THERMODYNAMIC AND KINETIC MODELING OF PRECIPITATION PHENOMENA IN P9 STEELS(2)

paperwehavesimulatedlong-termmicrostructuralchangesandtimedependantevolutionofmajorprecipitatesinsomeimportantferritic-martensiticsteelgrades.

Materialsandsimulationmethod

Fourdifferentferritic-martensiticheat-resistantsteelsarechosenforthepresentstudy.ChemicalcompositionsofthesesteelsaregiveninTable1.Theycontainabout9wt.%Cr,whichislowerthantheCrcontentofconventionalausteniticheat-resistantsteels.Theyareair-hardenablewhichcausesausten-itetotransformcompletelyintomartensite.Moimpartsim-provedthecreeprupturestrength,Nbforms neMXprecipitateswhichisstableevenatelevatedtemperature.PresenceofWinP92gradefurtherenhancescreeprupturestrengthandsteam-oxidationresistanceattemperaturesexceeding600 C.

RAFMsteelsareessentiallysimilartomediumorhighchromiumlowcarbonsteelssuchasV,Nbmodi ed9Cr-1Mosteel,butwithamajordifferencewithrespecttoelementspro-ducinglonghalf-lifetransmutantslikeNi,Mo,Nb,Cu,Co,Al,N,etc.Theseelementsarelargelysubstitutedbytheircompara-tivelyloweractivationcounterparts,suchasMn,W,V,Ta,andC.MoisreplacedbyWandNbbyTa.Strictcontrolisexercisedontheradioactivetrampelements(Mo,Nb,B,Cu,Ni,Al,Co,Ti)andontheelementsthatpromoteembrittlement(S,P,As,Sb,Sn,Zr,O).Theseelementsareusuallyrestrictedtoppmlevels.

Simulationoflong-termprecipitateevolutioninausteniticstainlesssteelshasalreadybeenattemptedbyShimetal.[4],usingMatCalcsoftwaredevelopedbyKozeschniketal.[5,6].Simulationofprecipitateevolutionincertainferritic-martensitic9-12%Crsteelsarealsoreportedintheliterature[7,8].Thepurposeofthisstudyistosimulatethelong-termprecipitateevolutioninsomeimportantgradesofferritic-martensiticheat-resistantsteelsforapplicationsaround600 CbyMatCalcsoft-ware,usinganindependentlydevelopedGibbsenergydatabaseforsteelsandamodi edversionofthemobilitydatabasethatisincludedwithMatCalc.

MatCalcusesclassicalnucleationtheoryalongwithOn-sager’sextremumprincipleforsimulatingprecipitateevolution.Ithasanumericalmodeltoclassifyprecipitatesofsameradiusandcompositionnucleatedindifferentintervalsoftime.IntheprecipitationkineticsapproachimplementedinMatCalc,thethemicrostructuralevolutionofthesystemissimulatedwithintheframeworkoftheKampmann-Wagnermodel[9].Accordingly,thetotaltimehistoryisbrokenintoadequatelysmall,isothermalsegments[6].Precipitatesofequalsizeandchemicalcompo-sitionaregroupedintoclasses,foreachofwhichtheevolutioninsizeandcompositioniscalculatedaccordingtotherateequa-tionsderivedfromthethermodynamicextremumprinciple[5].Nucleationofnewprecipitatesistakenintoaccountineachtimestepbasedonamulticomponentextensionofclassicalnucleationtheory[10,11].Accordingtothis,thetransientnucleationrateJ

de nesthenumberofnewnucleicreatedinthetimestep tasJ t.Jisgivenby

J=N0Zβ

exp( G t

kT)exp( τ

)

(1)

whereN0representsthetotalnumberofavailablenucleationsites,kistheBoltzmannconstant,Tisthetemperature,ZistheZeldovichfactor,β istheatomicattachmentrate,τistheincubationtimeandG isthecriticalnucleationenergygivenby

=

16πγ3

G3 G(2)

vol

whereγisthespeci cinterfacialenergyand Gvolisthevol-umeGibbsenergychangeonnucleiformation.γand Gvoland

theircompositionandtemperaturedependenciesareevaluatedusingtheGibbsenergydatabase.Bothquantitiesaremostes-sentialforachievingreliablecalculationofnucleationratesforprecipitationkineticssimulations.ThisissuehasrecentlybeendiscussedbyRadisetal.[10]inatreatmentofmultimodalsizedistributionsinNi-basesuperalloys.AllrequiredquantitiescanbecalculatedfromappropriateanalyticalexpressionsusingtheGibbsenergyandmobilitydatabases.DetailedexpressionsforallnucleationrelatedquantitiesaresummarizedbyJanssensetal.[11].ThenumberofpotentialnucleationsitesN0occurringinequation(1)isdependentonthechoiceiswhethernucleationishomogeneousorheterogeneous.Inthepresentsimulations,possiblechoiceshavebeenhomogeneousnucleationinthebulk,orheterogeneousnucleationondislocations,grainboundaries(GB),subgrainboundaries(SGB),grainboundaryedgesorgrainboundarycorners.Actualnumberofnucleationsitesisgivenbythetotalnumberofatomsinthesysteminthecaseofhomoge-neousnucleation,orbythenumberofatomslocatedatthehet-erogeneousnucleationsitesinallothercases.Fordislocations,thenumberofsitesisgivenbythenumberofatomslocatedatthedislocationlinesinaunitvolume.Thenumberofatomsinthegrainboundarycanbeestimatedfromthetotalgrainorsub-grainareas,whicharegivenbythegrain/subgraindiameterandtheelongationratio.Detailedexpressionsforcalculationofnu-cleationsitesinmicrostructuresarefoundelsewhere[7].Finally,thetotalnumberofpotentialnucleationsitesfromeitherhomo-geneousnucleation,ornucleationatdislocations,grainbound-aries,subgrainboundaries,edgesorcornersenterequation(1).

Inthekineticsimulationthematrixphaseisde ves,Z-phase,M23C6andMXareconsideredtobelikelyprecipitates.Thetransformationoftheaustenitematrixintomartensiteisnotconsidered.InsteadtheprecipitatesareallowedtonucleateintheferritematrixbelowAe1temperatureandal-lowedtogrowtillMstemperatureisreached,belowwhichthe

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