Mechanical properties of materials

Mechanical Properties of Materials

SOLID MECHANICS AND ITS APPLICATIONS

Volume 190

Series Editors: G.M.L. GLADWELL

Department of Civil Engineering

University of Waterloo

Waterloo, Ontario, Canada N2L 3GI

Aims and Scope of the Series

The fundamental questions arising in mechanics are: Why?, How?, and How

much? The aim of this series is to provide lucid accounts written by authoritative

researchers giving vision and insight in answering these questions on the subject of

mechanics as it relates to solids.

The scope of the series covers the entire spectrum of solid mechanics. Thus it

includes the foundation of mechanics; variational formulations; computational

mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations

of solids and structures; dynamical systems and chaos; the theories of elasticity,

plasticity and viscoelasticity; composite materials; rods, beams, shells and

membranes; structural control and stability; soils, rocks and geomechanics; fracture;

tribology; experimental mechanics; biomechanics and machine design.

The median level of presentation is the first year graduate student. Some texts

are monographs defining the current state of the field; others are accessible to final

year undergraduates; but essentially the emphasis is on readability and clarity.

For further volumes:

http://www.springer.com/series/6557

Joshua Pelleg

Mechanical Properties

of Materials

123

Joshua Pelleg

Materials Engineering

Ben Gurion University of the Negev

Ben Gurion Street

Beer Sheva

Israel

ISSN 0925-0042

ISBN 978-94-007-4341-0 ISBN 978-94-007-4342-7 (eBook)

DOI 10.1007/978-94-007-4342-7

Springer Dordrecht Heidelberg New York London

Library of Congress Control Number: 2012940227

© Springer Science+Business Media Dordrecht 2013

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does not imply, even in the absence of a specific statement, that such names are exempt from the relevant

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While the advice and information in this book are believed to be true and accurate at the date of

publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for

any errors or omissions that may be made. The publisher makes no warranty, express or implied, with

respect to the material contained herein.

Printed on acid-free paper

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

To my wife Ada, children Deenah, Ruth

and Asher and their families

Preface

As the title implies, the purpose of this textbook is to present a different approach

to the teaching of Materials Science and Engineering than the one that is now

commonly used. In earlier times, studies of materials were usually referred to

as “metallurgy”. Currently most textbooks still begin by introducing the student

to basic concepts, accompanied by laboratory exercises relevant to each concept.

These exercises are usually quite self-explanatory and have no special prerequisite –

except for some common sense – to perform them. In the preparation of this new

text, the author has been influenced by two guiding principles. The first is that the

student should begin by acquiring some degree of knowledge of and experience with

performing mechanical tests. Thus, Chap. 1 places its emphasis on developing this

skill. This lays the groundwork for the student to begin performing laboratory tests

simultaneously and in parallel with their studies of new concepts throughout the

course. Only after this chapter do we deal with basic concepts such as dislocations,

plastic deformation, etc.

The second guiding principle was the assumption that students exposed to a

course of mechanical behavior of materials in its various forms are if not at a junior

then at least at a sophomore level and sometimes even at a senior level. Thus they

should already have been exposed to the basic concepts of mechanical and structural

fundamentals. Consequently, in this text elements of the theory of elasticity and

plasticity are not covered, but rather the student is referred to appropriate books

or other publications. Inherent in this assumption is the belief that students at this

level are already familiar with the concepts of strain and stress tensors, principal

stresses, normal stress, and to the description of stress at a point. The same approach

is applied to other basic structural principles, and the elements of crystallography,

assuming familiarity of students with the fundamentals of materials science and

engineering materials.

Chapter 1 sets the framework of mechanical testing, excluding investigation

of dynamic stresses (fatigue) and the effect of temperature on applying static

load on materials (creep). These are considered separately. Chapter 2 introduces

the basic concept of dislocations that are needed to explain various observations

of mechanical behavior. Dislocations are essential in this regard and the chapter

vii

viii Preface

is devoted to describing this concept, their motion and generation. In Chap. 3,

plastic deformation is discussed in terms of dislocation motion; slip and slip

planes are introduced and their association with acting shear stress is considered.

Strengthening mechanisms such as strain (work) hardening are treated in Chap. 4.

Chapter 5 is completely devoted to creep, the effect of temperature on materials

which are loaded statically and which can lead to failure either by not being able

to carry the applied load or by stress rupture. The concept of cyclic or repeated

stress and its effect on material response in terms of fatigue failure is discussed in

Chap. 6. Fracture, both brittle and ductile, is considered in Chap. 7. It discusses

fracture occurring in static loading such as in simple tension, in creep as influenced

by the effect of time and temperature and fracture resulting from the application of

cyclic stresses. Finally, Chap. 8 is devoted to the mechanical behavior of small-size

specimens where the dimensions are in the micron and nano scales.

The book is intended as a text for materials engineering students in the junior

or possibly senior years of their studies. Students in other related disciplines such

as metallurgy or mechanical engineering can benefit from such a text. The scope

of the book makes it appropriate as a reference for graduate students as well and

for practicing engineers in industry who could use such a textbook to refresh their

knowledge in this field. In particular, when practicing engineers are required to

supplement or update their understanding in the field of mechanical properties of

materials, such a text can be invaluable in achieving these requirements.

I believe that there is sufficient material in this book for teaching at least a

three credit course per semester, but it can be extended for a second semester as

practiced in my university. In most universities where materials, metallurgy and

related engineering courses are being taught, this is about the level of credit hours

devoted to the subject of mechanical properties. The content of this textbook –

except for Chap. 8 dealing with specimens of small dimensions – is not new and it

can be found in many good text and reference books, or in research papers published

in journals. The book is based on my lectures given while I was teaching this course

at the Ben Gurion University of the Negev for junior undergraduate students, taught

as a three credit course for two semesters.

Finally I would like to express my gratitude to all publishers and authors for

permission to use and reproduce some of their illustrations and microstructures.

Beer Sheva, Israel Joshua Pelleg

Contents

1 Mechanical Testing of Materials ........................................... 1

1.1 Introduction ............................................................ 1

1.2 The Tension Test ....................................................... 2

1.2.1 Elastic Deformation and the Relations Between

Stress and Strain ............................................. 3

1.2.2 The Elastic and Proportional Limits ........................ 13

1.2.3 Plastic Deformation .......................................... 14

1.2.4 The True Stress/Strain Relation ............................. 16

1.2.5 Elongation .................................................... 18

1.2.6 The Reduction of Area....................................... 19

1.2.7 Necking ....................................................... 20

1.2.8 Instability in Tension......................................... 20

1.2.9 The Shear Stress and Shear Strain .......................... 23

1.2.10 The Elastic Strain Energy.................................... 25

1.2.11 Resilience..................................................... 27

1.2.12 Toughness .................................................... 28

1.2.13 Fracture Stress................................................ 29

1.3 Compression Stress.................................................... 30

1.3.1 Introduction .................................................. 30

1.3.2 The Compression of Brittle Materials....................... 30

1.3.3 The Compression of Ductile Materials ..................... 31

1.3.4 The Effect of Hydrostatic Pressure on Compression ....... 34

1.4 The Hardness Test ..................................................... 36

1.4.1 Indentation by Spherical (Ball) Indenters................... 37

1.4.2 Indentation by Pyramid and Cone Indenters................ 43

1.4.3 Indentation by Cone (or Spherical) Indenters .............. 46

1.4.4 Comments on Hardness Tests ............................... 50

1.5 The Torsion Test (Shear) .............................................. 50

1.5.1 Torsion in the Elastic Region ................................ 51

1.5.2 Torsion in the Plastic Region ................................ 55

ix

x Contents

1.5.3 Axial Change in Torsion ..................................... 62

1.5.4 Fracture by Torsion Test ..................................... 63

1.6 The Impact Tests....................................................... 64

1.7 Anelasticity ............................................................ 69

1.7.1 Introduction .................................................. 69

1.7.2 The Elastic After Effect...................................... 70

1.7.3 The Thermoelastic Effect .................................... 71

1.7.4 Energy Losses/Hysteresis Loop ............................. 73

1.7.5 Internal Friction .............................................. 73

Appendix I ............................................................. 78

Appendix II ............................................................ 80

References ..................................................................... 84

2 Introduction to Dislocations ................................................ 85

2.1 Introduction ............................................................ 85

2.2 The Theoretical Strength of Crystals ................................. 86

2.3 Seeing (Dislocations) Is Believing .................................... 88

2.3.1 Etch Pits ...................................................... 89

2.3.2 Transmission Electron Microscopy (TEM) ................. 92

2.3.3 Field Ion Microscopy (FIM)................................. 95

2.4 The Geometrical Characterization of Dislocations................... 97

2.5 The Formation of Dislocations........................................ 101

2.6 The Motion of Dislocations ........................................... 103

2.6.1 Conservative Motion ......................................... 105

2.6.2 Non-conservative Motion (Climb) .......................... 108

2.7 The Energy of Dislocations ........................................... 110

2.7.1 Screw Dislocation ............................................ 112

2.7.2 Edge Dislocation ............................................. 114

2.8 Line Tension ........................................................... 117

2.9 The Stress Field of a Dislocation ..................................... 118

2.9.1 Screw Dislocations........................................... 118

2.9.2 Edge Dislocations............................................ 120

2.10 The Forces Acting on Dislocations ................................... 122

2.10.1 The Glide Forces............................................. 122

2.10.2 Climb ......................................................... 124

2.11 The Forces Between Dislocations .................................... 125

2.11.1 Screw Dislocations........................................... 125

2.11.2 Edge Dislocations............................................ 126

2.12 The Intersection of Dislocations ...................................... 127

2.13 Dislocation Multiplication ............................................ 130

2.14 Partial Dislocations .................................................... 132

2.14.1 Shockley Partial Dislocations ............................... 133

2.14.2 Frank Partial Dislocations ................................... 136

2.14.3 The Cross Slip of Partial Dislocations ...................... 138

2.14.4 The Thompson Tetrahedron ................................. 139

2.14.5 Lomer-Cottrell Locks........................................ 140

Contents xi

2.15 Dislocation Pile-Ups................................................... 141

2.16 Low (Small)-Angle Grain Boundaries................................ 143

References ..................................................................... 145

3 Plastic Deformation .......................................................... 147

3.1 Introduction ............................................................ 147

3.2 Critical Resolved Shear Stress (CRSS) ............................... 147

3.3 Slip ..................................................................... 151

3.3.1 FCC Structures............................................... 151

3.3.2 BCC Structures............................................... 152

3.3.3 HCP Structures............................................... 153

3.4 The Slip in Polycrystalline Materials ................................. 155

3.5 Twinning ............................................................... 157

3.6 Yield Phenomena ...................................................... 163

3.6.1 Introduction .................................................. 163

3.6.2 Sharp Yield ................................................... 164

3.6.3 L¨uders Bands................................................. 165

3.6.4 Stain Aging ................................................... 166

3.6.5 The Cottrell-Bilby Theory ................................... 169

3.7 The Bauschinger Effect (BE) ......................................... 179

3.8 The Effect of Impurity (Solute), Temperature and Orientation ...... 180

3.9 Polygonization ......................................................... 184

3.10 Deformation in Polycrystalline Materials ............................ 186

3.10.1 Preferred Orientation (Texture).............................. 188

3.10.2 The Bauschinger Effect (BE)................................ 190

3.11 Grain Boundaries ...................................................... 192

References ..................................................................... 193

4 Strengthening Mechanisms ................................................. 195

4.1 Introduction ............................................................ 195

4.2 Strain Hardening ....................................................... 196

4.2.1 Stage I ........................................................ 197

4.2.2 Stage II ....................................................... 205

4.2.3 Stage III (Dynamic Recovery)............................... 210

4.3 Microstructure ......................................................... 214

4.4 Theories of Strain Hardening ......................................... 217

4.4.1 Stage I ........................................................ 219

4.4.2 Stage II ....................................................... 223

4.4.3 Stage III ...................................................... 233

4.5 Strain Hardening in Polycrystalline Materials ....................... 234

4.6 Solid Solution Strengthening.......................................... 236

4.6.1 Introduction .................................................. 236

4.6.2 Strengthening by Interstitial Atoms ......................... 237

4.6.3 Strengthening by Substitution Atoms....................... 237

4.7 Grain Boundaries and Grain Size ..................................... 239

xii Contents

4.8 Second-Phase Hardening (Precipitates and/or Other Particles) ..... 246

4.8.1 Introduction .................................................. 246

4.8.2 Orowan Loop Formation .................................... 247

4.8.3 The Strength of Obstacles and Break-Away Stress......... 249

4.8.4 Cutting Through the Second Phase ......................... 252

4.8.5 The Mott-Nabarro Concept .................................. 253

4.8.6 Summary of Second-Phase Strengthening .................. 255

References ..................................................................... 256

5 Time Dependent Deformation – Creep .................................... 259

5.1 Introduction ............................................................ 259

5.2 Creep in Single Crystals............................................... 260

5.3 Creep in Polycrystalline Materials.................................... 272

5.4 Mechanisms of Creep ................................................. 282

5.4.1 Nabarro-Herring Creep ...................................... 284

5.4.2 Dislocation Creep and Climb ................................ 288

5.4.3 Climb-Controlled Creep ..................................... 288

5.4.4 Glide via Cross-Slip ......................................... 291

5.4.5 Coble Creep .................................................. 296

5.5 Grain-Boundary Sliding ............................................... 298

5.6 Creep Rupture.......................................................... 307

5.7 Recovery (Relaxation)................................................. 314

5.8 The Prediction of Life-Time (Parametric Method)................... 318

5.8.1 The Larson-Miller Approach ................................ 318

5.8.2 The Manson-Haferd Approach .............................. 321

5.8.3 The Orr-Sherby-Dorn (OSD) Approach .................... 325

5.8.4 The Monkman-Grant Approach ............................. 329

5.9 Concepts of Designing (Selecting) Creep-Resistant Materials ...... 332

References ..................................................................... 335

6 Cyclic Stress – Fatigue....................................................... 339

6.1 Introduction ............................................................ 339

6.2 The Endurance Limit; S-N Curves.................................... 340

6.2.1 The Endurance Limit in Ferrous Metals .................... 345

6.2.2 The Endurance Limit in Non-ferrous Metals ............... 346

6.3 The Stress Cycles ...................................................... 347

6.3.1 Low-Cycle Fatigue Tests .................................... 348

6.3.2 High-Cycle Fatigue Tests.................................... 353

6.3.3 Very High Cycle Tests ....................................... 353

6.4 Fatigue Life ............................................................ 354

6.4.1 The Stress-Based Approach ................................. 354

6.4.2 Strain-Based Life-Times..................................... 355

6.5 Work Hardening (Softening) .......................................... 360

6.6 Hysteresis .............................................................. 371

6.7 The Mean Stress ....................................................... 381

Contents xiii

6.8 Underloading (UL), Overloading (OL), Coaxing

and Cumulative Damage .............................................. 385

6.8.1 Underloading (UL)........................................... 385

6.8.2 Overloading (OL) ............................................ 387

6.8.3 Coaxing....................................................... 391

6.8.4 Cumulative Damage ......................................... 392

6.8.5 Variable-Amplitude Loading (Intermittent Loading)....... 395

6.9 Structural Observations in Fatigued Specimens...................... 398

6.9.1 Progression Markings (Beach Marks) and Striations ...... 398

6.9.2 The Dislocation Structure in Fatigue........................ 400

6.10 The Notch Effect....................................................... 411

6.11 Failure Resulting from Cyclic Deformation (Fracture by Fatigue).. 415

6.12 The Effects of Some Materials and Process Variables ............... 416

6.12.1 Surface Effects on Fatigue ................................... 416

6.12.2 The Residual Stresses........................................ 417

6.12.3 Introduction to Residual Stresses............................ 418

6.13 Miscellaneous Variables............................................... 425

6.13.1 Grain Size .................................................... 426

6.13.2 The Effect of Temperature ................................... 430

6.13.3 Specimen Size ................................................ 432

6.13.4 The Environment............................................. 434

6.14 Thermal Fatigue ....................................................... 436

6.15 Design for Fatigue ..................................................... 442

References ..................................................................... 444

7 Fracture ....................................................................... 449

7.1 Introduction ............................................................ 449

7.2 Fracture Types ......................................................... 451

7.3 Brittle Fracture ......................................................... 454

7.4 Theories of Brittle Fracture ........................................... 455

7.4.1 Griffith’s Theory on Fracture ................................ 456

7.4.2 Orowan’s Fracture Theory................................... 459

7.4.3 Brittle Fracture in Crystalline Materials .................... 461

7.4.4 The Dislocation Theory of Brittle Fracture ................. 462

7.5 Factors Causing Embrittlement ....................................... 465

7.5.1 Liquid Metal Embrittlement (LME) ........................ 465

7.5.2 Hydrogen Embrittlement (HE) .............................. 466

7.5.3 Aqueous-Environment Embrittlement (AEE)

or Stress-Corrosion Cracking................................ 471

7.5.4 Temper Embrittlement (TE) ................................. 474

7.6 Fracture Toughness .................................................... 479

7.7 Ductile Fracture ........................................................ 490

7.7.1 Introduction .................................................. 490

7.7.2 The Process of Neck Formation ............................. 491

xiv Contents

7.8 Ductile-to-Brittle Transition (Transition Temperature) .............. 504

7.8.1 Introduction .................................................. 504

7.8.2 The Features.................................................. 505

7.9 Fatigue Fracture........................................................ 509

7.9.1 Crack-Tip Blunting .......................................... 509

7.9.2 The Effect of Inclusion ...................................... 512

References ..................................................................... 518

8 Mechanical Behavior in the Micron and Submicron/Nano Range ..... 521

8.1 Introduction ............................................................ 521

8.2 Mechanical Behavior in the Small-Size Range ...................... 521

8.2.1 An Explanation of the Size Effect........................... 522

8.3 The Static Properties................................................... 523

8.3.1 Single Crystals ............................................... 523

8.3.2 Polycrystalline Materials .................................... 530

8.3.3 Thin Films.................................................... 533

8.3.4 Free-Standing Films ......................................... 544

8.3.5 Whiskers...................................................... 549

8.3.6 Twinning ..................................................... 553

8.3.7 The Hall-Petch Relation (H-P) in Materials of

Small Dimensions............................................ 564

8.3.8 Superplasticity ............................................... 569

8.4 Time-Dependent Deformation (Creep) ............................... 584

8.5 Fatigue Behavior....................................................... 597

8.5.1 Introduction .................................................. 597

8.5.2 Fatigue in Micron-/Submicron-Sized Materials ............ 597

8.5.3 The Fatigue of Nanocrystalline (NC) Materials ............ 608

8.6 Fracture................................................................. 614

8.6.1 Introduction .................................................. 614

8.6.2 The Characteristics........................................... 615

8.7 Epilogue ................................................................ 623

Reference ...................................................................... 624

Index ............................................................................... 629