mechanical behaviour of material preface

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Mechanical Behaviorof Materials

Engineering Methods for Deformation,Fracture, and Fatigue

Fourth Edition

Norman E. DowlingEngineering Science and Mechanics Department, andMaterials Science and Engineering DepartmentVirginia Polytechnic Institute and State UniversityBlacksburg, Virginia

Boston Columbus Indianapolis New York San Francisco Upper Saddle RiverAmsterdam Cape Town Dubai London Madrid Milan Munich ParisMontreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong SeoulSingapore Taipei Tokyo

©2012 Pearson Education, Inc. Upper Saddle River, NJ. All Rights Reserved.

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VP/Editorial Director, Engineering/Computer Science: Marcia J. HortonExecutive Editor: Holly StarkSenior Marketing Manager: Tim GalliganMarketing Assistant: Jon BryantSenior Managing Editor: Scott DisannoProject Manager: Greg DullesOperations Specialist: Lisa McDowellSenior Art Director: Jayne ConteMedia Editor: Daniel SandinFull-Service Project Management:Composition: Integra Software ServicesPrinter/Binder: Courier/WestfordCover Printer: Lehigh-Phoenix Color/Hagerstown

Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear onappropriate page within text.

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Many of the designations by manufacturers and seller to distinguish their products are claimed as trademarks. Where thosedesignations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed ininitial caps or all caps.

Library of Congress Cataloging-in-Publication Data

About the Cover: Brake pedal made of alloy steel and designed for light weight and stiffness for use in race cars. After longuse, cracking occurred in some pedals, and the part was redesigned, preventing any failures. Contour plots (back cover) ofvon Mises equivalent stress for the original and modified designs show reduced stresses due to the redesign geometry change.No cracking has occurred for the redesign, and the part is expected to last 10 million cycles. Photos courtesy of Pratt & MillerEngineering, New Hudson, Michigan.

10 9 8 7 6 5 4 3 2 1

ISBN 13: 978-0-13-139506-0ISBN 10: 0-13-139506-8


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Contents

PREFACE ix

1 Introduction 1

1.1 Introduction 11.2 Types of Material Failure 21.3 Design and Materials Selection 101.4 Technological Challenge 161.5 Economic Importance of Fracture 181.6 Summary 19

References 20Problems and Questions 20

2 Structure and Deformation in Materials 22

2.1 Introduction 222.2 Bonding in Solids 242.3 Structure in Crystalline Materials 282.4 Elastic Deformation and Theoretical Strength 322.5 Inelastic Deformation 372.6 Summary 43


3 A Survey of Engineering Materials 47

3.1 Introduction 473.2 Alloying and Processing of Metals 483.3 Irons and Steels 543.4 Nonferrous Metals 623.5 Polymers 66

iii©2012 Pearson Education, Inc. Upper Saddle River, NJ. All Rights Reserved.

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iv Contents

3.6 Ceramics and Glasses 763.7 Composite Materials 823.8 Materials Selection for Engineering Components 873.9 Summary 93


4 Mechanical Testing: Tension Test and Other Basic Tests 100

4.1 Introduction 1004.2 Introduction to Tension Test 1054.3 Engineering Stress–Strain Properties 1104.4 Trends in Tensile Behavior 1194.5 True Stress–Strain Interpretation of Tension Test 1254.6 Compression Test 1334.7 Hardness Tests 1394.8 Notch-Impact Tests 1464.9 Bending and Torsion Tests 1514.10 Summary 157


5 Stress–Strain Relationships and Behavior 172

5.1 Introduction 1725.2 Models for Deformation Behavior 1735.3 Elastic Deformation 1835.4 Anisotropic Materials 1965.5 Summary 205


6 Review of Complex and Principal States of Stress and Strain 216

6.1 Introduction 2166.2 Plane Stress 2176.3 Principal Stresses and the Maximum Shear Stress 2276.4 Three-Dimensional States of Stress 2356.5 Stresses on the Octahedral Planes 2426.6 Complex States of Strain 2446.7 Summary 249



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Contents v

7 Yielding and Fracture under Combined Stresses 257

7.1 Introduction 2577.2 General Form of Failure Criteria 2597.3 Maximum Normal Stress Fracture Criterion 2617.4 Maximum Shear Stress Yield Criterion 2647.5 Octahedral Shear Stress Yield Criterion 2707.6 Discussion of the Basic Failure Criteria 2777.7 Coulomb–Mohr Fracture Criterion 2837.8 Modified Mohr Fracture Criterion 2937.9 Additional Comments on Failure Criteria 3007.10 Summary 303


8 Fracture of Cracked Members 316

8.1 Introduction 3168.2 Preliminary Discussion 3198.3 Mathematical Concepts 3268.4 Application of K to Design and Analysis 3308.5 Additional Topics on Application of K 3418.6 Fracture Toughness Values and Trends 3538.7 Plastic Zone Size, and Plasticity Limitations on LEFM 3638.8 Discussion of Fracture Toughness Testing 3728.9 Extensions of Fracture Mechanics Beyond Linear Elasticity 3738.10 Summary 380


9 Fatigue of Materials: Introduction and Stress-Based Approach 398

9.1 Introduction 3989.2 Definitions and Concepts 4009.3 Sources of Cyclic Loading 4119.4 Fatigue Testing 4129.5 The Physical Nature of Fatigue Damage 4179.6 Trends in S-N Curves 4239.7 Mean Stresses 4339.8 Multiaxial Stresses 4459.9 Variable Amplitude Loading 4509.10 Summary 460



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10 Stress-Based Approach to Fatigue: Notched Members 473

10.1 Introduction 47310.2 Notch Effects 47510.3 Notch Sensitivity and Empirical Estimates of k f 47910.4 Estimating Long-Life Fatigue Strengths (Fatigue Limits) 48310.5 Notch Effects at Intermediate and Short Lives 48810.6 Combined Effects of Notches and Mean Stress 49210.7 Estimating S-N Curves 50210.8 Use of Component S-N Data 50910.9 Designing to Avoid Fatigue Failure 51810.10 Discussion 52310.11 Summary 524


11 Fatigue Crack Growth 542

11.1 Introduction 54211.2 Preliminary Discussion 54311.3 Fatigue Crack Growth Rate Testing 55111.4 Effects of R = Smin/Smax on Fatigue Crack Growth 55611.5 Trends in Fatigue Crack Growth Behavior 56611.6 Life Estimates for Constant Amplitude Loading 57211.7 Life Estimates for Variable Amplitude Loading 58311.8 Design Considerations 58911.9 Plasticity Aspects and Limitations of LEFM for Fatigue Crack

Growth 59111.10 Environmental Crack Growth 59811.11 Summary 603


12 Plastic Deformation Behavior and Models for Materials 620

12.1 Introduction 62012.2 Stress–Strain Curves 62312.3 Three-Dimensional Stress–Strain Relationships 63112.4 Unloading and Cyclic Loading Behavior from Rheological

Models 64112.5 Cyclic Stress–Strain Behavior of Real Materials 65012.6 Summary 663



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13 Stress–Strain Analysis of Plastically Deforming Members 675

13.1 Introduction 67513.2 Plasticity in Bending 67613.3 Residual Stresses and Strains for Bending 68513.4 Plasticity of Circular Shafts in Torsion 68913.5 Notched Members 69213.6 Cyclic Loading 70413.7 Summary 715


14 Strain-Based Approach to Fatigue 727

14.1 Introduction 72714.2 Strain Versus Life Curves 73014.3 Mean Stress Effects 74014.4 Multiaxial Stress Effects 74914.5 Life Estimates for Structural Components 75314.6 Discussion 76314.7 Summary 771


15 Time-Dependent Behavior: Creep and Damping 784

15.1 Introduction 78415.2 Creep Testing 78615.3 Physical Mechanisms of Creep 79115.4 Time–Temperature Parameters and Life Estimates 80315.5 Creep Failure under Varying Stress 81515.6 Stress–Strain–Time Relationships 81815.7 Creep Deformation under Varying Stress 82315.8 Creep Deformation under Multiaxial Stress 83015.9 Component Stress–Strain Analysis 83215.10 Energy Dissipation (Damping) in Materials 83715.11 Summary 846


Appendix A Review of Selected Topics from Mechanics of Materials 862

A.1 Introduction 862A.2 Basic Formulas for Stresses and Deflections 862


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A.3 Properties of Areas 864A.4 Shears, Moments, and Deflections in Beams 866A.5 Stresses in Pressure Vessels, Tubes, and Discs 866A.6 Elastic Stress Concentration Factors for Notches 871A.7 Fully Plastic Yielding Loads 872

References 881

Appendix B Statistical Variation in Materials Properties 882

B.1 Introduction 882B.2 Mean and Standard Deviation 882B.3 Normal or Gaussian Distribution 884B.4 Typical Variation in Materials Properties 887B.5 One-Sided Tolerance Limits 887B.6 Discussion 889

References 890

ANSWERS FOR SELECTED PROBLEMS AND QUESTIONS 891

BIBLIOGRAPHY 903

INDEX 916


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Preface

Designing machines, vehicles, and structures that are safe, reliable, and economical requiresboth efficient use of materials and assurance that structural failure will not occur. It is thereforeappropriate 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 thejunior or senior undergraduate level, and it may also be employed at the first-year graduate levelby emphasizing the later chapters. The coverage includes traditional topics in the area, such asmaterials testing, yielding and plasticity, stress-based fatigue analysis, and creep. The relativelynew methods of fracture mechanics and strain-based fatigue analysis are also considered and are, infact, treated in some detail. For a practicing engineer with a bachelor’s degree, this book providesan understandable reference source on the topics covered.

Emphasis is placed on analytical and predictive methods that are useful to the engineeringdesigner in avoiding structural failure. These methods are developed from an engineering mechanicsviewpoint, 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 materialsproperty data requires some understanding of how the data are obtained, so their limitations andsignificance are clear. Thus, the materials tests used in various areas are generally discussed prior toconsidering the analytical and predictive methods.

In many of the areas covered, the existing technology is more highly developed for metals thanfor nonmetals. Nevertheless, data and examples for nonmetals, such as polymers and ceramics, areincluded where appropriate. Highly anisotropic materials, such as continuous fiber composites, arealso considered, but only to a limited extent. Detailed treatment of these complex materials is notattempted here.

The remainder of the Preface first highlights the changes made for this new edition. Thencomments follow that are intended to aid users of this book, including students, instructors, andpracticing engineers.

WHAT’S 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:

ix©2012 Pearson Education, Inc. Upper Saddle River, NJ. All Rights Reserved.

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• The end-of-chapter problems and questions are extensively revised, with 35% being new orsignificantly changed, and with the overall number increased by 54 to be 659. In each chapter, atleast 33% of the problems and questions are new or changed, and these revisions emphasize themore 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 theProblems and Questions where a numerical value or the development of a new equation isrequested.

• 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 alsoupdated 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 deformablebodies, provides an introduction to the subject of analyzing stresses and strains in engineeringcomponents, 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 providedhere. Some useful review and reference material in this area is given in Appendix A, along witha treatment of fully plastic yielding analysis.

Many engineering curricula include an introductory (again, typically sophomore) course inmaterials science, including such subjects as crystalline and noncrystalline structure, dislocationsand other imperfections, deformation mechanisms, processing of materials, and naming systems formaterials. Prior exposure to this area of study is also recommended. However, as such a prerequisitemay be missing, limited introductory coverage is given in Chapters 2 and 3.

Mathematics through elementary calculus is also needed. A number of the worked examplesand student problems involve basic numerical analysis, such as least-squares curve fitting, iterativesolution 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 numericalanalysis 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 readingand 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,


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the first author’s name and the year of publication are given, allowing the reference to be quicklyfound in the list at the end of that chapter.

Where specific data or illustrations from other publications are used, these sources are identifiedby information in brackets, such as [Richards 61] or [ASM 88], where the two-digit numbersindicate the year of publication. All such Bibliography items are listed in a single section nearthe 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 onlyto present typical data, not to give comprehensive information on materials properties. For actualengineering work, additional sources of materials properties, such as those listed at the ends ofvarious chapters, should be consulted as needed. Also, materials property values are subject tostatistical variation, as discussed in Appendix B, so typical values from this book, or from any othersource, need to be used with appropriate caution.

Where materials data are presented, any external source is identified as a bibliography item. Ifno source is given, then such data are either from the author’s research or from test results obtainedin laboratory courses at Virginia Tech.

UNITS

The International System of Units (SI) is emphasized, but U.S. Customary Units are also included inmost tables of data. On graphs, the scales are either SI or dual, except for a few cases of other unitswhere an illustration from another publication is used in its original form. Only SI units are givenin most exercises and where values are given in the text, as the use of dual units in these situationsinvites confusion.

The SI unit of force is the newton (N), and the U.S. unit is the pound (lb). It is often convenientto 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, whichin 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 = 1MN

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 frontcover. As an illustrative use of this listing, let us convert a stress of 20 ksi to MPa. Since 1 ksi isequivalent to 6.895 MPa, we have

20.0 ksi = 20.0 ksi

(6.895

MPa

ksi

)= 137.9 MPa


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xii 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. Strainsare most commonly given as straightforward ratios of length change to length, but percentages aresometimes used, ε% = 100ε.

MATHEMATICAL CONVENTIONS

Standard practice is followed in most cases. The function log is understood to indicate logarithmsto the base 10, and the function ln to indicate logarithms to the base e = 2.718 . . . (that is, naturallogarithms). 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 varietyof different symbols are used for certain variables that are needed. This situation is handled by usinga consistent set of symbols throughout, while following the most common conventions whereverpossible. However, a few exceptions or modifications to common practice are necessary to avoidconfusion.

For example, K is used for the stress intensity of fracture mechanics, but not for stressconcentration factor, which is designated k. Also, H is used instead of K or k for the strengthcoefficient describing certain stress–strain curves. The symbol S is used for nominal or averagestress, whereas σ is the stress at a point and also the stress in a uniformly stressed member. Dualuse 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 aregiven 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 topicsfor study. A semester-length course could include at least portions of all chapters through 11, andalso 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 isapplied to static fracture in Chapter 8, and to fatigue crack growth in Chapter 11. Also, Chapters 9and 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 fromChapter 14 on the strain-based approach to fatigue. If the students’ background in materials scienceis such that Chapters 2 and 3 are not needed, then Section 3.8 on materials selection may still beuseful.


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Particular portions of certain chapters are not strongly required as preparation for the remainderof that chapter, nor are they crucial for later chapters. Thus, although the topics involved areimportant in their own right, they may be omitted or delayed, if desired, without serious loss ofcontinuity. 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 toChapter 11, which extends the topic to fatigue crack growth. This can be done by passing overall of Chapters 9 and 10 except Sections 9.1 to 9.3. Also, various options exist for limited, butstill 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 whichcase 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 dependheavily on any other material beyond Chapter 4.

SUPPLEMENTS FOR INSTRUCTORS

For classroom instructors, as at academic institutions, four supplements are available: (1) a set ofprintable, downloadable files of the illustrations, (2) digital files of Microsoft Excel solutions forall but the simplest example problems worked in the text, (3) a manual containing solutions toapproximately half of the end-of-chapter problems for which calculation or a difficult derivationis required, and (4) answers to all problems and questions that involve numerical calculation ordeveloping a new equation. These items are posted on a secure website available only to documentedinstructors.

REFERENCES

ASTM. 2010. “American National Standard for Use of the International System of Units (SI): The ModernMetric System,” Annual Book of ASTM Standards, Vol. 14.04, No. SI10, ASTM International, WestConshohocken, PA.

CHAPRA, S. C. and R. P. CANALE. 2010. Numerical Methods for Engineers, 6th ed., McGraw-Hill,New York.

ACKNOWLEDGMENTS

I am indebted to numerous colleagues who have aided me with this book in a variety of ways. Thosewhose contributions are specific to the revisions for this edition include: Masahiro Endo (FukuokaUniversity), Maureen Julian (Virginia Tech), Kevin Kwiatkowski (Pratt & Miller Engineering),John Landes (University of Tennessee), Yung-Li Lee (Chrysler Group LLC), Marshal McCord III(Virginia Tech), and William Wright (Virginia Tech). As listed in the acknowledgments for previouseditions, many others have also provided valuable aid. I thank these individuals again and note thattheir contributions continue to enhance the present edition.

The several years since the previous edition of this book have been marked by the passing ofthree valued colleagues and mentors, who influenced my career, and who had considerable input


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into the development of the technology described herein: JoDean Morrow, Louis Coffin, and GaryHalford.

Encouragement and support were provided by Virginia Tech in several forms. I especially thankDavid Clark, head of the Materials Science and Engineering Department, and Ishwar Puri, headof the Engineering Science and Mechanics Department. (The author is jointly appointed in thesedepartments.) Also, I am grateful to Norma Guynn and Daniel Reed, two staff members in ESMwho 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 andmost helpful personal interaction.

I also thank Shiny Rajesh of Integra Software Services, and others working with her, for theircare 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 supportduring this work.


mechanical behaviour of material preface

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