薄膜力学8-断裂2.pdf
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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
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- 薄膜 力学 断裂
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