g E
E i ‘ x X x X 1‘ AY/E=0.01
.
0.5 ~: ’ ' ' xY/E=0.025
- "=03 (b) o YIE=0.1
O liwL
0 0.1 0.2 0.3 0.4 0.5 0.6
Elma/R
1.5
_ .Y/E=o.002
1 ' oY/E=0.005
5 r
E “ ° - 9 a I 3 YIE=OO1
5,, ~ I . g a x x i ‘ '
.C ” o o 0
0.5 ._ ’ ' ' ' ' xY/E=0.025
~ n=0.5 (c) . YIE=0.1
0 T T l T
0 02 0.4 06

150

 

1.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

~98 hum/R
1 °o 6 o 0.05
a A
E ° 0 o 0.2
.C
2 — ° .
0.5 a: 8 130.4
n=0.1 (d)
O r i . J. .
0 0.05 0.1 0.15
YIE
1.5 _
E 8 hmIR
g 1 - ° 9 00.05
E f o B 00.2
§ . °
': 05 ..L (30.4
: YIE=0.05 (e)
O r 4
0 0 1 0 2 0.3 0 4 0 5 0 6
n

Figure 4.4 Extent of piling-up (ho/hm,>1) and sinking-in (h/hmax<1) as a ﬁmction of
hmax/R (a-c), Y/E (d), and strain-hardening exponent n (e), in spherical indentation
simulations. Note that (a), (b) and (0) represent materials with strain-hardening exponent
n=0.1, 0.3 and 0.5, respectively, ((1) represents material with n=0.1, hm/R=0.05, 0.2 and
0.4, (e) represents materials with Y/E=0.05, hmax/R=0.05, 0.2 and 0.4. PU stands for
piling-up and SI stands for sinking-in.

151

 

80

Load (mN)
#- O)
O O

N
O
1 l l L 1 1

 

 

O: “'l'"'l""1r"'l"‘rr"r'
0 100 200 300 400 500 600

Displacement (nm)

 

Figure 4.5 Calculated load-displacement curves of a material with Y/E=0.025, v=O.2, and
n=0.5 at various indentation depths.

152

 

 

 

 

1 i1 (wt'wu)lwt=hflhmax
g 03 i R2=0.9995
g” 06;
E 0.4 : 6’00!
2 0°
0.2 E 0&6”
— e
OzkiﬁTIIIITTTTTITTIIIIIIIIIIIITII
0 0.2 0.4 0.6 0.8 1 1.2
I“flhmax

Figure 4.6 Finite element result shows that, for all the materials studied, a linear
relationship exists between h f /hnrm and (W,— Wu)/W,.

153

 

 

 

 

 

 

 

1.2 .
1 “MIle
1 i . 4 . ‘_ A 0.05
j\§k§' x01
"' 0.8 j $53?” .
E; . \2 “Q” A 0.15
g. 0.6 3 c \ ‘ o 0.2
g E \ ’ x025
0.4 3 o 0.3
0.23 .v . .04
3 ‘ o 0.5
O i I T 7 1 l l rT l i l T
0 0.05 0.1 0.15 0.2 0.25 0.3
HIE*

Figure 4.7 For each ﬁxed hum/R, a linear relationship exists between H/E* and (W,-
W.,)/W, for spherical indentation in elastic-plastic solids with work-hardening.

 

 

 

 

3
2 -:
09 I
c 1’
— 1 HI
; ln(-B) = -O.62ln(hmaxIR) + 0.523
OFILLILLllllllLllllll
-4 -3 -2 -1 0
|n(hmale)

Figure 4.8 A linear relationship between In (hm/R) and ln(-B).

154

 

 

 

 

 

 

 

 

1 g .r
O 8 a (Wt'wu)Nvt=hf,hmax
.. : R2=0.996 13
g 0.6 : A.“
3: j . .4}, " - FEM results
5 0.4 I ._ . ' 0 Cu
5 . ' El Al
0.2 3 .. «g; A W
.0" 0 Fused Silica
0 d T T T T T T l l l I T T T l I T T T T T T T fT
0 0.2 0.4 0.6 0.8 1
I"flhmax

Figure 4.9 Spherical indentation experiments show that a linear relationship exists
between h f /hmam and (W,— Wu)/W,. The ﬁnite element results are also shown in this ﬁgure.

155

 

160

 

 

 

j Cu
120
’2" i
g ..
ID 80 ‘—
m
o -
-' :
40 j
0 : j T T T V f T 7 T l T T T T l T T T T
O 500 1 000 1 500 2000
Displacement (nm)

Figure 4.10 Experimental load-displacement curves for spherical indentation in a copper
sample.

156

20000

 

 

 

 

 

15000 f
E E
E 10000 “E .
0‘ ; . R.,ﬂ=1915.6h,,,,,,°'2755

5000 -: R2=0.888

0 h““%‘i“i“L41L4‘*
0 500 1000 1500 2000
Displacement (nm)

Figure 4.11 Effective indenter radius, Ref], as a function of indentation depth, hm for an
imperfect spherical diamond indenter.

157

140

 

120 2 6061-T6 Aluminum
100

80 i
60
40
20

1111 11LL111

Load (mN)

111

(a)

11111141

 

 

 

0 I T Y T I Y T 1' T I 7 T 1 T I

0 500 1000 1 500 2000
Displacement (nm)

 

 

 

350 —~ — m.
300 Tungsten
250
200

150

Load (mN)

111111111111114111111111111

100
50

1111 1

0 rTTTIYTTTITTUTTTrTTITTrTI’TTYTIYFT

0 200 400 600 800 1000 1200 1400
Displacement(nm)

 

 

 

500

 

400 : Fused silica

111111

300

Load (mN)

200

100

11111111111

(e)

0 TUTTI—Tr‘IYITTTTTTTT—‘l—ITTTTITTj—TYYTTW

0 200 400 00 800 100012001400

Displacement (nm)

1

 

 

 

Figure 4.12 Experimental load-displacement curves obtained from instrumented
spherical indentation experiments in aluminum (a), tungsten (b), and fused silica (c).

158

 

400

 

 

 

 

 

 

 

 

 

7; L
0. : DAI
9, ~ H i
g 300 A? a: i i 0: a: ow
3 _
g 200 d: AFused Silica
2 C
3 T.
g 100 i
” E (I B a 8' a B B
'0 ~ g a
6‘2 _ (a)
0 1 1 1 1 1 ' 1 1 1 1 1 '
0 500 1000 1 500 2000
Displacement (nm)
8 L-
E 5
6 .L I § DAI
I I
: ti oW

IiiIII

A Fused silica

Hardness (GPa)
4:.

N

£Imuagm ‘3 u a me te- oCu

O
O 1111111111111 1111‘)
1 i l

0 500 1000 1 500 2000
Displacement (nm)

 

 

 

 

 

 

Figure 4.13 Measured composite reduced modulus (a) and hardness (b) using the energy-
based method together with indenter shape calibration. The error bar indicates the
standard deviation of the measured values.

159

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30,000
3 E=2006Pa,v=0.2
o. .
E 20.000 ‘: —stress~strain 1
g ; 0 1112.21
g 10,000 —:
1: 1 o (a)
O 111:11.1;1111#11111[1111
0 0.02 0.04 0.06 0.08 0.1
True Strain
2000 g
E E YIE=0.002, n=0.3
E 1500
3 I
g 1000 if
in E
g 500 _: —stress-strain
" 0 102.3 (b1
0 1 1 1 f1} 1 1 r 1 4 1 1 1 1 1 1 1 1
0 0.05 0.1 0.15 0.2
True strain
10000 .
a 8000 F YIE=0.025, n=0.3 O
o. “C O
:5 1E 000
+3 4000 -E O
o * O
E 2000 .: stress~strain
" 0 1112.0 (C)
o 1 L 1 1 1r 1 1 1 1 1 1 1 1 1 1 1 1 1 1_
0 0.05 0.1 0.15 0.2
True strain

Figure 4.14 Relationship between hardness and true stress for spherical indentation in
elastic material (a), material with Y/E=0.002, n=0.3, and (c) material with Y/E=0.025,

n=0.3. The horizontal axis represents true strain or representative strain of the same
value.

160

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15 : n=o_1 0 Y/E=0.002
‘6 3 “:
,3 : wwggmom <> 0 o o o o UY/E=0.005
.g 2 $2 AY/E=0.01
2 1 f oY/E=0.025
o ,
o (a) +Y/E=0.1
O 1111111111111111111111111
0 50 100 150 200 250 300
E*anR
4 1
g E "=03 o Y/E=0.002
o 3 ~
«I ; o o 0 o o D Y/E=0.005
E : @23me o o
'5 2 ﬂab AY/E=0.01
.. _
g 1 _~ oY/E=0.025
0 : (b) +Y/E=0.1
o ‘ 1 1,1 1 4 I 1 1 1 1
0 30 60 90 120 150
E*aloR
4 _
h : n=0.5 oY/E=0.002
O ..
~ 3 -— _
° El oo 0 o OWE-0.005
.3 41 @AMASUCFDOU o o o
.g 2 i 150% o AY/E=0.01
g 1 oY/E=0.025
o 1 -«
0 :
1 (c) +Y/E=O.1
O 1 1 141 11 1 ‘ 1 1 1
0 10 20 30 4O 50
E*anR

Figure 4.15 Constraint factors for various materials at different indentation depths: n=0.1
(a), n=0.3 (b) and n=0.5 (0). Note that the scale for x-axis is different in (a), (b) and (c).

161

REFERENCES

162

[1]

[2]

[3]

[41

[6]

[7]

[101

[11]

REFERENCES

W. J. Buehler and F. B. Wang, “Martensitic transformations in the TiNi
compound,” in Paper from Reactivity of Solids. New York, N.Y., American
Elsevier Publishing Co., 1965, pp. 79-90.

F. B. Wang, W. J. Buehler, and S. J. Pickart, “Crystal structure and a unique
martensitic transition of TiNi,” J. Appl. Phys, vol. 36, pp. 3232-3239, 1965.

W. J. Buehler and F. E. Wang, “A summary of recent research on the nitinol
alloys and their potential application in ocean engineering,” Ocean Eng, vol. 1,
pp. 105-120, 1968.

T. Duerig, K. N. Melton, D. Stockel, and C. M. Wayman, Engineering Aspect of
Shape Memory Alloys. Boston: Butterworth—heinemann, 1990.

K. Otsuka and C. M. Wayman, Shape Memory Alloys. Cambridge: Cambridge
University Press, 1998.

T. W. Duerig, “The use of superelasticity in modern medicine,” MRS Bulletin, pp.
101-104, 2002.

S. Miyazaki and A. Ishida, “Martensitic transformation and shape memory
behavior in sputter-deposited TiNi-base thin ﬁlms,” Materials Science and
Engineering, vol. A273-275, pp. 106-133, 1999.

P. Villars, Pearson 's Handbook Desk Edition: Crystallographic Data for
Intermetallic Phases, vol. 2. Materials Park, OH: ASM International, 1997.

V. I. Voronin, V. E. Naish, T. V. Novoselova, V. G. Pushin, and I. V. Sagaradze,
“Structures of Monoclinic phase in titanium nickelide: I. transformation cascade
B2-B19-B19',” The Physics of Metals and Metallography, vol. 89, pp. 12-18,
2000.

Y. Liu, J. V. Humbeeck, R. Stalrnans, and L. Delaey, “Some aspects of the
properties of NiTi shape memory alloy,” Journal of Alloys and Compounds, vol.
247, pp. 115-121,1997.

L. Orgeas and D. F avier, “Stress-induced martensitic transformation of a NiTi
alloy in isothermal shear, tension and compression,” Acta mater., vol. 46, pp.
5579-5591, 1998.

163

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[191

[201

[21]

[221

[23]

[24]

X. J iang, M. Hida, Y. Takemoto, A. Sakakibara, H. Yasuda, and H. Mori, “In situ
observation of stress-induced martensitic transformation and plastic deformation
in TiNi alloy,” Materials Science and Engineering, vol. A238, pp. 303-308, 1997.

H. C. Lin and S. K. Wu, “Determination of heat of transformation in a cold-rolled
martensitic TiNi alloy,” Metallurgical Transactions A, vol. 24A, pp. 293-299,
1 993.

M. Kao, S. Fariabi, R. Thoma, H. Ozkan, and C. L., “Characterization of NiTi
shape memory wires by differential scanning calorimetry and transmission X-ray
diffraction,” presented at Mat. Res. Soc. Symp. Proc., 1992.

Y. Matsukawa, T. Suda, S. Ohnuki, and C. Namba, “Microstructure and
mechanical properties of neutron irradiated TiNi shape memory alloy,” Journal of
Nuclear Materials, vol. 271-272, pp. 106—110, 1999.

V. Pelosin and A. Riviere, “Effect of thermal cycling on the R-phase and
martensitic transformations in a Ti-rich NiTi alloy,” Metallurgical and Materials
Transactions A, vol. 29A, pp. 1 175-1180, 1998.

Y. Liu and G. S. Tan, “Effect of deformation by stress-induced martensitic
transformation on the transformation behavior of NiTi,” Intermetallics, vol. 8, pp.
67-75, 2000.

J. L. J in and H. L. Wang, " Wear resistance of NiT i alloy," Acta. Metal]. Sinica,
vol. 24, No. 1, pp. A66-70, 1988.

P. Clayton, “Tribological behavior of a titanium nickel alloy,” Wear, vol. 162-
164, pp. 202-210, 1993.

J. Singh and A. T. Alpas, “Dry sliding wear mechanism in a Ti50Ni47Fe3
intermetallic alloy,” Wear, vol. 181-183, pp. 302-311, 1995.

D. Y. Li, “Wear behavior of TiNi shape memory alloys,” Scripta Materialia, vol.
34, pp. 195-200, 1996.

H. C. Lin, H. M. Liao, J. L. He, K. C. Chen, and K. M. Lin, “Wear characteristics
of TiNi Shape Memory Alloys,” Metallurgical and Materials Transaction A, vol.
28A, pp. 1871-1877, 1997.

Y. N. Liang, S. Z. Li, Y. B. Jin, W. J in, and S. Li, “Wear behavior of a TiNi
alloy,” Wear, vol. 198, pp. 236—241, 1996.

D. Y. Li and R. Liu, “The mechanism responsible for high wear resistance of
pseudo-elastic TiNi alloy - a novel tribo-material,” Wear, vol. 225-229, pp. 777-
783, 1999.

164

[25]

[261

[27]

[28]

[291

[30]

[31]

[32]

[331

[341

[35]

R. Liu and D. Y. Li, “A ﬁnite element model study on wear resistance of
pseudoelastic TiNi alloy,” Materials Science and Engineering A, vol. A277, pp.
169-175, 2000.

F. T. Cheng, P. Shi, and H. C. Man, “Correlation of cavitation erosion resistance
with indentation-derived properties for a NiTi alloy,” Scripta Materialia, vol. 45,
pp.1089,2001.

R. Liu and D. Li, “Modiﬁcation of Archard's equation by taking account of
elastic/pseudoelastic properties of materials,” Wear, vol. 250—251, pp. 956-964,
2001.

R. Liu and D. Y. Li, “Indentation behavior and wear resistance of pseudoelastic
Ti-Ni alloy,” Materials Science and Technology, vol. 16, pp. 328-332, 2000.

K. Gall, K. Juntunen, H. J. Maier, H. Sehitoglu, and Y. I. Chumlyakov,
“Instrumented micro-indentation of NiTi shape-memory alloys,” Acta mater., vol.
49, pp. 3205-3217, 2001.

K. Gall, M. Dunn, Y. Liu, P. Labossiiere, H. Sehitoglu, and Y. Chumlyakov,
“Micro and macro deformation of single crystal NiTi,” Transaction of ASME, vol.
124, pp. 238-245, 2002.

S. Moyne, c. Poilane, K. Kitarnura, S. Miyazaki, P. Delobelle, and C. Lexcellent,
“analysis of the therrnomechanical behavior of Ti-Ni shape memory alloy thin

ﬁlms by bulging and nanoindentation procedures,” Materials Science and
Engineering, vol. A273-275, pp. 727-732, 1999.

R. Liu, D. Y. Li, Y. S. Xie, R. Lewellyn, and H. M. Hawthorne, “Indentation
behavior of pseudoelastic TiNi alloy,” Scripta Materialia, vol. 41, pp. 691-696,
1999.

L. Chang, C. Hu-Simpson, D. S. Grummon, W. Pratt, and R. Loloee, “Structure
and Phase Transformations in Thermoelastic Ni sub (1--x) TiCu sub (x) Thin
Films Prepared by DC Magnetron Sputtering,” presented at Thin Film Structures
and Phase Stability, San Francisco, CA, USA, 1990.

D. Grummon and L. Chang, “Effect of Concurrent Ion Bombardment on Structure
and Composition of Ion Sputter—Deposited Ni--Ti Thin Films,” presented at
Materials Modiﬁcation by Energetic Atoms and Ions, San Francisco, CA, USA, ,
pp. 167-172, 1992.

L. Hou, T. J. Pence, and D. S. Grummon, “Structure and thermal stability in
titanium-nickel thin ﬁlms sputtered at elevated-temperature on inorganic and

165

 

1—1
'4)

[a
j,

[4

[4

[4

[<1

[4

[4

 

[36]

[37]

[38]

[39]

[40]

[41]

[42]

[43]

[44]

145]

[46]

polymeric substrates,” presented at Materials for Smart Systems, 28-30 Nov.
1994, Boston, MA, USA, pp. 369-374,1995.

L. Hou and D. S. Grummon, “Transformational superelasticity in sputtered
titanium-nickel thin ﬁlms,” Scr. Metal]. Mater., vol. 33, pp. 989-995, 1995.

D. S. Grummon, L. Hou, and T. J. Pence, “Progress on sputter-deposited
thermotractive titanium-nickel ﬁlms,” Journal de Physique (France) IV (France),
vol. 5, pp. 665-670, 1995.

D. S. Grummon, “Fabrication, microstructure and stress effects in sputtered TiNi
thin ﬁlms,” Materials Science Forum (Switzerland), vol. 327-328, pp. 295-302,
2000.

D. S. Grummon, R. Gotthardt, and T. Lagrange, “Planar extrinsic biasing of thin
ﬁlm shape-memory MEMS actuators,” presented at Surface Engineering 2002--
Synthesis, Characterization and Applications, Boston, Massachusetts, USA, 2003.

D. S. Grummon, J. Zhang, and T. J. Pence, “Relaxation and recovery of extrinsic
stress in sputtered titanium-nickel thin ﬁlms on (100)-Si,” Materials Science and
Engineering, vol. A273-275, pp. 722-726, 1999.

D. S. Grummon and T. J. Pence, “Thennotractive Titanium-Nickel Thin Films for
Microelectromechanical and Smart Materials Systems,” Proc. Mater. Res. Soc.
Symp, vol. 459, pp. 331, 1997.

D. S. Grummon and R. Gotthardt, “Latent sprain in titanium-nickel thin ﬁlms
modiﬁed by irradiation of the plastically-deformed martensite phase with 5 MeV
Ni2+,” Acta mater., vol. 48, pp. 635-646, 2000.

A. Ishida, M. Sato, and S. Miyazaki, “Mechanical properties of Ti-Ni shape
memory thin ﬁlms formed by sputtering,” Materials Science and Engineering,
vol. A273-275, pp. 754-757, 1999.

A. Ishida and S. Miyazaki, “Microstructure and mechanical properties of sputter-
deposited Ti-Ni alloy thin ﬁlms,” Journal of Engineering Materials and
Technology, vol. 121, pp. 2-8, 1999.

P. Surbled, C. Clerc, B. Piouﬂe, M. Ataka, and H. Fujita, “Effect of the
composition and thermal annealing on the transformation temperatures of the

sputtered TiNi shape memory alloy thin ﬁlms,” Thin solid films, vol. 401 , pp. 52-
59, 2001.

Y. Fu, W. Huang, H. Du, X. Huang, J. Tan, and X. Gao, “Characterization of

TiNi shape memory alloy thin ﬁlms for MEMS applications,” Surface Coatings
and Technology, vol. 145, pp. 107-112, 2001.

166

[47]

[48]

[49]

[50]

[51]

[52]

[53]

[54]

[55]

[56]

[57]

[58]

A. Ishida and V. Martynow, “Sputter-deposited shape memory alloy thin ﬁlms:
properties and applications,” MRS Bulletin, pp. 111-114, 2002.

J. J. Gill, D. T. Chang, L. A. Momoda, and G. P. Carman, “Manufacturing issues
of thin ﬁlm NiTi microwrapper,” Sensors and Actuators A, vol. 93, pp. 148-156,
2001.

M. Kohl, D. Dittmann, Q. E., B. Winzek, S. Miyazaki, and D. M. Allen, “Shape
memory microvalves based on thin ﬁlms or rolled sheets,” Materials Science and
Engineering, vol. A273-275, pp. 784-788, 1999.

V. Chemysh, V. Tuboltsev, and V. Kulikauskas, “Angular distributions of Ni and
Ti atoms sputtered from a NiTi alloy under He+ and Ar+ ion bombardment,”
Nuclear Instruments and Methods in Physics Research B, vol. 140, pp. 303-310,
1 998.

H. Noh, K. Lee, X. Cui, and C. Choi, “The composition and structure of TiNi thin
ﬁlm formed by electron beam evaporation,” Scripta mater, vol. 43, pp. 847-852,
2000.

K. Ho and G. Carman, “Sputter deposition of NiTi thin ﬁlm shape memory alloy
using a heated target,” Thin Solid Films, vol. 370, pp. 18-29, 2000.

M. Bendahan, J. Seguin, P. Canet, and H. Carchano, “NiTi shape memory alloy
thin ﬁlms: composition control using optical emission spectroscopy,” Thin Solid
Films, vol. 283, pp. 61-66, 1996.

J. He, K. Won, and J. Chang, “TiNi thin ﬁlms prepared by cathodic arc plasma
ion plating,” Thin Solid Films, vol. 359, pp. 46-54, 2000.

J. P. Chu, Y. W. Lai, T. N. Lin, and S. F. Wang, “Deposition and characterization
of TiNi-base thin ﬁlms by sputtering,” Materials Science and Engineering, vol.
A277, pp. 11-17, 2000.

A. Ishida, M. Sato, A. Takei, K. Nomura, and S. Miyazaki, “Effect of aging on
shape memory behavior ofTi-S 1.3 at. pct. Ni thin ﬁlms,” Metallurgical and
Materials Transactions A, vol. 27A, pp. 3753-3759, 1996.

T. Matsunaga, S. Kajiwara, O. K., K. T., and M. 8., “High strength Ti-Ni-base
shape memory thin ﬁlms,” Materials Science and Engineering A2 73-2 75, vol.
A273-275, pp. 745-748, 1999.

A. Ishida, K. Ogawa, M. Sato, and S. Miyazaki, “Microstructure of Ti- 48.2 at.

pct Ni shape memory thin ﬁlms,” Metallurgical and Materials Transactions A,
vol. 28A, pp. 1985-1991, 1997.

167

[59]

[60]

[61]

[62]

[63]

[64]

[65]

[66]

[67]

[68]

[69]

[70]

J. X. Zhang, M. Sato, and A. Ishida, “Structure of martensite in sputter-deposition
Ti-Ni thin ﬁlms coating Guinier-Preston zones,” Acta mater., vol. 49, pp. 3001-
3010, 2001.

A. Ishida, A. Takei, M. Sato, and S. Miyazaki, “Stress-strain curves of sputtered
thin ﬁlms of Ti-Ni,” Thin Solid Films, vol. 281-282, pp. 337-339, 1996.

H. Holleck, “Material selection for hard coatings,” J. Vac. Sci .Tech., vol. A4, pp.
2661-2669, 1986.

D. Dowson, “Thin Films in Tribology,” in A method for coating selection, A.
Matthews, K. Hohnberg, and S. and Franklin, Eds., Elservier Science Publishers,
1993.

M. F. Doemer and W. D. Nix, “Stress and deformation processes in thin ﬁlms on
substrates,” CRC Critical Reviews in Solid and Materials Science, vol. 14, pp.
225268, 1988.

F. Spaepen, “Interface and stresses in thin ﬁlms,” Acta mater., vol. 48, pp. 31-42,
2000.

A. A. Volinsky, N. R. Moody, and W. W. Gerberich, “Interfacial toughness
measurements for thin ﬁlms on substrates,” Acta Materiallia, vol. 50, pp. 441-
466, 2002.

R. H. Dauskardt, M. Lane, Q. Ma, and N. Krishna, “Adhesion and debonding of
multilayer thin ﬁlm structures,” Engineering Fracture Mechanics, vol. 61, pp.
141-162,1998.

M. Lane and D. R. H ., “Adhesion and reliability of copper interconnects with Ta
and TaN barrier layers,” J. Mater. Res, vol. 15, pp. 203-211, 2000.

H. Ollendorf, D. Schneider, T. Schwarz, G. Kirchhoff, and M. A., “A comparative
study of the mechanical properties of TiN coatings using the non-destructive
surface acoustic wave method, scratch tet and four-point bending test,” Surface
and Coatings Technology, vol. 84, pp. 458-464, 1996.

B. Navinsek, P. Panj an, M. Cekada, and D. T. Quinto, “Interface characterization
of combination hard solid/solid lubricant coatings by speciﬁc methods,” Surface
and Coatings Technology, vol. 154, pp. 194-203, 2002.

H. Ichimura and Y. Ishii, “Effects of indenter radius on the critical load in scratch
testing,” Surface and' Coatings Technology, vol. 165, pp. 1-7, 2003.

168

[71]

[72]

[73]

[74]

[75]

[76]

[77]

[78]

[79]

[80]

[81]

[82]

[83]

C. Subramanian, G. Cavallaro, and G. Winkelman, “Wear map of titanium nitride
coatings deposited on copper and brass with electroless nickel interlayers,” Wear,
vol. 241, pp. 228-233, 2000.

O. Glozman, G. Halperin, I. Etsion, A. Bemer, D. Shectman, and G. H. Lee,
“Study of the wear behavior and adhesion of diamond ﬁlms deposited on steel

substrates by use of a Cr-N interlayer,” Diamond and Related Materials, vol. 8,
pp. 859-864, 1999.

S. Hogmark, s. Jacobson, and M. Larsson, “Design and evaluation of tribological
coatings,” Wear, vol. 246, pp. 20-33, 2000.

Y. Xie and H. H. M., “A model for compressive coating stresses in the scratch
adhesion test,” Surface and Coatings Technology, vol. 141, pp. 15-25, 2001.

Y. Xie and H. M. Hawthorne, “Effect of contact geometry on the failure modes of

thin coatings in the scratch adhesion test,” Surface and Coatings Technology, vol.
155, pp. 121-129, 2002.

P. J. Burnett and D. S. Rickerby, “The relationship between hardness and scratch
adhesion,” Thin Solid Films, vol. 154, pp. 403-416, 1987.

W. Pan, G. Yu, and J. Huang, “Mechanical properties of ion-plated TiN ﬁlms on
AISI D2 steel,” Surface and Coatings Technology, vol. 110, pp. 111-119, 1998.

F. Ashraﬁzadeh, “Adhesion evaluation of PVD coatings to aluminum substrate,”
Surface and Coatings Technology, vol. 130, pp. 186-194, 2000.

J. Valli, U. Makela, A. Matthews, and V. Murawa, “TiN Coating Adhesion
Studies Using the Scratch Test Method,” J. Vac. Sci. Technol., vol. A3, pp. 2411-
2414, 1985.

I. M. Hutchings, Tribology: Friction and Wear of Engineering Materials. Boca
Raton, USA: CRC Press, 1992.

S. Veprek, “Conventional and new approaches towards the design of novel
superhard materials,” Surface and Coatings Technology, vol. 97, pp. 15-22, 1997.

G. Subhash and W. Zhang, “Investigation of the overall ﬁ'iction coefﬁcient in
single-pass scratch test,” Wear, vol. 252, pp. 123-134, 2002.

S. Hogmark, H. P., and S. Jacobson, “T ribological properties of thin hard

coatings: demands and evaluation,” Surface and coatings Technology, vol. 90, pp.
247-257, 1997.

169

[84]

[85]

[86]

[87]

[88]

[89]

[90]

[91]

[92]

[93]

[94]

[95]

[96]

A. Leyland and A. Matthews, “On the signiﬁcance of the H/E ratio in wear

control: a nanocomposite coating approach to optimized tribological behavior,”
Wear, vol. 246, pp. 1-11, 2000.

Y. T. Cheng and C. M. Cheng, “Relationships between hardness, elastic modulus,
and the work of indentation,” App]. Phys. Lett., vol. 73, pp. 614-616, 1998.

Y. T. Cheng and C. M. Cheng, “Scaling approach to conical indentation in elastic-
plastic solids with work hardening,” Journal of Applied Physics, vol. 84, pp.
1284-1291, 1998.

F. Wu, J. Li, and J. Duh, “Evaluation of the mechanical properties and
tribological behavior of the CrN coating deposited on mild steel modiﬁed with
electroless Ni interlayer,” Thin Solid ﬁlms, vol. 377-378, pp. 354-359, 2000.

J. Tang, L. Feng, and J. S. Zabinski, “The effect of metal interlayer insertion on
the friction, wear and adhesion of TiC coatings,” Surface and Coatings
Technology, vol. 99, pp. 242-247, 1998.

S. B. Hu, J. P. Tu, Z. Mei, Z. Z. Li, and X. B. Zhang, “Adhesion strength and high
temperature wear behavior of ion plating TiN composite coating with electric

brush plating Ni-W interlayer,” Surface and Coatings Technology, vol. 141, pp.
174-181, 2001.

E. A. Almond, “Aspects of Various Processes for Coating and Surface
Hardening,” Vacuum, vol. 34, pp. 835-842, 1984.

W. C. Oliver and G. M. Pharr, “An improved technique for determining hardness
and elastic modulus using load and displacement sensing indentation
experiments,” J. Mater. Res., vol. 7, pp. 1564-1583, 1992.

D. Tabor, The Hardness of Metals. London: Oxford University Press, 1951.

W. D. Nix, “Elastic and plastic properties of thin ﬁlms on substrates:
nanoindentation techniques,” Materials Science and Engineering, vol. A234-236,
pp. 37-44, 1997.

J. B. Savader, M. R. Scanlon, R. C. Cammarata, D. T. Smith, and C. Hayzelden,
“Nanoindentation study of sputtered nanocrystalline iron thin ﬁlms,” Scripta

Materialia, vol. 36, pp. 29-34, 1997.

A. J. Whitehead and T. F. Page, “Nanoindentation studies of thin ﬁlm coated
systems,” Thin Solid Films, vol. 220, pp. 277-283, 1992.

M. F. Doemer and W. D. Nix, “A method for interpreting the data from depth
sensing indentation instruments,”.l. Mater. Res., vol. 1, pp. 601-609, 1986.

170

 

[9

[9

[1

[l

 

 

[97]

[98]

[99]

[100]

[101]

[102]

[103]

[104]

[105]

[106]

[107]

[108]

[109]

Y. T. Cheng and C. M. Cheng, “Effect of 'sink in' and 'pile up' on estimating the
contact area under load in indentation,” Philosophical Magazine Letters, vol. 78,
pp. 115-120, 1998.

G. M. Pharr and A. Bolshakov, “Understanding nanoindentation unloading
curves,” J. Mater. Res., vol. 17, pp. 2660-2671, 2002.

I. N. Sneddon, Int. J. Eng. Sci, vol. 3, pp. 47, 1963.

C. M. Cheng and Y. T. Cheng, “On the initial unloading slope in indentation of
elastic-plastic solids by and indenter with an axisymmetric smooth proﬁle,” App].
Phys. Lett., vol. 71, pp. 2623-2625, 1997.

General Electric Fused Quartz Products Technical Data, vol. general catalog
number 7705-7725, 1985.

Y. T. Cheng and C. M. Cheng, “Further analysis of indentation loading curves:
effects of tip founding on mechanical property measurements,” J. Mater. Res.,
vol. 13, pp. 1059-1064, 1998.

Y. T. Cheng and C. M. Cheng, “Scaling relationships in conical indentation of
elastic-perfectly plastic solids,” International Journal of Solid Structures, vol. 36,
pp. 1231-1243, 1999.

Y. T. Cheng and C. M. Cheng, “Analysis of indentation loading curves obtained
using conical indenters,” Philosophical Magazine Letters, vol. 77, pp. 39-47,
1998.

Y. T. Cheng, “Can stress-strain relationships be obtained from indentation curves
using conical and pyramidal indenters?,” J. Mater. Res., vol. 14, pp. 3493-3496,
1999.

Y. T. Cheng, Z. Li, and C. M. Cheng, “Scaling relationship for indentation
measurements,” Philosophical Magazine, vol. 82, pp. 1821-1829, 2002.

A. Bolshakov and G. M. Pharr, “Inﬂuence of pileup on the measurement of
mechanical properties by load and depth sensing indentation techniques,” J.
Mater. Res., vol. 13, pp. 1049-1058, 1998.

T. A. Laursen and J. C. Simo, “A study of the mechanics of the microindentation
using ﬁnite elements,” J. Mater. Res., vol. 7, pp. 618-626, 1992.

Y. Y. Lim, M. M. Chaudhri, and Y. Enomota, “Accurate determination of the

mechanical properties of thin aluminum ﬁlms deposited on sapphire ﬂats using
nanoindentations,” J. Mater. Res., vol. 14, pp. 2314-2327, 1999.

171

[110]

[111]

[112]

[113]

[114]

[115]

[116]

[117]

[118]
[119]

[120]

[121]

[122]

[123]

Z. Li, Y. T. Cheng, H. T. Yang, and S. Chandrasekar, “On two indentation
hardness deﬁnitions,” Surface and Coatings Technology, vol. 154, pp. 124-130,
2002.

J. Malzbender and G. de With, “Indentation load-displacement curves, plastic
deformation, and energy,” J. Mater. Res., vol. 17, pp. 502-511, 2002.

Y. T. Cheng and C. M. Cheng, “What is indentation hardness?” Surface and
Coatings Technology, vol. 133-134, pp. 417-424, 2000.

K. L. Johnson, Contact Mechanics. Cambridge: Cambridge University Press,
1985.

M. M. Chaudhri, “Subsurface strain distribution around Vickers hardness

indentations in annealed polycrystalline copper,” Acta Mater., vol. 46, pp. 3047-
3056, 1998.

M. Mata, M. Anglada, and J. Alcala, “Contact deformation regimes around sharp
indentations and the concept of the characteristic strain,” J. Mater. Res., vol. 17,
pp. 964-976, 2002.

A. E. Giannakopoulos and S. Suresh, “Determination of elastoplastic properties
by instrumented sharp indentation,” Scripta Materialia, vol. 40, pp. 1191-1198,
1999.

T. A. Venkatesh, K. J. Van Vliet, A. E. Giannakopoulos, and S. Suresh,
“Determination of elasto-plastic properties by instrumented sharp indentation:

guidelines for property extraction,” Scripta mater, vol. 42, pp. 833-839, 2000.

B. W. Mott, Micro—indentation Hardness T esting. London; Butterworths, 1956.

A. C. Fischer-Cripps, Nanoindentation. New York: Springer-Verlag, 2002.

J. S. Field and M. V. Swain, “A simple predictive model for spherical
indentation,” J. Mater. Res., vol. 8, pp. 297-306, 1993.

A. C. Fischer-Cripps, “Study of analysis methods of depth-sensing indentation
test data for spherical indenters,” J. Mater. Res., vol. 16, pp. 1579-1584, 2001.

A. L. Norbury and T. Samuel, J. Iron Steel Inst, vol. 117, pp. 673, 1928.

R. Hill, B. Storakers, and A. B. Zdunek, “A Theoretical Study of the Brinell
Hardness Test,” presented at Proc. R. Soc., London, 1989.

172

[124]

[125]

[126]

[127]

[128]

[129]

[130]

[131]

[132]

[133]

[134]

[135]

J. S. Field and M. V. Swain, “Determining the mechanical properties of small
volumes of material from submicrometer spherical indentations,” J. Mater. Res.,
vol. 10, pp. 101-112,1995.

J. H. Ahn and D. Kwon, “Derivation of Plastic Stress-strain Relationship from

Ball Indentations: Examination of strain deﬁnition and pileup effect,” J. Mater.
Res., vol. 16, pp. 3170-3178, 2001.

T. A. Adler, “Elastic-plastic indentation of hard, brittle materials with spherical
indenters,”J. Am. Ceram. Soc., vol. 77, pp. 3177-3185, 1994.

S. Kucharski and Z. Mroz, “Indentation of plastic hardening parameters of metals
from spherical indentation tests,” Materials Science and Engineering, vol. A318,
pp. 65-76, 2001.

J. Alcala, A. E. Giannakopoulos, and S. and Suresh, “Continuous measurement of
load-penetration curves with spherical micrometers and estimation of mechanical
properties,” J. Mater. Res., vol. 13, pp. 1390-1400, 1998.

M. Beghini, L. Bertini, and V. and Fontanari, “On the possibility to obtain the
stress-strain curves for a strain-hardening material by spherical indentation,”

Intemationa] Journal of Computer Applications in Technology, vol. 15, pp. 168-
175, 2002.

M. Beghini, L. Bertini, and V. and Fontanari, “Evaluation of the ﬂow curve of

metallic materials by means of spherical indentation,” Computational Methods in
Contact Mechanics, vol. V, pp. 241-252, 2001.

E. G. Herbert, G. M. Pharr, W. C. Oliver, B. N. Lucas, and J. L. Hay, “On the
measurement of stress-strain curves by spherical indentation,” Thin Solid Films
(Switzerland), vol. 398—399, no. 0, pp. 331-335, 1 Nov. 2001, vol. 398-399, pp.
331-335, 2001.

D. Tabor, “A-simple theory of static and dynamic hardness,” Proc. Roy. Soc. A,
vol. 192, pp. 247-274, 1948.

D. Tabor, “Indentation hardness: F iﬁy years on indentation: A personal view,”
Philosophical Magazine A, vol. 74, pp. 1207-1212, 1996.

H. A. Francis, “Phenomenological analysis of plastic spherical indentation,”
Transactions of the ASME, Journal of Engineering Materials and Technology,
vol. 9, pp. 272-281, 1976.

Y. Tirupataiah and G. Sundararajan, “A Comprehensive analysis of the Static
indentation process,” Materials Science and Engineering, vol. 91, pp. 169-180,
1987.

173

[136]

[137]

[138]

[139]

[140]

[141]

[142]

[143]

[144]

[145]

[146]

[147]

Y. Tirupataiah and G. Sundararaj an, “On the constraint factor associated with the
indentation of work-hardening materials with a spherical ball,” Metallurgical
Transactions A, vol. 22A, pp. 2375-23 84, 1991.

A. Naybebi, R. E. Abdi, O. Bartier, and G. Mauvoisin, “New procedure to
determine steel mechanical parameters from the spherical indentation technique,”
Mechanics of Materials, vol. 34, pp. 243-254, 2002.

B. Taljat, T. Zacharia, and F. Kosel, “New analytical procedure to determine
stress-strain curve from spherical indentation data,” Int. J. Solid Structures, vol.
35, pp. 4411-4426, 1998.

S. D. Mesarovic and N. A. Fleck, “Spherical indentation of elastic-plastic solids,”
Proceedings of the Royal Society, vol. 455, pp. 2707-2728, 1999.

K. Durst, M. Goken, and G. M. Pharr, “Finite element simulation of spherical
indentation in the elastic-plastic transition,” Z. Metallke, vol. 93, pp. 857-861,
2002.

R. H. Richman and W. P. McNaughton, “A metallurgical approach to improved
cavitation-erosion resistance,” Journal of Materials Engineering and
Performance, vol. 6, pp. 633-641, 1997.

T. Zhang and D. Y. Li, “An experimental study on the erosion behavior of
pseudoelastic TiNi alloy in dry sand and in aggressive media,” Materials Science
and Engineering, vol. A293, pp. 208-214, 2000.

H. Hiraga, T. Inoue, H. Shimura, and A. Matsunawa, “Cavitation-erosion
mechanism of NiTi coatings made by laser plasma hybrid spraying,” Wear, vol.
231, pp. 272-278, 1999.

Y. Y. Lim and M. M. Chaudhri, “Nanohardness mapping of the curved surface of
spherical macroindentations in fully annealed polycrystalline oxygen-free
copper,” Physica Status Solidi (a), vol. 194, pp. 19-29, 2002.

J. E. Sundgren and H. T. G. Hentzell, “A review of the present state of art in hard

coatings grown from the vapor phase,” J. Vac. Sci. T echnol. A., vol. 4, pp. 2259-
2279, 1986.

M. D. Drory and J. W. Hutchinson, “Diamond Coating of Titanium Alloys,”
Science, vol. 263, pp. 1753-1755, 1994.

Y. T. Cheng, “Scaling relationships in indentation of power-law creep solids

using self—similar indenters,” Philosophical Magazine letters, vol. 81, pp. 9-16,
2001.

174

[148]

[149]

[150]

[151]

[152]

[153]

[154]

[155]

[156]

[157]

[158]

[159]

[160]

D. Brandon and W. D. Daplan, Joining Process: An introduction: John Wiley &
Sons Ltd., 1997.

K. Komvopoulos, N. Saka, and N. P. Suh, “The mechanism of ﬁiction in
boundary lubrication,” Journal of T ribology, vol. 107, pp. 452-462, 1985.

F. M. Haggag and G. E. Lucas, “Determination of Luders strains and ﬂow
properties in steels from hardness/microhardness tests,” Metall. Trans A, vol.
14A, pp. 1607-1613, 1983.

J. Alcala, A. E. Giannakopoulos, and S. Suresh, “Continuous measurements of
load-penetration curves with spherical microindenters and the estimation of
mechanical properties,” Journal of Materials Research, vol. 13, pp. 1390-1400,
1998.

M. M. Chaudhri and M. Winter, “The load-bearing area of a hardness
indentation,” J. Phys. D, App]. Phys, vol. 21, pp. 370-374, 1988.

G. E. Dieter, Mechanical Metallurgy, 3rd ed. New York: NcGraw-Hill, 1986.

G. I. Barenblatt, Scaling, Self-similarity, and Intermediate Asymptotics.
Cambridge: Cambridge University Press), 1996.

ABAQUS, Version 6.2 ed. Pawtucket, RI 02860: Hibbitt, Karlsson & Sorensen,
Inc.

K. A. Gschneidner, Solid State Physics, vol. 16, pp. 275, 1964.

G. Simmons and H. Wang, Single crystal elastic constants ad calculated
aggregate properties: A handbook, 2nd ed. Cambridge, MA: The MIT Press,
1971.

W. J. Poole, M. F. Ashby, and N. A. Fleck, “Micro-hardness of annealed and
work-hardened copper polycrystals,” Scripta Materialia, vol. 34, pp. 559-564,
1996.

K. W. McElhaney, J. J. Vlassak, and W. D. Nix, “Determination of indenter tip
geometry and indentation contact area for depth-sensing indentation
experiments,” Journal of Materials Research, vol. 13, pp. 1300-1306, 1998.

W. W. Gerberich, N. I. Tymiak, J. C. Grunlan, M. F. Horstemeyer, and M. I.

Baskes, “Interpretations of indentation size effects,” ASME International, Journal
of Applied Mechanics (Transactions of the ASME), vol. 69, pp. 433-442, 2001.

175

[161]

[162]

[163]

W. D. Nix and H. Gao, “Indentation size effects in crystalline materials: a law for
strain gradient plasticity,” Journal of the Mechanics and Physics of Solids, vol.
46, pp. 411-425, 1998.

J. G. Swadener, E. P. George, and G. M. Pharr, “The correlation of indentation
size effect measured with indenters of various shapes,” Journal of Mechanics and

Physics of Solids, vol. 50, pp. 681-694, 2002.

Y. T. Cheng, “Scaling, dimensional analysis, and indentation measurements,”
Materials Science and Engineering R, to be published.

176

   

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