THERMODYNAMIC AND KINETIC MODELING OF PRECIPITATION PHENOMENA IN P9 STEELS

Proceedings of ASME Turbo Expo 2011

GT2011

THERMODYNAMICANDKINETICMODELINGOFPRECIPITATIONPHENOMENAINP9STEELS

K.C.HariKumar V.B.Rajkumar

DepartmentofMetallurgicalandMaterialsEngineering

IndianInstitueofTechonlogyMadras

Chennai600036,INDIAEmail:kchkumar@iitm.ac.in

S.Raju

PhysicalMetallurgyDivision

IndiraGandhiCentreforAtomicResearch

Kalpakkam603102,INDIA

ABSTRACT

Thermo-kineticsimulationofprecipitateevolutionduringlong-termthermalexposureinfourdifferentferritic-martensiticheat-resistantpowerplantsteels(P91,P92,E9016,andRAFM)iscarriedoutusingMatCalcandThermo-Calcsoftwares,incom-binationwithanindependentlydevelopedGibbsenergydatabaseandamodi edversionofmobilitydatabaseforsteelsthatcomeswithMatCalc.MXandM23C6arepredictedtoremainasma-jorprecipitatesduringlong-termaginginthesesteels.AveragesizeofMXprecipitateisfoundtovarybetween10-100nmdur-ingtheaging,whileM23C6exceeds100nmafter100,000hofthermalexposureat600 C.Thesimulatedprecipitationsequenceandprecipitatesizeevolutionduringthermalexposureareingen-eralagreementwithavailableexperimentaldata.Itisexpectedthatthecalculationspresentedheregivesinsightintolong-termmicrostructuralstabilityofferritic-martensiticsteelsunderser-viceconditions,whichareotherwisedif cultestablishbyexper-imentsalone.

Introduction

Thereisanurgentneedtoimprovethethermalef ciencyoffossilfuelaswellasnuclearpowerplants,mainlyduetoen-vironmentalconsiderations.Thiscanbeachievedbyincreasingoperatingtemperatureandpressureofthepowerplants.Inthis

contextpipematerialsthatcanperformwellatelevatedtempera-tureandpressurearedesirable,withoutcompromisingsafetyas-pects.Plantoperationsathighertemperaturesinevitablyrequiresthedevelopmentofheat-resistantalloyswithahighercreeprup-turestrengthatanacceptablelevelofcreepductility.Inthisre-gard9-12%Crferritic-martensiticheatresistantsteelswithotheralloyingadditionsareidealmaterialsowingtotheirhighthermalconductivity,lowthermalexpansioncoef cientandlowsuscep-tibilitytothermalfatigue.

Itisgenerallyacceptedthatferriticandausteniticsteelsareusefuluptoabout620and675 C,respectively,purelyfromthecreepstrengthpointofviewatasteampressureofabout35MPa[1].Theroleofprecipitationphenomenoninenhancingcreepstrengthofheat-resistantsteelsiswellestablished[2].Inordertoimprovethecreepstrengthitisnecessarytoensureauni-formdistribution neprecipitateswithgoodlong-termhightem-peraturestability.Forexample,austeniticheat-resistantsteelsareknowntoexhibitquitecomplexprecipitationbehaviorin-volvingprecipitatessuchascarbides,nitridesandintermetallicphases[3].Inthecaseof9-12%Crferritic-martensiticsteels,thecreepstrengthisduetotheirspecialmicrostructuralfea-tures.Duetodiffusionprocessesatelevatedtemperatureser-vice,microstructuralchangestakesplaceleadingtodeteriorationinstrength.Inferritic-martensiticsteelsstrengthdeteriorationisattributedtocoarseningofM23C6precipitatesandtransfor-mationofMXprecipitatesintoZ-phase(Cr(V,Nb,Ta)N).Inthis Address

allcorrespondencetothisauthor.

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

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

precipitates.

P92steel:Figure5showsthevariationofthephasefrac-tionofprecipitatesduringtheheattreatmentandthethermalex-posureat600 CofP92steel.Fourprecipitates,MX,M23C6andZ-phaseandLavesphaseappearinthemicrostructure.Z-phasestartsnucleatingrightafterthetempering.TheamountofZ-phasestartstoincreaseslightlyafter10,000hofthermalexpo-sureandcontinuestoincreaseuntiltheserviceterminates,whichisincontrastwithMXandM23C6exhibitingthesaturationofprecipitationinashorttime[19].Lavesphase,thoughsmallinquantity,formsduringthethermalexposureandkeepsoncoars-ening(Figure6).ThisisattributedtohighamountofWandMointhissteel.TheaveragesizeoftheLavesphaseprecipitatesreaches～1µmatabout100,000h.TheprecipitationofLavesphasecanimprovecreepstrengthifitscoarseningdoesnotpro-ceedtoofast.ThispositivebehavioroftheLavesphaseisseeninNF616(similartoP92)steel.However,thepresenceoflargeM23C6andLavesphaseparticlesaboveapproximately0.5µmaregenerallyconsideredtobedeleterious[20].

E9016steel:Figure7showsthevariationofthephasefractionofprecipitatesinthecaseofE9016steel.LikeinthecaseofP91steel,fourkindsofprecipitates,MX,M23C6,LavesandZ-phase,appearduringthecourseofthermalexposure.PhasefractionofM23C6precipitatesremainconstantafterattainingtheequilibriumvalueduringthethermalexposure.Signi cantamountofLavesisseenfromabout100honwards.TheamountofZ-phasestartstoincreasesigni cantlyafter10,000hofther-malexposureandcontinuestoincreaseuntiltheservicetermi-nates.ItiswellknownthatduringserviceZ-phasegrowsattheexpenseofMXin9-12%Crferritic-martensiticheat-resistantsteelscontainingNborVandahighcontentofnitrogen[17].ThisfactisclearlyevidentfromFigure7.Althoughthereisnosigni cantcoarseningseeninthecaseofMXprecipitates,Z-phase,LavesandM23C6seemtoundergocoarseningoncontin-uedthermalexposure(Figure8).

Reducedactivationferritic-martensitic(RAFM)steel:Figure9showsthevariationofthephasefractionofprecipitatesasafunctionoftimeforRAFMsteel.TheamountofM23C6,whichappearsduringearlystagesoftheheattreat-ment,remainsnearlythesameevenafter100,000hofther-malexposure.PhasefractionofZ-phaseexceedsthatofMXallthroughout.IncreaseinfractionofZ-phasebeyond10,000hattheexpenseofMXprecipitateisclearlyidenti ableinFig-ure9.CoarseningoftheM23C6precipitatetowardslaterstagesofthermalexposureisevidentfromFigure10.ThereisslightreductionintheaveragesizeofMXprecipitatesbeyond10,000h.Figure11showsvariationinthecompositionofM23C6as

afunctionoftime.ItisseenthatitsCrcontentincreasesandthereisacorrespondingdecreasetheFecontentasthethermalexposureadvances[22].

Conclusions

Comparisonofcalculatedphasetransformationtempera-tureswithexperimentalvaluesshowsthattheGibbsenergydatabaseusedhereisreliableinpredictingphasetransformationfeaturesofferritic-martensiticsteels.M23C6isamajorcarbideinallthesteelsconsideredhere,followedbyMXcarbide.InP91andRAFM,Z-phaseisalmostnon-existent.Whenitispresent,itsamountincreasesattheexpenseofMXcarbidesduringther-malexposure.E9016ismostseriouslyaffectedwithcoarseningoftheZ-phase.InP92mostsigni cantcoarseningisfortheLavesphase,althoughitsamountisquitelow.InmostvarietiesofsteelconsideredhereM23C6tendstoresistcoarseninguptoabout10,000hafterwhichittendstocoarsen.ItisalsoseenthatinM23C6theamountofCrincreasesandthereisacorrespondingdecreasetheFecontentasthethermalexposureadvances.Thekineticsimulationagreeswiththeevolutionofelementalabun-danceintheM23C6phaseinRAFMsteelobservedexperimen-tally.

Acknowledgement

Authorsthankfullyacknowledgemanyfruitfule-maildis-cussionswithProfessorErnstKozeschnik,MatCalcdeveloper,ViennaUniversityofTechnology,Austria.

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POSITIONS(INWT.%)OFSELECTEDSTEELS.

ElementP91P92E9016RAFMAl0.011––0.0036C0.100.090.060.091Cr8.448.729.249.05Cu0.11––0.005Mn0.46–1.370.56Mo0.460.451.050.0036N0.0080.050.030.0206Nb–0.060.030.0039Ni0.17–0.095–P0.008–0.05–S0.002–0.001–Si0.490.160.30.05Ta–––0.063Ti–––0.0024V0.0010.0210.170.226W

–

1.87

–

1.00

[20]V´yrostkov´a,A.,Homolov´y,V.,Pecha,J.,andSvoboda,M.,

2008.“PhaseevolutioninP92andE911weldmetalsduringageing”.Mater.Sci.Eng.A,480(1–2),pp.289–298.

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E.,Vijayalakshmi,M.,Rao,K.B.S.,andRaj,B.,2010.“Developmentandcharacterizationofadvanced9Crfer-ritic/martensiticsteelsfor ssionandfusionreactors”.J.Nucl.Mater.,Inpress.

[22]Raj,B.,Rao,K.B.S.,andBhaduri,A.,2010.“Progressin

thedevelopmentofreducedactivationferritic-martensiticsteelsandfabricationtechnologiesinIndia”.FusionEng.andDes.,Inpress.

PARISONOFCALCULATEDTHERMOCHEMICALDATAANDPHASETRANSFORMATIONTEMPERATURESWITHCORRESPONDINGEXPERIMENTALDATAFROM[16].

Steelγ–start

C

γ– nish

C

Hα→γJg 1

Solidus

C

Liquidus

C

Tc

C

Ms

C

Exp.Ac1

P91P92E9016RAFM

Cal.Ae1789857673822

Exp.Ac3864886847871

Cal.Ae3857898799841

Exp.Cal.Exp.Cal.Exp.Cal.Exp.Cal.Exp.

820861799831

1710413

21.616.92020.8

1510151215201457

1430144814371452

1524152715311532

1502150814971509

768741731745

731738720732

400420425450

-Curietemperature

-Martensitestarttemperature

TABLE3.PARAMETERSUSEDFORKINETICSIMULATION.

SteelNormalization1050 C1h1070 C1h1050 C1h980 C0.5h

Tempering750 C2h775 C2h760 C2h760 C1h

Grainsize(µm)α

Subgrainsize

(µm)1

Dislocationdensity(m 2)α1014101410141014

γ

30

γ

1011101110111011

P9130

P9225250.5

E901625251

RAFM20201

TemperatureC

FIGURE1.

EQUILIBRIUMPHASEFRACTIONPLOTFORE9016STEEL.

o

Phasefractions

TemperatureC

FIGURE2.

EQUILIBRIUMPHASEFRACTIONPLOT

FORRAFMSTEEL.

o

FIGURE3.

EVOLUTIONOFPRECIPITATESINP91STEEL.

FIGURE4.

PRECIPITATESIZEDISTRIBUTIONINP91STEEL.

Time [h]

FIGURE5.PHASEFRACTIONPLOTFORP92STEEL.

Time [h]

FIGURE6.PRECIPITATESIZEDISTRIBUTIONINP92STEEL.

FIGURE7.

PHASEFRACTIONPLOTFORE9016STEEL.

FIGURE8.

PRECIPITATESIZEDISTRIBUTIONINE9016STEEL.

FIGURE9.PHASEFRACTIONPLOTFORRAFMSTEEL.

FIGURE10.

PRECIPITATESIZEDISTRIBUTIONINRAFMSTEEL.

FIGURE11.

Time [h]

ELEMENTFRACTIONINM23C6PRECIPITATEINRAFMSTEEL.

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