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1、MAE5553:FatigueandFractureLinearElasticFractureMechanics:ContinuedIIRamanP.SinghSchoolofMechanicalandAerospaceEngineeringOklahomaStateUniversityJanuary24,2013LinearElasticFractureMechanics:ContinuedIIRamanP.SinghOutlineStressFieldsStressFieldsTheWilliamsSolutionTheWilliamsSolutionTheWesterg

2、aardProblemTheWestergaardProblemTheStressIntensityFactorDefiningTheStressIntensityFactorDeterminingTheStressIntensityFactorTheStressIntensityFactorSuperpostionDefiningTheStressIntensityFactorDeterminingTheStressIntensityFactorSuperpostionLinearElasticFractureMechanics:ContinuedIIRamanP.SinghO

3、utlineStressFieldsStressFieldsTheWilliamsSolutionTheWilliamsSolutionTheWestergaardProblemTheWestergaardProblemTheStressIntensityFactorDefiningTheStressIntensityFactorDeterminingTheStressIntensityFactorTheStressIntensityFactorSuperpostionDefiningTheStressIntensityFactorDeterminingTheStressInte

4、nsityFactorSuperpostionTheWedgeProblemLinearElasticFractureMechanics:ContinuedIIRamanP.SinghOutlineStressFieldsTheWilliamsSolutionTheWestergaardProblemTheStressIntensityFactorDefiningTheStressIntensityFactorDeterminingTheStressIntensityFactorAwedgewithtractionfreeflanks[Sanford,2003]Superpost

5、ionWilliamssolvedthewedgeproblemusingastressfunctionformulation[Williams,1952]andwasthefirsttoshowtheuniversalnatureoftheinversesquare-rootpsingularity,O(1=r).TheCrackProblemLinearElasticFractureMechanics:ContinuedIIRamanP.SinghOutlineStressFieldsTheWilliamsSolutionTheWestergaardProblemThe

6、StressIntensityFactorDefiningTheStressIntensityFactorDeterminingTheStressIntensityFactorSuperpostionSetting=generatesthecrackproblem[Sanford,2003]Williamsextendedthewedgeproblemtosolvefortheelasticstressfieldssurroundingaremotelyloadedcracktip[Williams,1957].StressesForaCrackBasedontheWillia

7、msLinearElasticFractureMechanics:SolutionContinuedIIRamanP.SinghOutlineThestressesinpolarcoordinatesbecomeStressFieldsTheWilliamsSolution=r1(+1)f()+f00()TheWestergaardProblemrTheStress=(+1)r1f()IntensityFactorDefiningTheStressIntensityFacto