czm内聚力模型

,TheoreticalandComputationalAspectsofCohesiveZoneModeling,NAMASCHANDRADepartmentofMechanicalEngineeringFAMU-FSUCollegeofEngineeringFloridaStateUniversityTallahassee,Fl-32310,AMML,AMML,FractureMechanics-Linearsolutionsleadstosingularfields-difficulttoevaluateFracturecriteriabasedonNon-lineardomain-solutionsarenotuniqueAdditionalcriteriaarerequiredforcrackinitiationandpropagationBasicbreakdownoftheprinciplesofmechanicsofcontinuousmediaDamagemechanics-caneffectivelyreducethestrengthandstiffnessofthematerialinanaveragesense,butcannotcreatenewsurface,AMML,CZMcancreatenewsurfaces.Maintainscontinuityconditionsmathematically,despitethephysicalseparation.CZMrepresentsphysicsofthefractureprocessattheatomicscale.Itcanalsobeperceivedatthemeso-scaleastheeffectofenergydissipationmechanisms,energydissipatedbothintheforwardandthewakeregionsofthecracktip.Usesfractureenergy(obtainedfromfracturetests)asaparameterandisdevoidofanyad-hoccriteriaforfractureinitiationandpropagation.Eliminatessingularityofstressandlimitsittothecohesivestrengthofthethematerial.Itisanidealframeworktomodelstrength,stiffnessandfailureinanintegratedmanner.Applications:geomaterials,biomaterials,concrete,metallics,composites.,AMML,AMML,ConceptualFrameworkofCohesiveZoneModelsforinterfaces,Molecularforceofcohesionactingneartheedgeofthecrackatitssurface(regionII).TheintensityofmolecularforceofcohesionfisfoundtovaryasshowninFig.a.Theinteratomicforceisinitiallyzerowhentheatomicplanesareseparatedbynormalintermoleculardistanceandincreasestohighmaximumafterthatitrapidlyreducestozerowithincreaseinseparationdistance.EisYoungsmodulusandissurfacetension,(Barenblatt,G.I,(1959),PMM(23)p.434),Barenblatt(1959)wasfirsttoproposetheconceptofCohesivezonemodeltobrittlefracture,AMML,ForDuctilemetals(steel)CohesivestressintheCZMisequatedtoyieldstressYAnalyzedforplasticzonesizeforplatesundertensionLengthofyieldingzones,theoreticalcracklengtha,andappliedloadingTarerelatedintheform,(Dugdale,D.S.(1960),J.Mech.Phys.Solids,8,p.100),AMML,ThetheoryofCZMisbasedonsoundprinciples.HoweverimplementationofmodelforpracticalproblemsgrewexponentiallyforpracticalproblemswithuseofFEMandadventoffastcomputing.Modelhasbeenrecastasaphenomenologicaloneforanumberofsystemsandboundaryvalueproblems.Thephenomenologicalmodelscanmodeltheseparationprocessbutnottheeffectofatomicdiscreteness.,Hillerborgetal.1976Ficticiouscrackmodel;concreteBazantetal.1983crackbandtheory;concreteMorganetal.1997earthquakerupturepropagation;geomaterialPlanasetal,1991,concreteEisenmenger,2001,stonefragm-entationsqueezingbyevanescentwaves;brittle-biomaterialsAmruthrajetal.,1995,composites,Grujicic,1999,fracturebeha-viorofpolycrystalline;bicrystalsCostanzoetal;1998,dynamicfr.Ghosh2000,Interfacialdebo-nding;compositesRahulkumar2000viscoelasticfracture;polymersLiechti2001Mixed-mode,time-depend.rubber/metaldebondingRavichander,2001,fatigue,Tevergaard1992particle-matrixinterfacedebondingTvergaardetal1996elastic-plasticsolid:ductilefrac.;metalsBrocks2001crackgrowthinsheetmetalCamachobiomaterials,CZMessentiallymodelsfractureprocesszonebyalineoraplaneaheadofthecracktipsubjectedtocohesivetraction.Theconstitutivebehaviorisgivenbytraction-displacementrelationship,obtainedbydefiningpotentialfunctionofthetype,where,arenormalandtangentialdisplacementjump,Theinterfacetractionsaregivenby,y,AMML,AMML,AMML,Whatistherelationshipbetweenthephysics/mechanicsoftheseparationprocessandshapeofCZM?(Thereareasmanyshapes/equationsastherearenumberofinterfaceproblemssolved!)WhatistherelationshipbetweenCZMandfracturemechanicsofbrittle,semi-brittleandductilematerials?WhatistheroleofscalingparameterinthefidelityofCZMtomodelinterfacebehavior?Whatisthephysicalsignificanceof-ShapeofthecurveC-tmaxandinterfacestrength-SeparationdistancesepandCOD?-Areaunderthecurve,workoffracture,fracturetoughnessG(localandglobal),CriticalIssuesintheapplicationofCZMtointerfacemodels,AMML,CZMisanexcellenttoolwithsoundtheoreticalbasisandcomputationalease.Lackspropermechanicsandphysicsbasedanalysisandevaluation.Alreadywidelyusedinfracture/fragmentation/failure,AMML,AMML,AMML,AMML,Constructsymmetrictiltboundaries(STDB)byrotatingasinglecrystal(reflection)PeriodicboundaryconditioninXdirectionRestrainfewlayersinlowercrystalApplybodyforceontopcrystal,AMML,AsmallportionofCSLgrainbounarybeforeAndafterapplicationoftangentialforce,ShetC,LiH,ChandraN;InterfacemodelsforGBslidingandmigrationMATERSCIFORUM357-3:577-5852001,AMML,AsmallportionofCSLgrainboundarybeforeAndafterapplicationofnormalforce,AMML,Summarycompletedebondingoccurswhenthedistanceofseparationreachesavalueof2to3.For9bicrystaltangentialworkofseparationalongthegrainboundaryisoftheorder3andnormalworkofseparationisoftheorder2.6.For3-bicrystal,theworkofseparationrangesfrom1.5to3.7.Roseetal.(1983)havereportedthattheadhesiveenergy(workofseparation)foraluminumisoftheorder0.5andtheseparationdistance2to3Measuredenergytofracturecopperbicrystalwithrandomgrainboundaryisoftheorder54andfor11copperbicrystaltheenergytofractureismorethan8000,ImplicationsThenumericalvalueofthecohesiveenergyisverylowwhencomparedtotheobservedexperimentalresultsAtomisticsimulationgivesonlysurfaceenergyignoringtheinelasticenergiesduetoplasticityandothermicroprocesses.Itshouldalsobenotedthattheexper-imentalvalueoffractureenergyincludestheplasticworkinadditiontoworkofseparation(J.RRiceandJ.SWang,1989),AMML,AMML,Energybalanceandeffectofplasticityintheboundingmaterial,AMML,Motivation,ItisperceivedthatCZMrepresentsthephysicalseparationprocess.Asseenfromatomistics,fractureprocesscomprisesmostlyofinelasticdissipativeenergies.Therearemanyinelasticdissipativeprocessspecifictoeachmaterialsystem;someoccurwithinFPZ,andsomeintheboundingmaterial.Howtheenergyflowtakesplaceundertheexternalloadingwithinthecohesivezoneandneighboringboundingmaterialnearthecracktip?Whatisthespatialdistributionofplasticenergy?Istherealinkbetweenmicromechanicsprocessesofthematerialandcurve.,AMML,Plasticityvs.otherDissipationMechanisms,Sinceboundingmaterialhasitsowninelasticconstitutiveequation,whatistheproportionofenergydissipationwithinthatdomainandfractureregiongivenbyCZM.Roleofplasticityintheboundingmaterialisclearlyunique;andcannotbeassignedtoCZM.,AMML,Al2024-T3alloyTheinputenergyinthecohesivemodelarerelatedtotheinterfacialstressandcharacteristicdisplacementasTheinputenergyisequatedtomaterialparameterBasedonthemeasuredfracturevalue,Cohesivezoneparametersofaductilematerial,AMML,E=72GPa,=0.33,Stressstraincurveisgivenby,where,andfractureparameter,Materialmodelfortheboundingmaterial,Elasto-plasticmodelforAl2024-T3,AMML,Geometryandboundary/loadingconditions,a=0.025m,b=0.1m,h=0.1m,AMML,Finiteelementmesh,28189nodes,24340planestrain4nodeelements,7300cohesiveelements(widthofelementalongthecrackplanism,AMML,Globalenergydistribution,areconfinedtoboundingmaterial,AMML,Globalenergydistribution(continued),Analysiswithelasto-plasticmaterialmodel,AMML,WhatarethekeyCZMparametersthatgoverntheenergetics?,AMML,Globalenergydistribution(continued),Variationofcohesiveenergyandplasticenergyforvariousratios(2)(3)(4),AMML,Relationbetweenplasticworkandcohesivework,AMML,VariationofNormalTractionalongtheinterface,Thelengthofcohesivezoneisalsoaffectedbyratio.Thereisadirectcorrelationbetweentheshapeofthetraction-displacementcurveandthenormaltractiondistributionalongthecohesivezone.Forlowerratiosthetraction-separationcurveflattens,thistendtoincreasetheoverallcohesivezonelength.,AMML,Local/spatialEnergyDistribution,AMML,VariationofCohesiveEnergy,ThevariationofCohesiveEnergyintheWakeandForwardregionasthecrackpropagates.ThenumbersindicatetheCohesiveElementPatchnumbersFallingJustBelowthebindingelementpatches,AMML,VariationofElasticEnergy,VariationofElasticEnergyinVariousPatchofElementsasaFunctionofCrackExtension.ThenumbersindicatePatchnumbersstartingfromInitialCrackTip,Considerableelasticenergyisbuiltuptillthepeakofcurveisreachedafterwhichthecracktipadvances.AfterpassingC,thecohesiveelementsnearthecracktipareseparatedandtheelementsinthispatchbecomesapartofthewake.Atthisstage,thevaluesofnormaltractionreducesfollowingthedownwardslopeofcurvefollowingwhichthestressinthepatchreducesaccompaniedbyreductioninelasticstrainenergy.Thereductioninelasticstrainenergyisusedupindissipatingcohesiveenergytothosecohesiveelementsadjoiningthispatch.Theinitialcracktipisinherentlysharpleadingtohighlevelsofstressfieldsduetowhichhigherenergyforpatch1Cracktipbluntsforadvancingcracktipleadingtoalowerlevelsofstress,resultinginreducedenergylevelinotherpatches.,AMML,Variationofdissipatedplasticenergyinvariouspatchedasafunctionofcrackextension.Thenumberindicatepatchnumbersstartingfrominitialcracktip.,AMML,VariationofPlasticWork(),VariationofPlasticworkandElasticworkinvariouspatchofelementsalongtheinterfaceforthecaseof.Thenumbe