czm内聚力模型ppt课件.ppt

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1、资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值TheoreticalandComputationalAspectsofCohesiveZoneModelingNAMASCHANDRADepartmentofMechanicalEngineeringFAMU-FSUCollegeofEngineeringFloridaStateUniversityTallahassee,Fl-32310WhatisCZMandwhyisitimportantqInthestudyofsolidsanddesignofnano/micr

2、o/macrostructures,thermomechanicalbehaviorismodeledthroughconstitutiveequations.qTypicallyisacontinuousfunctionofandtheirhistory.qDesignislimitedbyamaximumvalueofagivenparameter()atanylocalpoint.qWhathappensbeyondthatconditionistherealmoffracture,damage,andfailuremechanics.qCZMoffersanalternativeway

3、toviewandfailureinmaterials.1.FractureMechanics-1.Linearsolutionsleadstosingularfields-difficulttoevaluate2.Fracturecriteriabasedon3.Non-lineardomain-solutionsarenotunique4.Additionalcriteriaarerequiredforcrackinitiationandpropagation2.Basicbreakdownoftheprinciplesofmechanicsofcontinuousmedia3.Damag

4、emechanics-1.caneffectivelyreducethestrengthandstiffnessofthematerialinanaveragesense,butcannotcreatenewsurfaceFracture/DamagetheoriestomodelfailureCZM can create new surfaces.Maintains continuity conditions mathematically,despite the physical separation.CZM represents physics of the fracture proces

5、s 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 fractu

6、reinitiation 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.CZMisanAlternativemet

7、hodtoModelSeparation资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值ConceptualFrameworkofCohesiveZoneModelsforinterfacesAMMLMolecularforceofcohesionactingneartheedgeofthecrackatitssurface(regionII).TheintensityofmolecularforceofcohesionfisfoundtovaryasshowninFig.a.Theinteratomicforceis

8、initiallyzerowhentheatomicplanesareseparatedbynormalintermoleculardistanceandincreasestohighmaximumafterthatitrapidlyreducestozerowithincreaseinseparationdistance.EisYoungsmodulusandissurfacetension(Barenblatt,G.I,(1959),PMM(23)p.434)Figure (a)Variation of Cohesive traction (b)I-inner region,II-edge

9、 regionDevelopmentofCZModels-HistoricalReviewq Barenblatt(1959)wasfirsttoproposetheconceptofCohesivezonemodeltobrittlefracture资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值ForDuctilemetals(steel)CohesivestressintheCZMisequatedtoyieldstressYAnalyzedforplasticzonesizeforplatesundertens

10、ionLengthofyieldingzones,theoreticalcracklengtha,andappliedloadingTarerelatedintheform(Dugdale,D.S.(1960),J.Mech.Phys.Solids,8,p.100)qDugdale(1960)independently developed the concept of cohesive stressqThetheoryofCZMisbasedonsoundprinciples.qHoweverimplementationofmodelforpracticalproblemsgrewexpone

11、ntiallyforpracticalproblemswithuseofFEMandadventoffastcomputing.qModelhasbeenrecastasaphenomenologicaloneforanumberofsystemsandboundaryvalueproblems.qThephenomenologicalmodelscanmodeltheseparationprocessbutnottheeffectofatomicdiscreteness.PhenomenologicalModelsHillerborgetal.1976Ficticiouscrackmodel

12、;concreteBazantetal.1983crackbandtheory;concreteMorganetal.1997earthquakerupturepropagation;geomaterialPlanasetal,1991,concreteEisenmenger,2001,stonefragm-entationsqueezingbyevanescentwaves;brittle-biomaterialsAmruthrajetal.,1995,compositesGrujicic,1999,fracturebeha-viorofpolycrystalline;bicrystalsC

13、ostanzoetal;1998,dynamicfr.Ghosh2000,Interfacialdebo-nding;compositesRahulkumar2000viscoelasticfracture;polymersLiechti2001Mixed-mode,time-depend.rubber/metaldebondingRavichander,2001,fatigueTevergaard1992particle-matrixinterfacedebondingTvergaardetal1996elastic-plasticsolid:ductilefrac.;metalsBrock

14、s2001crackgrowthinsheetmetalCamacho&ortiz;1996,impactDollar;1993Interfacialdebondingceramic-matrixcompLokhandwalla2000,urinarystones;biomaterialsAMMLqCZMessentiallymodelsfractureprocesszonebyalineoraplaneaheadofthecracktipsubjectedtocohesivetraction.qTheconstitutivebehaviorisgivenbytraction-displace

15、mentrelationship,obtainedbydefiningpotentialfunctionofthetypewherearenormalandtangentialdisplacementjumpTheinterfacetractionsaregivenbyFractureprocesszoneandCZMMaterialcracktipMathematicalcracktipxy资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增

16、值，其增值的这部分资金就是原有资金的时间价值Whatistherelationshipbetweenthephysics/mechanicsoftheseparationprocessandshapeofCZM?(Thereareasmanyshapes/equationsastherearenumberofinterfaceproblemssolved!)WhatistherelationshipbetweenCZMandfracturemechanicsofbrittle,semi-brittleandductilematerials?Whatistheroleofscalingparam

17、eterinthefidelityofCZMtomodelinterfacebehavior?Whatisthephysicalsignificanceof-ShapeofthecurveC-tmaxandinterfacestrength-SeparationdistancesepandCOD?-Areaunderthecurve,workoffracture,fracturetoughnessG(localandglobal)Critical Issues in the application of CZM to interface models资金是运动的价值，资金的价值是随时间变化而变

18、化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值CZMisanexcellenttoolwithsoundtheoreticalbasisandcomputationalease.Lackspropermechanicsandphysicsbasedanalysisandevaluation.Alreadywidelyusedinfracture/fragmentation/failureImportance of shape of CZMMotivationforstudyingCZMcriticalissuesaddressedhereScales-What

19、 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.资金是运动的价

20、值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值AtomisticsimulationstoextractcohesivepropertiesMotivationWhatistheapproximatescaletoexaminefractureinasolidvAtomisticatnmscaleorvGrainsatscaleorvContinuumatmmscaleArethestress/strainandenergyquantitiescomputedatonescalebevalidatotherscales?(canw

21、eevendefinestress-strainatatomicscales?)资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值Embedded Atom Method EnergyFunctions(D.J.Oh and R.A.Johnson,1989,Atomic Simulation of Materials,Edts:V Vitek and D.J.Srolovitz,p 233Edts:V Vitek and D.J.Srolovitz,p 233)Thetotalinternalenergyofthecr

22、ystalwhereandContributiontoelectrondensityofithatomandjth atom.Twobodycentralpotentialbetweenithatomandjth atom.InternalenergyassociatedwithatomiEmbeddedEnergyofatomi.资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值CONSTRUCTION OF COMPUTATIONAL CRYSTAL资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时

23、间的推移而增值，其增值的这部分资金就是原有资金的时间价值Boundary 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 AsmallportionofCSLgrainbounarybeforeAnda

24、fterapplicationoftangentialforce Curve in Shear directionShetC,LiH,ChandraN;InterfacemodelsforGBslidingandmigrationMATERSCIFORUM357-3:577-5852001资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值AsmallportionofCSLgrainboundarybeforeAndafterapplicationofnormalforceCurve in Normal directio

25、nSummarycomplete 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

26、 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 R

27、esultsanddiscussiononatomisticsimulationImplications 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

28、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)MaterialNomenclatureparticle sizeAluminiumalloys2024-T35135149001.22024-T85125.480001.2TitaniumalloysT2180489702-4T681301300002-4SteelMediumCarbon54126362-4Hi

29、ghstrengthalloys984161718Ni(300)maraging7625030Alumina4-834-24010SiCceramics6.10.11to1.28PolymersPMMA1.2-1.7220Tableofsurfaceandfractureenergiesofstandardmaterials资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值EnergybalanceandeffectofplasticityintheboundingmaterialMotivationItispercei

30、vedthatCZMrepresentsthephysicalseparationprocess.Asseenfromatomistics,fractureprocesscomprisesmostlyofinelasticdissipativeenergies.Therearemanyinelasticdissipativeprocessspecifictoeachmaterialsystem;someoccurwithinFPZ,andsomeintheboundingmaterial.Howtheenergyflowtakesplaceundertheexternalloadingwith

31、inthecohesivezoneandneighboringboundingmaterialnearthecracktip?Whatisthespatialdistributionofplasticenergy?Istherealinkbetweenmicromechanicsprocessesofthematerialandcurve.资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值Plasticityvs.otherDissipationMechanismsqSinceboundingmaterialhasits

32、owninelasticconstitutiveequation,whatistheproportionofenergydissipationwithinthatdomainandfractureregiongivenbyCZM.qRoleofplasticityintheboundingmaterialisclearlyunique;andcannotbeassignedtoCZM.资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值Al2024-T3alloyTheinputenergyinthecohesivemod

33、elarerelatedtotheinterfacialstressandcharacteristicdisplacementasTheinputenergyisequatedtomaterialparameterBasedonthemeasuredfracturevalueCohesivezoneparametersofaductilematerial资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值E=72GPa,=0.33,Stressstraincurveisgivenbywhereandfracturepara

34、meterMaterialmodelfortheboundingmaterialElasto-plasticmodelforAl2024-T3资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值Geometryandboundary/loadingconditionsa=0.025m,b=0.1m,h=0.1m资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值Finiteelementmesh28189nodes,24340planestrain4n

35、odeelements,7300cohesiveelements(widthofelementalongthecrackplanism资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值Globalenergydistributionareconfinedtoboundingmaterialiscohesiveenergy,asumtotalofalldissipativeprocessconfinedtoFPZandcannotberecoveredduringelasticunloadingandreloading.q

36、PurelyelasticanalysisTheconventionalfracturemechanicsusestheconceptofstrainenergyreleaserateUsingCZM,thisfractureenergyisdissipatedandnoplasticdissipationoccurs,suchthatGlobalenergydistribution(continued)IssuesFractureenergyobtainedfromexperi-mentalresultsissumtotalofalldissipativeprocessesinthemate

37、rialforinitiatingandpropagatingfracture.Shouldthisenergybedissipatedentirelyincohesivezone?Shouldbesplitintotwoidentifiabledissipationprocesses?TwodissipativeprocessPlasticitywithinBoundingmaterialMicro-separationProcessinFPZqAnalysiswithelasto-plasticmaterialmodelwhererepresentsotherfactorsarisingf

38、romtheshapeofthetraction-displacementrelationsImplicationsLeavesnoenergyforplasticworkintheboundingmaterialInwhatratioitshouldbedivided?Divisionisnon-trivialsinceplasticdissipationdependsongeometry,loadingandotherparametersasWhatarethekeyCZMparametersthatgoverntheenergetics?qincohesivezonedictatesth

39、estresslevelachievableintheboundingmaterial.qYieldintheboundingmaterialdependsonitsyieldstrengthanditspostyield(hardeningcharacteristics.qThusplaysacrucialroleindeterminingplasticityintheboundingmaterial,shapeofthefractureprocesszoneandenergydistribution.(otherparameterslikeshapemayalsobeimportant)资

40、金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值Globalenergydistribution(continued)Variationofcohesiveenergyandplasticenergyforvariousratios(1)(2)(3)(4)Recoverableelasticwork95to98%ofexternalworkPlasticdissipationdependsonElasticbehaviorplasticityoccurs.PlasticityincreaseswithRelationbe

41、tweenplasticworkandcohesivework(verysmallscaleplasticity),plasticenergy15%oftotaldissipation.Plasticityinducedattheinitialstagesofthecrackgrowthplasticityceasesduringcrackpropagation.Verysmallerrorisinducedbyignoringplasticity.plasticworkincreasesconsiderably,100to200%asthatofcohesiveenergy.Forlarge

42、scaleplasticityproblemstheamountoftotaldissipation(plasticandcohesive)ismuchhigherthan8000Plasticdissipationverysensitivetoratiobeyond2till3Crackcannotpropagatebeyondandcompletelyelasticbelow资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而增值，其增值的这部分资金就是原有资金的时间价值VariationofNormalTractionalongtheinterfaceThele

43、ngthofcohesivezoneisalsoaffectedbyratio.Thereisadirectcorrelationbetweentheshapeofthetraction-displacementcurveandthenormaltractiondistributionalongthecohesivezone.Forlowerratiosthetraction-separationcurveflattens,thistendtoincreasetheoverallcohesivezonelength.资金是运动的价值，资金的价值是随时间变化而变化的，是时间的函数，随时间的推移而

44、增值，其增值的这部分资金就是原有资金的时间价值Local/spatialEnergyDistributionAsetofpatchofelements(eachhavingapp.50elements)wereselectedintheboundingmaterial.Thepatchesareapproximatelysquares(130).Theyarespacedequallyfromeachother.Adjoiningthesepatches,patchesofcohesiveelementsareconsideredtorecordthecohesiveenergies.Vari

45、ationofCohesiveEnergyThevariationofCohesiveEnergyintheWakeandForwardregionasthecrackpropagates.ThenumbersindicatetheCohesiveElementPatchnumbersFallingJustBelowthebindingelementpatchesThecohesiveenergyinthepatchincreasesuptopointC(correspondingtoinFigure)afterwhichthecracktipispresumedtoadvance.Theen

46、ergyconsumedbythecohesiveelementsatthisstageisapproximately1/7ofthetotalcohesiveenergyforthepresentCZM.OncethepointCiscrossed,thepatchofelementsfallintothewakeregion.Therateofcohesivezoneenergyabsorptiondependsontheslopeofthecurveandtherateatwhichelasticunloadingandplasticdissipationtakesplaceinthea

47、djoiningmaterial.Thecurvesflattensoutoncetheentirecohesiveenergyisdissipatedwithinagivenzone.VariationofElasticEnergyVariationofElasticEnergyinVariousPatchofElementsasaFunctionofCrackExtension.ThenumbersindicatePatchnumbersstartingfromInitialCrackTipConsiderableelasticenergyisbuiltuptillthepeakofcur

48、veisreachedafterwhichthecracktipadvances.AfterpassingC,thecohesiveelementsnearthecracktipareseparatedandtheelementsinthispatchbecomesapartofthewake.Atthisstage,thevaluesofnormaltractionreducesfollowingthedownwardslopeofcurvefollowingwhichthestressinthepatchreducesaccompaniedbyreductioninelasticstrai

49、nenergy.Thereductioninelasticstrainenergyisusedupindissipatingcohesiveenergytothosecohesiveelementsadjoiningthispatch.Theinitialcracktipisinherentlysharpleadingtohighlevelsofstressfieldsduetowhichhigherenergyforpatch1Cracktipbluntsforadvancingcracktipleadingtoalowerlevelsofstress,resultinginreducede

50、nergylevelinotherpatches.Variationofdissipatedplasticenergyinvariouspatchedasafunctionofcrackextension.Thenumberindicatepatchnumbersstartingfrominitialcracktip.VariationofPlasticWork()plasticenergyaccumulatesconsiderablyalongwithelasticenergy,whenthelocalstressesboundingmaterialexceedstheyieldAfterr