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1、FractureandDamageMechanicsChapterFiveFracturecriterionformixedmodecrackChapterFiveFracturecriterionformixedmodecrackInthematerialmechanics,forthemultiaxialstressstate,fourstrengththeorieshavebeendeveloped.Inthefracturemechanicsforthemixedmodecrackproblem,weneedtodevelopthefracturetheoryaccording
2、ly.Manyfracturetheorieshavebeendeveloped.Twokeyquestionsmustbeanswered.(1)Whatdirectiondoesacrackpropagatealong?(2)Whatisthecriticalcase?Inwhatfollows,fivetheorieswillbeintroduced.§5-1MaximumnormalstresscriterionMaximumstresscriterioncanbeappliedtothemixedmodecrackofmodeIandmodeII.Theasymptotics
3、tresssolutionisByapplicationofthecoordinatetransformationformulas,wecanobtaintheexpressionsofthreestresscomponentsinthepolarcoordinates(r,q).ThecircumferentialnormalstressisThecircumferentialnormalstressintensityfactorisdefinedas77FractureandDamageMechanicsChapterFiveFracturecriterionformixedmod
4、ecrackHence,canbewrittenasAssumptions:(1)Crackinitiationdirectionisthedirectionofthemaximum;(2)Whenreachesitscriticalvalue,breakoccurs.isamaterialconstant.Thecrackinitiationanglecanbedeterminedfrom,TheresultisThecriticalconditionisDeterminationof:FormodeIcrack,,,,thecriticalconditionreducestoNot
5、ethatisamaterialconstant.When,and,therestillprevails.ThemaximumstresscriterionisexpressedasApplicationtomodeIIcrack:ForamodeIIcrack,and.Thecrackinitiationanglecanbesolved,77FractureandDamageMechanicsChapterFiveFracturecriterionformixedmodecrack.Fromonecanobtainthat,,ThefracturecriterionforModeII
6、crackcanbederivedfromthemaximumstresscriterionthatItisconvenientfortheengineeringapplication.However,thereisnodifferencebetweentheplanestressandplanestrain.§5-2MaximumnormalstraincriterionNearthecracktip,thecircumferentialnormalstrainis,,forplanestress;,,forplanestrain.Thecircumferentialnormalst
7、rainintensityfactorisdefinedas77FractureandDamageMechanicsChapterFiveFracturecriterionformixedmodecrackThen,Assumptions:(1)Crackinitiationdirectionisthedirectionofthemaximum;(2)Whenreachesitscriticalvalue,breakoccurs.isamate
