An anisotropic theory of elasticity for continuum damage mechanics.pdf

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1、InternationalJournalofFracture33:3-16(1987)3©MartinusNijhoffPublishers,Dordrecht-PrintedintheNetherlandsAnanisotropictheoryofelasticityforcontinuumdamagemechanicsC.L.ChowandJuneWang*DepartmentofMechanicalEngineering,UniversityofHongKong,HongKong,"onleavefromHuazhongUniversityofSc

2、ience&Technology,Wuhan,ChinaReceived13June1986;accepted11September1986AbstractThispaperpresentsthedevelopmentofananisotropicelasticdamagetheory.ThisisachievedbyderivingamodifieddamageeffecttensorM(D)fortheeffectivestressequationscapableofincludingtheeffectofanisotropicmaterialdam

3、age.Themodifiedtensorremovestherestrictionofaprioriknowledgeofthedirectionsofprincipalstressesimposedbyadamageeffecttensordevelopedearlierandcannowbemadeforgeneralpracticalengineeringapplicationsoffailureanalysis.Reductionoftheproposedtensortoascalarforisotropicdamageisshowntobep

4、ossiblewhenitisexpressednotonlyintheprincipaldirectionsbutalsoinanyarbitrarycoordinatesystem,anecessaryconditiontoverifythevalidityoftheproposedtensor.Uniaxialtensionandpuretorsionarechosentoillustratetheapplicationofthetheoryaswellasassociateddamagevariablesthatmaybeexperimental

5、lydeterminedusinglaboratorysizespecimens.Themeasureddamagevariablesconfirmthepresenceofanisotropicdamagefromaninitiallyisotropicmaterialspecimenandthemagnitudeismorepronouncedathigherstressesandstrains.1.IntroductionTheconceptofcontinuumdamagemechanicsduetoKachanov[1]hasbeendevel

6、opedtoastagewheretheconceptcanbeeffectivelyusedtosupplementthedesignofpracticalengineeringstructuresbasedonthetheoryoffracturemechanics[2-23].Althoughthedamagemechanicsprovideameasureofmaterialdegradationatthemicro-mechanicsscaleduetonucleationandcoalescenceofvoids,cavities,andmi

7、cro-cracks,thedamagevariablesareintroducedtoreflectaveragematerialdegradationinanelementatamacro-mechanicsscalenormallyassociatedwiththeclassicaltheoryofcontinuummechanics.Thisenablesthevariablestobemeasuredexperimentallyusinglaboratory-sizespecimensrecommendedforconventionaltest

8、ingstandards,thusmakingpossibletheapplic