An elastic-plastic cohesive zonemodel for metal-ce

Anelastic–plasticcohesivezonemodelformetal–ceramicinterfacesatfinitedeformationsQiangXu,ZixingLu⇑InstituteofSolidMechanics,BeihangUniversity(BUAA),Beijing100191,PRChinaarticleinfoArticlehistory:Received21June2012Receivedinfinalrevisedform4September2012Availableonline25September2012Keywords:InterfaceyieldingDamageMetalmatrixcompositesNumericalmodelingabstractThisstudyconcernsanelastic–plasticcohesivezonemodelformetal–ceramicinterfacesandthecorrespondingnonlinearfiniteelementimplementationforgeneralboundaryvalueproblemsthataccountsfornonlineartractionseparationconstitutiverelationinclud-ingfinescalemechanismsofthebondedinterfacesfailure.Theinterfacialmodel,formu-latedintermsofgeometricallynonlineartheoryofplasticity,allowsforlocalizationofplasticdeformation,ensuingdamageandfailure/fracturebehavioroftheinterfaceatfinitedeformations.Fromthenumericalsimulations,fiberismodeledasalinearlyelasticmate-rialwhiletheconstitutiverelationofmatrixmaterialismodeledusinglargedeformationofisotropicporousplasticmaterialwhichincludesthevoidsnucleate,growandcoalesce.Further,anextensiveparametricstudyisconductedinwhichtheeffectsofhardening/soft-ening,cohesiveyieldstressandthedamagedisplacementjumpsindeterminingstress-strainresponseofthecompositeandfiber/matrixdebondingprocessunderquasi-statictransverseloading.Moreover,theeffectsofinitialyieldstressandvoidvolumefractionintheporousmatrixarealsoconsidered.Resultsshowtherearesignificanteffectsofinter-faceyieldandfailure/fractureaswellasmatrixporousplasticityontheoveralldeforma-tionalandfailureresponseofcomposites.2012ElsevierLtd.Allrightsreserved.1.IntroductionMetalmatrixcomposites(MMCs)havebeenwidelyusedinrecentyearsduetotheirexcellentmechanicalproperties,suchashighspecificstrengthandstiffness,witharelativelylowweight.Thesepropertiesmakethemparticularlypopularinaerospaceapplications.InMMCs,themechanicalbehaviorischaracterizedintermsofthecompositemicrostructureandtheircorrespondingproperties.Moreover,MMCsalwaysdisplayinelasticresponseatthefinescale,whichoccurthroughthecomplexmechanismsthatinvolveinteractionbetweentheplasticdeformationofisotropicporousmatrixmaterialandtheirreversibleinelasticseparationoffiber/matrixinterfacewhensubjectedtotransverseloadingcondition.Numerical(see,e.g.,Bruzzietal.,2001;SaraevandSchmauder,2003;Venaetal.,2008;Fredrikssonetal.,2009;Doghrietal.,2010;Guoetal.,2011;ChenandGhosh,2012)andanalytical(ZhuandZbib,1995;VoyiadjisandThiagarajan,1996;WilliamsandPindera,1997;LiuandHu,2005;PyoandLee,2010)studieshavebeenconductedinwhichtherolesofparticlevolumefractionsandshapesaswellastheinelasticproperties(i.e.,porousandstraingradientplasticity,viscoplasticityanddamage)ofthematrixindeterminingtheoverallresponseofMMCsunderquasi-static,dynamicandcyclicloading.Butveryfewworks(Tanetal.,2005;BansalandPindera,2006;Siddiqetal.,2007;LegarthandNiordson,2010;KruchandChaboche,2011)devotedforstudyingtheinelasticanddamagebehavioroftheinterfaceinMMCs,despitetheexperimentalresultsavailabledemonstratingtheirimportance.Forexample,Xiaetal.(2009)observedthereverseplasticdisplacementsduring0749-6419/$-seefrontmatter2012ElsevierLtd.Allrightsreserved.⇑Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddresses:[e-mail](Q.Xu),[e-mail](Z.Lu).InternationalJournalofPlasticity41(2013)147–164ContentslistsavailableatSciVerseScienceDirectInternationalJournalofPlasticityjournalhomepage:(2009)experimentallyshowedthatlargeplasticdeformationscouldbeeffectivelygener-atednearthefibersbystronginterfacedebondinginafiberpush-outtestinMMCs.Thereforeitisimportanttocharacterizetheoverallperformanceofthecompositesbyincorporatingtheinelasticdebondingprocessoftheinterfaceatfinitedefor-mations.However,fiber/matrixdebondingfailureinMMCsis,ingeneral,verycomplicated.Insteadofmodelingthedebond-ingfractureprocessofMMCsbyfracturemechanicsmethod,cohesivezonemodels(CZMs)areusedfordecohesionoffiber/matrixinterface.Inthelasthalfcentury,anumberofcohesivezonemodelshavebeendevelopedformodellingtheinterfacialmechanicalresponse,e.g.,Chandraetal.(2002)andreferencestherein.Butveryfewcohesivemodelshavefocusedonthegeometricallynonlinear,inelasticanddamagebehaviorduetothecomplexityfailuremechanismsoflocalizedplasticdeformationaccu-mulationandthedamageevolutionintheductilematrixclosetotheinterfaceatfinitedeformations.Oneapproachtoaddressthenon-linearcohesivedecohesionbyrepresentingafunctionofnormalandtangentialtractionsaswellasfractureenergypotentialintermsofseparationdistances,e.g.,Needleman,1987,1990;TvergaardandHutchinson,1992;XuandNeedleman,1994.Althoughthesecohesivemodelswereappliedforhandlingawiderangeoffractureproblemsincludingdynamicdelaminationprocessinalaminate(Rahul-Kumaretal.,2000;Coriglianoetal.,20