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