THERMODYNAMIC AND KINETIC MODELING OF PRECIPITATION PHENOMENA IN P9 STEELS(3)

growthoftheprecipitateisverysluggish.Whereverpossiblewehavemadeuseofdislocationdensity,grainsizeofferrite,austen-ite,subgrainsizeandprecipitatenucleatingsitereportedintheliterature[18,21].

Theinterfacialenergyoftheprecipitatesisanimportantfac-tordeterminingtheirnucleationandgrowthrates.InMatCalc,interfacialenergyiscalculatedfromthermodynamicdata,basedonthegeneralizedbrokenbondmodel[12]takingintoaccountsizeeffectsofsmallprecipitates[13].Inthisstudy,theinter-facialenergyvaluesofcoherentandsemi-coherentprecipitateswereassumedtobe75-90%oftheonescalculatedforplanarandsharpinterfaces,respectively.Thisisdoneinordertotakeintoaccountofentropiccontributionsduetoatomicmixingacrosstheinterface,whichadditionallyreducestheinterfacialenergyascomparedtothesharpinterface.Nucleationconsideredhereisheterogeneous.Quantitiessuchasdislocationdensity,grainsize,subgrainsizeandtypeofnucleationsite,etc.havegreaterimpactonthesteadystatenucleationrate[7].SinceitisknownthatMX,M23C6,LavesphaseandZ-phasehaveanorientationrelation-shipwithferrite,theyareregardedassemi-coherentprecipitates.Forsimplicityofanalysis,theshapeoftheprecipitates[14]isassumedtobespherical,althoughsomeofthemdevelopcharac-teristicshapes.Duringthesimulation,precipitatesofacertainsizeandcompositionareconsideredasbelongingtoaparticularclass.Individualsizeclassesarecreated,rearrangedanddeletedduringsimulation[12],allowingtomodeltheevolutionofpre-cipitatessizedistribution.Inthisstudy25sizeclasseswereusedinordertoensuresuf cientaccuracyfortheprecipitatesizedis-tribution.

Heattreatmentforthesesteelsstartedwiththesolutioniz-ingaboveAe3.Itisassumedthatallconstituentelementsarehomogeneouslydistributedinthematrixandnoprecipitatesex-istatthesolutionizingtemperature.Afterthesolutionizingthesteelspecimenarecooledlinearlydowntoroomtemperatureatareasonablyhighcoolingrate.ThisisfollowedbytemperingatatemperaturebelowAe1andthencooledtoMstemperature.Finallysteelspecimenareheatedto600 C,whichcorrespondstothethermalexposure(service)temperature.Thethermalex-posureisdonefor100,000h.

Resultsanddiscussion

Thermodynamiccalculations

EquilibriumthermochemicaldataandphasetransformationtemperaturesarecalculatedusingtheGibbsenergydatabaseforsteels,employingThermo-Calc[15]software.ThedatabaseiscreatedaccordingtotheCalphadapproach.Itcontains20ele-mentsviz.Al,B,C,Co,Cr,Cu,Fe,Mn,Mo,N,Nb,Ni,O,P,S,Si,Ta,Ti,VandW.Maindifferencebetweentheexistingcom-mercialdatabasesforsteelsandtheoneusedhereistheinclusionofTaasanalloyingelement.

InTable2calculatedthermochemicaldataandphasetrans-

formationtemperaturesarecomparedwiththecalorimetricdatafrom[16].Calculatedvaluesagreereasonablywellwiththeex-perimentaldata.CalculatedequilibriumphasefractionplotsforE9016andRAFMsteelsareshowninFigure1andFigure2,respectively.

Kineticcalculations

Kineticsimulationsareperformedusingthethermodynamicdatabasetogetherwiththemobilitydatabase,employingMat-Calcsoftware.Themobilitydatabasewasmodi edtotakeintoaccountofpresenceoftantalum.Allsteelsconsideredhereareassumedtobeinnormalizedandtemperedcondition.Normal-izationtemperaturedecidestheaveragesizeofprioraustenitegrains.Thenormalizationtemperatureforthespeci edsteelsareselectedbasedonthecompletehomogenizationtemperature.Thegrainsizes,subgrainsizes,anddislocationdensitiesusedinthekineticcalculationsarelistedinTable3[18,21].PhasesconsideredforthermodynamicandkineticcalculationarelistedintheTable4.SinceMX,M23C6,Laves,Z-phasearethemajorphasesthatarepresentafterseveralhoursofthermalexposure,onlythesephasesareincludedinthekineticcalculations.ThechosennucleationsitesfortheseprecipitatesarealsogivenintheTable4.Thesefourphasesweremadetonucleateintheferrite(matrixphase).

Temperedmartensitehasacomplexmicrostructurethatcon-sistsofvariouskindsofinterfacessuchasprioraustenitebound-aries,martensitepacketboundaries,lath/twinboundariesandsubgrainboundariesinadditiontocarbidesalongboundaries.Thetemperedsteelretainsitshighdislocationdensityduringaustenitetomartensitetransformation.Inthesimulation,precip-itatesareassumedtogrowalongthegrainboundaries,subgrainboundariesanddislocations.Highdislocationdensity,grainandsubgrainfeaturearetakencarebyconsideringferriteasthema-trix.Theprecipitationbehaviorofsteelsselectedforthisstudy,asrevealedbythesimulations,arediscussedbelow.

P91steel:Figure3showsthevariationofthesimulatedphasefractionofprecipitatesduringtheheattreatmentandther-malexposureofP91steel.Fourkindsofprecipitates,viz.MX,M23C6,LavesandZ-phase,appearduringtheheattreatment.MXwhichformsondislocation,grainboundariesandsubgrainboundaries,vesphasestartsappearingatabout100h.MXandM23C6attainssaturationofprecipitationinashorttime.EarlycoarseningoftheM23C6precipitateisevidentfromFigure4.Itsaveragesizeremainsat～100nmduringmosttime.TheaveragesizeofMXprecipitateis～75nm.TheamountofZ-phaseisverysmall.NoticeablecoarseningofZ-phaseisseenafter10,000hofthermalexposureandcontinuestoincreaseinsize,whichisincontrastwiththebehaviorofMXandM23C6

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