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INTRODUCTIONWELDLINESAREFORMEDDURINGMOLDFILLINGWHENEVERTWOSEPARATEDMELTSTREAMSRECOMBINETHISOCCURSEITHERDUETOINJECTIONTHROUGHMULTIPLEGATESORASACONSEQUENCEOFFLOWAROUNDANOBSTACLETWOMAINTYPESOFWELDLINESAREUSUALLYDISTINGUISHEDCOLDOR‘‘STAGNATING’’WELDLINEISFORMEDBYAHEADONIMPINGEMENTOFTWOMELTFRONTSWITHOUTADDITIONALFLOWAFTERTHATHOTOR‘‘FLOWING’’WELDLINESOCCURWHENTWOMELTSTREAMSCONTINUETOFLOWAFTERTHEIRLATERALMEETINGSINCEWELDLINESOFTENRESULTINREDUCEDMECHANICALSTRENGTHSAND/ORPOOROPTICALSURFACEAPPEARANCEOFINJECTIONMOLDEDPARTSTHEREHAVEBEENAGREATNUMBEROFINVESTIGATIONSABOUTTHEEffECTOFPROCESSINGCONDITIONSONTHEWELDLINESMALGUARNERAANDMANISALI1981MEASUREDTHEWELDLINESTRENGTHFORSEVERALTYPESOFPOLYMERSANDFOUNDTHATMELTANDMOLDTEMPERATUREHADAREMARKABLEINFLUENCEONTHEWELDLINESTRENGTHCRIENSANDMOSLE1983INVESTIGATEDTHEINFLUENCEOFDESIGNANDPROCESSINGPARAMETERSONTHEMECHANICALPROPERTIESOFAPLATEWITHHOLETHEYRECOGNIZEDTHATTHEEffECTOFMELTTEMPERATURECHANGESFROMPOLYMERTOPOLYMERKIMANDSUH1986HAVESHOWNTHATINCREASINGMELTTEMPERATURECANLEADTOADETERIORATIONOFWELDLINESTRENGTHJUSTBELOWTHEDEGRADATIONTEMPERATUREINJECTIONPRESSURE,INJECTIONSPEED,HOLDINGTIMEANDHOLDINGPRESSUREHAVEALSOBEENINVESTIGATEDANDONLYLITTLEEffECTHASBEENOBSERVEDPICCAROLOANDSAIU1988RECENTLY,LIUETAL2000DESIGNEDTHEIREXPERIMENTSACCORDINGTOTHETAGUCHIC213SMETHODANDSHOWEDAGAINTHATTHEMELTANDMOLDTEMPERATUREARETHEPRINCIPLEFACTORSAffECTINGWELDLINEPROPERTIESOFINJECTIONMOLDEDTHERMOPLASTICSITSHOULDBENOTEDTHATTHESENSIBILITYOFWELDLINESDEPENDSNOTONLYONTHEMATERIALPROPERTIESANDTHEPROCESSINGCONDITIONS,BUTALSOONTHETESTINGMETHODSAPPLIEDSELDEN1997ALTHOUGHINTHELITERATUREMECHANICALWEAKNESSOFWELDLINESISUSUALLYEXPLAINEDBY1LACKOFDIffUSIONTHAMNGUYENCHUNGFLOWANALYSISOFTHEWELDLINEFORMATIONDURINGINJECTIONMOLDFILLINGOFTHERMOPLASTICSRECEIVED10FEBRUARY2003ACCEPTED22OCTOBER2003PUBLISHEDONLINE19DECEMBER2003C211SPRINGERVERLAG2003ABSTRACTTOSTUDYTHEWELDLINEFORMATIONOFCOLLIDINGFLOWFRONTSTHEFILLINGOFAMOLDCAVITYWASSIMULATEDTHETHERMORHEOLOGICALFINDINGSWEREUSEDTOINVESTIGATETHESOURCESOFWELDLINEWEAKNESSINTHISWAYCRITICALAREASOFTHEINTERFACEINREGARDTOTHELACKOFINTERDIffUSIONANDTHEINAPPROPRIATEMOLECULARORIENTATIONWEREFOUNDTOBEPLACEDNEARTHESURFACEOFTHEFINISHEDPARTSTHEMAINSOURCEFORTHEWELDLINEWEAKNESSSEEMSTOBETHEVNOTCHTHATARISESDUETOTHEPOORLYBONDEDREGIONNEARTHESURFACEINCOMBINATIONWITHTHELARGESHRINKAGEASARESULTOFEXTREMELYHIGHMOLECULARORIENTATIONSINDUCEDATTHEENDOFTHEFILLINGFURTHERMORE,THEEMPIRICALKNOWLEDGEWASCONFIRMEDTHATWELDLINESARERATHERMORESENSITIVETOTHELOCALFLOWSITUATIONTHANTHEGLOBALPROCESSINGCONDITIONSMELTANDMOLDTEMPERATURESCANBECONSIDEREDTOBETHEMOSTIMPORTANTFACTORSWHICHINFLUENCETHEWELDLINESTRENGTHKEYWORDSPOLYMERINJECTIONMOLDINGTHERMOPLASTICSWELDLINESIMULATIONRHEOLACTA200443240–245DOI101007/S0039700303392ORIGINALCONTRIBUTIONINPARTPRESENTEDATTHE6THEUROPEANCONFERENCEONRHEOLOGY,ERLANGEN,2002TNGUYENCHUNGINSTITUTFURALLGEMEINENMASCHINENBAUUNDKUNSTSTOffTECHNIK,CHEMNITZUNIVERSITYOFTECHNOLOGY,09107CHEMNITZ,GERMANYEMAILTHAMNGUYENCHUNGMBTUCHEMNITZDEOFPOLYMERMOLECULES,2UNFAVORABLEMOLECULARORIENTATIONATTHEINTERFACE,AND3FORMATIONOFAVNOTCHATTHESURFACEOFINJECTIONMOLDEDPARTSKIMANDSUH1986;FELLAHIETAL1995,LITTLEWASKNOWNABOUTTHEINTERRELATIONSHIPBETWEENTHESEFACTORSKIMANDSUH1986ANALYZEDTHEFIRSTANDSECONDFACTORSSEPARATELYANDTHENINTEGRATEDTHEMTOPREDICTTHESTRENGTHOFWELDLINESINTHEIRTHEORETICALAPPROACHFORTHEDIffUSIONPROCESSTHETEMPERATUREGRADIENTACROSSTHEPARTTHICKNESSWASNEGLECTEDTOMARIETAL1990CLARIFIEDTHEVNOTCHSTRUCTUREANDITSEffECTONTHESTRENGTHOFGENERALPURPOSEPOLYSTYRENEINJECTIONMOLDINGSTHEYMEASUREDTHEWELDSTRENGTHOFDOGBONETYPETENSILESPECIMENSTHESURFACEOFWHICHWASPARTIALLYELIMINATEDBYMILLINGTHEIRRESULTSSUGGESTEDTHATTHEVNOTCHEffECTISCAUSEDRATHERBYAPOORLYBONDEDLAYERNEARTHESURFACETHANTHEFINEGROOVEONTHESURFACEITISALSOWORTHNOTINGTHATTHEVNOTCHMAYBEALSOATTRIBUTEDTOTHEAIRENTRAPPEDATTHEINTERFACEBETWEENTHEFLOWFRONTSHAGERMAN1973ORVOLUMETRICSHRINKAGEDURINGCOOLINGPICCAROLOANDSAIU1988TODATE,MODELINGOFTHEWELDLINEMAINLYFOCUSESONPREDICTINGTHEWELDLINEPOSITIONANDINVESTIGATINGTHEINFLUENCEOFTHETHERMORHEOLOGICALSITUATIONONTHEMEASUREDWELDLINESTRENGTHSHOWEVER,MOSTOFTHESIMULATIONISBASEDONTHEPRESSUREDROPFORMULATION,WHICHDOESNOTGIVEDETAILEDINFORMATIONABOUTTHEFLOWSITUATIONATTHEADVANCINGFRONTTHEREHAVEBEENONLYAFEWPAPERSONSIMULATIONOFTHEWELDLINEFORMATIONCONSIDERINGTHEFULLFLOWHISTORYWEIETAL1987CALCULATEDTHESTRESSWHICHAVISCOELASTICMELTEXHIBITSINAFLOWPASTOBSTACLESBYASSUMINGTHATTHEKINEMATICSARECLOSETOTHOSEOFASHEARTHINNINGFLUIDSUCHASTHECARREAUMODELTHECALCULATEDVALUESOFMOLECULARORIENTATIONSHOWEDAHIGHLYORIENTEDREGIONSURROUNDINGTHEWELDINTERFACEJUSTDOWNSTREAMOFTHEOBSTACLE,WHICHWASVERIFIEDBYEXPERIMENTSUSINGTHERHEOOPTICALMETHODMAVRIDISETAL1988SIMULATEDTHESITUATIONOFCOLLIDINGFLOWFRONTSFORANEWTONIANFLUIDANDSHOWEDTHATTHEORIENTATIONOFPOLYMERMOLECULESATA‘‘STAGNATING’’WELDLINEISMAINLYDETERMINEDBYTHEFOUNTAINFLOWBEFORETHECOLLISIONOCCURSRECENTLY,NGUYENCHUNGETAL1998INVESTIGATEDTHEFLOWMECHANISMSBEHINDANOBSTACLECLARIFYINGTHEINFLUENCEOFTHETHERMORHEOLOGICALHISTORYOFTHEMELTONTHEPERFORMANCEOFTHEWELDLINETHEPRESENTEDPAPERREPRESENTSANONISOTHERMALSIMULATIONOFTHEWELDLINEFORMATIONDUETOCOLLISIONOFTWOFLOWFRONTSTHISWAYTHEAFOREMENTIONEDSOURCESOFTHEWELDLINEWEAKNESSANDTHEIRINTERRELATIONSHIPCANBEINVESTIGATEDWITHREGARDTOTHEFLOWHISTORYANDTHETHERMORHEOLOGICALSITUATION,WHICHASAWHOLEENABLESABETTERUNDERSTANDINGOFTHEMECHANISMSOFTHEWELDLINEFORMATIONSIMULATIONSIMULATIONHASBEENCARRIEDOUTOFAVISCOUSFLUIDFILLINGARECTANGULARCAVITYFROMBOTHENDSFIG1BYCONSIDERINGTHESYMMETRYAQUARTEROFTHECAVITYWASMODELEDASTWODIMENSIONALGEOMETRYNEGLECTINGGRAVITYANDSURFACETENSIONMEANSTHATTHEFREESURFACESCANBEASSUMEDTOBEINITIALLYFLAT,THEFLUIDBEINGATRESTTHEMASS,MOMENTUMANDENERGYCONSERVATIONEQUATIONSFORANINCOMPRESSIBLEFLUIDCANBEWRITTENASFOLLOWSRC1T01QTTTC1RTC18C19C0RPRC1C0S2QCPTTTC1RTC18C19RC1KRTC0S_C0C3WHERET,T,T,P,C0S,_C0C,Q,CPANDKDENOTETIME,VELOCITYVECTOR,TEMPERATURE,HYDROSTATICPRESSURE,DEVIATORICSTRESSTENSOR,RATEOFDEFORMATIONTENSOR,DENSITY,SPECIFICHEATANDHEATCONDUCTIVITYRESPECTIVELYTHECONSTITUTIVEEQUATIONFORAGENERALIZEDNEWTONIANFLUIDWASUSEDC0S2GT;_C_C0C;_C0C12RTRTT4WITHTHEVISCOSITYGIVENBYTHEBIRDCARREAUMODELBIRDETAL1977GG01KC_C2HINC012;_Cffiffiffiffiffiffiffiffiffiffiffiffi2_C0C_C0CP5FORTEMPERATUREDEPENDENCETHEARRHENIUSMODELWASAPPLIEDONTHEVISCOSITYATAREFERENCETEMPERATURET0G_C;TATGAT_C;T0;ATEXPA1TC01T0C18C19C20C216FIG1INITIALSTATETOPANDBOUNDARYCONDITIONSBOTTOMFORAFILLINGSIMULATIONOFARECTANGULARCAVITY241THEFOLLOWINGBOUNDARYCONDITIONSCOMPLETETHESTATEMENTOFTHEPROBLEMATTHEINLETACONSTANTVELOCITYANDACONSTANTTEMPERATUREOFTHEMELTAREASSUMED;NOSLIPCONDITIONANDACONSTANTMOLDTEMPERATUREAREIMPOSEDONTHEWALLTABLE1;ATTHESYMMETRYLINESSYMMETRYCONDITIONSAREAPPLIED;ATTHEFLOWFRONTZEROSURFACETRACTIONISAPPLIEDANDHEATTRANSPORTTHROUGHTHISSURFACEISNEGLECTEDWITHTHECOMMERCIALCODEFIDAPFLUENT1998,THEGALERKINFINITEELEMENTMETHODWASUSEDTOSOLVETHECONTINUITY,MOMENTUM,ANDENERGYEQUATIONSWHICHAREDISCRETIZEDBYSTANDARDPROCEDURES,USINGAMIXEDFORMULATIONINWHICHPRESSUREISINTERPOLATEDONEORDERLOWERTHANVELOCITYANDTEMPERATURETHEFREESURFACESARETRACKEDBYUSINGTHEVOFMETHODAPPLIEDONAFIXEDMESHHIRTANDNICHOLS1981ANADDITIONALEQUATIONISTOBESOLVEDTOGETHERWITHTHEGOVERNINGFLOWEQUATIONSFTTC1RF07WHEREBYFISDEFINEDASAMATERIALDENSITYFUNCTIONITHASAVALUEOFUNITYINAFILLEDSECTIONOFTHEFLOWDOMAINANDISZEROOUTSIDEOFTHEFLUIDATTHEFREESURFACEITSELFTHISFUNCTIONHASAVALUEBETWEEN0AND1ASMATERIAL,POLYSTYRENE165HSUPPLIEDBYBASF,LUDWIGSHAFEN,GERMANYHASBEENUSEDTHETHERMORHEOLOGICALPROPERTIESANDTHECOEffiCIENTSOFTHEVISCOSITYMODELARESHOWNINTABLE2RESULTSRESULTSWILLBESHOWNUSINGTHENONDIMENSIONALIZEDVARIABLESASFOLLOWSVC3VV0;TC3TT0;TC3TT0V0;_CC3_CV0T0;PC3PV0G0T0T08WITHACHARACTERISTICLENGTHV00004M,ACHARACTERISTICVELOCITYM001M/S,ANDAZEROSHEARRATEVISCOSITYG0T03760PASTHEFLOWFRONTSATDIffERENTTIMESFIG2SHOWTHATTHEWELDLINEISFORMEDASEXPECTEDFROMTHEMIDDLEOFTHECAVITYTOWARDSTHEWALLINFIG3THEPATHLINESOFSELECTEDMATERIALELEMENTSCANBEOBSERVEDWHICHAREORIGINALLYPOSITIONEDONTHEFLATFLOWFRONTTHEDISTANCEBETWEENTHEORIGINALLYFLATFLOWFRONTANDTHEWELDLINEPOSITIONISLARGEENOUGHSOTHATTHEFLOWFRONTHASBEENFULLYDEVELOPEDBEFORETHEWELDLINEISFORMEDITCANBESEENTHATTHEWELDLINECONSISTSOFTHEMATERIALELEMENTSCOMINGFROMTHECOREREGIONOFTHECAVITYWHERETHEYGENERALLYDIDNOTHAVEEXPERIENCEDLARGEDEFORMATIONSNGUYENCHUNGANDMENNIG2001ONLYDURINGTHETRANSITIONFROMTHEFLATTOTHEFULLYDEVELOPEDFLOWFRONTMAYDEFORMATIONSOCCUR,BUTTHATISRATHERANEXCEPTIONDUETOTHESPECIFICPROBLEMDEFINITIONONTHEWHOLE,DEFORMATIONSATTHEWELDLINEMUSTBEMOSTLYSUBJECTEDTOTHELOCALFLOWSITUATIONATTHEINTERFACETHEMATERIALELEMENTSCHANGETHEIRFLOWDIRECTIONANDCONTINUETOMOVEALONGTHETHICKNESSDIRECTIONDURINGTHESETIMESINTERDIffUSIONMAYOCCURINTHECORETHECONTACTTIMEABOVETHESOLIDIFICATIONTEMPERATUREISLONGERTHANINTHEOUTERREGIONSOTHATASTRONGERDEGREEOFINTERDIffUSIONCANBEEXPECTEDTHEREBYCONTRAST,INTHELAYERNEARTHEWALL,THECONTACTTIMEISVERYSHORTSINCETHEMATERIALELEMENTSARRIVINGTHEREWILLBEFROZENINIMMEDIATELYBEFORECONTACTWITHTHEIRCOUNTERPARTSCANBEESTABLISHEDFOREXAMPLETHEMATERIALELEMENTNUMBERED8THISRESULTSINALAYERWITHPOORBONDINGASFOUNDBYTOMARIETAL1990THEMOLECULARORIENTATIONHASBEENFREQUENTLYINVESTIGATEDBYTRACINGAGREATNUMBEROFMATERIALELEMENTSWHICHAREFIRSTLYPLACEDONASTRAIGHTLINECOYLEETAL1987HOWEVER,INTHATWAYITISNOTPOSSIBLETODISTINGUISHBETWEENTHEABSOLUTEDEFORMATIONSTHATSTRONGLYDEPENDONTHEOBSERVATIONTIMEANDTHERELATIVEDEFORMATIONSTHATAREAMEASUREMENTFORMOLECULARORIENTATIONINTHISWORK,SEVERALGROUPSOFMATERIALTABLE1PROCESSINGPARAMETERSPARAMETERSVALUESMELTTEMPERATURETF503C176KMOULDTEMPERATURETW333C176KINLETVELOCITYV001M/STABLE2MATERIALPROPERTIESOFPOLYSTYRENE165HPROPERTIESVALUESMELTDENSITYQ892KG/M3SPECIFICHEATCP1968J/KGKTHERMALCONDUCTIVITYK014W/MKREFERENCETEMPERATURET0503C176KZEROSHEARRATEVISCOSITYG0T03760PASTIMECONSTANTK015SPOWERLAWINDEXN023ARRHENIUSCOEffiCIENTA10,842FIG2DEVELOPMENTOFTHEFLOWFRONTS242ELEMENTSWERETRACEDEACHGROUPFORMSACIRCLEANDLOCATESORIGINALLYONTHESTRAIGHTFLOWFRONTFIG4BYCOMPARINGTHEDEFORMATIONSOFTHECIRCLESATDIffERENTTIMESTHERELATIVEDEFORMATIONSOFTHEMELTANDSOTHEDEVELOPMENTOFTHEFLOWINDUCEDMOLECULARORIENTATIONCANBEVISUALIZEDITSHOWSAGAINTHATTHEHIGHORIENTATIONATTHEWELDLINEISARESULTOFRATHERTHELOCALDEFORMATIONSALONGTHEINTERFACETHANOFTHEGENERALDEFORMATIO
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