Fracture_Lecture_Notes_02_Energy_Balance

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1、MAE5553:FatigueandFractureLinearElasticFractureMechanicsRamanP.SinghSchoolofMechanicalandAerospaceEngineeringOklahomaStateUniversityJanuary10,2013LinearElasticFractureMechanicsRamanP.SinghOutlineDevelopmentalConceptsDevelopmentalConceptsAtomicViewofFractureA

2、tomicViewofFractureCrackasaFiniteDefectCrackasaFiniteDefect(Hole)(Hole)TheGriffithEnergyBalanceTheGriffithEnergyBalanceTheEnergyReleaseRateEnergyDissipationDuringActualCrackGrowthTheEnergyReleaseRateConceptTheEnergyReleaseRateEnergyDissipationDuringActualCrack

3、GrowthTheEnergyReleaseRateConceptLinearElasticFractureMechanicsRamanP.SinghOutlineDevelopmentalConceptsDevelopmentalConceptsAtomicViewofFractureAtomicViewofFractureCrackasaFiniteDefectCrackasaFiniteDefect(Hole)(Hole)TheGriffithEnergyBalanceTheGriffithEnergyBal

4、anceTheEnergyReleaseRateEnergyDissipationDuringActualCrackGrowthTheEnergyReleaseRateConceptTheEnergyReleaseRateEnergyDissipationDuringActualCrackGrowthTheEnergyReleaseRateConceptFractureAsAtomicSeparationLinearElasticFractureMechanicsRamanP.SinghOutlineDevel

5、opmentalConceptsAtomicViewofFractureCrackasaFiniteDefect(Hole)TheGriffithEnergyBalanceTheEnergyReleaseRateEnergyDissipationDuringActualCrackGrowthTheEnergyReleaseRateConceptAtomicbondenergyandseparationforce[Anderson,1991]ForceNeededForAtomicSeparationLinearE

6、lasticFractureMechanicsRamanP.SinghOutlineBondenergyDevelopmentalZ1ConceptsAtomicViewofFractureEb=PdCrackasaFiniteDefect(Hole)0TheGriffithEnergyBalanceTheEnergyWecanapproximatetheseparationforce,P,asReleaseRateEnergyDissipationDuringActualCrackGrowthThe

7、EnergyReleaseRateP=PsinConceptcForsmalldisplacementsPcPPc=kwherekisthebondstiffnessStressNeededForAtomicSeparation—ILinearElasticFractureMechanicsRamanP.SinghOutlineNow,loadneededforseparation,DevelopmentalConceptsAtomicViewofFractureCrackasaFi

8、niteDefectk(Hole)Pc=TheGriffithEnergyBalanceTheEnergyReleaseRateDividebothsidesbynumberofatomicbondsperarea,EnergyDissipationDuringActualCrackGrowthandRHSbygagelengthTheEnergyReleaseRate0Conce