Fracture Mechanics

306 Pages·2012·3.108 MB·English

by  C T Sun, Z H Jin

Fracture Mechanics

Fracture Mechanics
C. T. Sun
School of Aeronautics and Astronautics
Purdue University
West Lafayette, Indiana
Z.-H. Jin
Department of Mechanical Engineering
The University of Maine
Orono, Maine
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Contents
Preface............................................................................... xiii
AbouttheAuthors................................................................... xvii
CHAPTER 1 Introduction ....................................................... 1
1.1 FailureofSolids .................................................. 1
1.2 FractureMechanicsConcepts.................................... 2
1.3 HistoryofFractureMechanics................................... 5
1.3.1 GriffithTheoryofFracture................................ 5
1.3.2 FractureMechanicsasanEngineeringScience.......... 6
1.3.3 RecentDevelopmentsinFractureMechanics
Research ................................................... 7
References.............................................................. 8
CHAPTER 2 GriffithTheoryofFracture........................................ 11
2.1 TheoreticalStrength.............................................. 11
2.1.1 AnAtomisticModel....................................... 11
2.1.2 TheEnergyConsideration................................. 13
2.2 TheGriffithTheoryofFracture.................................. 14
2.3 ARelationamongEnergies...................................... 17
References.............................................................. 22
Problems ............................................................... 22
CHAPTER 3 TheElasticStressFieldaroundaCrackTip.................... 25
3.1 BasicModesofFractureandStressIntensityFactor ........... 25
3.2 MethodofComplexPotentialforPlaneElasticity
(TheKolosov-MuskhelishviliFormulas)........................ 27
3.2.1 BasicEquationsofPlaneElasticityandAiry
StressFunction ............................................ 27
3.2.2 AnalyticFunctionsandCauchy-Riemann
Equations .................................................. 29
3.2.3 ComplexPotentialRepresentationoftheAiry
StressFunction ............................................ 30
3.2.4 StressandDisplacement................................... 32
vii
viii Contents
3.3 WestergaardFunctionMethod ................................... 34
3.3.1 SymmetricProblems(ModeI)............................ 34
3.3.2 Skew-SymmetricProblems(ModeII).................... 36
3.4 SolutionsbytheWestergaardFunctionMethod................. 38
3.4.1 ModeICrack............................................... 38
3.4.2 ModeIICrack.............................................. 43
3.4.3 ModeIIICrack............................................. 46
3.4.4 ComplexRepresentationofStressIntensityFactor...... 48
3.5 FundamentalSolutionsofStressIntensityFactor............... 50
3.5.1 AFiniteCrackinanInfinitePlate ........................ 51
3.5.2 StressIntensityFactorsforaCrackSubjected
toArbitraryCrackFaceLoads............................ 53
3.5.3 ASemi-infiniteCrackinanInfiniteMedium............. 54
3.6 FiniteSpecimenSizeEffects..................................... 55
3.7 Williams’CrackTipFields....................................... 56
3.7.1 Williams’CrackTipStressandDisplacement
Fields:ModeIandII...................................... 57
3.7.2 Williams’CrackTipStressandDisplacement
Fields:ModeIII ........................................... 63
3.8 K-Dominance..................................................... 66
3.9 Irwin’sK-BasedFractureCriterion.............................. 68
References.............................................................. 71
Problems ............................................................... 72
CHAPTER 4 EnergyReleaseRate.............................................. 77
4.1 TheConceptofEnergyReleaseRate............................ 77
4.2 TheRelationsbetweenGandK bytheCrackClosure
Method............................................................ 78
4.3 TheJ-Integral..................................................... 82
4.3.1 JasEnergyReleaseRate.................................. 83
4.3.2 Path-Independence......................................... 86
4.3.3 RelationbetweenJandK ................................. 87
4.3.4 Examples................................................... 89
4.4 StressIntensityFactorCalculationsUsingtheFinite
ElementMethod.................................................. 92
4.4.1 DirectMethod.............................................. 92
4.4.2 ModifiedCrackClosureTechnique....................... 93
Contents ix
4.5 Three-DimensionalFieldnearCrackFront ..................... 94
4.5.1 DistributionofStressIntensityFactorover
Thickness .................................................. 95
4.5.2 PlaneStrainZoneattheCrackFront ..................... 99
References.............................................................. 101
Problems ............................................................... 102
CHAPTER 5 MixedModeFracture............................................. 105
5.1 ASimpleEllipticalModel ....................................... 105
5.2 MaximumTensileStressCriterion(MS-Criterion) ............. 108
5.3 StrainEnergyDensityCriterion(S-Criterion)................... 111
5.4 MaximumEnergyReleaseRateCriterion
(ME-Criterion).................................................... 115
5.5 ExperimentalVerifications ....................................... 117
References.............................................................. 119
Problems ............................................................... 120
CHAPTER 6 CrackTipPlasticity............................................... 123
6.1 YieldCriteria...................................................... 124
6.1.1 TrescaYieldCriterion ..................................... 124
6.1.2 vonMisesYieldCriterion................................. 125
6.2 ConstitutiveRelationshipsinPlasticity.......................... 125
6.2.1 FlowTheoryofPlasticity ................................. 126
6.2.2 DeformationTheoryofPlasticity......................... 128
6.3 Irwin’sModelforModeIFracture .............................. 130
6.3.1 PlasticZoneSize........................................... 130
6.3.2 EffectiveCrackLengthandAdjustedStress
IntensityFactor............................................ 133
6.3.3 CrackTipOpeningDisplacement......................... 134
6.4 TheDugdaleModel .............................................. 134
6.4.1 Small-ScaleYielding ...................................... 135
6.4.2 ACrackinanInfinitePlate................................ 137
6.5 PlasticZoneShapeEstimateAccordingtotheElastic
Solution........................................................... 140
6.5.1 PrincipalStresses .......................................... 140
6.5.2 PlaneStressCase .......................................... 141