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ASIMPLIFIEDMODELFORHEATTREATMENTSIMULATIONJoséRisso*,AlbertoCardona*andAndresAnca**CIMEC-INTEC(UNL/Conicet)Güemes3450,(3000)SantaFe,Argentinae-mail:acardona@intec.unl.edu.arKeywords:HeatTreatment,ThermalStresses,SolidMechanicsAbstract.Thisworkpresentsasimplifiedmodeltopredictstrainandstressesproducedduringheattreatmentofferrousalloys,usingthefiniteelementmethod.Fromacomputationalpointofview,thisproblemrequirescoupledthermal-metallurgical-mechanicalanalysis,modeledasnon-stationaryandnonlinearprocesses.Calculationofmetallurgicalpropertiesiscoupleddirectlywiththermalanalysis,becausethermalpropertiesdependonmicrostructuralcomposition.Metallurgicaltransformationsoccurringduringtheprocessareimportantinthedevelopmentofinternalstressesanddistortions,becausetheychangemechanicalpropertiesofthemetal,butalsoinvolvespecificvolumechangesthatarecoupledtothermaldilatations.Themicrostructuresformedduringheattreatmentdependonalloycomposition,temperaturesandcoolingrate,ascanbeobservedinTTTorCCTdiagrams.Foragivenmaterial,theirpropertiescouldbeconsideredasfunctionsoftemperatureandmicrostructuralcompositionand,inasecondanalysis,asfunctionsoftemperatureandtime.Takingintoaccountthedifficultiestoobtainmaterialparameterstomodelaccuratelytheirpropertieswithmoresophisticatedmodels,apiecewiselinearmodelisproposed.Anumericalexampleappliedtoarealcaseispresented.Mec´anicaComputacionalVol.XXIIIG.Buscaglia,E.Dari,O.Zamonsky(Eds.)Bariloche,Argentina,November200411INTRODUCTIONHeattreatmentofmetallicalloysisacomplexthermomechanicalprocessinvolvingsolidstatemetallurgicaltransformationsthatchangeboththermalandmechanicalpropertiesofmaterials.Thisprocessiswidelyusedinindustrialapplications,toreleaseinternalstresses,reducefragility,improvemachinabilityormodifypropertieslikehardnessorstrength,tosatisfytherequirementsofadefiniteapplication.However,heattreatmentcancause,duringorafterthem,undesirablestrainsandstresses,andalsocrackingofparts.Thisfactmustbetakenintoaccountwhendesigningtheheatingandcoolingsequenceoftheprocess.Numericalsimulationofheattreatmentwassubjectofmanyresearchworks.Someofthemfocusedonthermalandmechanicalanalysisoftheprocess3,4,12,whiletheothersfocusedonaspectsofmaterialmodeling1,8,9,13.Materialmodelswiththeabilitytoaccountforvariationsinthermalandmechanicalpropertiesduetotemperatureandmetallurgicalstructurechangesareakeypointtosimulateaccuratelythethermomechanicalevolutionofpartssubjectedtoheattreatment.Severalmodelsdescribematerialpropertiesasfunctionsofalloycomposition,temperatureandmicrostructure.Othermodelsdescribetheevolutionofmicrostructureasafunctionofalloycompositionandcoolingtime,reproducingTTTorCCTdiagramsfordifferentalloysandchemicalcompositions.Eventhoughadvancedmaterialmodelsareveryusefultocoverabroadrangeofchemicalcompositionsforsomewell-knownalloys(carbonsteels,low-alloysteels,austeniticstainlesssteels),theirefficacyforotheralloysisverylimitedbecauseofthedifficultytoobtainallthecoefficientsneededtorepresentaccuratelytheirbehavior(e.g.forhigh-alloywhiteiron).Inthiswork,wefollowanalternativesimplifiedwaytosimulateheattreatment,usingmaterialpropertiesdefinedasfunctionsoftimeandtemperature,obtainedbymergingTTT/CCTdiagramswithcurvesofdependencyofthermomechanicalpropertieswithtemperature.SimulationsweredoneusingthecommercialfiniteelementsoftwareSAMCEF.Section2.1describesthenumericalmodelusedtosimulatethermomechanicalprocessesinheattreatmentofferrousmetals.Insection2.2,adescriptionoftheproposedmaterialmodelisgiven.Section3presentsanapplicationofthismodeltosimulationofheattreatmentofcentrifugallycast,three-layer,Hi-Chromeworkrolls,commonlyusedinsteelmills.2NUMERICALMODEL2.1ThermomechanicalmodelNumericalanalysisofheattreatmentprocessescanbemadebymodelingthetimeevolutionoftwocoupledproblems:1)athermalone,thatinvolvesheatingandcoolingofpartsandmusttakeintoaccountvariationsinmaterialproperties(thermalconductivityandenthalpy)duetotemperatureandmicrostructuraltransformations,andalsoheatreleasing/absorptionJ.Risso,A.Cardona,A.Anca2(relatedwithlatentheat)duringmetallurgicaltransformations.2)amechanicalone,topredictstressesandstrainsgeneratedbythermalexpansion/contractionproducedbytemperaturechangesandalsobymetallurgicalphasetransformations.Thethermalproblemisnon-linear,becausethermalparametersaredependentoftemperature.Themechanicalproblemisalsonon-linear,becausethermalandtransformation-inducedstrainsoftengenerateplasticdeformations.Inabsenceofverystrongmechanicalperturbationsthatcouldinducemetallurgicaltransformations(e.g.transformationofretainedaustenitetomartensite,inducedbystressesgeneratedbyexternalloads),mechanicalphenomenadonotaffectthermalproperties.Thisfactreleasesthedependencyofthethermalmodelonmechanicalvariables,andenablesustoperformanuncoupledthermalanalysis,followedbyamechanicalanalysisthattakesthermalresultsasinputs.Thedependenceofthethermalproblemonmetallurgicaltransformationsissimulatedwithanenthalpymodelthattakesintoaccountheatcapacityofmetal,andlatentheatexchangeoccurringduringphasechanges.Thedifferentialequationde