Indentaion Test- Theory

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Mechanical Engineering Series

Series Editors

Ward O. Winer

Arthur E. Bergles

Georgia A. Klutke

Kuo K. Wang

Iain Finnie

J. R. Welty

Michael D. Bryant

Henry T. Yang

Van C. Mow

Frederick A. Leckie

Dietmar Gross

For further volumes:

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Mechanical Engineering Series

Frederick F. Ling

Editor-in-Chief

The Mechanical Engineering Series features graduate texts and research monographs to

address the need for information in contemporary mechanical engineering, including areas

of concentration of applied mechanics, biomechanics, computational mechanics, dynami-

cal systems and control, energetics, mechanics of materials, processing, production systems,

thermal science, and tribology.

Advisory Board/Series Editors

Applied Mechanics F.A. Leckie

University of California,

Santa Barbara

D. Gross

Technical University of Darmstadt

Biomechanics V.C. Mow

Columbia UniversityComputational Mechanics H.T. Yang

University of California,

Santa Barbara

Dynamic Systems and Control/ D. Bryant

Mechatronics University of Texas at Austin

Energetics J.R. Welty

University of Oregon, Eugene

Mechanics of Materials I. Finnie University of California, Berkeley

Processing K.K. Wang

Cornell University

Production Systems G.-A. Klutke

Texas A&M University

Thermal Science A.E. Bergles

Rensselaer Polytechnic Institute

Tribology W.O. Winer Georgia Institute of Technology


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Anthony C. Fischer-Cripps

Nanoindentation

Third Edition

1 3


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ISSN 0941-5122 e-ISSN 2192-063XISBN 978-1-4419-9871-2 e-ISBN 978-1-4419-9872-9DOI 10.1007/978-1-4419-9872-9Springer New York Dordrecht Heidelberg London

Springer Science+Business Media, LLC 2011All rights reserved. This work may not be translated or copied in whole or in part without the written

permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connec-tion with any form of information storage and retrieval, electronic adaptation, computer software, or bysimilar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are

not identified as such, is not to be taken as an expression of opinion as to whether or not they are subjectto proprietary rights.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

Anthony C. Fischer-CrippsFischer-Cripps Laboratories Pty Ltd.Londonderry Drive 292087 Killarney Heights, New South WalesAustralia

[email protected]


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To Dianne, Raymond and Henry


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vii

Series Preface

Mechanical engineering, an engineering discipline forged and shaped by the needsof the industrial revolution, is once again asked to do its substantial share in the call

for industrial renewal. The general call is urgent as we face profound issues of pro-

ductivity and competitiveness that require engineering solutions. The Mechanical

Engineering Series features graduate texts and research mono-graphs intended to

address the need for information in contemporary areas of mechanical engineering.

The series is conceived as a comprehensive one that covers a broad range of con-

centrations important to mechanical engineering graduate education and re-search.

We are fortunate to have a distinguished roster of consulting editors on the advisory

board, each an expert in one of the areas of concentration. The names of the consult-

ing editors are listed on the facing page of this volume. The areas of concentration

are applied mechanics, biomechanics, computational me-chanics, dynamic systems

and control, energetics, mechanics of materials, processing, production systems,

thermal science, and tribology.

New York, New York Frederick F. Ling


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Preface

There has been considerable interest in the last two decades in the mechanical char-acterisation of thin film systems and small volumes of material using depth-sensing

indentation tests utilising either spherical or pyramidal indenters. Usually, the prin-

cipal goal of such testing is to obtain values for elastic modulus and hardness of the

specimen material from experimental readings of indenter load and depth of pen-

etration. The forces involved are usually in the millinewton range and are measured

with a resolution of a few nanonewtons. The depths of penetration are in the order

of nanometres, hence the term nanoindentation.

This third edition of Nanoindentation adds the results of new research in this

field, and includes more information about nanoindentation instrumentation and

applications. The book is intended for those who are entering the field for the first

time and to act as a reference for those already conversant with the technique.

In preparing this book, I was encouraged and assisted by many friends and col-

leagues. Particular thanks to Ben Beake, Trevor Bell, Avi Bendavid, Alec Bendeli,

Robert Bolster, Andy Bushby, Yanping Cao, Yang-Tse Cheng, Christophe Comte,

Peter Cusack, John Field, Asa Jamting, Nigel Jennett, Brian Lawn, Boon Lim,

Alfonso Ngan, Darien Northcote, Paul Rusconi, Sergio Santos, Doug Smith, Jim

Smith, Eric Thwaite, Stan Veprek, Yvonne Wilson, David Vodnick, Oden Warren,

and Thomas Wyrobek for their advice and assistance. I thank Hysitron Inc. and

Micro Materials Ltd for their important contributions. I gratefully acknowledge the

support of the CSIRO Division of Telecommunications and Industrial Physics and,

in particular, Ken Hews-Taylor who supported the UMIS instrument for many years

in his management portfolio, the staff of the library, and the Chief of the Division

for his permission to use the many figures that appear in this book. I also thank the

many authors and colleagues who publish in this field from whose work I have

drawn and without which this book would not be possible. Finally, I thank the edito-

rial and production team at Springer-Verlag New York, Inc., for their very profes-

sional and helpful approach to the whole publication process.

Sydney, Australia Anthony C. Fischer-Cripps


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Contents

1 Contact Mechanics ....................................................................................... 11.1 Introduction ........................................................................................... 1

1.2 Elastic Contact ...................................................................................... 1

1.3 Geometrical Similarity .......................................................................... 6

1.4 ElasticPlastic Contact .......................................................................... 8

1.4.1 The Constraint Factor ................................................................ 8

1.4.2 Indentation Response of Materials ............................................ 9

1.4.3 ElasticPlastic Stress Distribution ............................................ 10

1.4.4 Hardness Theories ..................................................................... 11

1.5 Indentations at the Nanometre Scale ..................................................... 14

References ...................................................................................................... 17

2 Nanoindentation Testing.............................................................................. 21

2.1 Nanoindentation Test Data .................................................................... 21

2.2 Indenter Types ....................................................................................... 21

2.3 Indentation Hardness and Modulus ....................................................... 24

2.3.1 Spherical Indenter ..................................................................... 25

2.3.2 Vickers Indenter ........................................................................ 26

2.3.3 Berkovich Indenter .................................................................... 27

2.3.4 Cube Corner Indenter ................................................................ 28

2.3.5 Knoop Indenter .......................................................................... 28

2.4 Load-Displacement Curves ................................................................... 29

2.5 Experimental Techniques ...................................................................... 32

2.5.1 Instrument Construction and Installation .................................. 33

2.5.2 Indenters .................................................................................... 34

2.5.3 Specimen Mounting .................................................................. 35

2.5.4 Working Distance and Initial Penetration ................................. 35

2.5.5 Test Cycles ................................................................................ 36

References ...................................................................................................... 37


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3 Analysis of Nanoindentation Test Data.................................................... 39

3.1 Analysis of Indentation Test Data ..................................................... 39

3.2 Analysis Methods .............................................................................. 39

3.2.1 Cylindrical Punch Indenter ................................................... 39

3.2.2 Conical IndenterCylindrical Punch Approximation.......... 413.2.3 Spherical Indenter ................................................................. 43

3.2.4 Berkovich Indenter................................................................ 47

3.2.5 Knoop Indenter ..................................................................... 52

3.2.6 Effective Indenter Shape ....................................................... 55

3.2.7 Energy Methods .................................................................... 59

3.2.8 Dynamic Methods ................................................................. 67

3.2.9 Other Methods of Analysis ................................................... 68

References .................................................................................................... 72

4 Factors Affecting Nanoindentation Test Data......................................... 77

4.1 Introduction ....................................................................................... 77

4.2 Thermal Drift..................................................................................... 77

4.3 Initial Penetration Depth ................................................................... 78

4.4 Instrument Compliance ..................................................................... 81

4.5 Indenter Geometry ............................................................................ 84

4.6 Piling-Up and Sinking-In .................................................................. 88

4.7 Indentation Size Effect ...................................................................... 91

4.8 Surface Roughness ............................................................................ 934.9 Tip Rounding ..................................................................................... 95

4.10 The Plastic Depth .............................................................................. 97

4.11 Residual Stresses ............................................................................... 99

4.12 Friction and Adhesion ....................................................................... 101

4.13 Specimen Preparation........................................................................ 102

References .................................................................................................... 103

5 Simulation of Nanoindentation Test Data................................................ 105

5.1 Introduction ....................................................................................... 1055.2 Spherical Indenter ............................................................................. 105

5.3 Berkovich Indenter ............................................................................ 107

5.4 Conical and Power Law Indenters .................................................... 108

5.5 Finite Element Analysis .................................................................... 111

5.6 Comparison of Simulated and Experimental Data ............................ 113

References .................................................................................................... 117

6 Scaling Relationships in Nanoindentation............................................... 119

6.1 Scaling Relationships in Nanoindentation ........................................ 119

References .................................................................................................... 123

Contents


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7 Time-dependent Nanoindentation.......................................................... 125

7.1 Introduction ..................................................................................... 125

7.2 Dynamic Indentation Testing .......................................................... 126

7.2.1 Single Frequency Dynamic Analysis ................................ 126

7.2.2 Multiple Frequency Dynamic Analysis ............................. 1347.3 Creep ............................................................................................... 136

References .................................................................................................. 144

8 Nanoindentation of Thin Films and Small Volumes of Materials....... 147

8.1 Introduction ..................................................................................... 147

8.2 Testing of Thin Films ...................................................................... 147

8.2.1 Elastic Modulus ................................................................. 148

8.2.2 Hardness ............................................................................ 150

8.2.3 Film Adhesion ................................................................... 1528.3 Scratch Testing ................................................................................ 155

8.4 Small Volumes of Materials ............................................................ 158

References .................................................................................................. 159

9 Other Techniques in Nanoindentation................................................... 163

9.1 Introduction ..................................................................................... 163

9.2 Acoustic Emission Testing .............................................................. 163

9.3 Constant Strain Rate Testing ........................................................... 165

9.4 Fracture Toughness ......................................................................... 1669.5 High-Temperature Nanoindentation Testing ................................... 169

9.6 Strain-hardening Exponent ............................................................. 172

9.7 Impact ............................................................................................. 174

9.8 Residual Stress ................................................................................ 174

9.9 Surface Forces ................................................................................. 177

References .................................................................................................. 178

10 Nanoindentation Test Standards............................................................ 181

10.1 Nanoindentation Test Standards ...................................................... 18110.2 ISO 14577 ....................................................................................... 181

10.2.1 ISO 14577 Part 1: Test Method ......................................... 183

10.2.2 ISO 14577 Part 2: Verification and Calibration

of Machines ....................................................................... 191

10.2.3 ISO 14577 Part 3: Calibration of Reference Blocks ......... 194

10.2.4 ISO 14577 Part 4: Test Method for Coatings .................... 194

References .................................................................................................. 198

11 Nanoindentation Instrumentation.......................................................... 199

11.1 Specifications of Nanoindentation Test Instruments ....................... 199

11.2 Head Design .................................................................................... 202

11.2.1 Actuator ............................................................................. 203

11.2.2 Force Measurement ........................................................... 204

11.2.3 Depth Measurement .......................................................... 206

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11.3 Frame Construction ....................................................................... 208

11.4 Specimen Positioning .................................................................... 208

11.5 Imaging .......................................................................................... 210

11.6 Scratch Testing ............................................................................... 210

References .................................................................................................. 211

12 Applications of Nanoindentation............................................................ 213

12.1 Introduction ................................................................................... 213

12.2 Fused Silica.................................................................................... 214

12.3 Titanium Dioxide Thin Film .......................................................... 215

12.4 Superhard Thin Film ...................................................................... 216

12.5 Diamond-like Carbon (DLC) Thin Film ....................................... 217

12.6 Creep in Polymer Film .................................................................. 218

12.7 Fracture and Delamination of a Silicon Oxide Film...................... 22012.8 High-temperature Testing .............................................................. 221

12.9 Adhesion Measurement ................................................................. 222

12.10 Dynamic Hardness ......................................................................... 222

12.11 Repeatability Testing ..................................................................... 223

12.12 Bone ............................................................................................... 224

12.13 AFM Imaging ................................................................................ 226

12.14 Conductive Nanoindentation ......................................................... 226

12.15 Thermal Barrier Coating ................................................................ 227

12.16 Hardness of Diamond .................................................................... 22712.17 Variation in H/E

rwith Temperature ............................................... 229

12.18 Impact Indentation of Wear Resistant Coatings ............................ 230

12.19 Mechanical Property Mapping ...................................................... 231

12.20 Other Applications ......................................................................... 231

References .................................................................................................. 232

13 Appendices 17......................................................................................... 235

13.1 Elastic Indentation Stress Fields .................................................... 235

13.1.1 Contact Pressure Distributions ......................................... 23513.1.2 Indentation Stress Fields .................................................. 236

13.2 Surface Forces, Adhesion and Friction .......................................... 238

13.2.1 Adhesion Forces in Nanoindentation ............................... 238

13.2.2 Forces in Nature ............................................................... 239

13.2.3 Interaction Potentials ........................................................ 239

13.2.4 Van der Waals Forces ....................................................... 241

13.2.5 Surface Interactions .......................................................... 241

13.2.6 Adhesion ........................................................................... 243

13.2.7 Friction ............................................................................. 247

13.3 Common Indenter Geometries....................................................... 250

13.3.1 Berkovich Indenter ........................................................... 250

13.3.2 Vickers Indenter ............................................................... 251

Contents


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13.3.3 Knoop Indenter .............................................................. 252

13.3.4 Sphero-Conical Indenter ................................................ 253

13.4 Non-linear Least Squares Fitting ................................................... 253

13.5 Properties of Materials................................................................... 257

13.6 Frequently Asked Questions .......................................................... 25813.7 Specifications for a Nanoindenter ................................................. 269

13.7.1 Instrument Function ....................................................... 270

13.7.2 Basic Specifications and Construction ........................... 271

13.7.3 Specimen Positioning ..................................................... 272

13.7.4 Specimen Mounting ....................................................... 272

13.7.5 Optical Microscope and Imaging ................................... 273

13.7.6 Software ......................................................................... 273

13.7.7 Accessories ..................................................................... 274

13.7.8 Instrument Mounting and Isolation ................................ 27413.7.9 Delivery, Calibration and Warranty ............................... 274

13.7.10 Instrument/Supplier Checklist ........................................ 275

References .................................................................................................. 276

Index.................................................................................................................. 277

Contents


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List of Symbols

cone semi-angle, geometry correction factor for Knoop indenter analysis,surface roughness parameter, thin film hardness parameter, buckling pa-

rameter

indenter cone inclination angle, indenter geometry shape factor

phase angle between force and depth in oscillatory indentation tests

distance of mutual approach between indenter and specimen

strain

half of the total energy required to separate two surfaces

gamma function

coefficient of viscosity

angle

number density of molecules

normal stress

I indentation stress

r residual stress

s maximum asperity height

z normal pressure underneath the indenter

shear stress

coefficient of friction

Poissons ratio

frequency

a radius of circle of contact, constant for linear fit

A contact area, constant forPvs hrelationship

ac radius of circle of contact at transition from elastic to plastic deformation

with spherical indenter

Af portion of contact area carried by film

Ai area of contact that would be obtained for an ideal indenter at a particular

penetration depth

ao contact radius obtained for smooth surfacesA

p projected contact area

As portion of contact area carried by substrate


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B length of the short diagonal of the residual impression made by a Knoop

indenter, Burgers vector, constant for linear fit

C constraint factor, coefficients for area function expansion

Ce power law coefficient for elastic response

Cp power law coefficient plastic responseC

0 size of plastic zone

Cf load frame compliance

d length of diagonal of residual impression, diameter of residual impression,

length of long side of impression from a Knoop indenter

D diameter of spherical indenter, damping factor

E elastic modulus

E*Er combined or reduced elastic modulus

Eeff

effective modulus of film and substrate combination

Ef film modulusE

s substrate modulus

F force

FL

lateral force (normal to scratch)

FN

normal force

FT tangential force (parallel to scratch)

G shear modulus, storage modulus, loss modulus

H indentation depth

H hardness

h*

characteristic length for depth dependence on hardnessh

a depth of circle of contact measured from specimen free surface

he elastic depth of penetration for unloading

Heff

effective hardness of filmsubstrate combination

Hf film hardness

hi initial penetration depth

ho amplitude of oscillatory depth reading

Ho hardness measured without presence of dislocations

hc depth of circle of contact measured from maximum depth h

max(the contact

depth)hr depth of residual impression

hrc

contact depth of penetration for an equivalent punch

hs penetration depth at unloading forceP

s, depth at which spherical indenter

tip meets conical support measured from indenter tip

Hs substrate hardness

hmax

total indentation depth measured from specimen free surface

Io weighting function for thin film analysis

K constant for determining initial penetration depth, Boltzmanns constant,

bulk modulus, intercept correction factor, coefficient for stressstrain

response in uniaxial plastic regime

Kc fracture toughness

Ks stiffness of indenter support springs

L,l length or distance

List of Symbols


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m mass of oscillating components, power law exponent that describes the

form of the loading and unloading curves

n Meyers index, slope of logarithmic method of determining hI

P indenter load (force), hydrostatic pressure

Pc critical load at onset of plastic deformation with spherical indenter, pull-offload due to adhesive forces

PI indenter load at initial penetration

pm mean contact pressure

po amplitude of oscillatory force

Pmax

maximum load in an indentation test

Ps indenter load at partial unload

R spherical indenter radius

r radial distance measured from axis of symmetry

R+ equivalent rigid indenter radius for contact involving a deformable indenterof radius R

Ri radius of indenter

Ro initial radius of curvature

Rr radius of curvature of residual impression

S contact stiffness dP/dh

SL

slope of loading curve

SU slope of unloading curve

T temperature, interfacial shear strength

t time, film thicknesstc coating (film) thickness

tf film thickness

ts substrate thickness

U energy, work

uz displacement

V volume

w interaction potential

W work

x strain-hardening exponentY yield stress

Yf yield stress of film

Ys yield stress of substrate

zo equilibrium spacing in the Lennard-Jones potential

List of Symbols


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Introduction

Indentation testing is a simple method that consists essentially of touching the mate-rial of interest whose mechanical properties such as elastic modulus and hardness

are unknown with another material whose properties are known. The technique has

its origins in Mohs hardness scale of 1822 in which materials that are able to leave

a permanent scratch in another were ranked harder material with diamond assigned

the maximum value of 10 on the scale. The establishment of the Brinell, Knoop,

Vickers, and Rockwell tests all follow from a refinement of the method of indenting

one material with another. Nanoindentation is simply an indentation test in which

the length scale of the penetration is measured in nanometres (109m) rather than

microns (106m) or millimetres (103m), the latter being common in convention-

al hardness tests. Apart from the displacement scale involved, the distinguishing

feature of most nanoindentation testing is the indirect measurement of the contact

areathat is, the area of contact between the indenter and the specimen. In conven-

tional indentation tests, the area of contact is calculated from direct measurements

of the dimensions of the residual impression left in the specimen surface upon the

removal of load. In nanoindentation tests, the size of the residual impression is of

the order of microns and too small to be conveniently measured directly. Thus, it is

customary to determine the area of contact by measuring the depth of penetration of

the indenter into the specimen surface. This, together with the known geometry of

the indenter, provides an indirect measurement of contact area at full load. For this

reason, nanoindentation testing can be considered a special case of the more general

terms: depth-sensing indentation (DSI) or instrumented indentation testing (IIT).

It is not only hardness that is of interest to materials scientists. Indentation tech-

niques can also be used to calculate elastic modulus, strain-hardening exponent,

fracture toughness (for brittle materials), and viscoelastic properties. How can such

a wide variety of properties be extracted from such a simple test, which, in many

respects, can be considered a non-destructive test method? Consider the load-dis-

placement response shown in Fig. 1. This type of data is obtained when an indenter,

shaped as a sphere, is placed into contact with the flat surface of the specimen witha steadily increasing load. Both load and depth of penetration are recorded at each

load increment (ultimately providing a measure of modulus and hardness as a func-

tion of depth beneath the surface). Following the attainment of the maximum load,
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xxii Introduction

in the material shown in Fig. 1a, the load is steadily removed and the penetrationdepth recorded. The loading part of the indentation cycle may consist of an initial

elastic contact, followed by plastic flow, or yield, within the specimen at higher

loads. Upon unloading, if yield has occurred, the load-displacement data follow a

different path until at zero applied load, a residual impression is left in the specimen

surface. The maximum depth of penetration for a particular load, together with the

slope of the unloading curve measured at the tangent to the data point at maximum

load, lead to a measure of both hardness and elastic modulus of the specimen mate-

rial. In some cases, it is possible to measure elastic modulus from not only the un-

loading portion, but also the loading portion of the curve. For a viscoelastic materi-al, the relationship between load and depth of penetration is not linearly dependent.

That is, for a given load, the resulting depth of penetration may depend upon the rate

of application of load as well as the magnitude of the load itself. For such materi-

als, the indentation test will be accompanied by creep, and this manifests itself

as a change in depth for a constant applied load as shown in Fig. 1b. An analysis of

the creep portion of the load-displacement response yields quantitative information

about the elastic solid-like properties of the specimen, and also the fluid-like or

out-of-phase components of the specimen properties. In brittle materials, crack-

ing of the specimen may occur, especially when using a pyramidal indenter such asthe three-sided Berkovich or the four-sided Vickers indenter. As shown in Fig. 1c,

the length of the crack, which often begins at the corners of the indentation impres-

sion, can be used to calculate the fracture toughness of the specimen material.

More advanced methods can be employed to study residual stresses in thin films,

the properties of materials at high temperatures, scratch resistance and film adhesion,

and, in some cases, van der Waals type surface forces. In this book, all these issues

are examined and reported beginning with a description of the method of test and the

basis upon which the analysis is founded. Later chapters deal with the various correc-

tions required to account for a number of instrumental and materials related effects

that are a source of error in the measurement, theoretical aspects behind the constitu-

tive laws that relate the mechanical properties to the measurement quantities, recent

attempts at formulating an international standard for nanoindentation, examples of

applications, and a brief description of how nanoindentation instruments are designed.

Fig. 1 Load-displacement curves for (a) an elastic plastic solid and (b) a viscoelastic solid for a

spherical indenter and (c) cracks emanating from the corners of the residual impression in a brittle

material
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