IntroductionWeldlinesareformedduringmoldfillingwhenevertwoseparatedmeltstreamsrecombine.Thisoccurseitherduetoinjectionthroughmultiplegatesorasaconse-quenceofflowaroundanobstacle.Twomaintypesofweldlinesareusuallydistinguished.Coldorstagnat-ingweldlineisformedbyahead-onimpingementoftwomeltfrontswithoutadditionalflowafterthat.Hotorflowingweldlinesoccurwhentwomeltstreamscontinuetoflowaftertheirlateralmeeting.Sinceweldlinesoftenresultinreducedmechanicalstrengthsand/orpooropticalsurfaceappearanceofinjectionmoldedpartstherehavebeenagreatnumberofinvestigationsabouttheeectofprocessingcondi-tionsontheweldlines.MalguarneraandManisali(1981)measuredtheweldlinestrengthforseveraltypesofpolymersandfoundthatmeltandmoldtemperaturehadaremarkableinfluenceontheweldlinestrength.CriensandMosle(1983)investigatedtheinfluenceofdesignandprocessingparametersonthemechanicalpropertiesofaplatewithhole.Theyrec-ognizedthattheeectofmelttemperaturechangesfrompolymertopolymer.KimandSuh(1986)haveshownthatincreasingmelttemperaturecanleadtoadeteriorationofweldlinestrengthjustbelowthedegradationtemperature.Injectionpressure,injectionspeed,holdingtimeandholdingpressurehavealsobeeninvestigatedandonlylittleeecthasbeenobserved(PiccaroloandSaiu1988).Recently,Liuetal.(2000)designedtheirexperimentsaccordingtotheTaguchiC213smethodandshowedagainthatthemeltandmoldtemperaturearetheprinciplefactorsaect-ingweldlinepropertiesofinjectionmoldedthermo-plastics.Itshouldbenotedthatthesensibilityofweldlinesdependsnotonlyonthematerialpropertiesandtheprocessingconditions,butalsoonthetestingmethodsapplied(Selden1997).Althoughintheliteraturemechanicalweaknessofweldlinesisusuallyexplainedby(1)lackofdiusionThamNguyen-ChungFlowanalysisoftheweldlineformationduringinjectionmoldfillingofthermoplasticsReceived:10February2003Accepted:22October2003Publishedonline:19December2003C211Springer-Verlag2003AbstractTostudytheweldlineformationofcollidingflowfrontsthefillingofamoldcavitywassim-ulated.Thethermo-rheologicalfindingswereusedtoinvestigatethesourcesofweldlineweakness.Inthiswaycriticalareasoftheinter-faceinregardtothelackofinter-diusionandtheinappropriatemolecularorientationwerefoundtobeplacednearthesurfaceofthefinishedparts.ThemainsourcefortheweldlineweaknessseemstobetheV-notchthatarisesduetothepoorlybondedregionnearthesur-faceincombinationwiththelargeshrinkageasaresultofextremelyhighmolecularorientationsinducedattheendofthefilling.Further-more,theempiricalknowledgewasconfirmedthatweldlinesarerathermoresensitivetothelocalflowsit-uationthantheglobalprocessingconditions.Meltandmoldtemper-aturescanbeconsideredtobethemostimportantfactorswhichinflu-encetheweldlinestrength.KeywordsPolymerInjectionmoldingThermoplasticsWeldlineSimulationRheolActa(2004)43:240245DOI10.1007/s00397-003-0339-2ORIGINALCONTRIBUTIONInpartpresentedatthe6thEuropeanCon-ferenceonRheology,Erlangen,2002T.Nguyen-ChungInstitutfurAllgemeinenMaschinenbauundKunststotechnik,ChemnitzUniversityofTechnology,09107Chemnitz,GermanyE-mail:tham.nguyen.chungmb.tu-chemnitz.deofpolymermolecules,(2)unfavorablemolecularori-entationattheinterface,and(3)formationofaV-notchatthesurfaceofinjectionmoldedparts(KimandSuh1986；Fellahietal.1995),littlewasknownabouttheinterrelationshipbetweenthesefactors.KimandSuh(1986)analyzedthefirstandsecondfactorsseparatelyandthenintegratedthemtopredictthestrengthofweldlines.Intheirtheoreticalapproachforthediusionprocessthetemperaturegradientacrossthepartthicknesswasneglected.Tomarietal.(1990)clarifiedtheV-notchstructureanditseectonthestrengthofgeneralpurposepolystyreneinjectionmol-dings.Theymeasuredtheweldstrengthofdogbonetypetensilespecimensthesurfaceofwhichwaspar-tiallyeliminatedbymilling.TheirresultssuggestedthattheV-notcheectiscausedratherbyapoorlybondedlayernearthesurfacethanthefinegrooveonthesurface.ItisalsoworthnotingthattheV-notchmaybealsoattributedtotheairentrappedattheinterfacebetweentheflowfronts(Hagerman1973)orvolumetricshrinkageduringcooling(PiccaroloandSaiu1988).Todate,modelingoftheweldlinemainlyfocusesonpredictingtheweldlinepositionandinvestigatingtheinfluenceofthethermo-rheologicalsituationonthemeasuredweldlinestrengths.However,mostofthesimulationisbasedonthepressuredropformulation,whichdoesnotgivedetailedinformationabouttheflowsituationattheadvancingfront.Therehavebeenonlyafewpapersonsimulationoftheweldlinefor-mationconsideringthefullflowhistory.Weietal.(1987)calculatedthestresswhichaviscoelasticmeltexhibitsinaflowpastobstaclesbyassumingthatthekinematicsareclosetothoseofashear-thinningfluidsuchastheCarreaumodel.Thecalculatedvaluesofmolecularorientationshowedahighlyorientedregionsurroundingtheweldinterfacejustdownstreamoftheobstacle,whichwasverifiedbyexperimentsusingtherheo-opticalmethod.Mavridisetal.(1988)simulatedthesituationofcollidingflowfrontsforaNewtonianfluidandshowedthattheorientationofpolymermoleculesatastagnatingweldlineismainlydeter-minedbythefountainflowbeforethecollisionoccurs.Recently,Nguyen-Chungetal.(1998)investigatedtheflowmechanismsbehindanobstacleclarifyingtheinfluenceofthethermo-rheologicalhistoryofthemeltontheperformanceoftheweldline.Thepresentedpaperrepresentsanon-isothermalsimulationoftheweldlineformationduetocollisionoftwoflowfronts.Thiswaytheaforementionedsourcesoftheweldlineweaknessandtheirinterrelationshipcanbeinvesti-gatedwithregardtotheflowhistoryandthethermo-rheologicalsituation,whichasawholeenablesabetterunderstandingofthemechanismsoftheweldlineformation.SimulationSimulationhasbeencarriedoutofaviscousfluidfillingarectan-gularcavityfrombothends(Fig.1).Byconsideringthesymmetryaquarterofthecavitywasmodeledastwo-dimensionalgeometry.Neglectinggravityandsurfacetensionmeansthatthefreesurfacescanbeassumedtobeinitiallyflat,thefluidbeingatrest.Themass,momentumandenergyconservationequationsforanincompressiblefluidcanbewrittenasfollows:rC1t01qtttC1rtC18C19C0rprC1C0s2qcpTttC1rTC18C19rC1krTC0s:_C0c3wheret,t,T,p,C0s,_C0c,q,cpandkdenotetime,velocityvector,temperature,hydrostaticpressure,deviatoricstresstensor,rateofdeformationtensor,density,specificheatandheatconductivityrespectively.TheconstitutiveequationforageneralizedNewtonianfluidwasused:C0s2gT；_c_C0c；_C0c12rtrtT4withtheviscositygivenbytheBird-Carreaumodel(Birdetal.1977):gg01kc_c2hinC012；_c2_C0c:_C0cp5FortemperaturedependencetheArrheniusmodelwasappliedontheviscosityatareferencetemperatureT0:g_c；TaTgaT_c；T0；aTexpa1TC01T0C18C19C20C216Fig.1Initialstate(top)andboundaryconditions(bottom)forafillingsimulationofarectangularcavity241Thefollowingboundaryconditionscompletethestatementoftheproblem:attheinletaconstantvelocityandaconstanttem-peratureofthemeltareassumed；no-slipconditionandaconstantmoldtemperatureareimposedonthewall(Table1)；atthesym-metrylinessymmetryconditionsareapplied；attheflowfrontzerosurfacetractionisappliedandheattransportthroughthissurfaceisneglected.WiththecommercialcodeFIDAP(Fluent1998),theGalerkinfiniteelementmethodwasusedtosolvethecontinuity,momentum,andenergyequationswhicharediscretizedbystandardprocedures,usingamixedformulationinwhichpressureisinterpolatedoneorderlowerthanvelocityandtemperature.ThefreesurfacesaretrackedbyusingtheVOFmethodappliedonafixedmesh(HirtandNichols1981).Anadditionalequationistobesolvedtogetherwiththegoverningflowequations:FttC1rF07wherebyFisdefinedasamaterialdensityfunction.Ithasavalueofunityinafilledsectionoftheflowdomainandiszerooutsideofthefluid.Atthefreesurfaceitselfthisfunctionhasavaluebetween0and1.Asmaterial,polystyrene165H(suppliedbyBASF,Ludwigshafen,Germany)hasbeenused.Thethermo-rheologicalpropertiesandthecoecientsoftheviscositymodelareshowninTable2.ResultsResultswillbeshownusingthenon-dimensionalizedvariablesasfollows:vC3vv0；tC3tt0；tC3tt0v0；_cC3_cv0t0；pC3pv0g0T0t08withacharacteristiclengthv0=0.004m,acharacteristicvelocitym0=0.1m/s,andazero-shear-rateviscosityg0(T0)=3760Pas.Theflowfrontsatdierenttimes(Fig.2)showthattheweldlineisformedasexpectedfromthemiddleofthecavitytowardsthewall.InFig.3thepathlinesofselectedmaterialelementscanbeobservedwhichareoriginallypositionedontheflatflowfront.Thedistancebetweentheoriginallyflatflowfrontandtheweldlinepositionislargeenoughsothattheflowfronthasbeenfullydevelopedbeforetheweldlineisformed.Itcanbeseenthattheweldlineconsistsofthematerialelementscomingfromthecoreregionofthecavitywheretheygenerallydidnothaveexperiencedlargedeformations(Nguyen-ChungandMennig2001).Onlyduringthetransitionfromtheflattothefullydevelopedflowfrontmaydeformationsoccur,butthatisratheranexceptionduetothespecificproblemdefinition.Onthewhole,deformationsattheweldlinemustbemostlysubjectedtothelocalflowsituation.Attheinterfacethematerialelementschangetheirflowdirectionandcontinuetomovealongthethicknessdirection.Duringthesetimesinterdiusionmayoccur.Inthecorethecontacttimeabovethesolidificationtemperatureislongerthanintheouterregionsothatastrongerdegreeofinterdiusioncanbeexpectedthere.Bycontrast,inthelayernearthewall,thecontacttimeisveryshortsincethematerialelementsarrivingtherewillbefrozen-inimmediatelybeforecontactwiththeircounterpartscanbeestablished(forexamplethemate-rialelementnumbered8).ThisresultsinalayerwithpoorbondingasfoundbyTomarietal.(1990).Themolecularorientationhasbeenfrequentlyinvestigatedbytracingagreatnumberofmaterialele-mentswhicharefirstlyplacedonastraightline(Coyleetal.1987).However,inthatwayitisnotpossibletodistinguishbetweentheabsolutedeformationsthatstronglydependontheobservationtimeandtherelativedeformationsthatareameasurementformolecularorientation.Inthiswork,severalgroupsofmaterialTable1ProcessingparametersParametersValuesMelttemperatureTF503C176KMouldtemperatureTW333C176KInletvelocityv00.1m/sTable2Materialpropertiesofpolystyrene165HPropertiesValuesMeltdensityq892kg/m3Specificheatcp1968J/kgKThermalconductivityk0.14W/mKReferencetemperatureT0503C176KZero-shear-rateviscosityg0(T0)3760PasTimeconstantk0.15sPowerlawindexn0.23Arrheniuscoecienta10,842Fig.2Developmentoftheflowfronts242elementsweretraced.Eachgroupformsacircleandlocatesoriginallyonthestraightflowfront(Fig.4).Bycomparingthedeformationsofthecirclesatdierenttimestherelativedeformationsofthemeltandsothedevelopmentoftheflowinducedmolecularorientationcanbevisualized.Itshowsagainthatthehighorienta-tionattheweldlineisaresultofratherthelocaldeformationsalongtheinterfacethanofthegeneraldeformationattheflowfront.Inthepast,Mavridisetal.(1988)alsorecognizedthattherewassignificantexten-sionaldeformationatthesurfaceoftheadvancingflowfrontwhichwouldleadtoaperpendicularorientationtothewall.TheauthorspointedouttheanalogyofthecollidingflowfrontstotheplanarstagnationflowwhichwasoriginallyusedbyTadmor(1974)asamodeltodescribethefountainflow.However,inthesamepaperMavr