Mechanical behavior of materials: engineering methods for deformation fracture and fatigue

Mechanical Behavior

of Materials

This page intentionally left blank

Mechanical Behavior

of Materials

Engineering Methods for Deformation,

Fracture, and Fatigue

Fourth Edition

Norman E. Dowling

Frank Maher Professor of Engineering

Engineering Science and Mechanics Department, and

Materials Science and Engineering Department

Virginia Polytechnic Institute and State University

Blacksburg, Virginia

International Edition contributions by

Katakam Siva Prasad

Assistant Professor

Department of Metallurgical and Materials Engineering

National Institute of Technology

Tiruchirappalli

R. Narayanasamy

Professor

Department of Production Engineering

National Institute of Technology

Tiruchirappalli

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Authorized adaptation from the United States edition, entitled Mechanical Behavior of Materials, Engineering Methods for Deformation,

Fracture, and Fatigue, 4th edition, ISBN 978-0-13-139506-0 by Norman E. Dowling published by Pearson Education c 2012.

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ISBN 10: 0-273-76455-1

ISBN 13: 978-0-273-76455-7

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A catalogue record for this book is available from the British Library

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Contents

PREFACE 11

ACKNOWLEDGMENTS 17

1 Introduction 19

1.1 Introduction 19

1.2 Types of Material Failure 20

1.3 Design and Materials Selection 28

1.4 Technological Challenge 34

1.5 Economic Importance of Fracture 36

1.6 Summary 37

References 38

Problems and Questions 38

2 Structure and Deformation in Materials 40

2.1 Introduction 40

2.2 Bonding in Solids 42

2.3 Structure in Crystalline Materials 46

2.4 Elastic Deformation and Theoretical Strength 50

2.5 Inelastic Deformation 55

2.6 Summary 61

References 62

Problems and Questions 63

3 A Survey of Engineering Materials 65

3.1 Introduction 65

3.2 Alloying and Processing of Metals 66

3.3 Irons and Steels 72

3.4 Nonferrous Metals 80

3.5 Polymers 84

5

6 Contents

3.6 Ceramics and Glasses 94

3.7 Composite Materials 100

3.8 Materials Selection for Engineering Components 105

3.9 Summary 111

References 113

Problems and Questions 114

4 Mechanical Testing: Tension Test and Other Basic Tests 118

4.1 Introduction 118

4.2 Introduction to Tension Test 123

4.3 Engineering Stress–Strain Properties 128

4.4 Trends in Tensile Behavior 137

4.5 True Stress–Strain Interpretation of Tension Test 143

4.6 Compression Test 151

4.7 Hardness Tests 157

4.8 Notch-Impact Tests 164

4.9 Bending and Torsion Tests 169

4.10 Summary 175

References 176

Problems and Questions 177

5 Stress–Strain Relationships and Behavior 190

5.1 Introduction 190

5.2 Models for Deformation Behavior 191

5.3 Elastic Deformation 201

5.4 Anisotropic Materials 214

5.5 Summary 223

References 225

Problems and Questions 225

6 Review of Complex and Principal States of Stress and Strain 234

6.1 Introduction 234

6.2 Plane Stress 235

6.3 Principal Stresses and the Maximum Shear Stress 245

6.4 Three-Dimensional States of Stress 253

6.5 Stresses on the Octahedral Planes 260

6.6 Complex States of Strain 262

6.7 Summary 267

References 269

Problems and Questions 269

Contents 7

7 Yielding and Fracture under Combined Stresses 275

7.1 Introduction 275

7.2 General Form of Failure Criteria 277

7.3 Maximum Normal Stress Fracture Criterion 279

7.4 Maximum Shear Stress Yield Criterion 282

7.5 Octahedral Shear Stress Yield Criterion 288

7.6 Discussion of the Basic Failure Criteria 295

7.7 Coulomb–Mohr Fracture Criterion 301

7.8 Modified Mohr Fracture Criterion 311

7.9 Additional Comments on Failure Criteria 318

7.10 Summary 321

References 322

Problems and Questions 323

8 Fracture of Cracked Members 334

8.1 Introduction 334

8.2 Preliminary Discussion 337

8.3 Mathematical Concepts 344

8.4 Application of K to Design and Analysis 348

8.5 Additional Topics on Application of K 359

8.6 Fracture Toughness Values and Trends 371

8.7 Plastic Zone Size, and Plasticity Limitations on LEFM 381

8.8 Discussion of Fracture Toughness Testing 390

8.9 Extensions of Fracture Mechanics Beyond Linear Elasticity 391

8.10 Summary 398

References 401

Problems and Questions 402

9 Fatigue of Materials: Introduction and Stress-Based Approach 416

9.1 Introduction 416

9.2 Definitions and Concepts 418

9.3 Sources of Cyclic Loading 429

9.4 Fatigue Testing 430

9.5 The Physical Nature of Fatigue Damage 435

9.6 Trends in S-N Curves 441

9.7 Mean Stresses 451

9.8 Multiaxial Stresses 463

9.9 Variable Amplitude Loading 468

9.10 Summary 478

References 479

Problems and Questions 481

8 Contents

10 Stress-Based Approach to Fatigue: Notched Members 491

10.1 Introduction 491

10.2 Notch Effects 493

10.3 Notch Sensitivity and Empirical Estimates of k f 497

10.4 Estimating Long-Life Fatigue Strengths (Fatigue Limits) 501

10.5 Notch Effects at Intermediate and Short Lives 506

10.6 Combined Effects of Notches and Mean Stress 510

10.7 Estimating S-N Curves 520

10.8 Use of Component S-N Data 527

10.9 Designing to Avoid Fatigue Failure 536

10.10 Discussion 541

10.11 Summary 542

References 544

Problems and Questions 545

11 Fatigue Crack Growth 560

11.1 Introduction 560

11.2 Preliminary Discussion 561

11.3 Fatigue Crack Growth Rate Testing 569

11.4 Effects of R = Smin/Smax on Fatigue Crack Growth 574

11.5 Trends in Fatigue Crack Growth Behavior 584

11.6 Life Estimates for Constant Amplitude Loading 590

11.7 Life Estimates for Variable Amplitude Loading 601

11.8 Design Considerations 607

11.9 Plasticity Aspects and Limitations of LEFM for Fatigue Crack

Growth 609

11.10 Environmental Crack Growth 616

11.11 Summary 621

References 623

Problems and Questions 624

12 Plastic Deformation Behavior and Models for Materials 638

12.1 Introduction 638

12.2 Stress–Strain Curves 641

12.3 Three-Dimensional Stress–Strain Relationships 649

12.4 Unloading and Cyclic Loading Behavior from Rheological

Models 659

12.5 Cyclic Stress–Strain Behavior of Real Materials 668

12.6 Summary 681

References 683

Problems and Questions 684

Contents 9

13 Stress–Strain Analysis of Plastically Deforming Members 693

13.1 Introduction 693

13.2 Plasticity in Bending 694

13.3 Residual Stresses and Strains for Bending 703

13.4 Plasticity of Circular Shafts in Torsion 707

13.5 Notched Members 710

13.6 Cyclic Loading 722

13.7 Summary 733

References 734

Problems and Questions 735

14 Strain-Based Approach to Fatigue 745

14.1 Introduction 745

14.2 Strain Versus Life Curves 748

14.3 Mean Stress Effects 758

14.4 Multiaxial Stress Effects 767

14.5 Life Estimates for Structural Components 771

14.6 Discussion 781

14.7 Summary 789

References 790

Problems and Questions 791

15 Time-Dependent Behavior: Creep and Damping 802

15.1 Introduction 802

15.2 Creep Testing 804

15.3 Physical Mechanisms of Creep 809

15.4 Time–Temperature Parameters and Life Estimates 821

15.5 Creep Failure under Varying Stress 833

15.6 Stress–Strain–Time Relationships 836

15.7 Creep Deformation under Varying Stress 841

15.8 Creep Deformation under Multiaxial Stress 848

15.9 Component Stress–Strain Analysis 850

15.10 Energy Dissipation (Damping) in Materials 855

15.11 Summary 864

References 867

Problems and Questions 868

Appendix A Review of Selected Topics from Mechanics of Materials 880

A.1 Introduction 880

A.2 Basic Formulas for Stresses and Deflections 880

10 Contents

A.3 Properties of Areas 882

A.4 Shears, Moments, and Deflections in Beams 884

A.5 Stresses in Pressure Vessels, Tubes, and Discs 884

A.6 Elastic Stress Concentration Factors for Notches 889

A.7 Fully Plastic Yielding Loads 890

References 899

Appendix B Statistical Variation in Materials Properties 900

B.1 Introduction 900

B.2 Mean and Standard Deviation 900

B.3 Normal or Gaussian Distribution 902

B.4 Typical Variation in Materials Properties 905

B.5 One-Sided Tolerance Limits 905

B.6 Discussion 907

References 908

ANSWERS FOR SELECTED PROBLEMS AND QUESTIONS 909

BIBLIOGRAPHY 920

INDEX 933

Preface

Designing machines, vehicles, and structures that are safe, reliable, and economical requires

both efficient use of materials and assurance that structural failure will not occur. It is therefore

appropriate for undergraduate engineering majors to study the mechanical behavior of materials,

specifically such topics as deformation, fracture, and fatigue.

This book may be used as a text for courses on mechanical behavior of materials at the

junior or senior undergraduate level, and it may also be employed at the first-year graduate level

by emphasizing the later chapters. The coverage includes traditional topics in the area, such as

materials testing, yielding and plasticity, stress-based fatigue analysis, and creep. The relatively

new methods of fracture mechanics and strain-based fatigue analysis are also considered and are, in

fact, treated in some detail. For a practicing engineer with a bachelor’s degree, this book provides

an understandable reference source on the topics covered.

Emphasis is placed on analytical and predictive methods that are useful to the engineering

designer in avoiding structural failure. These methods are developed from an engineering mechanics

viewpoint, and the resistance of materials to failure is quantified by properties such as yield strength,

fracture toughness, and stress–life curves for fatigue or creep. The intelligent use of materials

property data requires some understanding of how the data are obtained, so their limitations and

significance are clear. Thus, the materials tests used in various areas are generally discussed prior to

considering the analytical and predictive methods.

In many of the areas covered, the existing technology is more highly developed for metals than

for nonmetals. Nevertheless, data and examples for nonmetals, such as polymers and ceramics, are

included where appropriate. Highly anisotropic materials, such as continuous fiber composites, are

also considered, but only to a limited extent. Detailed treatment of these complex materials is not

attempted here.

The remainder of the Preface first highlights the changes made for this new edition. Then

comments follow that are intended to aid users of this book, including students, instructors, and

practicing engineers.

WHAT IS NEW IN THIS EDITION?

Relative to the third edition, this fourth edition features improvements and updates throughout.

Areas that received particular attention in the revisions include the following:

11

12 Preface

• The end-of-chapter problems and questions are extensively revised, with 35% being new or

significantly changed, and with the overall number increased by 54 to be 659. In each chapter, at

least 33% of the problems and questions are new or changed, and these revisions emphasize the

more basic topics where instructors are most likely to concentrate.

• New to this edition, answers are given near the end of the book for approximately half of the

Problems and Questions where a numerical value or the development of a new equation is

requested.

• The end-of-chapter reference lists are reworked and updated to include recent publications,

including databases of materials properties.

• Treatment of the methodology for estimating S-N curves in Chapter 10 is revised, and also

updated to reflect changes in widely used mechanical design textbooks.

• In Chapter 12, the example problem on fitting stress–strain curves is improved.

• Also in Chapter 12, the discussion of multiaxial stress is refined, and a new example is added.

• The topic of mean stress effects for strain-life curves in Chapter 14 is given revised and updated

coverage.

• The section on creep rupture under multiaxial stress is moved to an earlier point in Chapter 15,

where it can be covered along with time-temperature parameters.

PREREQUISITES

Elementary mechanics of materials, also called strength of materials or mechanics of deformable

bodies, provides an introduction to the subject of analyzing stresses and strains in engineering

components, such as beams and shafts, for linear-elastic behavior. Completion of a standard

(typically sophomore) course of this type is an essential prerequisite to the treatment provided

here. Some useful review and reference material in this area is given in Appendix A, along with

a treatment of fully plastic yielding analysis.

Many engineering curricula include an introductory (again, typically sophomore) course in

materials science, including such subjects as crystalline and noncrystalline structure, dislocations

and other imperfections, deformation mechanisms, processing of materials, and naming systems for

materials. Prior exposure to this area of study is also recommended. However, as such a prerequisite

may be missing, limited introductory coverage is given in Chapters 2 and 3.

Mathematics through elementary calculus is also needed. A number of the worked examples

and student problems involve basic numerical analysis, such as least-squares curve fitting, iterative

solution of equations, and numerical integration. Hence, some background in these areas is useful,

as is an ability to perform plotting and numerical analysis on a personal computer. The numerical

analysis needed is described in most introductory textbooks on the subject, such as Chapra (2010),

which is listed at the end of this Preface.

REFERENCES AND BIBLIOGRAPHY

Each chapter contains a list of References near the end that identifies sources of additional reading

and information. These lists are in some cases divided into categories such as general references,

sources of materials properties, and useful handbooks. Where a reference is mentioned in the text,

Preface 13

the first author’s name and the year of publication are given, allowing the reference to be quickly

found in the list at the end of that chapter.

Where specific data or illustrations from other publications are used, these sources are identified

by information in brackets, such as [Richards 61] or [ASM 88], where the two-digit numbers

indicate the year of publication. All such Bibliography items are listed in a single section near

the end of the book.

PRESENTATION OF MATERIALS PROPERTIES

Experimental data for specific materials are presented throughout the book in numerous illustrations,

tables, examples, and problems. These are always real laboratory data. However, the intent is only

to present typical data, not to give comprehensive information on materials properties. For actual

engineering work, additional sources of materials properties, such as those listed at the ends of

various chapters, should be consulted as needed. Also, materials property values are subject to

statistical variation, as discussed in Appendix B, so typical values from this book, or from any other

source, need to be used with appropriate caution.

Where materials data are presented, any external source is identified as a bibliography item. If

no source is given, then such data are either from the author’s research or from test results obtained

in laboratory courses at Virginia Tech.

UNITS

The International System of Units (SI) is emphasized, but U.S. Customary Units are also included in

most tables of data. On graphs, the scales are either SI or dual, except for a few cases of other units

where an illustration from another publication is used in its original form. Only SI units are given

in most exercises and where values are given in the text, as the use of dual units in these situations

invites confusion.

The SI unit of force is the newton (N), and the U.S. unit is the pound (lb). It is often convenient

to employ thousands of newtons (kilonewtons, kN) or thousands of pounds (kilopounds, kip).

Stresses and pressures in SI units are thus presented in newtons per square meter, N/m2, which

in the SI system is given the special name of pascal (Pa). Millions of pascals (megapascals, MPa)

are generally appropriate for our use. We have

1 MPa = 1

MN

m2 = 1

N

mm2

where the latter equivalent form that uses millimeters (mm) is sometimes convenient. In U.S. units,

stresses are generally given in kilopounds per square inch (ksi).

These units and others frequently used are listed, along with conversion factors, inside the front

cover. As an illustrative use of this listing, let us convert a stress of 20 ksi to MPa. Since 1 ksi is

equivalent to 6.895 MPa, we have

20.0 ksi = 20.0 ksi

6.895

MPa

ksi

= 137.9 MPa

14 Preface

Conversion in the opposite direction involves dividing by the equivalence value.

137.9 MPa = 137.9 MPa



6.895 MPa

ksi  = 20.0 ksi

It is also useful to note that strains are dimensionless quantities, so no units are necessary. Strains

are most commonly given as straightforward ratios of length change to length, but percentages are

sometimes used, ε% = 100ε.

MATHEMATICAL CONVENTIONS

Standard practice is followed in most cases. The function log is understood to indicate logarithms

to the base 10, and the function ln to indicate logarithms to the base e = 2.718 ... (that is, natural

logarithms). To indicate selection of the largest of several values, the function MAX( ) is employed.

NOMENCLATURE

In journal articles and in other books, and in various test standards and design codes, a wide variety

of different symbols are used for certain variables that are needed. This situation is handled by using

a consistent set of symbols throughout, while following the most common conventions wherever

possible. However, a few exceptions or modifications to common practice are necessary to avoid

confusion.

For example, K is used for the stress intensity of fracture mechanics, but not for stress

concentration factor, which is designated k. Also, H is used instead of K or k for the strength

coefficient describing certain stress–strain curves. The symbol S is used for nominal or average

stress, whereas σ is the stress at a point and also the stress in a uniformly stressed member. Dual

use of symbols is avoided except where the different usages occur in separate portions of the book.

A list of the more commonly used symbols is given inside the back cover. More detailed lists are

given near the end of each chapter in a section on New Terms and Symbols.

USE AS A TEXT

The various chapters are constituted so that considerable latitude is possible in choosing topics

for study. A semester-length course could include at least portions of all chapters through 11, and

also portions of Chapter 15. This covers the introductory and review topics in Chapters 1 to 6,

followed by yield and fracture criteria for uncracked material in Chapter 7. Fracture mechanics is

applied to static fracture in Chapter 8, and to fatigue crack growth in Chapter 11. Also, Chapters 9

and 10 cover the stress-based approach to fatigue, and Chapter 15 covers creep. If time permits,

some topics on plastic deformation could be added from Chapters 12 and 13, and also from

Chapter 14 on the strain-based approach to fatigue. If the students’ background in materials science

is such that Chapters 2 and 3 are not needed, then Section 3.8 on materials selection may still be

useful.