Mechanical behavior of materials 4th ed norman e dowling (pearson, 2013)

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

Boston Columbus Indianapolis New York San Francisco Upper Saddle River
Amsterdam Cape Town Dubai London Madrid Milan Munich Paris
´
˜ Paulo Sydney Hong Kong Seoul
Montreal
Toronto Delhi Mexico City Sao
Singapore Taipei Tokyo


VP/Editorial Director, Engineering/Computer Science: Marcia J. Horton
Executive Editor: Holly Stark
Senior Marketing Manager: Tim Galligan
Marketing Assistant: Jon Bryant
Senior Managing Editor: Scott Disanno
Project Manager: Greg Dulles
Publisher, International Edition: Angshuman Chakraborty
Acquisitions Editor, International Edition: Somnath Basu
Publishing Assistant, International Edition: Shokhi Shah
Print and Media Editor, International Edition: Ashwitha Jayakumar
Project Editor, International Edition: Jayashree Arunachalam
Operations Specialist: Lisa McDowell
Senior Art Director: Jayne Conte
Media Editor: Daniel Sandin
Full-Service Project Management: Integra Software Services Pvt. Ltd.
Cover Printer: Lehigh-Phoenix Color/Hagerstown
Pearson Education Limited
Edinburgh Gate
Harlow

Essex CM20 2JE
England
and Associated Companies throughout the world
Visit us on the World Wide Web at:
www.pearsoninternationaleditions.com
c Pearson Education Limited 2013
The right of Norman E. Dowling to be identified as author of this work has been asserted by him in accordance with the Copyright, Designs
and Patents Act 1988.
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.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any
means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence
permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6–10 Kirby Street,
London EC1N 8TS.
All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or
publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement
of this book by such owners.
Microsoft R and Windows R are registered trademarks of the Microsoft Corporation in the U.S.A. and other countries. Screen shots and
icons reprinted with permission from the Microsoft Corporation. This book is not sponsored or endorsed by or affiliated with the Microsoft
Corporation.
ISBN 10: 0-273-76455-1
ISBN 13: 978-0-273-76455-7
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
10 9 8 7 6 5 4 3 2 1
14 13 12 11 10
Typeset in Times-Roman by Integra Software Services Pvt. Ltd.
Printed and bound by Courier/Westford in The United States of America
The publisher’s policy is to use paper manufactured from sustainable forests.

Contents
PREFACE

11

ACKNOWLEDGMENTS

17

1

19

Introduction
1.1
1.2
1.3
1.4
1.5
1.6

2

Structure and Deformation in Materials
2.1
2.2
2.3
2.4
2.5

2.6

3

Introduction 19
Types of Material Failure 20
Design and Materials Selection 28
Technological Challenge 34
Economic Importance of Fracture 36
Summary 37
References 38
Problems and Questions 38

Introduction 40
Bonding in Solids 42
Structure in Crystalline Materials 46
Elastic Deformation and Theoretical Strength
Inelastic Deformation 55
Summary 61
References 62
Problems and Questions 63

A Survey of Engineering Materials
3.1
3.2
3.3
3.4
3.5

Introduction 65

Alloying and Processing of Metals
Irons and Steels 72
Nonferrous Metals 80
Polymers 84

40

50

65

66

5


6

Contents

3.6
3.7
3.8
3.9

4

Introduction 190
Models for Deformation Behavior
Elastic Deformation 201

Anisotropic Materials 214
Summary 223
References 225
Problems and Questions 225

190

191

Review of Complex and Principal States of Stress and Strain
6.1
6.2
6.3
6.4
6.5
6.6
6.7

118

Introduction 118
Introduction to Tension Test 123
Engineering Stress–Strain Properties 128
Trends in Tensile Behavior 137
True Stress–Strain Interpretation of Tension Test 143
Compression Test 151
Hardness Tests 157
Notch-Impact Tests 164
Bending and Torsion Tests 169
Summary 175

References 176
Problems and Questions 177

Stress–Strain Relationships and Behavior
5.1
5.2
5.3
5.4
5.5

6

105

Mechanical Testing: Tension Test and Other Basic Tests
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10

5

Ceramics and Glasses 94
Composite Materials 100

Materials Selection for Engineering Components
Summary 111
References 113
Problems and Questions 114

Introduction 234
Plane Stress 235
Principal Stresses and the Maximum Shear Stress
Three-Dimensional States of Stress 253
Stresses on the Octahedral Planes 260
Complex States of Strain 262
Summary 267
References 269
Problems and Questions 269

245

234


7

Contents

7

Yielding and Fracture under Combined Stresses
7.1
7.2
7.3

7.4
7.5
7.6
7.7
7.8
7.9
7.10

8

9

Introduction 275
General Form of Failure Criteria 277
Maximum Normal Stress Fracture Criterion 279
Maximum Shear Stress Yield Criterion 282
Octahedral Shear Stress Yield Criterion 288
Discussion of the Basic Failure Criteria 295
Coulomb–Mohr Fracture Criterion 301
Modified Mohr Fracture Criterion 311
Additional Comments on Failure Criteria 318
Summary 321
References 322
Problems and Questions 323

Fracture of Cracked Members
8.1
8.2
8.3
8.4

8.5
8.6
8.7
8.8
8.9
8.10

334

Introduction 334
Preliminary Discussion 337
Mathematical Concepts 344
Application of K to Design and Analysis 348
Additional Topics on Application of K 359
Fracture Toughness Values and Trends 371
Plastic Zone Size, and Plasticity Limitations on LEFM 381
Discussion of Fracture Toughness Testing 390
Extensions of Fracture Mechanics Beyond Linear Elasticity 391
Summary 398
References 401
Problems and Questions 402

Fatigue of Materials: Introduction and Stress-Based Approach
9.1
9.2
9.3
9.4
9.5
9.6
9.7

9.8
9.9
9.10

275

Introduction 416
Definitions and Concepts 418
Sources of Cyclic Loading 429
Fatigue Testing 430
The Physical Nature of Fatigue Damage
Trends in S-N Curves 441
Mean Stresses 451
Multiaxial Stresses 463
Variable Amplitude Loading 468
Summary 478
References 479
Problems and Questions 481

435

416


8
10

Contents

Stress-Based Approach to Fatigue: Notched Members

10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11

11

11.10
11.11

12

Introduction 491
Notch Effects 493
Notch Sensitivity and Empirical Estimates of k f 497
Estimating Long-Life Fatigue Strengths (Fatigue Limits) 501
Notch Effects at Intermediate and Short Lives 506
Combined Effects of Notches and Mean Stress 510
Estimating S-N Curves 520
Use of Component S-N Data 527
Designing to Avoid Fatigue Failure 536
Discussion 541
Summary 542

References 544
Problems and Questions 545

Fatigue Crack Growth
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9

12.5
12.6

560

Introduction 560
Preliminary Discussion 561
Fatigue Crack Growth Rate Testing 569
Effects of R = Smin /Smax on Fatigue Crack Growth 574
Trends in Fatigue Crack Growth Behavior 584
Life Estimates for Constant Amplitude Loading 590
Life Estimates for Variable Amplitude Loading 601
Design Considerations 607
Plasticity Aspects and Limitations of LEFM for Fatigue Crack
Growth 609
Environmental Crack Growth 616

Summary 621
References 623
Problems and Questions 624

Plastic Deformation Behavior and Models for Materials
12.1
12.2
12.3
12.4

491

Introduction 638
Stress–Strain Curves 641
Three-Dimensional Stress–Strain Relationships 649
Unloading and Cyclic Loading Behavior from Rheological
Models 659
Cyclic Stress–Strain Behavior of Real Materials 668
Summary 681
References 683
Problems and Questions 684

638


9

Contents

13

Stress–Strain Analysis of Plastically Deforming Members
13.1
13.2
13.3
13.4
13.5
13.6
13.7

14

15

Introduction 693
Plasticity in Bending 694
Residual Stresses and Strains for Bending 703
Plasticity of Circular Shafts in Torsion 707
Notched Members 710
Cyclic Loading 722
Summary 733
References 734
Problems and Questions 735

Strain-Based Approach to Fatigue
14.1
14.2
14.3
14.4
14.5

14.6
14.7

Introduction 745
Strain Versus Life Curves 748
Mean Stress Effects 758
Multiaxial Stress Effects 767
Life Estimates for Structural Components
Discussion 781
Summary 789
References 790
Problems and Questions 791

745

771

Time-Dependent Behavior: Creep and Damping
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
15.10
15.11

Appendix A
A.1
A.2

693

Introduction 802
Creep Testing 804
Physical Mechanisms of Creep 809
Time–Temperature Parameters and Life Estimates
Creep Failure under Varying Stress 833
Stress–Strain–Time Relationships 836
Creep Deformation under Varying Stress 841
Creep Deformation under Multiaxial Stress 848
Component Stress–Strain Analysis 850
Energy Dissipation (Damping) in Materials 855
Summary 864
References 867
Problems and Questions 868

802

821

Review of Selected Topics from Mechanics of Materials
Introduction 880
Basic Formulas for Stresses and Deflections

880

880


10

Contents

A.3
A.4
A.5
A.6
A.7

Appendix B
B.1
B.2
B.3
B.4
B.5
B.6

Properties of Areas 882
Shears, Moments, and Deflections in Beams 884
Stresses in Pressure Vessels, Tubes, and Discs 884
Elastic Stress Concentration Factors for Notches 889
Fully Plastic Yielding Loads 890
References 899
Statistical Variation in Materials Properties
Introduction 900
Mean and Standard Deviation 900

Normal or Gaussian Distribution 902
Typical Variation in Materials Properties
One-Sided Tolerance Limits 905
Discussion 907
References 908

900

905

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,


13

Preface

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
N
=1
2
m
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.


Preface

15

Particular portions of certain chapters are not strongly required as preparation for the remainder
of that chapter, nor are they crucial for later chapters. Thus, although the topics involved are
important in their own right, they may be omitted or delayed, if desired, without serious loss of

continuity. These include Sections 4.5, 4.6 to 4.9, 5.4, 7.7 to 7.9, 8.7 to 8.9, 10.7, 11.7, 11.9,
and 13.3.
After completion of Chapter 8 on fracture mechanics, one option is to proceed directly to
Chapter 11, which extends the topic to fatigue crack growth. This can be done by passing over
all of Chapters 9 and 10 except Sections 9.1 to 9.3. Also, various options exist for limited, but
still coherent, coverage of the relatively advanced topics in Chapters 12 through 15. For example,
it might be useful to include some material from Chapter 14 on strain-based fatigue, in which
case some portions of Chapters 12 and 13 may be needed as prerequisite material. In Chapter 15,
Sections 15.1 to 15.4 provide a reasonable introduction to the topic of creep that does not depend
heavily on any other material beyond Chapter 4.
SUPPLEMENTS FOR INSTRUCTORS
For classroom instructors, as at academic institutions, four supplements are available: (1) a set of
printable, downloadable files of the illustrations, (2) digital files of Microsoft Excel solutions for
all but the simplest example problems worked in the text, (3) a manual containing solutions to
approximately half of the end-of-chapter problems for which calculation or a difficult derivation
is required, and (4) answers to all problems and questions that involve numerical calculation or
developing a new equation. These items are posted on a secure website available only to documented
instructors.
Instructor resources for the International Edition are available at www.
pearsoninternationaleditions.com/dowling.
REFERENCES
ASTM. 2010. “American National Standard for Use of the International System of Units (SI): The Modern
Metric System,” Annual Book of ASTM Standards, Vol. 14.04, No. SI10, ASTM International, West
Conshohocken, PA.
C HAPRA, S. C. and R. P. C ANALE. 2010. Numerical Methods for Engineers, 6th ed., McGraw-Hill,
New York.


This page intentionally left blank

Acknowledgments

I am indebted to numerous colleagues who have aided me with this book in a variety of ways. Those
whose contributions are specific to the revisions for this edition include: Masahiro Endo (Fukuoka
University, Japan), Maureen Julian (Virginia Tech), Milo Kral (University of Canterbury, New
Zealand), Kevin Kwiatkowski (Pratt & Miller Engineering), John Landes (University of Tennessee),
Yung-Li Lee (Chrysler Group LLC), Marshal McCord III (Virginia Tech), George Vander Voort
(Vander Voort Consulting), and William Wright (Virginia Tech). As listed in the acknowledgments
for previous editions, many others have also provided valuable aid. I thank these individuals again
and note that their contributions continue to enhance the present edition.
The several years since the previous edition of this book have been marked by the passing of
three valued colleagues and mentors, who influenced my career, and who had considerable input
into the development of the technology described herein: JoDean Morrow, Louis Coffin, and Gary
Halford.
Encouragement and support were provided by Virginia Tech in several forms. I especially thank
David Clark, head of the Materials Science and Engineering Department, and Ishwar Puri, head
of the Engineering Science and Mechanics Department. (The author is jointly appointed in these
departments.) Also, I am grateful to Norma Guynn and Daniel Reed, two staff members in ESM
who were helpful in a variety of ways.
The photographs for the front and back covers were provided by Pratt & Miller Engineering,
New Hudson, Michigan. Their generosity in doing so is appreciated.
I thank those at Prentice Hall who worked on the editing and production of this edition,
especially Gregory Dulles, Scott Disanno, and Jane Bonnell, with whom I had considerable and
most helpful personal interaction.
I also thank Shiny Rajesh of Integra Software Services, and others working with her, for their
care and diligence in assuring the accuracy and quality of the book composition.
Finally, I thank my wife Nancy and family for their encouragement, patience, and support
during this work.
The publishers would like to thank Professor Manoj Kumar Mitra of the Department of

Metallurgical and Material Engineering, Jadavpur University, Kolkata, for reviewing the content
of the International Edition.

17


This page intentionally left blank


1
Introduction
1.1
1.2
1.3
1.4
1.5
1.6

INTRODUCTION
TYPES OF MATERIAL FAILURE
DESIGN AND MATERIALS SELECTION
TECHNOLOGICAL CHALLENGE
ECONOMIC IMPORTANCE OF FRACTURE
SUMMARY

OBJECTIVES
•

Gain an overview of the types of material failure that affect mechanical and structural design.
Understand in general how the limitations on strength and ductility of materials are dealt

with in engineering design.
• Develop an appreciation of how the development of new technology requires new materials
and new methods of evaluating the mechanical behavior of materials.
• Learn of the surprisingly large costs of fracture to the economy.
•

1.1 INTRODUCTION
Designers of machines, vehicles, and structures must achieve acceptable levels of performance and
economy, while at the same time striving to guarantee that the item is both safe and durable. To
assure performance, safety, and durability, it is necessary to avoid excess deformation—that is,
bending, twisting, or stretching—of the components (parts) of the machine, vehicle, or structure.
In addition, cracking in components must be avoided entirely, or strictly limited, so that it does not
progress to the point of complete fracture.
The study of deformation and fracture in materials is called mechanical behavior of materials.
Knowledge of this area provides the basis for avoiding these types of failure in engineering
applications. One aspect of the subject is the physical testing of samples of materials by applying
forces and deformations. Once the behavior of a given material is quantitatively known from
testing, or from published test data, its chances of success in a particular engineering design can
be evaluated.
19


20

Chapter 1

Introduction

The most basic concern in design to avoid structural failure is that the stress in a component
must not exceed the strength of the material, where the strength is simply the stress that causes a

deformation or fracture failure. Additional complexities or particular causes of failure often require
further analysis, such as the following:
1. Stresses are often present that act in more than one direction; that is, the state of stress is
biaxial or triaxial.
2. Real components may contain flaws or even cracks that must be specifically considered.
3. Stresses may be applied for long periods of time.
4. Stresses may be repeatedly applied and removed, or the direction of stress repeatedly
reversed.
In the remainder of this introductory chapter, we will define and briefly discuss various types
of material failure, and we will consider the relationships of mechanical behavior of materials to
engineering design, to new technology, and to the economy.
1.2 TYPES OF MATERIAL FAILURE
A deformation failure is a change in the physical dimensions or shape of a component that is
sufficient for its function to be lost or impaired. Cracking to the extent that a component is separated
into two or more pieces is termed fracture. Corrosion is the loss of material due to chemical
action, and wear is surface removal due to abrasion or sticking between solid surfaces that touch.
If wear is caused by a fluid (gas or liquid), it is called erosion, which is especially likely if the
fluid contains hard particles. Although corrosion and wear are also of great importance, this book
primarily considers deformation and fracture.
The basic types of material failure that are classified as either deformation or fracture are
indicated in Fig. 1.1. Since several different causes exist, it is important to correctly identify the
ones that may apply to a given design, so that the appropriate analysis methods can be chosen to
predict the behavior. With such a need for classification in mind, the various types of deformation
and fracture are defined and briefly described next.

Figure 1.1 Basic types of deformation and fracture.


Section 1.2

Types of Material Failure

21

Figure 1.2 Axial member (a) subject to loading and unloading, showing elastic deformation
(b) and both elastic and plastic deformation (c).

1.2.1 Elastic and Plastic Deformation
Deformations are quantified in terms of normal and shear strain in elementary mechanics of
materials. The cumulative effect of the strains in a component is a deformation, such as a bend, twist,
or stretch. Deformations are sometimes essential for function, as in a spring. Excessive deformation,
especially if permanent, is often harmful.
Deformation that appears quickly upon loading can be classed as either elastic deformation or
plastic deformation, as illustrated in Fig. 1.2. Elastic deformation is recovered immediately upon
unloading. Where this is the only deformation present, stress and strain are usually proportional.
For axial loading, the constant of proportionality is the modulus of elasticity, E, as defined in
Fig. 1.2(b). An example of failure by elastic deformation is a tall building that sways in the wind and
causes discomfort to the occupants, although there may be only remote chance of collapse. Elastic
deformations are analyzed by the methods of elementary mechanics of materials and extensions of
this general approach, as in books on theory of elasticity and structural analysis.
Plastic deformation is not recovered upon unloading and is therefore permanent. The difference
between elastic and plastic deformation is illustrated in Fig. 1.2(c). Once plastic deformation begins,
only a small increase in stress usually causes a relatively large additional deformation. This process
of relatively easy further deformation is called yielding, and the value of stress where this behavior
begins to be important for a given material is called the yield strength, σo .
Materials capable of sustaining large amounts of plastic deformation are said to behave in a
ductile manner, and those that fracture without very much plastic deformation behave in a brittle
manner. Ductile behavior occurs for many metals, such as low-strength steels, copper, and lead,
and for some plastics, such as polyethylene. Brittle behavior occurs for glass, stone, acrylic plastic,

22

Chapter 1

Introduction

Figure 1.3 Tension test showing brittle and ductile behavior. There is little plastic deformation
for brittle behavior, but a considerable amount for ductile behavior.

and some metals, such as the high-strength steel used to make a file. (Note that the word plastic
is used both as the common name for polymeric materials and in identifying plastic deformation,
which can occur in any type of material.)
Tension tests are often employed to assess the strength and ductility of materials, as illustrated
in Fig. 1.3. Such a test is done by slowly stretching a bar of the material in tension until it breaks
(fractures). The ultimate tensile strength, σu , which is the highest stress reached before fracture,
is obtained along with the yield strength and the strain at fracture, ε f . The latter is a measure
of ductility and is usually expressed as a percentage, then being called the percent elongation.
Materials having high values of both σu and ε f are said to be tough, and tough materials are
generally desirable for use in design.
Large plastic deformations virtually always constitute failure. For example, collapse of a steel
bridge or building during an earthquake could occur due to plastic deformation. However, plastic
deformation can be relatively small, but still cause malfunction of a component. For example, in
a rotating shaft, a slight permanent bend results in unbalanced rotation, which in turn may cause
vibration and perhaps early failure of the bearings supporting the shaft.
Buckling is deformation due to compressive stress that causes large changes in alignment of
columns or plates, perhaps to the extent of folding or collapse. Either elastic or plastic deformation,
or a combination of both, can dominate the behavior. Buckling is generally considered in books on
elementary mechanics of materials and structural analysis.
1.2.2 Creep Deformation

Creep is deformation that accumulates with time. Depending on the magnitude of the applied stress
and its duration, the deformation may become so large that a component can no longer perform its


Section 1.2

Types of Material Failure

23

Figure 1.4 A tungsten lightbulb filament sagging under its own weight. The deflection
increases with time due to creep and can lead to touching of adjacent coils, which causes
bulb failure.

function. Plastics and low-melting-temperature metals may creep at room temperature, and virtually
any material will creep upon approaching its melting temperature. Creep is thus often an important
problem where high temperature is encountered, as in gas-turbine aircraft engines. Buckling can
occur in a time-dependent manner due to creep deformation.
An example of an application involving creep deformation is the design of tungsten lightbulb
filaments. The situation is illustrated in Fig. 1.4. Sagging of the filament coil between its supports
increases with time due to creep deformation caused by the weight of the filament itself. If too much
deformation occurs, the adjacent turns of the coil touch one another, causing an electrical short and
local overheating, which quickly leads to failure of the filament. The coil geometry and supports are
therefore designed to limit the stresses caused by the weight of the filament, and a special tungsten
alloy that creeps less than pure tungsten is used.
1.2.3 Fracture under Static and Impact Loading
Rapid fracture can occur under loading that does not vary with time or that changes only slowly,
called static loading. If such a fracture is accompanied by little plastic deformation, it is called a
brittle fracture. This is the normal mode of failure of glass and other materials that are resistant to
plastic deformation. If the loading is applied very rapidly, called impact loading, brittle fracture is

more likely to occur.
If a crack or other sharp flaw is present, brittle fracture can occur even in ductile steels or
aluminum alloys, or in other materials that are normally capable of deforming plastically by large
amounts. Such situations are analyzed by the special technology called fracture mechanics, which is
the study of cracks in solids. Resistance to brittle fracture in the presence of a crack is measured by
a material property called the fracture toughness, K I c , as illustrated in Fig. 1.5. Materials with high


24

Chapter 1

Introduction

Figure 1.5 Fracture toughness test. K is a measure of the severity of the combination of
crack size, geometry, and load. KIc is the particular value, called the fracture toughness,
where the material fails.

K Ic , Fracture Toughness, MPa m

200

TRIP steels
150

Low alloy
Q and T
steels

Maraging steels

100

P-H stainless steels
50
1000

1500
2000
σo , Yield Strength, MPa

Figure 1.6 Decreased fracture toughness, as yield strength is increased by heat treatment,
for various classes of high-strength steel. (Adapted from [Knott 79]; used with permission.)

strength generally have low fracture toughness, and vice versa. This trend is illustrated for several
classes of high-strength steel in Fig. 1.6.
Ductile fracture can also occur. This type of fracture is accompanied by significant plastic
deformation and is sometimes a gradual tearing process. Fracture mechanics and brittle or ductile
fracture are especially important in the design of pressure vessels and large welded structures,
such as bridges and ships. Fracture may occur as a result of a combination of stress and chemical