czm内聚力模型(ppt文档).ppt

TheoreticalandComputationalAspectsofCohesiveZoneModelingNAMASCHANDRADepartmentofMechanicalEngineeringFAMU-FSUCollegeofEngineeringFloridaStateUniversityTallahassee,Fl-32310AMMLWhatisCZMandwhyisitimportantqInthestudyofsolidsanddesignofnano/micro/macrostructures,thermomechanicalbehaviorismodeledthroughconstitutiveequations.qTypicallyisacontinuousfunctionofandtheirhistory.qDesignislimitedbyamaximumvalueofagivenparameter()atanylocalpoint.qWhathappensbeyondthatconditionistherealmoffracture,damage,andfailuremechanics.qCZMoffersanalternativewaytoviewandfailureinmaterials.AMML1.FractureMechanics-1.Linearsolutionsleadstosingularfields-difficulttoevaluate2.Fracturecriteriabasedon3.Non-lineardomain-solutionsarenotunique4.Additionalcriteriaarerequiredforcrackinitiationandpropagation2.Basicbreakdownoftheprinciplesofmechanicsofcontinuousmedia3.Damagemechanics-1.caneffectivelyreducethestrengthandstiffnessofthematerialinanaveragesense,butcannotcreatenewsurfaceFracture/DamagetheoriestomodelfailureAMMLCZM can create new surfaces.Maintains continuity conditions mathematically,despite the physical separation.CZM represents physics of the fracture process at the atomic scale.It can also be perceived at the meso-scale as the effect of energy dissipation mechanisms,energy dissipated both in the forward and the wake regions of the crack tip.Uses fracture energy(obtained from fracture tests)as a parameter and is devoid of any ad-hoc criteria for fractureinitiation and propagation.Eliminates singularity of stress and limits it to the cohesive strength of the the material.It is an ideal framework to model strength,stiffness and failure in an integrated manner.Applications:geomaterials,biomaterials,concrete,metallics,composites.CZMisanAlternativemethodtoModelSeparationAMMLAMMLConceptualFrameworkofCohesiveZoneModelsforinterfacesAMMLMolecularforceofcohesionactingneartheedgeofthecrackatitssurface(regionII).TheintensityofmolecularforceofcohesionfisfoundtovaryasshowninFig.a.Theinteratomicforceisinitiallyzerowhentheatomicplanesareseparatedbynormalintermoleculardistanceandincreasestohighmaximumafterthatitrapidlyreducestozerowithincreaseinseparationdistance.EisYoungsmodulusandissurfacetension(Barenblatt,G.I,(1959),PMM(23)p.434)Figure (a)Variation of Cohesive traction (b)I-inner region,II-edge regionDevelopmentofCZModels-HistoricalReviewq Barenblatt(1959)wasfirsttoproposetheconceptofCohesivezonemodeltobrittlefractureAMMLForDuctilemetals(steel)CohesivestressintheCZMisequatedtoyieldstressYAnalyzedforplasticzonesizeforplatesundertensionLengthofyieldingzones,theoreticalcracklengtha,andappliedloadingTarerelatedintheform(Dugdale,D.S.(1960),J.Mech.Phys.Solids,8,p.100)qDugdale(1960)independently developed the concept of cohesive stressAMMLqThetheoryofCZMisbasedonsoundprinciples.qHoweverimplementationofmodelforpracticalproblemsgrewexponentiallyforpracticalproblemswithuseofFEMandadventoffastcomputing.qModelhasbeenrecastasaphenomenologicaloneforanumberofsystemsandboundaryvalueproblems.qThephenomenologicalmodelscanmodeltheseparationprocessbutnottheeffectofatomicdiscreteness.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,fatigueTevergaard1992particle-matrixinterfacedebondingTvergaardetal1996elastic-plasticsolid:ductilefrac.;metalsBrocks2001crackgrowthinsheetmetalCamacho&ortiz;1996,impactDollar;1993Interfacialdebondingceramic-matrixcompLokhandwalla2000,urinarystones;biomaterialsAMMLqCZMessentiallymodelsfractureprocesszonebyalineoraplaneaheadofthecracktipsubjectedtocohesivetraction.qTheconstitutivebehaviorisgivenbytraction-displacementrelationship,obtainedbydefiningpotentialfunctionofthetypewherearenormalandtangentialdisplacementjumpTheinterfacetractionsaregivenbyFractureprocesszoneandCZMMaterialcracktipMathematicalcracktipxyAMMLAMMLAMMLWhatistherelationshipbetweenthephysics/mechanicsoftheseparationprocessandshapeofCZM?(Thereareasmanyshapes/equationsastherearenumberofinterfaceproblemssolved!)WhatistherelationshipbetweenCZMandfracturemechanicsofbrittle,semi-brittleandductilematerials?WhatistheroleofscalingparameterinthefidelityofCZMtomodelinterfacebehavior?Whatisthephysicalsignificanceof-ShapeofthecurveC-tmaxandinterfacestrength-SeparationdistancesepandCOD?-Areaunderthecurve,workoffracture,fracturetoughnessG(localandglobal)Critical Issues in the application of CZM to interface modelsAMMLCZMisanexcellenttoolwithsoundtheoreticalbasisandcomputationalease.Lackspropermechanicsandphysicsbasedanalysisandevaluation.Alreadywidelyusedinfracture/fragmentation/failureImportance of shape of CZMMotivationforstudyingCZMcriticalissuesaddressedhereScales-What range of CZM parameters are valid?vMPaorGPaforthetractionvJorKJforcohesiveenergyvnmorforseparationdisplacementWhat is the effect of plasticity in the bounding material on the fracture processesEnergy-Energy characteristics during fracture process and how energy flows in to the cohesive zone.AMMLAtomisticsimulationstoextractcohesivepropertiesMotivationWhatistheapproximatescaletoexaminefractureinasolidvAtomisticatnmscaleorvGrainsatscaleorvContinuumatmmscaleArethestress/strainandenergyquantitiescomputedatonescalebevalidatotherscales?(canweevendefinestress-strainatatomicscales?)AMMLEmbedded Atom Method EnergyFunctions(D.J.Oh and R.A.Johnson,1989,Atomic Simulation of Materials,EdtsEdts:V:V Vitek Vitek and D.J.and D.J.SrolovitzSrolovitz,p 233,p 233)ThetotalinternalenergyofthecrystalwhereandContributiontoelectrondensityofithatomandjth atom.Twobodycentralpotentialbetweenithatomandjth atom.InternalenergyassociatedwithatomiEmbeddedEnergyofatomi.AMMLCONSTRUCTION OF COMPUTATIONAL CRYSTALAMMLBoundary Conditions for GB Slidingq Construct symmetric tilt boundaries(STDB)by rotating a single crystal(reflection)q Periodic boundary condition in X directionq Restrain few layers in lower crystalqApply body force on top crystal AMMLAsmallportionofCSLgrainbounarybeforeAndafterapplicationoftangentialforce Curve in Shear directionShetC,LiH,ChandraN;InterfacemodelsforGBslidingandmigrationMATERSCIFORUM357-3:577-5852001AMMLAsmallportionofCSLgrainboundarybeforeAndafterapplicationofnormalforceCurve in Normal directionAMMLSummarycomplete debonding occurs when the distance of separation reaches a value of 2 to 3 .For 9 bicrystal tangential work of separation along the grain boundary is of the order 3 and normal work of separation is of the order 2.6 .For 3-bicrystal,the work of separation ranges from 1.5 to 3.7 .Rose et al.(1983)have reported that the adhesive energy(work of separation)for aluminum is of the order 0.5 and the separation distance 2 to 3 Measured energy to fracture copper bicrystal with random grain boundary is of the order 54 and for 11 copper bicrystal the energy to fracture is more than 8000 ResultsanddiscussiononatomisticsimulationImplications The numerical value of the cohesive energy is very low when compared to the observed experimental results Atomistic simulation gives only surface energy ignoring the inelastic energies due to plasticity and other micro processes.It should also be noted that the exper-imental value of fracture energy includes the plastic work in addition to work of separation (J.R Rice and J.S Wang,1989)AMMLMaterialNomenclatureparticle sizeAluminiumalloys2024-T35135149001.22024-T85125.480001.2TitaniumalloysT2180489702-4T681301300002-4SteelMediumCarbon54126362-4Highstrengthalloys984161718Ni(300)maraging7625030Alumina4-834-24010SiCceramics6.10.11to1.28PolymersPMMA1.2-1.7220TableofsurfaceandfractureenergiesofstandardmaterialsAMMLEnergybalanceandeffectofplasticityintheboundingmaterialAMMLMotivationItisperceivedthatCZMrepresentsthephysicalseparationprocess.Asseenfromatomistics,fractureprocesscomprisesmostlyofinelasticdissipativeenergies.Therearemanyinelasticdissipativeprocessspecifictoeachmaterialsystem;someoccurwithinFPZ,andsomeintheboundingmaterial.Howtheenergyflowtakesplaceundertheexternalloadingwithinthecohesivezoneandneighboringboundingmaterialnearthecracktip?Whatisthespatialdistributionofplasticenergy?Istherealinkbetweenmicromechanicsprocessesofthematerialandcurve.AMMLPlasticityvs.otherDissipationMechanismsqSinceboundingmaterialhasitsowninelasticconstitutiveequation,whatistheproportionofenergydissipationwithinthatdomainandfractureregiongivenbyCZM.qRoleofplasticityintheboundingmaterialisclearlyunique;andcannotbeassignedtoCZM.AMMLAl2024-T3alloyTheinputenergyinthecohesivemodelarerelatedtotheinterfacialstressandcharacteristicdisplacementasTheinputenergyisequatedtomaterialparameterBasedonthemeasuredfracturevalueCohesivezoneparametersofaductilematerialAMMLE=72GPa,=0.33,StressstraincurveisgivenbywhereandfractureparameterMaterialmodelfortheboundingmaterialElasto-plasticmodelforAl2024-T3AMMLGeometryandboundary/loadingconditionsa=0.025m,b=0.1m,h=0.1mAMMLFiniteelementmesh28189nodes,24340planestrain4nodeelements,7300cohesiveelements(widthofelementalongthecrackplanismAMMLGlobalenergydistributionareconfinedtoboundingmaterialiscohesiveenergy,asumtotalofalldissipativeprocessconfinedtoFPZandcannotberecoveredduringelasticunloadingandreloading.qPurelyelasticanalysisTheconventionalfracturemechanicsusestheconceptofstrainenergyreleaserateUsingCZM,thisfractureenergyisdissipatedandnoplasticdissipationoccurs,suchthatAMMLGlobalenergydistribution(continued)IssuesFractureenergyobtainedfromexperi-mentalresultsissumtotalofalldissipativeprocessesinthematerialforinitiatingandpropagatingfracture.Shouldthisenergybedissipatedentirelyincohesivezone?Shouldbesplitintotwoidentifiabledissipationprocesses?TwodissipativeprocessPlasticitywithinBoundingmaterialMicro-separationProcessinFPZqAnalysiswithelasto-plasticmaterialmodelwhererepresentsotherfactorsarisingfromtheshapeofthetraction-displacementrelationsImplicationsLeavesnoenergyforplasticworkintheboundingmaterialInwhatratioitshouldbedivided?Divisionisnon-trivialsinceplasticdissipationdependsongeometry,loadingandotherparametersasAMMLWhatarethekeyCZMparametersthatgoverntheenergetics?qincohesivezonedictatesthestresslevelachievableintheboundingmaterial.qYieldintheboundingmaterialdependsonitsyieldstrengthanditspostyield(hardeningcharacteristics.qThusplaysacrucialroleindeterminingplasticityintheboundingmaterial,shapeofthefractureprocesszoneandenergydistribution.(otherparameterslikeshapemayalsobeimportant)AMMLGlobalenergydistribution(continued)Variationofcohesiveenergyandplasticenergyforvariousratios(1)(2)(3)(4)Recoverableelasticwork95to98%ofexternalworkPlasticdissipationdependsonElasticbehaviorplasticityoccurs.PlasticityincreaseswithAMMLRelationbetweenplasticworkandcohesivework(verysmallscaleplasticity),plasticenergy15%oftotaldissipation.Plasticityinducedattheinitialstagesofthecrackgrowthplasticityceasesduringcrackpropagation.Verysmallerrorisinducedbyignoringplasticity.plasticworkincreasesconsiderably,100to200%asthatofcohesiveenergy.Forlargescaleplasticityproblemstheamountoftotaldissipation(plasticandcohesive)ismuchhigherthan8000Plasticdissipationverysensitivetoratiobeyond2till3CrackcannotpropagatebeyondandcompletelyelasticbelowAMMLVariationofNormalTractionalongtheinterfaceThelengthofcohesivezoneisalsoaffectedbyratio.Thereisadirectcorrelationbetweentheshapeofthetraction-displacementcurveandthenormaltractiondistributionalongthecohesivezone.Forlowerratiosthetraction-separationcurveflattens,thistendtoincreasetheoverallcohesivezonelength.AMMLLocal/spatialEnergyDistributionAsetofpatchofelements(eachhavingapp.50elements)wereselectedintheboundingmaterial.Thepatchesareapproximatelysquares(130).Theyarespacedequallyfromeachother.Adjoiningthesepatches,patchesofcohesiveelementsareconsideredtorecordthecohesiveenergies.AMMLVariationofCohesiveEnergyThevariationofCohesiveEnergyintheWakeandForwardregionasthecrackpropagates.ThenumbersindicatetheCohesiveElementPatchnumbersFallingJustBelowthebindingelementpatchesThecohesiveenergyinthepatchincreasesuptopointC(correspondingtoinFigure)afterwhichthecracktipispresumedtoadvance.Theenergyconsumedbythecohesiveelementsatthisstageisapproximately1/7ofthetotalcohesiveenergyforthepresentCZM.OncethepointCiscrossed,thepatchofelementsfallintothewakeregion.Therateofcohesivezoneenergyabsorptiondependsontheslopeofthecurveandtherateatwhichelasticunloadingandplasticdissipationtakesplaceintheadjoiningmaterial.Thecurvesflattensoutoncetheentirecohesiveenergyisdissipatedwithinagivenzone.AMMLVariationofElasticEnergyVariationofElasticEnergyinVariousPatchofElementsasaFunctionofCrackExtension.ThenumbersindicatePatchnumbersstartingfromInitialCrackTipConsiderableelasticenergyisbuiltuptillthepeakofcurveisreachedafterwhichthecracktipadvances.AfterpassingC,thecohesiveelementsnearthecracktipareseparatedandtheelementsinthispatchbecomesapartofthewake.Atthisstage,thevaluesofnormaltractionreducesfollowingthedownwardslopeofcurvefollowingwhichthestressinthepatchreducesaccompaniedbyreductioninelasticstrainenergy.Thereductioninelasticstrainenergyisusedupindissipatingcohesiveenergytothosecohesiveelementsadjoiningthispatch.Theinitialcracktipisinherentlysharpleadingtohighlevelsofstressfieldsduetowhichhigherenergyforpatch1Cracktipbluntsforadvancingcracktipleadingtoalowerlevelsofstress,resultinginreducedenergylevelinotherpatches.AMMLVariationofdissipatedplasticenergyinvariouspatchedasafunctionofcrackextension.Thenumberindicatepatchnumbersstartingfrominitialcracktip.VariationofPlasticWork()plasticenergyaccumulatesconsiderablyalongwithelasticenergy,whenthelocalstressesboundingmaterialexceedstheyieldAfterreachingpeakpointConcurvetractionreducesandplasticdeformationceases.Accumulatedplasticworkisdissipativeinnature,itremainsconstantafterdebonding.AlltheenergytransferinthewakeregionoccursfromelasticstrainenergytothecohesivezoneTheaccumulatedplasticworkdecreasesuptopatch4fromthatof1asaconsequenceofreductionoftheinitialsharpnessofthecrack.Mechanicalworkisincreasedtopropagatethecrack,duringwhichthedoesnotincreaseresultinginincreasedplasticwork.Thatincreaseinplasticworkcausestheincreaseinthestoredworkinpatches4andbeyondAMMLVariationofPlasticWork()VariationofPlasticworkandElasticworkinvariouspatchofelementsalongtheinterfaceforthecaseof.Thenumbersindicatestheenergyinvariouspatchofelementsstartingfromthecracktip.,thereisnoplasticdissipation.plasticworkisinducedonlyinthefirstpatchofelementNoplasticdissipationduringcrackgrowthplaceintheforwardregionInitialsharpcracktipprofileinduceshighlevelsofstressandhenceplasticityinboundingmaterial.Duringcrackpropagation,tipbluntsresultingreducedlevelofstressesleadingtoreducedelasticenergiesandnoplasticitycondition.AMMLContourplotofyieldlocusaroundthecohesivecracktipatthevariousstagesofcrackgrowth.AMMLSchematicofcra