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1、FractureandDamageMechanicsChapterFiveFracturecriterionformixedmodecrackChapterFiveFracturecriterionformixedmodecrackInthematerialmechanics,forthemultiaxialstressstate,fourstrengththeorieshavebeendeveloped.Inthefracturemechanicsforthemixedmodecrackproblem,weneedtodevelopthefracturetheory
2、accordingly.Manyfracturetheorieshavebeendeveloped.Twokeyquestionsmustbeanswered.(1)Whatdirectiondoesacrackpropagatealong?(2)Whatisthecriticalcase?Inwhatfollows,fivetheorieswillbeintroduced.§5-1MaximumnormalstresscriterionMaximumstresscriterioncanbeappliedtothemixedmodecrackofmodeIandmod
3、eII.TheasymptoticstresssolutionisByapplicationofthecoordinatetransformationformulas,wecanobtaintheexpressionsofthreestresscomponentsinthepolarcoordinates(r,q).ThecircumferentialnormalstressisThecircumferentialnormalstressintensityfactorisdefinedas77FractureandDamageMechanicsChapterFiveF
4、racturecriterionformixedmodecrackHence,canbewrittenasAssumptions:(1)Crackinitiationdirectionisthedirectionofthemaximum;(2)Whenreachesitscriticalvalue,breakoccurs.isamaterialconstant.Thecrackinitiationanglecanbedeterminedfrom,TheresultisThecriticalconditionisDeterminationof:FormodeIcrack
5、,,,,thecriticalconditionreducestoNotethatisamaterialconstant.When,and,therestillprevails.ThemaximumstresscriterionisexpressedasApplicationtomodeIIcrack:ForamodeIIcrack,and.Thecrackinitiationanglecanbesolved,77FractureandDamageMechanicsChapterFiveFracturecriterionformixedmodecrack.Fromon
6、ecanobtainthat,,ThefracturecriterionforModeIIcrackcanbederivedfromthemaximumstresscriterionthatItisconvenientfortheengineeringapplication.However,thereisnodifferencebetweentheplanestressandplanestrain.§5-2MaximumnormalstraincriterionNearthecracktip,thecircumferentialnormalstrainis,,forp
7、lanestress;,,forplanestrain.Thecircumferentialnormalstrainintensityfactorisdefinedas77FractureandDamageMechanicsChapterFiveFracturecriterionformixedmodecrackThen,Assumptions:(1)Crackinitiationdirectionisthedirectionofthemaximum;(2)Whenreachesitscriticalvalue,breakoccurs.isamate
