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 FrankMaherProfessorofEngineering EngineeringScienceandMechanicsDepartment,and MaterialsScienceandEngineeringDepartment VirginiaPolytechnicInstituteandStateUniversity Blacksburg,Virginia International Edition contributions by KatakamSivaPrasad AssistantProfessor DepartmentofMetallurgicalandMaterialsEngineering NationalInstituteofTechnology Tiruchirappalli R.Narayanasamy Professor DepartmentofProductionEngineering NationalInstituteofTechnology Tiruchirappalli Boston Columbus Indianapolis NewYork SanFrancisco UpperSaddleRiver Amsterdam CapeTown Dubai London Madrid Milan Munich Paris Montre´al TorontoDelhi MexicoCity Sa˜oPaulo Sydney HongKong Seoul Singapore Taipei Tokyo VP/EditorialDirector,Engineering/ComputerScience:MarciaJ.Horton ExecutiveEditor:HollyStark SeniorMarketingManager:TimGalligan MarketingAssistant:JonBryant SeniorManagingEditor:ScottDisanno ProjectManager:GregDulles Publisher,InternationalEdition:AngshumanChakraborty AcquisitionsEditor,InternationalEdition:SomnathBasu PublishingAssistant,InternationalEdition:ShokhiShah PrintandMediaEditor,InternationalEdition:AshwithaJayakumar ProjectEditor,InternationalEdition:JayashreeArunachalam OperationsSpecialist:LisaMcDowell SeniorArtDirector:JayneConte MediaEditor:DanielSandin Full-ServiceProjectManagement:IntegraSoftwareServicesPvt.Ltd. 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Contents PREFACE 11 ACKNOWLEDGMENTS 17 1 Introduction 19 1.1 Introduction 19 1.2 TypesofMaterialFailure 20 1.3 DesignandMaterialsSelection 28 1.4 TechnologicalChallenge 34 1.5 EconomicImportanceofFracture 36 1.6 Summary 37 References 38 ProblemsandQuestions 38 2 StructureandDeformationinMaterials 40 2.1 Introduction 40 2.2 BondinginSolids 42 2.3 StructureinCrystallineMaterials 46 2.4 ElasticDeformationandTheoreticalStrength 50 2.5 InelasticDeformation 55 2.6 Summary 61 References 62 ProblemsandQuestions 63 3 ASurveyofEngineeringMaterials 65 3.1 Introduction 65 3.2 AlloyingandProcessingofMetals 66 3.3 IronsandSteels 72 3.4 NonferrousMetals 80 3.5 Polymers 84 5 6 Contents 3.6 CeramicsandGlasses 94 3.7 CompositeMaterials 100 3.8 MaterialsSelectionforEngineeringComponents 105 3.9 Summary 111 References 113 ProblemsandQuestions 114 4 MechanicalTesting:TensionTestandOtherBasicTests 118 4.1 Introduction 118 4.2 IntroductiontoTensionTest 123 4.3 EngineeringStress–StrainProperties 128 4.4 TrendsinTensileBehavior 137 4.5 TrueStress–StrainInterpretationofTensionTest 143 4.6 CompressionTest 151 4.7 HardnessTests 157 4.8 Notch-ImpactTests 164 4.9 BendingandTorsionTests 169 4.10 Summary 175 References 176 ProblemsandQuestions 177 5 Stress–StrainRelationshipsandBehavior 190 5.1 Introduction 190 5.2 ModelsforDeformationBehavior 191 5.3 ElasticDeformation 201 5.4 AnisotropicMaterials 214 5.5 Summary 223 References 225 ProblemsandQuestions 225 6 ReviewofComplexandPrincipalStatesofStressandStrain 234 6.1 Introduction 234 6.2 PlaneStress 235 6.3 PrincipalStressesandtheMaximumShearStress 245 6.4 Three-DimensionalStatesofStress 253 6.5 StressesontheOctahedralPlanes 260 6.6 ComplexStatesofStrain 262 6.7 Summary 267 References 269 ProblemsandQuestions 269 Contents 7 7 YieldingandFractureunderCombinedStresses 275 7.1 Introduction 275 7.2 GeneralFormofFailureCriteria 277 7.3 MaximumNormalStressFractureCriterion 279 7.4 MaximumShearStressYieldCriterion 282 7.5 OctahedralShearStressYieldCriterion 288 7.6 DiscussionoftheBasicFailureCriteria 295 7.7 Coulomb–MohrFractureCriterion 301 7.8 ModifiedMohrFractureCriterion 311 7.9 AdditionalCommentsonFailureCriteria 318 7.10 Summary 321 References 322 ProblemsandQuestions 323 8 FractureofCrackedMembers 334 8.1 Introduction 334 8.2 PreliminaryDiscussion 337 8.3 MathematicalConcepts 344 8.4 ApplicationofK toDesignandAnalysis 348 8.5 AdditionalTopicsonApplicationofK 359 8.6 FractureToughnessValuesandTrends 371 8.7 PlasticZoneSize,andPlasticityLimitationsonLEFM 381 8.8 DiscussionofFractureToughnessTesting 390 8.9 ExtensionsofFractureMechanicsBeyondLinearElasticity 391 8.10 Summary 398 References 401 ProblemsandQuestions 402 9 FatigueofMaterials:IntroductionandStress-BasedApproach 416 9.1 Introduction 416 9.2 DefinitionsandConcepts 418 9.3 SourcesofCyclicLoading 429 9.4 FatigueTesting 430 9.5 ThePhysicalNatureofFatigueDamage 435 9.6 TrendsinS-N Curves 441 9.7 MeanStresses 451 9.8 MultiaxialStresses 463 9.9 VariableAmplitudeLoading 468 9.10 Summary 478 References 479 ProblemsandQuestions 481 8 Contents 10 Stress-BasedApproachtoFatigue:NotchedMembers 491 10.1 Introduction 491 10.2 NotchEffects 493 10.3 NotchSensitivityandEmpiricalEstimatesofk 497 f 10.4 EstimatingLong-LifeFatigueStrengths(FatigueLimits) 501 10.5 NotchEffectsatIntermediateandShortLives 506 10.6 CombinedEffectsofNotchesandMeanStress 510 10.7 EstimatingS-N Curves 520 10.8 UseofComponentS-N Data 527 10.9 DesigningtoAvoidFatigueFailure 536 10.10 Discussion 541 10.11 Summary 542 References 544 ProblemsandQuestions 545 11 FatigueCrackGrowth 560 11.1 Introduction 560 11.2 PreliminaryDiscussion 561 11.3 FatigueCrackGrowthRateTesting 569 11.4 Effectsof R = S /S onFatigueCrackGrowth 574 min max 11.5 TrendsinFatigueCrackGrowthBehavior 584 11.6 LifeEstimatesforConstantAmplitudeLoading 590 11.7 LifeEstimatesforVariableAmplitudeLoading 601 11.8 DesignConsiderations 607 11.9 PlasticityAspectsandLimitationsofLEFMforFatigueCrack Growth 609 11.10 EnvironmentalCrackGrowth 616 11.11 Summary 621 References 623 ProblemsandQuestions 624 12 PlasticDeformationBehaviorandModelsforMaterials 638 12.1 Introduction 638 12.2 Stress–StrainCurves 641 12.3 Three-DimensionalStress–StrainRelationships 649 12.4 UnloadingandCyclicLoadingBehaviorfromRheological Models 659 12.5 CyclicStress–StrainBehaviorofRealMaterials 668 12.6 Summary 681 References 683 ProblemsandQuestions 684 Contents 9 13 Stress–StrainAnalysisofPlasticallyDeformingMembers 693 13.1 Introduction 693 13.2 PlasticityinBending 694 13.3 ResidualStressesandStrainsforBending 703 13.4 PlasticityofCircularShaftsinTorsion 707 13.5 NotchedMembers 710 13.6 CyclicLoading 722 13.7 Summary 733 References 734 ProblemsandQuestions 735 14 Strain-BasedApproachtoFatigue 745 14.1 Introduction 745 14.2 StrainVersusLifeCurves 748 14.3 MeanStressEffects 758 14.4 MultiaxialStressEffects 767 14.5 LifeEstimatesforStructuralComponents 771 14.6 Discussion 781 14.7 Summary 789 References 790 ProblemsandQuestions 791 15 Time-DependentBehavior:CreepandDamping 802 15.1 Introduction 802 15.2 CreepTesting 804 15.3 PhysicalMechanismsofCreep 809 15.4 Time–TemperatureParametersandLifeEstimates 821 15.5 CreepFailureunderVaryingStress 833 15.6 Stress–Strain–TimeRelationships 836 15.7 CreepDeformationunderVaryingStress 841 15.8 CreepDeformationunderMultiaxialStress 848 15.9 ComponentStress–StrainAnalysis 850 15.10 EnergyDissipation(Damping)inMaterials 855 15.11 Summary 864 References 867 ProblemsandQuestions 868 AppendixA ReviewofSelectedTopicsfromMechanicsofMaterials 880 A.1 Introduction 880 A.2 BasicFormulasforStressesandDeflections 880