聚合物复合材料应力场模拟.docx

聚合物复合材料应力场模拟.docx

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聚合物复合材料应力场模拟

FiniteElementSimulationofTensileBehaviorsintheElasticRegionForPP/nano-TiO2Composites

Abstract：

Polypropylene（PP）/nano-TiO2compositeswerepreparedbythemeltintercalationmolding.Basedontheassumptionofcontinuummechanicsmodelformaterials,afiniteelementanalysismodelforthecompositeswasconstructedusingANSYS11.0software.Inthestageofdeformation（pre-yieldregime）theresponsemechanismofthestressandthestrainforcompositeswasinvestigated,andthevonmisesstressfieldofPP/nano-TiO2compositeshasalsobeensimulated.ItwasfoundthatthesimulationresultsareConsistentwiththetestingresultsatlowvolumestrainlevel.Comparingwiththe3Dmodel,theresultssimulatedusingthe2Dmodelareaccuratewiththeexperimentalresults.Ifthevolumefractionofparticlesisless,otherparticleshavelittleinfluenceonthelocalstressfieldofacertainparticle,noobviousoverlaporcrossofthestressfieldcouldbefoundbetweentwoneighboringparticles.Whileapplyingdifferentloads,thestressjumpstomaximumstressvalueintheinteractionregionofthetwophasefirstly,andthenitoccursthattheparticlesdebondwiththematrix.

Keywords：

Polypropylene（PP）；TiO2；elasticregion；tensilebehavior；finiteelementanalysis

1.Introduction

Manydecadeshasseengreatdevelopmentsininorganicfillersusedaspolymermodifiers.Atthebeginning,thekeyaimiseithertobeusedasamajorreinforcingandfillingsystem,forexampleinrubberusingcarbonblackandsilica,ortocheapenthecompoundsusingsilicate,carbonate,sulfateandothermaterials,nowadayslikenanotubes,nanoparticlesandlayeredsilicatesaremorewidelyusedtoimprovethetensileandimpactpropertiesofthepolymercomposites[1-4].Greatfocuswillbelaidonthisresearchinthefuture.Althoughtheformerworkshasprovidedmanychancesforthedesigningofhighpropertiescomposites,researchthatlaysonpredictionofamulti-phasecompositesusingafiniteelementmethodwerestillonastartingstage.

Basedonafiniteelementanalysis（FEA）modelconstructedusingtheANSYSsoftware,M.Hoffman[5]providedanewmethodtoevaluateboththeuniaxialtensilebehaviorandenhancedtoughnessofthenanocomposites,andclaimedthattheenhancedfracturepropertieswerecausedbytheassistedvoidformationattheparticleswhichissupportedbyamicrostructure-basedfiniteelementmodelingbaseduponelastic–plasticdeformationaroundweaklybondedparticles.YuDong[6]capturedmorphologicalimagesusingbothSEMandTEMtogeneratethegeometricinformation,andthenpredictedtheelasticmodulusofpolypropylene（PP）/claynanocompositesbyusinganObject-Orientedfiniteelementanalysis.Itshowedthattheresultsnumericalsimulatedhavegoodagreementcomparedwiththeexperimentaldataandtheavailablecompositestheoreticalmodels.Onshapeanddistributionassumptionoftheparticles,amicrostructure-based（FEA）modelforPP/nano-TiO2compositeswasconstructedinthispaper,usingthismodeltheresponsemechanismofthestressandthestrainpre-yieldregimewasinvestigated,andwealsosimulatedthevonmisesstressfieldofthecomposites.

2.Experimentalprocedures

Commercial-graderawmaterialsconsistingofisotacticpolypropylene（PP）homopolymerT30S,suppliedbyMaomingPetrochemicalIndustrialCo.，China,Ithasameltflowindex（MFI）of3.2g/10min（2.16kgat230℃）.Theprecipitatednano-TiO2wassuppliedbyKenanewmaterialsCo.,Chinaanddynamiclightscatteringmeasurementssuggeststhatthemicellesizeisapproximately20nm.

Nano-TiO2weredriedinaincubatorat80℃for24h,andthenwereputinasolutionmixedwithethanolandtitanatecouplingagentNDZ-201（200:

1byvolumeratio）,heatthemixturetoboilinguntiltheethanolwerefullyvolatilized.ThenwegotthemodifiedTiO2particles.“Masterbatch”ofParticles/monomer（20/100）werefirstlypreparedusingatwin-screwextruderwiththetemperaturesofthesuccessivezonesfromthefeedertothediesetto180,200and210°Crespectivelyandascrewspeedof300rpm,thenPP/1wt.%TiO2waspreparedthroughthesamemethod.

Thenaninjectionmoldingmachinewasusedtomoldthecompoundsintostandardbarsformechanicaltesting.Thedimensionofthedeformableregionofthetensiledumbbellspecimenswas25.0×3.2×2.0mm3.Sixtensiledumbbellspecimenswereusedfortesting.TensilepropertiesofthecompositesweredeterminedwithaGT-TCS-2000universaltesteratacrossheadspeedof50mm/minaccordingtoAS1145.1-2001.Toassessdispersionofthenanoparticlesinthepolypropylenematrix,ultrathinsectionsofthecompoundswereexaminedbyaTecnaiGF2transmissionelectronmicroscope（TEM）.SampleswerepreparedusingaReichertJungultra-microtomeequippedwithadiamondknifetocutfilmsof80–100nmthicknessat-80℃byLiquidnitrogencooling.Thecutsectionswereplacedonaformvar-coatedcoppergridforobservationintheTEM.

2numericalmethod

2.1Microstructuralcharacterisation

Inordertopreparehigh-performancenanocomposites,amainfactorwastomakeinorganicparticlesdispersedinthematrixuniformly;anotherfactorwastheformingofelasticinterfacebetweenparticlesandthematrixwhichcouldtransferthestressloadedfreely.Theinterfacewasnottakenintoconsiderationinthispaperandthemodelwassimplifiedasatwo-phasecompositesystemaccordingtothecontinuummechanicstheory[7].Itwasassumedthattheparticlesisdispersedinthematrixuniformlyandthebondingbetweentheparticlesandthematrixisveryweak,totheextentthattheparticlescanbeassumedtobevoidsinamatrixaroundwhichastressconcentrationisinducedonloading,alsoboththePPmatrixandclayparticleswasassumedtobehaveaslinearelasticmaterialswithaperfectinterfacialbondingbetweentwoconstituents.Theunitvolume（

）modeledbytheFEmethodcouldbedescribedbasedonparticlesradius（

）andvolumefractions（

）ofparticlesasfollows[8]:

（2-1）

Toascertaintheresponsemechanismofstressandstrainatamicrostructurallevel,arepresentativevolumeelement（RVE）modelandatwo-dimensionalplanemodelwereconstructedseparately.Thenthefiniteelementmeshwasoperated,moreover,anadaptivemeshrefinementwasemployedtorefinethegridsatthematrix-particleinterfaceswherethehigheststressgradientscouldarise,andthusahighdegreeofrefinementmightberequiredtopreciselycapturefluctuationsinthestressandstrainfields.Aftermeshingthemodeltheforce-balanceequationwasactivatedforthelinearsolver.Asdepictedinequation2-2,theboundaryconstraintswasappliedsothatthedisplacementsXandYontheleftboundarycouldbefullyconstrainedandonlydisplacementsXwereemployedontherightboundary.

（2-2）

Atlastaccordingtoahomogenizedmethod,theaverageofstressandstrainwesimulatedcouldbeequaltotheengineeringstressandstrainofthecompositesasdescribedinequation2-3，

istheunitvolumeofthemodel.

（2-3）

WhileapplyingloadsonPP/nano-TiO2composites,eventheloadswereverysmall,manymicro-voidsandcrackswouldhaveformedaroundtheparticles.Ifmaterialswererichindefects,thebearingstressachievedadominantpositioninallloadsappliedatthesametime,themicromechanicaldeformationprocessescouldbedescribedasfollows[9,10]:

Themodifierparticlesactasstressconcentrators,thestressconcentrationleadstothedevelopmentofatriaxialstressintheinorganicparticlesandtodilatation.Ahigherhydrostaticortriaxialstressbuildsupinsideparticlesandgivesrisetovoidformationthroughcavitationinsideparticlesordebondingattheparticlematrixinterface.Withcontinuousgrowthofvoids,theycomeintoawholeintheend,thecompositesfailuresimultaneously.FracturecriterionandstrainenergyreleaseratecriterionaremainlytwokindsofCriterionusedforevaluatingthecrackpropagation.Inthispaper,theyieldbehaviorofthecompositeswerestudiedusingvonmisescriterion[7],sothestrengthcriterioncouldbedescribedasfollowsCorrespondingly:

=

（2-4）

Intheequation2-4,

、

、

wereNo.1,No.2,No.3principalstressseparately,

≥

≥

;

wasthevonmisesstressinthepaperand

representstheintrinsicstrengthofthecomposites.

2.2Constructionoffiniteelementanalysismodel

Inthisstudy,onlyisotropicelasticmaterialpropertieswereassignedwiththeelasticconstantsofYoung’smodulusandPoisson’sratio.Basedonlotsofexperimentaldataandmicrostructuralcharacterization,wesetmaterial1aspolypropylene,itsmodulusandPoisson’sratiowaschosentobe605MPaand0.36;material2wassettobenano-TiO2,whichwerehandledasmicro-voids（Fig.1（a））duringthesimulationprocess.Representativevolumeelementmodel（RVE）wereconstructedandthenmeshedusingquadratic3Dsolidlinearelements,8nodeSOLID185（enhancedstrainformulation，axisymmetricoption）asshowninFig.1（a）,thenthefiniteelementmeshwasoperatedandmodified,resultsshowedthatthismodelhas1242nodesand1236elements.Tocomparewiththe3Dmodel,weconstructed2-dimensionalmodelandmeshedwithquadratic2Dsolidlinearelements,8nodePLANE82withthesuperpositionofasymmetricgridofquadrilateralelements,whilemeshingthemodelthewidthoftheboundarywereassigned,weget83201nodesand82500elements.ArrowsrepresentthedirectionandsizeoftheloadsimposedinFig.2.ThispaperwouldstudytherelationshipbetweenMechanicalpropertiesandmicrostructureofcompositesbasedontwoFEmodelsabove.

（a）ThevolumeusedforFEManalysisis1/8oftheunitcell（b）TheplaneusedforFEManalysisis1/4oftheunitcell

Fi