czm内聚力模型

AMMLTheoreticalandComputationalAspectsofCohesiveZoneModelingNAMASCHANDRADepartmentofMechanicalEngineeringFAMU-FSUCollegeofEngineeringFloridaStateUniversityTallahassee,Fl-32310WhatisCZMandwhyisitimportantInthestudyofsolidsanddesignofnano/micro/macrostructures,thermomechanicalbehaviorismodeledthroughconstitutiveequations.Typicallyisacontinuousfunctionofandtheirhistory.Designislimitedbyamaximumvalueofagivenparameter()atanylocalpoint.Whathappensbeyondthatconditionistherealmof‘fracture’,‘damage’,and‘failure’mechanics.CZMoffersanalternativewaytoviewandfailureinmaterials.,,f(,,)FractureMechanics-Linearsolutionsleadstosingularfields-difficulttoevaluateFracturecriteriabasedonNon-lineardomain-solutionsarenotuniqueAdditionalcriteriaarerequiredforcrackinitiationandpropagationBasicbreakdownoftheprinciplesofmechanicsofcontinuousmediaDamagemechanics-caneffectivelyreducethestrengthandstiffnessofthematerialinanaveragesense,butcannotcreatenewsurfaceFracture/DamagetheoriestomodelfailureICICICK,G,J,CTOD,...ED1,Effectivestress=E1DCZMcancreatenewsurfaces.Maintainscontinuityconditionsmathematically,despitethephysicalseparation.CZMrepresentsphysicsofthefractureprocessattheatomicscale.Itcanalsobeperceivedatthemeso-scaleastheeffectofenergydissipationmechanisms,energydissipatedbothintheforwardandthewakeregionsofthecracktip.Usesfractureenergy(obtainedfromfracturetests)asaparameterandisdevoidofanyad-hoccriteriaforfractureinitiationandpropagation.Eliminatessingularityofstressandlimitsittothecohesivestrengthofthethematerial.Itisanidealframeworktomodelstrength,stiffnessandfailureinanintegratedmanner.Applications:geomaterials,biomaterials,concrete,metallics,composites….CZMisanAlternativemethodtoModelSeparationAMMLContactWedgingContactSurface(friction)PlasticWakePlasticityinducedcrackclosureFibril(MMCbridgingOxidebridgingPlasticzoneCleavagefractureWakeofcracktipForwardofcracktipExtrinsicdissipationIntrinsicdissipationMetallicCeramicCrackMeanderingThicknessofceramicinterfaceMicrovoidcoalescencePlasticwakePrecipitatesCrackDeflectionCrackMeanderingCyclicloadinducedcrackclosureMicrocrackinginitiationMicrovoidgrowth/coalescenceDelaminationCorneratomsBCCBodycenteredatomsFacecenteredatomsFCCCorneratomsPhasetransformationGrainbridgingFibril(polymers)bridgingInter/transgranularfractureActivedissipationmechanisimsparticipatingatthecohesiveprocesszoneDissipativeMicromechanisimsActinginthewakeandforwardregionoftheprocesszoneattheInterfacesofMonolithicandHeterogeneousMaterialCWAKEFORWARDsepdmaxdDdCOHESIVECRACKTIPACTIVEPLASTICZONEINACTIVEPLASTICZONE(Plasticwake)ELASTICSINGULARITYZONEMATHEMATICALCRACKTIPMATERIALCRACKTIPAEDxyDdmaxdsepdmaxyWAKEFORWARDLOCATIONOFCOHESIVECRACKTIPdˆABDENOMATERIALSEPARATIONl1l2COMPLETEMATERIALSEPARATIONC,XConceptofwakeandforwardregioninthecohesiveprocesszoneConceptualFrameworkofCohesiveZoneModelsforinterfacesisaninterfacesurfaceseparatingtwodomains(identical/separateconstitutivebehavior).Afterfracturethesurfacecompriseofunseparatedsurfaceandcompletelyseparatedsurface(e.g.);allmodeledwithinthecon-ceptofCZM.Suchanapproachisnotpossibleinconventionalmechanicsofcon-tinuousmedia.112,*1Molecularforceofcohesionactingneartheedgeofthecrackatitssurface(regionII).Theintensityofmolecularforceofcohesion‘f’isfoundtovaryasshowninFig.a.Theinteratomicforceisinitiallyzerowhentheatomicplanesareseparatedbynormalintermoleculardistanceandincreasestohighmaximumafterthatitrapidlyreducestozerowithincreaseinseparationdistance.EisYoung’smodulusandissurfacetensionoT(Barenblatt,G.I,(1959),PMM(23)p.434)mofET/bE/10Figure(a)VariationofCohesivetraction(b)I-innerregion,II-edgeregionDevelopmentofCZModels-HistoricalReviewBarenblatt(1959)wasfirsttoproposetheconceptofCohesivezonemodeltobrittlefractureAMMLForDuctilemetals(steel)CohesivestressintheCZMisequatedtoyieldstressYAnalyzedforplasticzonesizeforplatesundertensionLengthofyieldingzone‘s’,theoreticalcracklength‘a’,andappliedloading‘T’arerelatedintheform2sTa4Y2sin()(Dugdale,D.S.(1960),J.Mech.Phys.Solids,8,p.100)Dugdale(1960)independentlydevelopedtheconceptofcohesivestressThetheoryofCZMisbasedonsoundprinciples.HoweverimplementationofmodelforpracticalproblemsgrewexponentiallyforpracticalproblemswithuseofFEMandadventoffastcomputing.Modelhasbeenrecastasaphenomenologicaloneforanumberofsystemsandboundaryvalueproblems.Thephenomenologicalmodelscanmodeltheseparationprocessbutnottheeffectofatomicdiscreteness.PhenomenologicalModelsHillerborgetal.1976Ficticiouscrackmodel;concreteBazantetal.1983crackbandtheory;concreteMorganetal.1997earthquakerupturepropagation;geomaterialPlanasetal,1991,concreteEisenmenger,2001,stonefragm-entationsqueezingbyevanescentwaves;brittle-biomaterialsAmruthrajetal.,1995,compositesGrujicic,1999,fracturebeha-viorofpolycrystalline;bicrystalsCostanzoetal;1998,dynamicfr.Ghosh2000,Interfacialdebo-nding;compositesRahulkumar2000viscoelasticfracture;polymersLiechti2001Mixed-mode,time-depend.rubber/metaldebondingRavichander,2001,fatigueTevergaard1992part