薄膜力学8-断裂2.pdf

薄膜力学8-断裂2.pdf

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EM397:

ThinFilmMechanicsVIII.FilmCrackingunderTensionNanshuLuTheUniversityofTexasatAustinFall2013CracknucleationandgrowthSubstrateFilmAthree-dimensionalprocess:

crackgrowsinbothparallelandperpendiculardirections,withacurvedcrackfront.CuttingandChannelingCutting:

acrackgrowingperpendiculartotheinterface;aplanestrainproblem,assuminglongintheparalleldirection.Channeling:

crack（s）growingparalleltotheinterface,assumingaconstantdepthintheperpendiculardirection.ElasticmismatchForelasticfilmsandsubstrates,thecrackbehaviordependsontheelasticmismatchbetweenthem.Dundursparameters:

sfsffssffssfEEEE11111111fssffssfPlanestrain:

21EE43Nomismatch:

=0;Stifffilmoncompliantsubstrate:

0;Compliantfilmonstiffsubstrate:

0;Iff=s=0.5,=0;Iff=s=1/3,=/4;Bothandchangesignswhenthematerialsareswitched.1-1-0.250.25PartiallycrackedfilmsSubstrateFilmStressintensityfactoratthecracktip:

hhaFKI,a/hF01000When=0ora/h0:

aKI12.1Stifffilmoncompliantsubstrate:

SIFincreasesmonotonically;Compliantfilmonstiffsubstrate:

SIFattainsamaximumneartheinterfaceBeuth,IJSS29,1657-1675（1992）.FullycrackedfilmsSubstrateFilma=h:

thecracktipisattheinterface,differentcrack-tipfieldduetoelasticmismatch.sxxrhCr）0,（Thestresssingularityexponent,s,dependsontheelasticmismatch（ZakandWilliams,1963）:

01）1（12）cos（222ssWhen=0,s=0.5;For0,s0,s0.5（moresingular）;For1,s1.s-11010.5Penetrationordeflection?

SubstrateFilmspGidGWhenbothconditionsaresatisfied,thecrackislikelytopenetrateintothesubstrateif1idspGGHeandHutchinson,IJSS25,1053-1067,1989.Boththeenergyreleaseratesdependontheelasticmismatchbetweenthefilmandthesubstrate.Energyreleaseratea/h01000ffhEG2SubstrateFilmSubstrateFilmCrackchannelingSubstrateFilm0hAssumethecrackcutsthroughthefilm,withnosubstratepenetration,interfacedebonding,orspalling.Thecrackgrowsparalleltotheinterface,withacurvedchannelfront.Three-dimensionalanalysisisrequiredtodeterminetheshapeofthechannelfront（NakamuraandKamath,1992）.Thecrackreachesasteadystatewhenthelengthexceedsafewtimesthefilmthickness.Steady-statechannelingcracksSubstrateFilm0hThechannelfrontmaintainsitsshapeasitadvances,andthecrosssection（opening）profilebehindthefrontattainstheequilibriumshapeofaplane-straincrack.Thus,thesteady-stateenergyreleaserateofachannelingcrackcanbeobtainedfromtheplanestrainproblem,andthefractureresistanceisthefilmtoughness.Steady-stateenergyreleaserate0FilmSubstrateSubstrateh0Film（z）（b）zxAheadofthechannelfrontFarbehindthechannelfrontEnergyreleaserate:

hSSdzzhG00）（21hSSdzaGhG0）（1orFromdimensionalanalysis:

fSSEhZG20）,（Numericalresults-1-0.500.510510152025303540Elasticmismatch,Dimensionlessenergyreleaserate,（GSSE1*）/（02h）Beuth21XFEM=/4Beuth,IJSS29,1657-1675（1992）;Huangetal.,EngineeringFractureMech.70,2513-2526（2003）.fSSEhZG20）,（976.1ZParallelchannelingcracksfSSEhShZG20）,（Assumesimultaneousgrowthandhomogeneoussystem.SHuangetal.,EngineeringFractureMech.70,2513-2526（2003）.Elasticshear-lagapproximation0000（x）fhxxuEfuksuhEkxuffs220）0（u0）2/（SsffkhEl2lSElSuftanh）2/（20Averagecrackopening:

Energyreleaserate:

lSElGfSStanh221200SXiaandHutchinson,JMPS48,1107-1131（2000）.Shear-laglengthlSElGfSStanh220Fromtheshear-lagmodel,sffkhEl2Forthicksubstrates,comparethesteady-stateenergyreleaseratewithnumericalsolutions.ForS:

fffSSEhZElG2020）,（2fhZl）,（2Forathinsubstratewiththelowersurfacefixed:

ssshkssffhhEl2haaaEG21Free-standingfilmEffectofsubstrateconstrainthEG22FilmonelasticsubstratehahTheenergyreleaserateincreasesifthecrackpenetratesintothesubstrateorifthefilmdebond.LossofconstraintunderlayerCreepingorviscousunderlayer:

theconstraintisgraduallylostovertime.Plasticunderlayer:

thesubstrateconstraintispartiallylost,andthedrivingforceforchannelcracksincreases.Ratchetingunderlayer:

theconstraintisgraduallylostoverthermalcycles,analogoustocreep.CrackgrowthmodulatedbycreepTensileFilmCreepinglayerRigidsubstrateWhent0,4/121103.1）（ssfffthhEtKForastationarylongcrack:

225.0cssKHhEVSteady-statevelocity:

Huang,etal.,ActaMater.50,4137（2002）;Liangetal.,ExperimentalMechanics43,269-279（2003）.Numericalsimulationofcrackgrowth00.511.522.5300.51K/Kc00.511.522.5300.511.5a/00.511.522.5300.20.40.6Vt0/t/t0TransientstateStationarycrack4/1）（DttKSteadystategrowth0tVStresscontourascrackgrowsUniformmesh,200by20035initialcracksSubcriticalCrackingKcKthKVAfter100timesteps1sinh220thKKVVKineticlaw:

Onelasticsubstrate（nocreep）ExtendedFiniteElementMethod（XFEM）Liangetal.,Int.J.SolidsStruct.40,2343（2003）.MeasurementoffilmtoughnessGeneratepre-cracks,e.g.,byagentlescratching;Measurecrackvelocityundercontrolledstresses,usingabendingfixture.Thresholdtoughness,GthToughnessforfastfracture,GcSubcriti