coppercornerradius

AnalysisofthermomechanicalbehaviourinbilletcastingwithdifferentmouldcornerradiiJ.
K.
Park,B.
G.
Thomas,andI.
V.
SamarasekeraTwodecadesofoperatingexperiencehaveshownthatreducingthecornerradiusfrom12–16mmto3or4mmAfiniteelementthermalstressmodeltocomputeisbenecialinreducinglongitudinalcornercracking.
4Inthethermomechanicalstateofthesolidifyingshelladditiontolesseningcrackfrequency,decreasingthecornerduringcontinuouscastingofsteelinasquarebilletradiusalsotendstomovethecracklocationfromthecastingmouldhasbeenappliedtoinvestigatecorneritselftotheocornerregion.
Unfortunately,billetslongitudinalcracks.
Atwo-dimensionalwithsharpedgestendto'foldover'duringtherollingprocess.
5thermoelastoviscoplasticanalysiswascarriedoutTherefore,moulddesignersstruggletosatisfythesetwocon-withinahorizontalsliceofthesolidifyingstrandictingrequirements.
Abetterwaytosolvethelongitudinalwhichmovesverticallywithinandjustbelowthecornercrackproblemsisdesirable.
Animportantsteptowardsmould.
Themodelcalculatesthetemperaturethisendistheachievementofanaccurate,quantitativedistributions,thestresses,thestrainsintheunderstandingofthecrackformationmechanism(s).
Thissolidifyingshell,andtheintermittentairgapunderstandingwouldaidmoulddesignoptimisation,especiallybetweenthecastingmouldandthesolidifyingforhighspeedcasting.
strand.
ModelpredictionswereverifiedwithbothOvertheyears,manymathematicalmodelshavebeenananalyticalsolutionandaplanttrial.
Themodelwasthenappliedtostudytheeffectofmoulddevelopedtohelptounderstandtheoriginofdefectsincornerradiusonlongitudinalcrackformationforcomplexprocessessuchascontinuouscasting.
6–11How-castinginatypical0·75%/mtaperedmouldwithever,quantitativeunderstandingofthere-entrantcornerbothoilandmouldpowderlubrication.
Withthisphenomenonofthesolidifyingshellinthebilletmouldhasinadequatelineartaper,agapformsbetweenthereceivedrelativelylittleattention.
Furthermore,theeectshellandthemouldinthecornerregion.
Astheofthebilletmouldcornerradiusonthetemperature,cornercornerradiusofthebilletincreasesfrom4to15mm,gap,andstressdevelopmenthasnotbeenstudied.
thisgapspreadsfurtheraroundthecornertowardsInthepresentwork,athermal–elastic–plastic–creepnitethecentreofthestrandandbecomeslarger.
Thiselementmodelhasbeendevelopedtostudythethermal–leadstomoretemperaturenon-uniformityaroundmechanicalbehaviourofthesolidifyingshellinandjustthebilletperimeterassolidificationproceeds.
belowabilletmould.
ThemodelwasvalidatedwithplantLongitudinalcornersurfacecracksarepredictedtomeasurementsincludingsolidshellthicknessandmouldformonlyinthelargecornerradiusbillet,owingthermocoupletemperatures.
Themodelwasthenappliedtotensioninthehotterandthinnershellalongthetothere-entrantcornerphenomenontoinvestigatethecornerduringsolidificationinthemould.
Offcornerinuenceofcornerradiusonlongitudinalcrackformation.
internalcracksformmorereadilyinthesmallcornerradiusbillet.
Theyarecausedbybulgingbelowthemould,whichbendsthethin,weakshellPREVIOUSWORKaroundthecorner,creatingtensilestrainonthesolidificationfrontwheretheselongitudinalcracksLongitudinalcracksareultimatelyobserved.
I&S/1675Longitudinalcracksareoneofthemostcommonmouldrelatedqualityproblemsencounteredinbilletcasting.
TheyDrParkisattheUniversityofBritishColumbia,141–2355EastMall,areassociatedwithhottearingclosetothesolidicationVancouver,BC,Canada,ProfessorThomas(bgthomas@uiuc.
edu)front,2andaremanifestedinatleasttwodierentforms:isintheDepartmentofMechanicalandIndustrialEngineering,'longitudinalcornercracks'and'ocornerinternalcracks'.
UniversityofIllinoisatUrbana–Champaign(UIUC),1206WGreenStreet,Urbana,IL,61801,USA,andProfessorSamarasekeraisinLongitudinalcornercracksrunalongthesurfaceneartheDepartmentofMetalsandMetallurgicalEngineering,Universitytheexactcornerofthebilletandareusually1–2mmofBritishColumbia,111–2355EastMall,Vancouver,BC,Canada.
indepth,12asshowninFig.
1a.
AlthoughseveralstudiesManuscriptreceived27February2002;accepted16July2002.
suggestthatlongitudinalcornercracksarerelatedtothe2002IoMCommunicationsLtd.
PublishedbyManeyfortherhomboidconditionofthebillet,12,14–17thesecracksalsoInstituteofMaterials,MineralsandMiningoccurintheabsenceofrhomboidity,asaresultofimpropercornerradius12,18ormoulddistortionandwear.
14,15AketaandUshijima18observedthatwithalargecornerradius,thelongitudinalcornercracksappearalongthecorner,INTRODUCTIONwhilewithsmallerradii,thesesurfacecracksformmoreDuringthecontinuouscastingofsteelbillets,thecornerfrequentlyattheocornerregion.
Theysuggestedthatregionsofthecastsectionoftenexperiencelocalthinning.
theoptimalcornerradiustominimiselongitudinalcrackThisphenomenon,sometimesreferredtoas're-entrantformationshouldbeone-tenthofthesectionsize.
2However,corners',resultsfromthecomplexbehaviouroftheairgap,SamarasekeraandBrimacombe12believedthatthemodernwhichformsbetweenthemouldandthesolidifyingshellintrendofsmallercornerradiisuchas3or4mmmaysolvethecornerregion.
Thiscommonoccurrencecanleadtothelongitudinalcornercrackingproblem,butattheexpenseproblemssuchaslongitudinalcracksnearthebilletcorner,ofcreatingmoreocornercracks.
Mori15observedthatespeciallyathighcastingspeed.
1–3Inextremecases,thetheincidenceoflongitudinalcornercracksincreaseswithcornersmaybesothinthatabreakoutoccurs,eventhoughthetimethatamouldisinserviceduringacampaign.
Hetheaverageshellthicknessiseasilylargeenoughtowithstandtheferrostaticpressureatthemouldexit.
suggestedthatoverallreverseoftapermaybeanimportantDOI00.
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Thermomechanicalbehaviourinbilletcastingoftheshellbulgingwasguessedtobethermaldistortionorwearinthelowerregionofthemould.
Thisbulgingcouldariseifimproperlysetfootrollsorwobblingofthemouldduringitsoscillationcyclecausesthestrandtomoveaboutinthelowerregionofthemould.
MathematicalstressmodelsDuringcontinuouscasting,solidicationofthesteelshellinthemouldregioninvolvesmanycomplexphenomenasuchasuidow,interactionofshrinkageoftheshellandferrostaticpressure,whichleadstointermittentcontactwiththemould,andinteractionofinterfacialheattransferwithairgapformation.
Overtheyears,manymathematicalmodelshaveinvestigatedthethermalandmechanicalbehaviourofthesolidifyingshellwithairgapformationinthecontinuouscastingofsteelinabilletmould.
6–11Grilletal.
6appliedanelastic–plasticmodelofthebilletstrandtostudyitsthermomechanicalbehaviourandtoexplaininternalcrackformation.
Theycalculatedtheheattransfercoecientinthecornerregionandwereabletopredictcornercracksinthebilletbycouplingheatowtotheairgapcomputedfromstressanalysis.
ThemodelwasimprovedlaterbySorimachiandBrimacombe7withbettermaterialpropertydata.
Theyobservedthatinternalcrackscouldbecausedbysurfacereheatingbelowthemould.
KristianssonandZetterlund8,9simulatedbilletcastingusingastepwisecoupledtwo-dimensionalthermalandmechanicalmodel,whichalsocalculatedthesizeoftheshell–mouldgaparoundeachportionofthestrandperipheryateachtime.
Themodelwasappliedtoinvestigatetheformationoflongitudinalsubsurfacecracksinthesolidify-ingshell.
Theysuggestedthatlargeairgaps,whichmayformowingtowearormisalignmentofthemould,causelargestrainsinthesolidifyingshellandahighriskofcracking.
Kellyetal.
10developedacoupledtwo-dimensionalaxi-symmetricthermomechanicalmodelforsteelshellbehaviourinroundbilletcastingmouldsusingacombinationofmodelsFIDAPandNIKED2D.
Theirmodelwasfullycoupledthroughtheinterfacegap,includedmoulddistortion,andassumedelastic–plasticmechanicalbehaviour.
Theirresultssuggestedthatthermalshrinkageassociatedwiththephasechangefromdferritetoaustenitein0·1%Csteelaccountsforthedecreasedheattransferobservedinthisalloyaswellasitssusceptibilitytocracking.
Tszengetal.
11calculatedbillettemperatureeldsusingatemperaturerecoverysolidicationmethod,followedbyanuncoupledstressanalysiswithplanestrainintheMARCmodel.
Theyinterpretedtheresultstoobtainqualitativeideasaboutpossiblebilletdefects.
OhnakaandYashima19studiedtheeectofmouldtaperandmouldcornerradiionthetemperatureandstressabeldsinslabcastingusinganelastoplasticmodel,whichalongitudinalcornercrack;boffcornerinternalcracksconsideredtheferrostaticpressure,mouldtaper,andinter-1Appearanceoflongitudinalcracksinbilletcasting12,13actionbetweenthesolidifyingshellandmould.
Thismodeldemonstratedthatshelldeformationowingtothermalstressandferrostaticpressurechangestheshell–mouldcontributor.
Thiswasattributedtopermanentcreepdis-tortionoftheuppermouldtowardsthesteel,andwearinthermalresistance,resultingintensilestressneartheslabcorner,whichmaycauselongitudinalcracks.
Theyalsothelowermouldwithlongerservicetime.
Althoughlongitudinalcornercracksarebelievedtoformsuggestedthatalargermouldcornerradiusshoulddecreasetheinterfacialgapthicknessandtensilestressintheshellinthemould,2,5ocornerinternalcracksarebelievedtoformbelowthemouldinthespraycoolingzone.
3Theseandtherebyhelptopreventcracks.
Inthepresentwork,athermoelastoviscoplasticnitecracks,13showninFig.
1b,arelocated~15mmfromagivencornerstartingatadepthof4–11mmfromthebilletelementmodelhasbeendevelopedtosimulatetemperatureandstressinatransverseslicethroughthesolidifyingshellsurfaceandextendingtoadepthof13–20mm.
3,12Byanalysingthemicrostructureofabilletobtainedfromofatypicalbilletcaster.
Theevolutionoftheairgaphasbeencalculatedfromthedeformationofthestrandandindustrialtrialsusingheatowcalculations,Brimacombeetal.
3deducedthatcrackscanformasaresultofbulgingthetaperedanddistortedmould.
Itscoupledeectonthetemperaturedistributionhasbeentakenintoaccountwithofthesolidshellinthelowerpartofthemould.
Theyproposedthatasbulgingoccurs,ahingingactiondevelopsadistancedependentheattransfercoecientbetweenthemouldandstrand.
Theaccuracyofthetwo-dimensionalnearthecoldandstrongcorners,causingocornertensilestressesnearthesolidicationfront,andcracking.
Thecause(2D)slicemodelformulationinthisanalysishasalsobeenIronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcasting3investigatedthroughcomparisonwithbothananalyticalsolutionandmeasurementsfromaplanttrial.
Finally,themodelhasbeenappliedtothespecicproblemofhowthecornerradiusofthemouldaectsthethermal,deformation,andstresseldsofalowcarbonsteelbilletcontinuouslycastusingbothoillubricantandmouldpowderpractices.
Theimplicationsforlongitudinalcrackformationarediscussed.
PLANTTRIALSCasterdetailsandnominaloperatingpracticeAplanttrialwasconductedatPOSCO,Pohangworks,SouthKorea,relatingtoa120mmsquaresectionof0·04%Csteelcontinuouslycastat2·2mmin1.
Themouldwasmanufacturedfromrelativelypure,deoxidisedhighpurity(DHP)copperwithawallthicknessof6mm,acornerradiusof4mm,andasingle'linear'taperof0·75%/m.
OtheroperatingparametersandmouldgeometrydetailsareprovidedinTable1.
MouldtemperaturemeasurementThemouldtubewasinstrumentedwith12Ktypethermo-couplesontheinsideradiusfaceasshowninFig.
2.
Theywerearrangedinthreecolumnsalongthecentrelineand±45mmfromthecentreline,andinfourrowslocatedat120,170,400,and700mmbelowthetopofthe800mmlengthmould.
Thethermocoupleswereembeddedinthemouldwalltoadepthof3mmfromthehotface.
Themouldwatertemperatureincreasewasnotrecordedatthetime,butisestimatedtobe30Kbasedonrecentmeasurementsforthesameconditions.
SolidshellmeasurementToinvestigatesolidshellgrowth,FeStracerwassuddenlyaddedintotheliquidpoolduringsteadystatecasting.
BecauseFeScannotpenetratethesolidshell,thepositionofthesolidshellfrontatthatinstantcanbeclearlyrecognisedaftercastingusingasulphurprint.
2PhotographofthermocoupleinstrumentedmouldtubeMATHEMATICALMODELDESCRIPTIONToinvestigatethethermomechanicalbehaviourofthecon-tinuouscastbilletandmould,a2Dtransientthermoelasto-asaresultofthermalstrains,whileheattransferacrosstheviscoplasticniteelementmodel(AMEC2D)20–22hasbeengapdependsontheamountofshrinkageofthesolidifyingdeveloped.
Thismodeltracksthethermalandmechanicalshell.
Duringeachstepoftheanalysis,thetemperaturebehaviourofatransverseslicethroughthecontinuouslyeldsofthemouldandstrandarecalculatedsimultaneously,caststrandasitmovesdownthroughthecaster.
Themodelextrapolatingfromthepreviousstep,neglectingaxialcon-includesseparateniteelementmodelsofheattransferandduction.
Then,thestressanalysiscalculatesdeformationofstressgenerationthatarestepwisecoupledthroughthesizethestrand,stress,andtheairgapsize.
Iterationcontinuesandpropertiesoftheinterfacialgap.
Stressesariseprimarilyuntiltheheattransfercoecientdeterminedfromthecalculatedgapisconverged.
Table1CastingandmouldconditionsinplanttrialMicrosegregationanalysisGenerally,thesolidicationofsteelduringcontinuousCastingconditionscastingdoesnotexactlyfollowthepathoftheequilibriumbilletsize120mm2Nominalcastingspeed2·2mmin1binaryFe–CphasediagramowingtotherapidcoolingMeniscuslevel100mmandmicrosegregationofothersoluteelements.
TodetermineOscillationtypeSinusoidalthevariationofliquid,d-Fe,andc-Fefractionswithtemper-Strokelength8mmature,themicrosegregationofsoluteelementsofsteelwasSubmergedentrynozzleOpenpouringMachineradius8manalysedusingthedirectnitedierencemethodofKim23andUeshimaetal.
24asdescribedelsewhere.
25Figure3showsMouldconditionsMaterialDeoxidisedhighpurityCuthecalculatedliquid,d-Fe,andc-FefractionsasafunctionMouldlength800mmoftemperatureduringsolidicationofthelowcarbonsteelThickness6mmgradeusedintheplanttrial(Fe–0·04C–0·2Si–0·25Mn–ConstructionTube0·010P–0·015S,wt-%)andthecorrespondingthermallinearTaper(linear)0·75%/mCornerradius4mmexpansion(TLE)functionusedinthepresentstudy.
TheseCoolingwater1100lmin1resultswereusedtodeterminethethermophysicalpropertiesCoolingwatervelocity9·2ms1ofthesteelgivenbelow.
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Thermomechanicalbehaviourinbilletcasting5Heattransfercoefficientacrossstrand/mouldforvarious3Calculatedsolidfractionfs,d-Fefraction,c-Fefraction,airgapsizesandgivensurfacetemperaturesandthermallinearexpansionasfunctionoftemperatureforlowcarbon(C=0·04wt-%)steelwhereRTisthethermalresistance,KgisthethermalHeatflowanalysisconductivityofthegapmedium(assumedtobe100%airTheheatowmodelsolvesthe2Dtransientheatcon-inthepresentstudy),giveninTable2,dgapisthethick-ductionequationforthetemperaturedistributioninthenessofthegap,andhradistheheattransfercoecientforsolidifyingshell.
Theeectsofsolidicationandsolidstateradiativeheatowwhenanairgapexistsbetweenthephasetransformationontheheatowareincorporatedstrandandthemouldsuchthatthroughatemperaturedependententhalpyfunctionashrad=sSBe(Ts+Tm)(T2s+T2m3)showninFig.
4.
Thisgurealsoshowsthetemperaturedependentconductivityfunction.
wheresSBistheStefan–Boltzmannconstant,TsistheshellThefollowingassumptionsareusedinthiscalculation:surfacetemperature,andTmisthemouldhotfacetemper-(i)theincomingmetaltemperature,liquidlevel,andature.
Theaverageemissivityeoftheshellandmouldcastingspeedareconstantandaxialheatconductionsurfaceisassumedtobe0·8.
27IfthevalueofhCcomputedisignoredfromequation(2)exceedsthevalueassociatedwithdirect(ii)mouldoscillationandfrictionbetweentheshellandcontact,itistruncatedtothatvalue.
ThevalueofhCthemouldareneglectedfordirectcontactistakentobe2500Wm2K1,which(iii)theeectofconvectiveheatowintheliquidregionrepresentsaminimumcontactresistanceoraveragegapistakenintoaccountusingtheeectivethermalassociatedwithoscillationmarksof0·02mmdepth.
10conductivitykeffformoltensteel26Figure5showsplotsofthisheattransfercoecientfunctionversusairgapsize,assumingstrandsurfacetemperatureskeff=27[1+6(1fs)2]1)of1500and1000°Candmouldhotfacetemperaturesofwherefsisthesolidfraction.
300and200°C.
OilcastinginterfaceheattransferPowdercastinginterfaceheattransferHeatextractionfromthesolidshellsurfaceinthemouldisTostudytheeectofusingmouldpowderasalubricant,primarilycontrolledbyheatconductionacrosstheinterfacesimulationswerealsoperformedusingthefollowingbetweenthemouldandthesolidifyingsteelshell.
Thisisexpressionforthermalresistancebetweenthesolidifyingmodelledasaninternalboundarycondition,usingtheshellsurfaceandthemould,consistingoffourtermsinterfacialheattransfercoecienthCasafunctionofairgapthicknessandsurfacetemperatureofthestrand,accordingRT=1hm+dgapKg+dfluxKflux+1hshell4)totherelationshipofKellyetal.
10Therstthermalresistance(rstterminequation(4))hC=hrad+1RTisthecontactresistancebetweenthemouldwallsurfaceandthemouldux,wherehmisthecontactheattransfer=hrad+Kg/dgap2)coecientsetto2500Wm2K1.
Thesecondresistanceisconductionthroughtheairgap,whichisthesameascalculatedforoilcasting.
Thethirdresistanceisconductionthroughthemoulduxlm,withathermalconductivityKfluxof1·0Wm1K1.
21Thethicknessofthemoulduxlayerdfluxisassumedtobe0·1mm.
28Thenaltermisthecontactresistancebetweenthemoulduxandthestrandsurface,wheretheheattransfercoecienthshelldependsTable2Conductivityofgapmedium(air)withtemperatureTemperature,°CConductivity,Wm1K12000·0324000·0396000·0458000·05110000·05712000·0634Enthalpyandconductivityoflowcarbonsteel14000·068(C=0·04wt-%)usedinpresentmodelIronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcasting5greatlyontemperature,becauseofthelargechangeinviscosityofthemoulduxoverthetemperaturerangeofthestrandsurface.
ThetemperaturedependencyofhshellisgiveninTable3.
29SpraycoolingToinvestigatebulgingofthebilletbelowthemould,thermalcalculationswereextendedto200mmbelowthemouldexit,assumingavalueof500Wm2K1fortheheattransfercoecientatthebilletsurfaceandambienttemperatureof30°C.
Thisvaluewaschosentorepresentatypicalspraycoolingcoecient,whichrangesfrom200to600Wm2K1intheliterature.
30MouldtemperatureTemperatureinthemouldwasassumedtobesteadywithin6Profilesofmoulddistortionandtaperusedinpresenteachtimestepandslice.
ItwascalculatedinAMEC2DmodelbyapplyingthewaterheattransfercoecienttothecoldfaceofthemouldbasedonthecorrelationofDittusandBoelter.
31Thisanalysisignoresaxialheatconduction.
Thus,transferanalysisandthethermallinearexpansionofsteelasecondmodel,CON1D,32wasappliedtovalidatethe(TLE),whichcanbedeterminedinturnfromthephaseheatuxprole.
Thismodeltakesintoaccountaxialheatfractionsfoundbymicrosegregationanalysisandthespecicconductioninthemould,sogivesmoreaccuratemouldvolumeVofeachphaseofthesteeltemperaturepredictionsthanAMEC2D.
TLE(T)=AVVref1B1/36)StressanalysisThestressandstraindistributionsassociatedwithtemper-V=(fdVd+fcVc)fs+Vlfl7)aturechangeinthetransversesliceofthesolidifyingshellarecalculatedbythesolvingthestandardequilibrium,whereVrefisthespecicvolumeatthereferencetemper-stress–strain,andsmallstraindisplacementequations.
Theature,andfd,fc,andflarefractionsofd,c,andliquidsliceisassumedtobeinaplanestraincondition,inwhichphase,respectively.
Thereferencetemperatureischosentostrainalongthecastingdirectionisneglected.
Thetemper-correspondwiththesolidfractionof0·8.
ThespecicaturescalculatedbythethermalmodelareinputtothevolumeofthevariousphasesisgiveninTable4,andwereincrementalthermalstressmodel.
obtainedfromWray.
34MouldtaperanddistortionEffectiveplasticstrainandflowstressincarbonsteelMoulddistortionduetothermalexpansion,whichisaddedAthighertemperatures,importanttostressdevelopmenttothemouldtapertodenethemouldwallposition,isduringsolidication,inelasticstrainfromplasticityandcalculatedfromcreepisalsoimportant.
ThefollowingconstitutiveequationproposedbyHanandco-workers35–37isusedtorelatetheowstressofdandcphasesatvarioustemperaturesTDxmould=amouldAmouldwidth2BATcold+Thotc2TrefBandstrainratese˙p5)e˙p=Aexp(Q/RT)[sinh(bK)]l/m8)whereamouldisthemouldthermallinearexpansions=Kenp9)coecient(1·6*105K1),TcoldisthemouldcoldfacewhereAandbareconstants,QandRaretheactivationtemperature(°C),Thotcisthemouldhotfacetemperatureenergyfordeformationandthegasconstant,respectively,(°C),andTrefistheaveragemouldtemperatureatthemisthestrainratesensitivity,Kisthestrengthcoecient,meniscus(°C).
nisthestrainhardeningexponent,sistheowstress,andForequation(5),themouldtemperatureisbasedontheepistheeectiveplasticstrain.
Table5givestheparametersresultsoftheCON1Dmodel,33whichmatcheswellwithintheaboveequationfordferriteandcaustenitephasesthemeasuredtemperature.
Figure6showsprolesoftheofsteel.
Thetotalstrainrateisthuscomposedofthismoulddistortion,0·75%/mlinearproleofthemouldviscoplasticstrainratetogetherwiththethermalandelastictaper,andtheactualmouldwallshapeadoptedinthestrainrates.
presentworkasthewallboundarycondition.
ThermalstrainThermalstrainarisesfromthevolumechangescausedbyTable4Specificvolumeofd-Fe,c-Fe,andliquidsteel34changingtemperatureandphasetransformation.
ThiswasPhaseSpecificvolume,cm3g1calculatedfromthetemperaturedeterminedintheheatd0·1234+[9·38*106(T20)]c0·1255+[9·45*106(T20)]+(7·688*106)Liquidsteel1/7·035Table3Temperaturedependenceofheattransfercoefficientbetweenmouldfluxandstrandsurface29Temperature,°Chshell,Wm2K1Table5Parametersforconstitutiveequation37PhaseA,s1b,MPa1Q,kJmol1mnMouldfluxcrystallinetemperature,1030°C1000Mouldfluxsofteningtemperature,1150°C2000Metalsolidustemperature,1511°C10000d6·754*1080·0933216·90·10280·0379c1·192*10100·0381373·40·23630·2100Metalliquidustemperature,1529°C20000IronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcasting7Finiteelementmeshoftwo-dimensionalhorizontalquarterdomainforbilletstrandandmouldanditsboundaryconditions:hheattransfercoefficient,TtemperatureElasticmoduluscalculatedtoshowthetransversestress–straincomponentorientedparalleltotheperimeteroftheshell.
TocalculateTheelasticmodulusofsteeldecreasessignicantlywithincreasingtemperature.
Thereisstilluncertaintyconcerningthesehoopvalues,rst,theangleoftheheatuxdirectionwwithrespecttotheglobalxandyaxesisobtainedfromthebestvalueofEathightemperatures.
ThefollowingexpressionofKinoshitaetal.
38isusedinthepresentworkthetemperatureresults.
Thestress–straincomponentper-pendiculartothatdirection,i.
e.
h=90°w,isthenderivedE=1·38*102T2225·6T+3·146*105(kgcm2)from10)sh=sx+sy2+sxsy2cos2h+txysin2h.
.
.
(11)TreatmentofliquidSinceelementsmaybeliquid,solid,ormushy,andthevolumeofliquidinthedomainmayvary,specialcareiswheresxisthexstress,syistheystress,andtxyistheneededtohandletheliquidregion.
Inthepresentmodel,shearstress.
negligible(0·5*104MPa)stinessisassignedtothoseNotethatalongthehorizontalshell,h=0°,sothehoopGaussianintegrationpointswhosetemperatureisabovestressbecomessx.
Thehoopstressbecomessyalongthethecoherencetemperature,assumedtocorrespondtoaverticalshell,ash=90°.
Similarcalculationsareappliedtosolidfractionof0·7.
Inaddition,thermalexpansionisndthehoopstraineh.
assumedtobezerofortemperaturescorrespondingtoasolidfractionof0·8orabove.
StrandandmoulddomainFigure7showstheniteelementmeshofthe2DhorizontalSolidshell–mouldcontactsectionofthebilletstrandandmouldanditsboundaryInteractionbetweentheshellandthemouldaectsnotconditions.
Atwofoldsymmetryassumptionallowsaonlytheloadingontheexteriorpositionoftheshell,butquartertransversesectionofthebillettobemodelled.
Thisalsoinuencestheheattransfersignicantly.
Acontactdomainconsistsof5273nodesand5135fournodeiso-algorithmisappliedtorestraintheshellelementsfromparametricquadrilateralelementsinthebillet,and207penetratingthemould,39whosepositionisdenedinFig.
6.
nodesand136elementsinthemouldforthe4mmradiusAteachiteration,suchpenetrationsareevaluated,anewmould.
Forthe15mmradiusmould,theniteelementglobalmatrixisgenerated,andstressesareresolved.
Tomeshcontains8947nodesand8775elementsinthebillet,achieveconvergence,thepenetrationparameterissettoand243nodesand160elementsinthemould.
Theelement5·0,andthefrictioncoecientto0·2.
equationsareassembledusingasingleintegrationpoint,FerrostaticpressureandbulgingandtheequationsaresolvedusingNewton–RaphsonFerrostaticpressurefromtheverticalgravityforceontheiteration.
Furthermodeldetailsaregivenelsewhere.
39TheliquidpushestheinsidesurfaceofthesolidifyingshellboundaryconditionsusedarealsoshowninFig.
7.
Furthertowardsthemouldwalls,andgreatlyaectsgapsizeandsimulationconditionsfortheplanttrialaredescribedinmouldheattransfer.
ItincreasesinproportiontotheTable6.
distancebelowthemeniscus.
InAMEC2D,thispressureisappliedtoeveryliquidelementinthedomainatalltimes.
ThispressureisallowedtocausebulgingbelowthemouldTable6Simulationconditionsforplanttrialsimplybyremovingthemouldcontactconstraintcon-ditions.
ThisapproachneglectstheeectsofaxialbendingSteelgradeC=0·04wt-%Liquidustemperature401529°Cmomentsandguiderolls,sorepresentsanextremecaseofSolidustemperature401511°Cpoorguiderollalignment.
Superheat25KContactheattransfercoefficient2500Wm2K1CrackcriterionMould–waterheattransfercoefficient29400Wm2K1Castingspeed2·2mmin1Tostudythesusceptibilityofcornercrackoccurrence,Taper0·75%/m'hoopstress'shand'hoopstrain'ehcomponentswereIronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcasting79ComparisonofcalculatedstressprofileswithanalyticalsolutionsComparisonwithplanttrialThe2Dtransverseslicemodelforsimulatingbilletcast-ingundertheplanestrainconditiondescribedabovewasvalidatedbycomparingwithmeasurementsfromtheplanttrial,basedontheconditionsgiveninTable6,featuringoilcastingwitha4mmcornerradius.
TemperatureAxialmould–temperatureproleswerecalculatedusingboththeAMEC2DandCON1Dmodels.
Figure10comparesthepredictionswiththemeasuredtemperatureproleatemperature;bstressdownthemould,foundbyaveragingthethermocouple8Comparisonofnumericalandanalyticalsolutionsvaluesacrosseachofthefourrows.
TheheatuxproleintheCON1Dmodelwasadjustedcarefully,tomatchMODELVALIDATIONthetemperaturesaccurately.
TheAMEC2Dmodelignoresaxialheatconductionsoisnotexpectedtomatchexactly,Comparisonwithanalyticalsolutionbutstillagreesreasonablywell.
Figure10alsoincludestheTheinternalconsistencyoftheniteelementmodeldevelopedhotandcoldfacetemperatures.
inthepresentwork(AMEC2D)hasbeenvalidatedwithThecorrespondingheatuxprolespredictedbybothanalyticalsolutionsundertheconditionofplanestrainmodelsarecomparedinFig.
11.
TheaccurateCON1Dusinganelementmeshsizeof0·3mm,asshowninFig.
7.
modelcurveshowsaslightdipandreboundinheatuxWeinerandBoley41developedanexactanalyticalsolutionbetween~20and100mmbelowthemeniscus.
Thisisaofthermalstressduringone-dimensionalsolidicationofaresultoftheunexpectedlowertemperaturemeasuredbysemi-inniteelastic–perfectlyplasticbodyafterasuddenthehighestthermocouple.
Itisinterestingtonotethatthisdecreaseinsurfacetemperature.
Table7givesthedetaileddropcorrespondsapproximatelytotheregionofnegativeconditionsforvericationoftheanalyticalsolution.
moulddistortion,suggestingthatthisnegativetaperattheFigure8comparesthissolutionwithnumericalcalcu-meniscusmightplayarole.
Thisheatuxdipphenomenonlationsforvarioussolidicationtimes.
Althoughthetemper-hasbeenobservedbyothers.
13,44,45TheAMEC2DcurveatureproleofAMEC2Dagreescloselywiththeanalyticalshowstheclassicmonotonicallydecreasingprole,whichsolution(Fig.
8a),themaximumtensileandcompressiveismorecommonlyobserved.
stressesare6·5MPaand22·9MPa,whichdierfromTheheatuxforthemouldpowdercastingcaseistheanalyticalsolutionby34%and11·5%,respectivelyalsoincludedinFig.
11.
Itsoverallproleismuchlower(Fig.
8b).
Thisdiscrepancyiscausedbytheassumptionofthanthatfortheoilcastingcase.
ThisresultalsoagreesplanestraininAMEC2D,whichisdierentfromthetruestateofgeneralisedplanestrainintheanalyticalsolution.
However,comparingAMEC2DresultswiththoseoftheCON2Dmodel42,43usinganemeshsizeof0·1mm,asseeninFig.
9,bothshowalmostthesamestressprole,whichimpliesthatthemeshsizeadoptedinthepresentworkisadequate.
Table7Simulationconditionsforanalyticalsolutiontest41Density7400kgm3Specificheat700Jkg1K1Thermalconductivity33Wm1K1Latentheat272kJkg1Initialtemperature1469°CLiquidustemperature1469°CSolidustemperature1468°CSurfacetemperature1300°CYoung'smodulus40GPaPoisson'sratio0·35Thermalexpansioncoefficient20*106K110ComparisonofmeasuredandcalculatedmouldYieldstressatsurfacetemperature20MPatemperaturesIronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcasting11Heatfluxprofilesdownmouldforgivencasting13Comparisonofmeasuredandcalculatedsolidshellconditionsandmodelsthicknesseswithcastingtime:Vccastingspeedwithotherwork.
46Thislowerheatuxiscausedbythethesulphurprint.
Thisagreementappearstovalidatetheinsulatingeectofthemoulduxlayerbetweenthemouldremainingfeaturesofthepresentmodel,includingairgapandstrand.
formationinthecornerregion.
TheshellthicknessisplottedinFig.
13asafunctionHeatbalanceofresidencetimeinthemould.
AlsoplottedinFig.
13areTovalidatetheheatuxproles,acomparisonwasmadetheplanttrialmeasurements,bymeansofthetracertest.
withanenergybalancecarriedoutforthecoolingwater.
ItcanbeseeninFig.
13thatthepredictedsolidshellThemodelpredictionsofaverageheatux,foundfromthegrowthisreasonable,consideringtheuncertaintyabouttheareasunderthecurvesinFig.
11,are1·84and1·80MWm2penetrationdepthofthetracerintothemushyzoneoftheforCON1DandAMEC2D,respectively.
Themeasuredsolidifyingshell.
coolingwatertemperatureincreaseof8Kcorrespondstoanaverageheatuxof1·84MWm2,whichagreeswellwithbothmodelpredictions.
SolidshellthicknessFigure12comparesthemeasuredsolidshellthicknessinatransversesectionthroughthebilletwiththecorrespond-ingmodelprediction.
Thetransversesectionwastakenat285mmbelowthemeniscus,whichcorrespondstoasimulationtimeof7·8s.
ThedeformedshapeofthestrandissuperimposedwithtemperaturecontoursinFig.
12.
Shellthicknessisdenedinthemodelastheisothermcorrespond-ingtothecoherencytemperature,assumedtobe70%solid.
Thegeneralshapesofthepredictedandmeasuredsolidshellmatchreasonably.
Itisnotedthatthemodelcanalsopredictthere-entrantcornereect,observedinacentre;boffcorner;ccorner12Comparisonofcalculatedandmeasuredsolidshellthicknesses:C=0·04wt-%,285mmbelowmeniscus,14Evolutionofsurfacetemperatureprofilesatgivenbilletpositionsfor4mmcornerradiuscastingspeed2·2mmin1IronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcasting915Surfacetemperatureprofilesalong4mmcorner17Temperatureandtransversestressprofilesthroughradiusbilletatgiventimesshellthicknessat19sofcastingtimefor4mmcornerradiusmouldBulgingbelowmouldBulgingbelowthemoulddependsonthetemperatureandhighercastingspeedsandlackofsupportcanmakeitstrengthoftheshellatthemouldexit.
Inthemould,thesignicant.
Thisbulgingcancauseinternalstraininthesurfacetemperatureofthestrandisgovernedbythecontactshell,dependingonbilletgeometryfeaturessuchascornerbetweenthestrandandthemould,whichdenesthegapradiusandtaper.
Figure16showstheevolutionofdisplace-betweenthem.
Thisisinuencedbythemouldtaper,soamentatthecentreandcornerofthebilletsurface.
AsseensimulationwasalsodonefortheextremecaseofnomouldinFig.
16,thebulgingatthecentreofthebilletispredictedtaper.
Figure14showsaxialprolesofthesurfacetemper-tobe~1·4mmfor4mmcornerradiusofbilletwithatureatthestrandcentre,corner,and5mmocorner.
Regardlessoftaper,thecentrelinesurfacetemperaturehasthesameprole,decreasingmonotonicallyto900°Catthemouldexit(Fig.
14a).
Thisisbecausethebilletstrandisalwaysingoodcontactwiththemouldatthestrandcentre.
Thetemperaturereboundbelowthemouldissimplyduetotheslowerrateofheatremovalbythesprays.
Atthecornerregion,thetemperaturereboundsafter~1sforbothcases,owingtoairgapformation.
Thistimecorrespondstoinitialformationoftheairgap,andisdelayedbyapplyingthetaper,asshowninFig.
14c.
Anairgapstillforms,becausethetaperof0·75%/misnotsucienttomatchtheshrinkageoftheshell.
Figure15depictstransversetemperatureprolesalongthebilletsurfaceatvariouscastingtimes,withtaper.
Aftertheinitialsolidicationstage(0·5s),thetemperaturearoundthecornerregionisshowntoremainhigherthroughoutcasting.
ThiswasnotobservedbyBrimacombeetal.
,3whodidnotsimulateairgapformationduringthecalculation.
Theyattributedocornerinternalcrackstoahingingactionaroundacold,strongcorner.
However,Fig.
15impliesthatthecornerregionhasahighersurfacetemperature,whichenhanceshingingbelowthemould.
Thestrandshellexitingthemouldisweakandhot,sotheinternalliquidpressurebulgestheshelloutwardsbelowthemould.
Althoughitmightbesupposedthatthisbulginginbilletcastingissmall,comparedwithslabcasting,theaamicrostructureofoffcornercrack;bhoopstressdistribution;cequivalentplasticstraincontours16Evolutionofbilletsurfacedisplacementshowing18Comparisonofcracklocationandmodelcalculationsat100mmbelowmouldexitbulgingbelowmouldexitwithgivencornerradiiRIronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcastinga4mmcornerradius;b15mmcornerradius19VariationofshellprofilesandtemperaturecontoursincornerregionIronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcasting11respecttodisplacementofthebilletcorner.
Bulgingofthebilletduringtheplanttrialwasalsomeasured,basedonthedistancefromthebilletcentretothenon-bulgedlineextendingbetweenthetwobilletocornerlocations(4mmfromeachedge).
Thesemeasurementsweremadeonthecoldsection,andrangedgreatlyfrom0toover2mm.
Consideringtheuncertaintieswhenevaluatingthebulging,thecalculatedbulgingamountseemstobeconsistentwiththemeasuredvalue.
StressandcrackpredictionToillustratethestressstatethroughthesolidifyingshell,transversestressessxareplottedatvariousstrandpositionsat19sofcastingtime(mouldexit)inFig.
17.
Thepeaktensilestressis~3MPa,andisfoundbeneaththesurface.
Inthemould,itissimilararoundthebilletperimeterexceptnearthecorner.
Thepeakcompressivestressisfoundatthesurface,andismuchhigheratthecentreregionthanat20Evolutionofairgapsizeprofileswithgivencornertheocornerandcorner.
Thisisbecauseofthehugedropradiiofsurfacetemperature,resultingfromgoodcontactbetweenthestrandandthemould,whichincreasestheshellstrength.
Thesuperimposedtemperatures(Fig.
17)throughtheshellTheairgapsizeforbothmouldsisplottedatvariousshowthatthepeakstressclearlycorrespondstothedcastingtimesinFig.
20.
Astimeprogresses,withincreasingferriteregion,asindicatedbythehorizontallines.
Thisdistancebelowthemeniscus,thegapspreadsfurtheragreeswiththendingsofMoitraetal.
,43thatthesuddenaroundthecorner.
Bythemouldexit,thegapsizeextendsshrinkagefromthedtothecphaseproducesthesetensileto~1·3mmaroundthecornerofthe4mmradiusbilletpeaks,whichmaycausesubsurfacecracks.
and1·4mmforthe15mmradiusbillet.
Infact,thegapDuringtheplanttrial,billetsampleswerealsotakensizeinthe15mmradiusmouldislargerthanthatoftheunderthesamecastingconditionsasdescribedinTable1,4mmradiusmouldateverytime.
Thisleadstoahigherandtheirmicrostructurewasinvestigated.
Figure18com-surfacetemperature,asshowninFig.
19.
Theairgapgrowsparesthetypicalmicrostructureofanocornercrackwiththermalcontractionofthecircumferenceofthelong,thatwasfoundinthisplanttrialwithstressandstrainthinshell.
Thecircumferentiallengthalongthebilletsurfacedevelopmentat100mmbelowthemouldexit.
Usually,is118·3mmand113·6mmforthe4mmand15mmradiussolidicationcrackingorhottearingcanoccurwhenthemould,respectively.
Shellshrinkageis2·38mmforthesteelinthemushyzoneisundertensionbeyondsome4mmand1·95mmforthe15mmradiusbillet.
The15mmsmallcriticallimit,owingtotheexistenceofaliquidlm.
radiusbilletshrinksalittlelessbecauseitsshellisslightlyPeakhooptensilestresses,whichpullapartdendritesandhotter.
However,thepresentstudyshowsthatthe4mmresultinhottears,takeplacebothatthecentreandatthecornerradiusisassociatedwithasmallerairgapsize.
Thisocornerofthebillet,asshowninFig.
18b.
EectiveresultisoppositetothatofOhnakaandYashima,19whoplasticstrainishighestattheocornerlocation(Fig.
18c).
simulatedslabcastingandreportedthattheairgapsizeItisinterestingtonotethatthepeakstrainoccursinadecreasedwithincreasingcornerradius,resultinginlowerregionoftensilehoopstress,andcorrespondsroughlytostressnearthecorner.
thepositionofcrackoccurrence.
TheexactlocationofthisThelargerairgapsizepredictedforthelargecornercrackobviouslymatchesthesurfacedepression.
radiusinthepresentworkisconsistentwiththesimpleanalysisofthestrandgeometrydescribedintheAppendix.
EFFECTOFMOULDCORNERRADIUSForagivenamountofshrinkage,theshellperimeteraroundthelargeradiuscornermustpullfurtherawayfromNext,themodelwasappliedtocomparethethermo-thewallthaninthesmallradiuscase,whichgeneratesmechanicalbehavioursofsteelcastin4mm(small)and'slack'moreeasily.
Thislargerairgapcanalsobeguessed15mm(large)cornerradiusmoulds.
Theresultshavebeenfromtheextremecaseoflargecornerradius:aroundevaluatedaccordingtotheeectsonheattransferandgapsectionbillet,whereanairgaptendstoformaroundtheformation,longitudinalcornersurfacecracks,andlongitudinalentireperimeter.
ocornersubsurfacecracks.
HeattransferLongitudinalcornersurfacecracksFigure21comparescontoursofhoopstressandhoopFigure19showstemperaturecontourswiththedeformedshapesofbothbilletsnearthecornerregion,atfourplasticstrainofbothbilletsnearthecornerregionatthecastingtimeof8s.
AscanbeseeninFig.
21,bothhooplocationsdownthemould.
Bothbilletsexperienceincreasingsolidshellthinningatthecorner,andtheassociatedevolutionvaluesaremuchhigherinthe15mmradiusbillet.
Thedevelopmentofhoopplasticstrainwithtimeisshownofanairgap,withincreasingcastingtime.
Duringinitialsolidication,auniformsolidifyingshellformsasaresultinFig.
22atacriticalcornerlocation,1mmbeneaththecornersurface,wherelongitudinalcornercrackswereofgoodcontactbetweenthestrandandmould.
Afterlessthan1s,theshellstartstoshrinkawayfromthebilletandfound.
Figure22revealsthatthelargecornerradiusbilletdevelopstensileplasticstrainfrom4to14sinthemouldanairgapformsnearthecorner.
Thisreducesthelocalheatowfromthestrandtothemould.
Thisraisesthe(150–520mmbelowthemeniscus).
Thisisconsistentwithbreakoutshellobservations,inwhichcornercracksbegintemperatureofthecornerregions22mmbelowthemeniscus,asshowninFig.
14.
Closerexaminationofthetemperaturesomedistancebelowthemeniscus.
Compressionisfoundbothbeforeandafterthistime.
Belowthemould,bulgingprolearoundthecornerrevealsthatthe15mmcornerradiusbilletdevelopsbothhighersurfacetemperatureatcausestheshelltohingearoundthecorner,forcingthecornersurfaceintocompression.
Thesmallradiusbilletthecornerandmoreseverenon-uniformtemperaturecon-toursalongthebilletsurfaceassolidicationproceeds.
Thisexperiencescompressiveplasticstrainatthislocationthroughoutcasting,owingtotwo-dimensionalcoolingatre-entrantcornereectpersistsevenbelowthemouldexit.
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Thermomechanicalbehaviourinbilletcastinga4mmcornerradius;b15mmcornerradius21Contoursofhoopstressandhoopplasticstrainat8sofcastingtimeforoilcastingthecorner.
Thisndingofhighersusceptibilitytosurfacebothbillets.
Thelocationofthepeakstrainalsomovesfromthecornertoocornerwithdecreasingcornerradius.
crackswithalargercornerradiuscorrespondswellwithotherplantobservations.
1–2ItisalsonotedfromFig.
22Thismovementofthepeakstrainlocationisdirectlyrelatedtotheshellbehaviouratthecorner.
Theshellisthatusingthemouldpowderasalubricantcanreducetheplasticstrainowingtotheformationofamoreuniformthickeratthecornerthanattheocornerforthesmallradiusbillet,whiletheshellinthelargeradiusbilletisshell,resultinginlesscrackoccurrence.
thinnest,hottest,andweakestattheexactcentreofthecorner.
Therefore,thesmallradiusbilletismoresusceptibleLongitudinaloffcornerinternalcrackstoocornersubsurfacecracksthanthelargeradiusbillet,Figures23and24comparecontoursofhoopstressandassuggestedbySamarasekeraandBrimacombe.
12Further-hoopplasticstrainofbothbilletsnearthecornerregionatmore,thehighpeakstrainbeneaththecornerofthelargethemouldexitand100mmbelowthemould.
Allresultsradiusbilletbelowthemouldsuggeststhatsurfacecornerindicatecompressionatthesurface,whichimpliesthatnocracks,whichinitiateeasilyinthemouldasindicatedsurfacecrackscanformatthemouldexitorbelow.
Bothabove,maygrowmoreseverebelowthemould,asshownbilletsdevelopsimilarmaximumtensilehoopstressesofinFig.
1a.
~3MPa,locatedclosetothesolidicationfronteverywhereexceptnearthecorner.
AlthoughthestresschangeslittleEFFECTOFCASTINGWITHMOULDFLUXbetweenmouldandbelow,thehoopplasticstrainchangesdramatically.
At100mmbelowthemould,bulgingoftheFinally,asimulationwascarriedouttostudytheeectbilletcausesthefacetohingearoundthecorner.
Thisofmouldpowderlubricationonthethermomechanicalcausessubsurfacetensilestrain,increasingfromapeakofbehaviourofsteelcastinthetwodierentcornerradiusonly0–0·1%atmouldexittoover0·4%at100mmformouldsbutwiththesameinadequatelineartaper.
Figure25comparesthesolidshellcontoursatthemouldexit.
Bothbilletsshowmoreuniformshellsolidicationwithmouldux,leadingtoasmallerairgapsize,despitehavingathinneraverageshellowingtothelowerheatuxassociatedwithathickergap.
Thesmallerairgapsizeisaresultoflessshrinkageofthehottershell.
Inoilcasting,thisextrauniformitycouldbeachievedbyincreasingthetaper.
Changingthelubricantfromoiltopowderdoesnotchangethenatureofthestressandstraindevelopment,orthesusceptibilityoflargeandsmallcornerradiusbilletstocornerandocornercracks,respectively.
The15mmcornerradiusbilletdevelopspeakhoopstressandstrainatthecornerandthe4mmcornerradiusbilletgeneratesbothpeaksattheocornerregion.
Figure26showstheevolutionofhoopstressandstrainwithcastingtimeforthe15mmcornerradiusbillet.
Withpowder,theheatuxislowerandthesolidifyingshellishotterandweaker.
Thus,allofthestressesandstrains,andtheassociated22Evolutionofhoopplasticstrainat1mmbelowbilletcornersurfaceforgivencastingconditionssurfacedefects,areexacerbatedslightly.
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Thermomechanicalbehaviourinbilletcasting13amouldexit;b100mmbelowmould23Hoopstressandhoopplasticstraincontoursfor4mmcornerradius:oilcastingamouldexit;b100mmbelowmould24Hoopstressandhoopplasticstraincontoursfor15mmcornerradius:oilcastingIronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcastinga4mmcornerradius;b15mmcornerradius25ComparisonofsolidshellcontoursatmouldexitwithgivenlubricantsandcornerradiusInthepresentanalysis,theuxlayerisassumedtomain-dendritesintheocornerregion,leadingtolongitudinalsubsurfaceocornercracksinbilletscastinthesemoulds.
tainconstantthicknessduringgapformation.
Inreality,itAlthoughtheaboveanalysisignorestheimportanteectsislikelythatliquiduxwillbuilduptollthegap.
Thisofasymmetry,rhomboidityphenomena,andlowerductilitywouldincreasethecornerheatuxrelativetothepre-fromcopperpickuponthesedefects,thesemechanismssug-dictionshere,whichwouldgiverisetoevenmoreuniformgestmoreaboutmouldoperation.
Applyingmouldpowdershellthickness.
Therefore,forthesameaverageheatuxasthelubricantallowstheshelltosolidifymoreuniformly,andshellthicknessatthemouldexit,thepowdercastingwhichcouldpotentiallyreducebothofthesetypesofpracticeisexpectedtobelesssusceptibletocracks,owingcracks.
Employinganoptimisedparabolicmouldtapercouldtobetteruniformityofthesolidifyingshell.
achievethesamebenet.
Mouldweareectivelyreducesthetaperandprobablyworsensbothcrackingproblems.
MECHANISMOFLONGITUDINALCRACKMouldwearatthecornerwouldcauseamoreseveregap,FORMATIONleadingtoahotterandthinnershellthere,whichwouldThenumericalanalysiscarriedoutinthepresentstudyincreasesusceptibilitytocornersurfacecracks.
Mouldwearindicatestwodistinctmechanismstogeneratelongitudinalatthecentrewouldallowbilletbulgingtooccurinsidethecornercracksorlongitudinalocornerinternalcracksinmould.
Thiscouldallowthehingeactioninsidethemould,thecastingofsteelbilletswithinadequatelineartaper.
andincreasesusceptibilitytoocornersubsurfacecracks.
LongitudinalcornercracksarepredictedtoariseonlyinMisalignedormissingguiderollswouldalsoaggravatethelargecornerradiusbillets,owingtotensiondevelopingbelowmouldbulgingandhingingmechanism.
acrossthehotterandthinnershellalongtheexactcentreofFinally,thepresentworksuggeststhatmouldcornerthecornerduringsolidicationinthemould.
Suchsurfaceradiuscontrolshowlongitudinalcracksaremanifested,butcrackscouldextenddeeperbecauseofsolidshellbulgingisnottherootcauseoftheproblem.
Thismeansthatlargebothinthemould,owingtomouldwear,orbelow,owingtocornerradiusmouldscouldbeusedeectivelytoimprovepooralignmentoftheguiderolls.
Ontheotherhand,smallsmoothrollingoperationswhilestillmaintainingqualitycornerradiusbilletsallowtheformationofathinnershellbilletsfreeoflongitudinalcracks,aslongasothercastingattheocornerregioninsidethemould.
Thisexacerbatesparametersareoptimised.
Specically,anoptimisedparabolicthehingingactionthataccompaniesbulgingbelowthemouldtapershouldbeemployedtogetherwithawellmain-tainedmouldshape(freeofwearandpermanentdistortion),mould.
ThiscauseshighplastictensilestrainacrosstheIronmakingandSteelmaking2002Vol.
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Thermomechanicalbehaviourinbilletcasting15ahoopstress;bhoopplasticstrain26Evolutionofcalculatedstressandstraincontoursfor15mmcornerradiuswithpowdercastingmouldpowderlubrication,andadequatelyalignedfootthecentreofthestrandandbecomeslarger.
Theaccom-rolls.
Morestudyisneededtoachievetheserequirementspanyingdropinheatuxleadstomorenon-uniformityinfordierentcastingspeeds,sectionsizes,andmouldlengths.
temperaturearoundthebilletperimeterassolidicationproceeds.
3.
Longitudinalcornercracksarepredictedonlyinthelargecornerradiusbillet.
TheyformasaresultoftensionCONCLUSIONwithinthehotterandthinnershellalongthecornerduringUsingatwo-dimensionalcoupledthermoelastoviscoplasticsolidicationinthemould(150–520mmdownthemould).
niteelementmodelofaslicethroughthecontinuouscastThesesurfacecrackscouldextenddeeperbysolidshellstrand,thethermomechanicalbehaviourofasquarebilletbulgingowingtomouldwear,orpooralignmentofguidehasbeenanalysed.
Calculatedresultsoftemperatureoftherollsbelowthemould.
mould,heatux,thicknessofthesolidifyingshell,bulging4.
Longitudinalocornersubsurfacecracksarepredicteddeformation,andlocationoflongitudinalcrackformationtoformmoreeasilyinthesmallcornerradiusbillet.
Theyareingoodagreementwithexperimentalobservations.
Thearecausedbyhingingofthethin,weakshellaroundthefollowingconclusionsarebasedonsimulationsof4mmcornerattheocornerregion,asaresultofbulgingand15mmradiuscornersof120mmsquarebilletsoflowallowedeitherinthemouldbymouldwear,orbelowthecarbonsteelwithonly0·75%/mlineartaperandcastatmouldbypoorguiderollalignment.
2·2mmin1.
5.
Changingfromoillubricationtopowdercastingwith1.
Agapformsinthecornerregionoflineartapergoodinltrationandhighgapconductivityand/oroptimisingmouldsowingtoinsucienttaper.
mouldtaperleadstoamoreuniformshellinthemould,2.
Asthecornerradiusofthebilletincreasesfrom4to15mm,thisgapspreadsfurtheraroundthecornertowardswithpotentialbenetsforreducinglongitudinalcracks.
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Thermomechanicalbehaviourinbilletcasting6.
Withoptimisedparabolictaper,nomouldwear,Solvingequation(15),thegapsizeDE=HIfora4mmproperpowderlubrication,andadequatesubmouldguideradiusbilletis0·79mm.
rollsupport,largecornerradiusbilletsshouldbecastablewithoutlongitudinalcracks,withthebenetofasmoothercornerforrollingoperations.
ACKNOWLEDGEMENTSTheauthorswouldliketoacknowledgethenancialandtechnicalsupportofPOSCO.
TheywouldalsoliketoAPPENDIXthankProfessorK.
H.
Oh(SeoulNationalUniversity)forThegapsizeof4mmand15mmcornerradiusmouldsforpermissiontousethemodeldiscussedhere.
Theauthorscasting120mmsquarebilletswasapproximatedgeometricallyarealsogratefulforthesupportofDrT.
J.
Yeo(formerlyassuming:post-doctorialatUniversityofBritishColumbia)and(i)shrinkageis0·5%Y.
Meng(graduatestudentatUniversityofIllinois)inthe(ii)circumferentiallengthofthegapis11·78mmmodeldevelopment.
MrJ.
Shaver(graduatestudentat(p*15/4mm).
UniversityofBritishColumbia)isalsothankedforhelpfulFigure27ashowsaschematicdiagramofthecornerregiondiscussion.
Supportofoneoftheauthors(BGT)fromofa15mmradiusbillet,whereBFistheinitialradiustheContinuousCastingConsortiumattheUniversityof(15mm),AF=ADisthenewradius,EFistheinitialhalfIllinois,theNationalScienceFoundation(GrantDMIperimeterofthe15mmradius,andDFisthenewhalf98–00274),andtheNationalCenterforSupercomputingperimeterofthenewradius.
ApplicationsatUIUCisalsoacknowledged.
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.
,.
.
,and.
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billet.
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