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Computer Model of Phase Transformation From Hot-Deformed Austenite in Niobium Microalloyed Steels

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Computer Model of Phase Transformation From Hot-Deformed Austenite in Niobium Microalloyed Steels

    Computer Model of Phase Transformation

    From Hot-Deformed Austenite in

    Niobium Microalloyed Steels

    Availableonlineatwww.sciencedirect.com

    .,,

    ?:,ScienceDirect

    JOURNALOFIRONANDSTEELRESEARCH,INTERNATIONAL.

    2007,14(2):6669

    ComputerModelofPhaseTransformationFromHot-Deformed

    Aus.

    teniteinNiobiumMicroalloyedSteels

    xuYunbo,YUYongmei,LIUXianghua,WANGGuo-dong

    (StateKeyLabofRollingandAutomation,NortheasternUniversity,Shenyang110004,Liaoning,China)

    Abstract:Basedonthermodynamicsandkinetics,anewmathematicalmodelwasdevelopedtocalculatetheCCTdia

    gramsandthetransformationkineticsinlowcarbonniobiumsteels,inwhichtheeffectofdeformationonthedegree

    ofsupercoolingwastakenintoaccount.Theundercoolingcausedbydeformationisthemajorreasonfortheincrease

    oithestartingtransitiontemperatureduringcontinuouscooling.Thecriticalcoolingrateofbainiteformationiswith

    in25?

    /sforthestudiedniobiumsteelsanddeformationissuitablefortheoccurrenceofDearlite.Theferritevo1

    umefractionincreaseswiththeincreaseoftheausteniteboundaryarea,anddecreaseswiththe

increaseofthecooling

    rate.ThecalculatedCCTdiagramsandthevolumefractionofeachphaseareingoodagreemen

    twiththemeasure

    ments.

    Keywords:lowcarbonniobiumsteel;thermodynamics;supercoolingdegree;continuousco

    olingtransformation:

    computermodel

    Highstrengthlowalloy(HSLA)steelwith

    goodlowtemperaturetoughnessandlowweld

    crackingsusceptibilityisdemandedforstructural use.Thethermomechanicalcontrolprocess(TM

    CP)hasbecomeamajorprocessforproducinghigh strengthsteelplates['.Hence.thecontrolofmi

    crostructurethroughanoptimizationofthechemis

    tryandthemanufacturingprocessisimprtantforthe bestuseofTMCPandtheimprovementoftheme

    chanicalpropertiesofHSLAsteelplates.

    Continuouscoolingtransformationdiagrams andtransformationkineticsplayanimportantrolein selectingareasonablethermomechaniealcontroIprocess. Basedonthesuperelementmodel,Cahnstheory[.and

    Scheilsrulee.thetransformationstarttemperature of7PF,WF,B,andPinlowcarbonniobium

    steelsduringcontinuouscoolingafterhotdeforma

    tionwerepredicted.Furthermore,theeffectsofhot deformationandthecoolingrateorlCCTdiagrams andtransformationkineticswerealsoanalyzed.The predictedresultsareinreasonableagreementwith themeasuredones.Thepresentmodelcanprovidea theoreticalbasisfortheapplicationofTMCP.

1ThermodynamicDescription

    Thermodynamicdatasuchastheequilibrium temperature,thedrivingforcefornucleation,and thefreeenergychangeassociatedwithphasetrans

    formation,theequilibriumcompositionsetc.arees

    sentialrequirementsforthetheoreticalsimulationof transformationkinetics.Inthepresentstudy,the superelementmodelisadoptedowingtoitssimplici

    tyandpopularity.Inthepresentthermodynamic program,FeEX(XiMn,Si,etc.)canbetrea

    tedasasuperelementS,andthemethodsimilarto binaryalloyisusedtocalculatethethermodynamic parameters.

    Deformationcanincreasethedislocationdensity andcanresultinachangeofthefreeenergyof7, andcanmoveupthefreeenergy-compositioncurve. Theincreaseofchemicalpotentialof7,?,caused

    bydeformationis[5]:

    ?一0.5.v(1)

    whereandbareshearmodulusandBurgersvec

    FoundationItem:ItemSponsoredbyNationalNaturalScienceFoundationofChina(505040

    07,50474086,50334010)andDoctorStartup FoundationofLiaoningProvinceofChina(20041009) Biography:XUYumbo(1976

    ),Male,Doctor,AssodateProfessor;E-mail:xuyunbo@mail.neu.edu.en;RevisedDate:

    November24,2005

No.2ComputerModelofPhaseTransformationFromHot

    DeformedAusteniteinNiobiumMicroalloyedSteels?67?

tor,respectively;andDisthedislocationdensity

    (1/cm.);VTismolarvolumeof7.

    2DeterminationofIncubationPeriod

    Duringcontinuouscoolingtransformation, whenthetemperatureislowerthanA3,7isinthe incubationperiodoftransformation,andwhenthe temperatureislowerthanA|3,thedproeutectoid transformationstarts.Thepearliteandbainite transformationshavesimilarprocesses. Scheilsadditivityruleprovidesamathematical relationbetweenthenonisothermalandisothermal

    transformations.Transformationincontinuouscool

    ingcanbeconsideredasthesumoffewisothermal transformations.Thestartingtransitiontemperature duringcontinuouscoolingcanbecalculatedusing Eqn.(2).

    \

    '1一一一'

    ,

    I////.

    k,f

    Time

    Fig.1Diagramdepictingincubationperiodand degreeofsupercoolingunderundeformed anddeformedconditions

    BhadeshiainRef.I-6].

    (2)3TransformationKineticsModel

    whereAtfisslightincrementintime;andrisincu bationtimeoftransformationatdifferenttempera tures.

    Theincubationperiod,r,isdeterminedby rA(3)

    where?Tisdegreeofsupercooling;andA,Q,and maretheconstantsrelatedtothealloyingcomposi

    tion.Forthestudiedsteelgrade,theseconstants canbeobtainedbyexperiment.Fig.1showsthe effectofhotdeformationontheincubationperiod andthedegreeofsupercooling,where,Ad3isthe thermodynamicequilibriumtemperatureofaustenite toferritetransformationwhileconsideringdeforma

    tion.Ifdeformationisnotconsidered,thistempera

    tureisAe3.Deformationcanincreasethethermodynam

    icequilibriumtemperatureandthedegreeofsupercoo

    1ing.Hence,whendeformationoccurs,Eqn.(4)is satisfied.

    ?T一?Ti+?Tid(4)

    where?Tiistotaldegreeofsupercooling,andATi and?Tidaredegreesofsupercoolingduetocooling anddeformation,respectively.Thedetermination methodofpearlitetransformationstartis:whenthe carboncontentinaustenite,XachievesX,and the7Ptransformationincubationperiodisachieved. TheKRCmodelcanbeusedtocalculatetheequilib

    riumcarboncontentofcementiteformation(X). Theonsetofwidmanst~tternferriteandbainitetrans

    formationisdeterminedusingthemethodproposedby Attheearlierstageofdtransformation,the processiscontrolledbythenucleationgrowthmech——

    anism.AccordingtoCahnstransformation,theki

    neticsequationisexpressedas

XF11exp(7tIsSG;/3)(5)

    Atthelatterstage,thekineticsequationispro

    videdaccordingtothesitesaturationmechanism.

    XF21exp(2S,GFt)(6)

    whereXF1andXF2arethetransformedfractionsin theearlyandlatestageofaustenitetoferritetrans

    formationrespectively.andtistheisothermalhold

    ingtime.Thecontinuouscoolingtransformationis consideredasthesumoftheshortholdingtimesat successivetemperatures.S7istheequivalentgrain surfaceareaofunitvolumeof7,thatis,thebound

    aryareaofthedeformed7grainplusthedeforma

    tionband.Thecalculationmethodisshowninthe followingequation:

    s12j..(1--p)/一一{l+[(1

    Y./(1--p)3/El(1--p).z.

    y./(1p).]}.dxdy+Ae.(7)

    wherePisreduction;Aisconstant;d7isaverage austenitegrainsize;istruestrain;andIsisnucle

    ationrateof,anditsdeterminationmethodcanbe foundinRef.E73.

    Is-XeXpeXpl

    whereRandTaregas

    perature,respectively;

    K2]

    RT(AGF).l(8)

    constantandabsolutetern

    K1andK2areconstantsto

    ?ll&??g?

L

    

    ??

?68?JournalofIronandSteelResearch,InternationalVo1.14

    bedeterminedbyexperiment;D.isdiffusivityofC in7;andGFisgrowthrateofa,whichcanbecalcu

    latedusingtheZenerHillertequation~.

    Gr一警?u下一i9)

    whereandzareequilibriumconcentrationsof Cin7anda,respectively;zisaustenitematrix concentration;andK3isaconstant.

    Assumingthatpearliteandbainitetransforma

    tionsarecontrolledbythesaturationofthenuclea

    tionsite,thesecanbeexpressedbysimilarequa

    tions[.

    XP(B)1exp(2STGP(B))(10)

    whereGp(B)isgrowthrateofpearlite(bainite). 4ResultandDiscussion

    CCTdiagramsoftheinvestigatedsteelfromde

    formedausteniteandundeformedaustenitewere measuredusingtheGleeblel500thermomechanical simulator.Thefirstprocedureisasfollows:rehea

    tingthespecimensto1150?.holdingfor5minfor

    austenitizing,coolingto1000?.andthenafter

    holdingfor5s,coolingthespecimenstoroomtem

    peraturewithvariouscoolingrates(0.520?/s).

    Thesecondprocedureis:afteraustenitizing,defor

    mingto42at920?and33at850?,andsub

    sequentlycoolingwithvariouscoolingrates.The

    phasetransformationpointsweremeasuredusinga dilatometerandmetallography.

    4.1InfluenceofdeformationonCCTcurve Thecomputedcontinuoustransformation-time

    (CCT)diagramof0.11C-O.85Mn-0.024Nb(mass percent)steelisshowninFig.2;Fig.2(a)repre- sentstheCCTdiagramfromundeformedaustenite, andFig.2(b)representsthatfromdeformedaus

    tenite.Thestartingtemperaturesofa,WF,P, Bdecreasewithincreasingcoolingrate,andthenin

    creasebecauseofthedeformation.Forthestudied niobiumsteel,thetransformedphaseconsistsoffer

    riteandalittlepearliteatlowcoolingrates,and bainitebecomesthesecondphaseinsteadofpearlite whenthecoolingratesarehigherthanonefixedval

    He.Thevalueis2?/sforundeformedaustenite.

    andishigherforthedeformedaustenite.Inother words,deformationissuitablefortheOCCurrenceof pearlitetosomeextent.Thereasonisthatdeforma

    tionpromotestheformationofferrite,increasesthe carboncontentinaustenite,and?acceleratesthepre

    cipitationofcementite.ThecomputedCCTdiagram isingoodagreementwiththatobserved.asshown inFig.2.

    10100

    4.2Influenceofdeformationandcoolingontrans

    formationkinetics

    Austenitetoferritetransformationisacceler

    atedwiththerefinementoftheaustenitegrainsize and/ortheincreaseoftheamountofdeformationin

    thelowtemperatureausteniteregion.Thegrain boundariesandthedeformedsubstructuresinthe graininterioractasnucleationsitesofferrite.Hence, theeffectiveausteniteboundaryareaperunitvol

    ume,ST,iscloselyrelatedtothekineticsoftrans

    formationfromdeformedaustenite.

    Fig.3showstheinfluenceofthecoolingrate andtheeffectiveboundaryareaontheferritetrans

    formationfractionfor0.11C-0.85Mn-0.024Nbstee1. AtlowSvalue,i.e.1ightcontrolledrolling,the transformedvolumefractionofferritephaseisrela- tivelysmal1.Thevolumefractionofferritephasein

    creaseswiththeincreaseoftheSvaluebytheheav

    Ycontrolledrolling.Theeffectofthecoolingrateon Timps

    (a)Fromundeformedaustenite;(b)Fromdeformedaustenite Fig.2Computedcontinuous-transformation-timediagramof0.11(2-0.85Mn-0.024Nbstee

    l

    p/aBJau10

No.2ComputerModelofPhaseTransformationFromHot-DeformedAusteniteinNiobium

    MicroalloyedSteels?69?

    Fig.3Influenceofcoolingrateandeffectiveboundary areaontransformationfraction

    thevolumefractionislargerthantheSTvalue.With theincreaseofthecoolingrate,theferritevolume fractiondecreases.Thecomparisonofthecalculated Volumefractionofthetransformedmicrostructure withthemeasuredoneisshowninFig.4.Thecal

    culatedresultsareinreasonableagreementwiththe

measuredresults.

    5Conclusions

    Onthebasisofthermodynamicsandkinetics,fl newmodelhasbeendevelopedtopredicttheeffectof hotdeformationandcoolingonthetransformation 0204060100

    Predictedphasefracfion~%

    4Cmnm~ofcalculatedvolumefractionoftransformed microstructurewithmeasuredone

    kineticsinlowcarbonniobiumstee1.Thefollowing conclusionsareobtainedbasedonthecalculatedand measuredresults:

    (1)Theeffectivedegreeofsupercoolingbefore transformationconsistsoftwoparts:Oneisthe temperatureundercooling,andtheotheristhede- formationundercooling.Thelatteristhemainrea

    sonfortheincreaseofthestartingtransitiontemper

    atureduringcontinuouscoolingunderthedeforma- tioncondition.

    (2)Thecriticalcoolingrateofbainiteforma

    tioniswithin25?/sforlowcarbonniobium

    steels.Deformationissuitablefortheoccurrenceof pearlitetoflcertainextent.

    (3)Thevolumefractionoftheferritephase increaseswiththeincreaseoftheSvalue,andde

    creaseswiththeincreaseofthecoolingrate.The effectofthecoolingrateonthevolumefractionis largerthanthatofSTvalue.

    (4)ThecalculatedCCTdiagramsandthevol

    umefractionofeachphaseareingoodagreement

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