Carbon content evolution in austenite during austenitization studied by in situ synchrotron X-ray diffraction of a hypoeutectoid steel

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To cite this version:

Denand, B. and Esin, V.A. and Dehmas, M.

and Geandier, G. and Denis, S. and Sourmail, T. and Aeby-Gautier,

E. Carbon content evolution in austenite during austenitization

studied by in situ synchrotron X-ray diffraction of a hypoeutectoid

steel.

(2020) Materialia, 10. 100664. ISSN 25891529

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Full Length Article

Carbon

content

evolution

in

austenite

during

austenitization

studied

by

in

situ

synchrotron

X-ray

diﬀraction

of

a

hypoeutectoid

steel

B. Denand

a,c,∗

_{, V.A. Esin}

b

_{, M. Dehmas}

d

_{, G. Geandier}

a,c

_{, S. Denis}

a,c

_{, T. Sourmail}

e

_,

E. Aeby-Gautier

a,c

a_Institut_Jean_Lamour,_UMR7198_CNRS,_{Université de}_Lorraine,_Nancy,_France

b_MINES_ParisTech,_PSL_University,_Centre_des_Matériaux_(CMAT),_UMR₇₆₃₃_CNRS,_Evry,_France

c_Laboratory_of_Excellence_for_Design_of_Alloy_Metals_for_Low-mass_Structures_(‘DAMAS’_Labex),_{Université de}_Lorraine,_France d_CIRIMAT,_{Université de}_Toulouse,_CNRS,_Toulouse,_France

e_{Ascometal-CREAS}_(Research_Centre),_Hagondange,_France

a

r

t

i

c

l

e

i

n

f

o

Keywords:

Austenitization

InsitusynchrotronX-raydiﬀraction Latticeparameter

Carboncontent Thermo-Calc

a

b

s

t

r

a

c

t

UsinginsituhighenergyX-raydiﬀractionstudyofausteniteformationinhypoeutectoidsteelwiththree diﬀer-entinitialmicrostructures(ferrite-pearlite,temperedmartensiteandbainite),thelatticeparametersofferrite, cementiteandausteniteareexaminedonheatingat0.25,10and100°C/s.

Thelatticeparametersofferrite,cementiteandaustenitedonotvarylinearlywiththetemperature,especially, inthetemperaturerangewheretheaustenitizationtakesplace.Fortheaustenite,itissuggestedthatthedeviation fromthelinearityismainlyassociatedtothecarboncontentvariation.UsingDysonandHolmesequation,the carboncontentinausteniteisevaluatedforanymomentoftheausteniteformationforeachinitialmicrostructure andallheatingrates.

Fortheferrite-pearlitemicrostructureheatedat0.25°C/s,thecarboncontentinausteniteaftercomplete cementitedissolutioncorrespondstothatofpearlite.Moreover,arapiddecreaseincarboncontentintheaustenite isobservedduringtheﬁrststageoftheaustenitization(simultaneousdissolutionofferriteandcementite)followed byaslowfurtherdecreaseduringthetransformationoftheremainingferrite.Theobtainedresultsarediscussed usingthermodynamiccalculations.

1. Introduction

Theservicelifeofcrankshaftsforautomotive industrycan be in-creasedbysurfacehardeningvia aninduction heattreatment [1,2]. Suchalocalheattreatmentleadstoaformationofaustenitecloseto thesurfacewhichfurthertransformsintomartensiteuponsubsequent quenching.Therefore,theresultingsurfacelayerhasahigherhardness incomparisonwiththatofthebulk.Inaddition,retainedcompressive stressesaregeneratedinthesurfacelayer(mainlyduetothemartensitic transformationinthatarea),optimalforthepropertiesofcrankshafts use[3].

Therequiredheattreatmentshouldbefastenoughtolimitthe vol-umeofthematerialtransformedintoaustenite(closetothesurface)on heating.Typicalheatingratesvaryfrom30toover100°C/s.Inthese conditions,theinitialmicrostructureofthesteelmayaffectthe austeni-tizationkineticsduetodifferencesininterfacemigrationandinterstitial andsubstitutionalelementsredistributionindifferentmicrostructures. Evenforafullyausteniticlayer,thechemicalcompositionmaypresent localheterogeneitiesduetoinitialmicrostructurefeaturesleadingthus

tolocaldifferencesinfinalmicrostructurewithdifferentlocal mechani-calproperties.Itisworthnoting,thatmostofinvestigationsreportedin literaturehavebeencarriedoutontheaustenitizationofsteelswith ini-tialferrite-pearlitemicrostructure[4–14].Theanalysisofaustenite for-mationforthesamesteelhavingdifferentinitialmicrostructuresandfor differentheatingratesisoftechnologicalandfundamentalimportance. Inthis scope,ourprevious studyreportedon thekineticsof austen-iteformationconsideringthreeinitialmicrostructures(ferrite-pearlite, temperedmartensiteandbainite)ofthesamehypoeutectoidsteeland fiveheatingrates(0.25,1,10,60and100°C/s)[15].TheuseofHigh EnergysynchrotronX-RayDiffraction(HE-XRD)[16]allowedto char-acterizethephasefractionevolutionofallphasesandhighlightedtwo stepsintheausteniteformation[15]:(i)thesimultaneous transforma-tionofferriteandcementiteintoaustenite,and(ii)thetransformationof theremainingferriteintoaustenite.Foragivenheatingrate,thekinetics ofeachstepwasshowntobedependentontheinitialmicrostructure.

Inadditiontothenatureandamountofphasesformed,theRietveld refinementofdiffractionpatternsgivesalsoinformationaboutthe lat-ticeparametersandwidthsofdiffractionspeaksfordifferentphasesfor

∗_{Corresponding}_author_at:_Institut_Jean_Lamour,_Université_de_Lorraine,_CNRS,_UMR7198,₅₄₀₁₁_Nancy_Cedex,_France.

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Table 1

Chemicalcomposition(wt.%)ofthe37MnCr4-3steelused.

Fe C Si Mn S Ni Cr V Mo Cu Al

Bal. 0.356 0.253 1.285 0.024 0.208 0.652 0.005 0.065 0.172 0.018

anymomentduringheatingandtheausteniteformation.Togetinsight intothetransformationfeatures,thepresentpaperfocusesonthe evo-lutionoflatticeparametersofaustenite,ferriteandcementitetobeable toestimatethecarboncontentevolutionsinthephases.

It is worth noting that a recent studyattempted to analyze the evolutionof austenitelatticeparameterduringaustenitizationof the same50CrMo4steelhavingferrite-pearliteandsoftannealedinitial mi-crostructuresclosetoequilibriumstate[14].InsituHE-XRDwasused onheatingwiththeratesof1,10and100°C/s.Adecreaseinaustenite latticeparameterwasobservedatthebeginningof theaustenite for-mationuntilaminimumvaluefollowedbyfurtherlinearincreasewith temperature.Suchachange inaustenitelatticeparameterwas quali-tativelyattributedtotheevolutionofaustenitechemicalcomposition. However,anyattemptwasnotdonetoquantifyaustenitecarbon con-tentorlatticeparameterevolutionofferritecementiteandaustenite, andonlypossibleexplanationsweregiven.

InthepresentworkanaccurateanalysisofX-raydataiscarriedout usingRietveldrefinement.Differentassumptionsconcerningthe evolu-tionoflatticeparametersofferrite,cementiteandausteniteare care-fullyanalyzedtobeabletoobtaintheaustenitecarboncontentatany momentofthetransformationfordifferentheatingrates.Besides, non-equilibriumtemperedmartensiteandbainitemicrostructuresare inves-tigatedtogetherwithferrite-pearliteinitialmicrostructure.

2. Material

Thesteelusedinthepresentworkisa37MnCr4-3,whichwas man-ufacturedbyAscometalCREAS.Thechemicalcompositionwas charac-terizedonforgedbarsusingopticalemissionspectrometryand combus-tion(LECO)analysisforaccuratemeasurementsofcarbonandsulphur contents(Table1).Thesteelwasmadeavailableashotforgedbarsof approximatediameter40mm.Detailsofthefabricationprocesshave alreadybeenreportedin[15].

Toproducediﬀerentinitial microstructures,theforgedbarswere austenitizedat850 °Cfor1handfurthersubjectedtodiﬀerentheat treatments.These thermal treatments have already been detailedin [15],butwillneverthelessbesummarizedforeaseoflegibility.To ob-tainferrite-pearliteinitialmicrostructure,thesteelwasaircooledfrom austenitizingtemperaturedownto625°Candheldatthistemperature for1h.Thetemperedmartensiterequiredoilquenchingatroom tem-peraturefromaustenitedomainfollowedbyatemperingat500°C dur-ing1h.Thebainitemicrostructurewasobtainedduringanisothermal soakinginasaltbathat450°Cduring30minafteraustenitizing.

Thesamplesusedinthisstudyweretakenatthemidradiusofthe barsforeachinitial microstructurein ordertoavoid decarburization phenomenonatthesurfaceofthesebars.Theseinitialmicrostructures obtainedbyScanningElectronMicroscopy(SEM)arepresentedinFig.1. Fig.1(a)showstheinitialferrite-pearlitemicrostructurewhereblack regionsarethefreeferriteandgreyregionsarethepearlite.Volume frac-tionofferriteandpearlitecanbedeterminedbyimageanalysisbased oncontrast threshold.Themeanphase fractionobtainedforthefree ferriteis20%andthatforthepearliteis80%.Theinterceptsmethod allowedustoestimatethesizeofmeanpro-eutectoidferritegrainsto beof10μm.Fortheinitialtemperedmartensiteandbainite microstruc-tures(Fig.1(b)and(c)),itwasnotpossibletodistinguishthediﬀerent phasesbySEM.

HE-XRDanalysisrevealedthepresenceofabout2–3wt.%of cemen-titeforthethreeinitialmicrostructuresand3wt.%ofretainedaustenite inthebainiticmicrostructure.

3. Experimentaltechniques

Experiments were carried out at the Deutsches Elektronen-Synchrotron(DESY,Hamburg,Germany)onthebeamlineP07 of PE-TRAIII.ADIL805A/DdilatometerfromTAInstrumentwasusedto ap-plythethermal treatments.Threelinearheatingrates (0.25,10 and 100°C/s)wereimposeduntil900°Cfollowedbygasquenching.

Thesampleswerehollowcylindersof10mmlengthwhosethe ex-ternaldiameterwas4mmandthethicknesswas0.5mminorderto reduceradialthermalgradient.

Induction heatingwasemployed duringtheexperiments and the temperaturewascontrolledusingS-typethermocouplecentrallywelded atthesurfaceofthehollowcylinder.Inordertohaveagood correla-tionbetweenthetemperatureacquisitionandtheDebye-Sherrerrings recordedduringthethermaltreatment,theX-raybeamcrossedthe sam-pleintheareaclosetothermocouple.TheDebye-Scherrerringswere ob-tainedbyusingamonochromaticbeamof100keVand2Dimageplate detectorsituatedatabout1.5mawayfromthesample.Apreliminary calibrationwithCeO2powderwascarriedouttodeterminethevalues

requiredforfurtherX-raydataanalysissuchasthedistancebetweenthe sampleandthedetectororthewavelengthwhichwas0.123984Å inthis case.Thebeamsizeof1.0×1.0mm2_allowed_getting_a_reasonably_good resolutionandfastacquisitiontimeforthehighheatingrates.Indeed, twomodeswereemployedtothediﬀractionpatternrecording:aslow modewithanacquisitiontimeof3.5sfortheheatingrateof0.25°C/s andafastmodewithanacquisitiontimeof0.1sfortheheatingratesof 10and100°C/s.Fortheslowmode,theacquisitiontimeincludedthe shutteropeningandclosing,theacquisitionofexternalparameterasthe temperature,andthedataerasingfromthedetector.Inthefastmode, theshutteropenedatthebeginningoftheexperimentandclosedatthe end;anyexternalparameterwasnotrecordedduringtheacquisition.

Thefastmodeledthustoanuncertaintyintemperaturevaluewhich canbecalculatedasΔ𝑇=±0.1 × 𝑉_ℎ,whereV_h(°C/s)istheheating rateand0.1(s)istheacquisitiontimeinfastmode.

Itisworthnotingthatforthepresentstudythreeheatingrateswere selected:0.25,10and100°C/swhile1and60°C/sheatingrateswere usedaswellinthestudyonaustenitizationkineticsinthesamesteelin [15].

TheDebye-Scherrer ringsgiveinformationonthesample crystal-lographyatanymomentduringthethermalpath.Thecomplete inte-grationoftheseringsleadingtoconventional1-Ddiffractogramswere madeusingtheFit2Dsoftware.Then,thediffractogramswereanalyzed byRietveldrefinement[17,18]withtheFullProfsoftware[19].

ThestartingstructuresfortheRietveldanalysisconsistedofferrite andcementitefortheinitialferrite-pearliteandtemperedmartensite microstructures,andofferrite,cementiteandaustenitefortheanalysis ofthebainiticmicrostructure.Moredetailsconcerningtheprocedureof Retvieldreﬁnementcanbefoundin[15]

ForeachXRDpattern,thefollowingparameterswerereﬁned:scale factors,massfractions,FWHM(fullwidthathalfmaximum)andlattice parameters.

4. Results

Thekineticsofausteniteformationasfunctionofinitial microstruc-ture andheatingratewasreportedin detailsin[15].Werecallhere themainresultsandconclusionsrequiredforthefurtheranalysisofthe latticeparametersevolutions.

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B.Denand,V.A.EsinandM.Dehmasetal.

Fig. 1. Initial(a)ferrite-pearlite,(b)bainiteand(c)temperedmartensitemicrostructuresoftheinvestigatedsteelasobservedbySEM(standardmetallography preparationand2%Nitaletching).

Table 2

Thetemperaturesofthestart(AC1)andend(AC3)ofausteniteformationonheatingaswellasthetemperatureoftheendoftheﬁrststageofausteniteformation (T1)accordingtothedataobtainedfromHE-XRDexperimentsin[15]fordiﬀerentinitialmicrostructuresandheatingrates.

Heatingrate(°C/s) Ferrite-pearlite Temperedmartensite Bainite

AC1(°C) T1(°C) AC3(°C) AC1(°C) T1(°C) AC3(°C) AC1(°C) T1(°C) AC3(°C)

0.25 740 753 790 736 758 774 736 763 770

10 761 792 822 743 763 779 741 769 790

100 781 843 854 753 788 810 743 789 810

Table 3

Volumecoeﬃcientofthermalexpansionofcementiteinthetemperaturerangefrom450to600°C,andlinearcoeﬃcientofthermalexpansionofferriteandaustenite inthetemperaturerangewherenotransformationoccurs.

Coeﬃcientofthermalexpansion(10−6_K−1₎ _Initial_{microstructure} _Literature_data

Ferrite– pearlite Bainite Temperedmartensite

Volume,cementite 54 56 54 46[25],58[26]

Linear,ferrite 16.4 16.2 16.1 14–16[20,21],16.3[23],16.8pureiron[23],16[25]

Linear,austenite 24.7 24.9 24.4 20–23[20],24[21]

Thetemperaturerangeofausteniteformationonheatingfor diﬀer-entconditionsisgiveninTable2.Inordertoobtainagoodconﬁdence onthesetemperatures,thestartofaustenitization(AC1)istakenfora

massfractionof3%ofaustenitecreatedandtheferritedissolutionis consideredascompleted(AC3)for95%ofausteniteformation.

ThedatareportedinTable2clearlyevidencethatthe transforma-tionkineticsisdependingontheinitialmicrostructure,mainlythesize ofthedifferentmicrostructureconstituents[15].Thephasefraction evo-lutionsshowtwostagesinthekineticsofausteniteformation.Thefirst onecorrespondstothesimultaneousdissolutionofferriteand cemen-tite;thesecondonetothedissolutionoftheremainingferrite.The tem-peratureoftheendofthefirststage(T1)isrecalledinTable2.This

temperatureisdependentontheinitialmicrostructureandheatingrate anditsvariationwasattributedtodiﬀerentsizeofcementiteparticles indiﬀerentinitialmicrostructures[15].

Togetherwithphasefractions,theresultsofRietveldrefinement in-formaboutevolutionofthemeanlatticeparametersofferrite,cementite andaustenite.Thosearefurtheranalyzedanddiscussedconsideringthe differentoriginsoflatticeparameterevolution:thetemperature varia-tion,theelasticstrainsand/orthevariationofchemicalcompositionof differentphasesduringaustenitization.

4.1. Meanlatticeparametersonheating

Thevariationofmeanlatticeparametersofferriteandaustenite dur-ingheatingwitharateof0.25°C/sisgiveninFig.2forthethreeinitial microstructures.Forcementite,thechangeinunitcellvolumeon heat-ingisreportedinFig.3forthesameconditions.Thevaluesofapparent coeﬃcientsofthermalexpansion,obtainedinthetemperatureranges

wherenotransformationoccurred,aresummarizedinTable3forall phases.1

Fortheferrite-pearliteandtemperedmartensiteinitial microstruc-turesthatcontainamixtureofferriteandcementite,themeanlattice parameterofferriteincreaseslinearlywithtemperatureupto735°C. Between735°Candaround760°C,intheﬁrststageoftheaustenite formation,themeanlatticeparameterofferriteslightlydeviatesfrom thelinearbehavior,withadecreaseintheapparentCoeﬃcientof Ther-malExpansion(CTE).Above760°C(Fig.2(b)),inthesecondstageof thetransformation,thelatticeparameterofferritedecreaseswitha neg-ativeapparentCTE.Forbothferrite-pearliteandtemperedmartensite microstructures,theunit cellvolumeof cementiteincreaseswith in-creasingtemperature:alinearbehaviorisonlyobservedbetween450 and735°C(Fig.3).Above735°Cwherecementitedissolutionoccurs, adecreaseintheunitcellvolumeofcementiteisobserved.Forthe bai-nitemicrostructure,theinitialstatecontainsamixtureofthreephases (ferrite,cementiteandretainedaustenite).Duringtheheatingbetween 240and410°C,thetransformationofretainedausteniteintoferriteand cementiteoccurs.Between410and735°C,theamountofferriteand cementiteremainsconstant.Nevertheless,themeanlatticeparameters offerriteandcementitehavealmostasimilarevolutionthantheone obtainedforferrite-pearliteandtemperedmartensitemicrostructures.

1_The_volume_thermal_expansion_coefficients_of_cementite_were_measured_in thetemperaturerange450–600°Cfortworeasons:(i)thesestemperaturesare higherthancementiteCurietemperature(Tc≈227°C)[20](magnetictransition hasasignificanteffectonthethermalexpansioncoefficientinatemperature rangeofabout200°CaroundTc);(ii)fortheinitialbainitemicrostructuresome transformationoftheretainedausteniteoccurredfortemperatureslowerthan 450°Candmayaffecttheapparentthermalcoefficientofcementite.

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Fig. 2. Meanlatticeparametersofferriteandausteniteonheatingwithaheatingrateof0.25°C/sforinitialmicrostructuresofferrite-perlite(solid),bainite(dashed) andtemperedmartensite(dotted):(a)before,duringandafteraustenitizationand(b)zoomtothetemperaturerangewheretheausteniteformationoccurs.

Fig. 3. Unitcellvolumeofcementitebeforeandduringaustenitizationwitha heatingrateof0.25°C/sforinitialmicrostructuresofferrite-pearlite(blue), bai-nite(red)andtemperedmartensite(black).(Forinterpretationofthereferences tocolorinthisﬁgurelegend,thereaderisreferredtothewebversionofthis article.)

Fortheevolutionofaustenitelatticeparameter, twotemperature rangesshould bedistinguished:(i)above730°C whereamixture of ferriteandcementite transforms intoaustenite (ferrite-pearlite, tem-peredmartensiteandbainitemicrostructures),and(ii)between240and 410°Cwhereretainedaustenitetransformsintoferriteandcementite (bainitemicrostructureonly).

Acomplexnon-linearevolutionofaustenitelatticeparameterwith temperatureisobservedduringtheferrite+cementite→austenite trans-formationwhatevertheinitialmicrostructure(Fig.2(b)).Asigniﬁcant decreasein austenitelatticeparameteris observedbetween 735and 760°C,duringtheﬁrststageofthetransformation.Above760°C, dur-ingthesecondstageofthetransformation,theaustenitelattice param-eterincreases.TheCTEofausteniteincreasesuntilreachingaconstant valueof25×10−6_K−1_once_the_{transformation}_is_completed.

Forinitialbainiticmicrostructure,theCTEofretainedaustenite ob-tainedbetweenroomtemperatureand240°Cisequalto21×10−6_K−1

whichislowerthantheCTEmeasuredaftercompleteaustenitization, couldindicatethattheretainedausteniteisunderacompressivestress

state[27].Above240°C,theapparentCTEincreasesupto41×10−6_K−1

wheretheretainedaustenitetransformsintoferriteandcementite. Inthetemperatureranges whereno transformationoccurred,the coeﬃcientsofthermalexpansionobtainedfortheferrite,cementiteand austeniteareingoodagreementwiththosefoundinliterature(Table3, [20–26]).

Asimilarevolutionofferrite,cementiteandaustenitelattice parame-terswithtemperaturewasobservedforheatingratesof10and100°C/s forthediﬀerentinitialmicrostructuresasillustratedforferrite-pearlite microstructureinFig.4.

Thecomplexvariationsofmeanlatticeparametersofeachphasecan beduetoseveralfactors:changeintemperature(thermalexpansion), elasticstrainandchangeinchemicalcomposition.Asthetemperature wasmeasuredallalongtheexperimentandthermalgradientswere neg-ligible,thosevariationscanbefurtheranalyzedsubtractingthethermal contributionusingthedatareportedinTable3.

4.2. Ferriteandcementitelatticeparametersbeforethe ferrite+cementite→austenitetransformation

First,themeanlatticeparameterofferriteobtainedonheatingfor the threeinitial microstructuresis comparedwith thatof pureiron, heated on the same apparatusand in the same conditions (Fig. 5). Theabsolutevaluesofferritelatticeparameterforthethreeinitial mi-crostructuresareslightlydifferentandareslightlylowerascompared tothelatticeparameterofferriteinpureiron.Thosedifferencescanbe attributedtodifferencesinchemicalcompositionoftheferriteaswell astointernalstresses.

The diﬀerences in CTE of ferrite in comparison with pure iron are within 3.6% above 450 °C (16.4 × 10−6 _K−1 _in _{ferrite-pearlite}

microstructure, 16.2 × 10−6 _K−1 _in _the _tempered _martensite _and

16.1×10−6_K−1_in_the_bainite,_Fig.₅_).

Comparing cementite at room temperature in three initial mi-crostructuresandapurecementitepowder[28,29],themeanlattice parametersarequitesimilar(thediﬀerencesarewithin1%,Table4). Moreover,inthetemperaturerangebetween200and327°C,the vol-umeCTEofcementitereportedin[28]iscloseto42×10−6_K−1_,_which

isingoodagreementwiththeCTEofcementiteobtainedforthethree initialmicrostructuresinthesametemperaturerange:42×10−6_K−1_for

temperedmartensiteandlowerthan48×10−6_K−1_for_{ferrite-pearlite}

microstructure.Forthetemperaturerangefrom450to600°C,the ob-tainedvolumeCTEofcementite(Table3)isingoodagreementwith literaturedata.

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Fig. 4. Ferrite(black)andaustenite(blue)latticeparametersand cementiteunitcellvolume(green)asfunctionoftemperaturein ini-tialferrite-pearlitemicrostructureonheatingwithdiﬀerentheating rates.(Forinterpretationofthereferencestocolorinthisﬁgure leg-end,thereaderisreferredtothewebversionofthisarticle.)

Fig. 5. Comparisonofferritemeanlatticeparameterbeforeausteniteformation forthethreeinitialmicrostructuresandforthepureironobtainedonheating witharateof0.25°C/s.InsettablegivesCTEobtainedfromtheexperimental curvesforthetemperaturesbetween450°CandAC1.

Table 4

Meanlatticeparametersofcementiteatroomtemperaturefordiﬀerentinitial microstructuresofa37MnCr4-3steelincomparisonwiththoseforpure cemen-titepowder[28,29]. Microstructure a(Å) b(Å) c(Å) Ferrite-pearlite 5.0858 6.7374 4.5292 Bainite 5.0860 6.7420 4.5301 Temperedmartensite 5.0709 6.7295 4.5484 Cementitepowder[28] 5.0809 6.7530 4.5150 Cementitepowder[29] 5.0901 6.7456 4.5262

4.3. Meanlatticeparametersduringtheferrite+cementite→austenite transformation

Inordertoanalyzethelatticeparameterevolutionsinthe transfor-mationtemperaturerangewithoutthethermalcontribution,the param-etersΔa_𝛼,Δa𝛾andΔV𝜃 weredeﬁnedasfollows:foreachphase,the

con-tributionduetothermalexpansionalonewasextrapolatedfrom temper-atureregionswherethisphenomenonwassoleactiveorpredominant, thediﬀerencewas thencalculated betweenactual measurementand thermalcontributionalone.ThisisschematicallyillustratedinFig.6.

ThiswasdoneassumingaconstantlinearCTEforferriteandconstant volumeCTEforcementitegiveninTable3.

Foraustenite,thevariationsoflatticeparameterwerecalculated tak-ingausteniteinthesingleaustenitedomainasareference.Thisisalso illustratedin Fig.6,wheretheextrapolatedchangesin austenite pa-rametersareshownasatangentlinetothemeasurementsforthehigh temperature,austenitedomain.

The resulting variationsof Δa_𝛾, Δa_𝛼 andΔV_𝜃 areplotted versus austeniteweightfractioninFig.7(a)forferrite-pearlitemicrostructure andinFig.7(b)forallthreeinitialmicrostructures(Δa_𝛾andΔa_𝛼only).

Δa_𝛼slightlydecreasesatthebeginningoftheausteniteformation andremainsnearlyconstantandequalto−1.5×10−4_{Å between}₂₀

and85wt.%ofaustenite.Adropto-1×10−3_{Å is}_observed_between₈₅

and100wt.%ofaustenite,whatevertheinitialmicrostructure. TheΔa_𝛾 variationsareoppositeinsigntothoseofferrite,andten timeslarger.Δa_𝛾presentsthehighestvalueatthebeginningofthe trans-formation(0.01Å)andthendecreasesasausteniteamountincreasesto reach 0Å oncethetransformationiscompleted whatevertheinitial microstructure. Thedecrease is largerat thebeginningof the trans-formation.ΔV_𝜃 decreases continuouslywithtransformationprogress. Themaximalvalueisnear−0.28Å3_{corresponding}_to_a_relative_volume

changeof5.210−3_.

Thedecreaseinthemeanlatticeparameterofferriteandcementite duringthetransformation,whichissmallbutsigniﬁcantcanbe associ-atedwiththedevelopmentofcompressivestresses[30]orwithachange initschemicalcomposition.

Sincetheaustenitehasalowyieldstressinthetemperaturerange wherethetransformationoccurs,thechangesinitslatticeparameters shouldbemainlyassociatedwithchemicalcompositionvariation.

4.4. Austenitechemicalcompositionduringaustenitization

Consideringonlythesoluteelementsinthestudiedsteel,weusedthe relationproposedbyDysonandHolmes[31],asdonein[32–34],forthe latticeparameteroftheausteniteasafunctionofchemicalcomposition (inwt.%)atroomtemperature:

𝑎𝛾 =3.5847+0.0330 × [C]+0.00095 × [Mn]−0.0002 × [Ni]

+ 0.0006 × [Cr]+0.0015 × [Cu] (1)

where3.5847Å correspondstotheaustenitelatticeparameterinthe pureironatroomtemperature.

UsingthecompositionprovidedinTable1,theaustenitelattice pa-rametercanbecalculatedto3.59789Å.Thisis0.01319Å greaterthan forpureiron,withacontributionof0.01175 ˚Aduetocarbonalone,and of0.00144 ˚Aduetothesubstitutionalelements.Giventhatthecarbon

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Fig. 6. Ferriteandaustenitelatticeparametersandcementiteunit cellvolumeobtainedforferrite-pearliteinitialmicrostructureon heatingof0.25°C/s.Δa_𝛼,Δa𝛾andΔV𝜃areschematizedbyarrows.

Fig. 7. Variationsofmeanlatticeparametersofferriteandaustenitewithoutthermalcontribution(Δa 𝜶andΔa 𝜸,respectively)andunitcellvolumeofcementite (ΔV _𝜽)asafunctionofausteniteweightfractiononheatingof0.25°C/sfor(a)ferrite-pearliteand(b)threeinitialmicrostructures.

inﬂuenceistherefore10timeslargerthanthatofthesubstitutional el-ements,thevariationsofΔa_𝛾,maybeassumedtobemainlyrelatedto changesincarbonconcentrationinaustenite(Δwc𝛾).Thisisexplicited

inEq.(2):

Δ𝑎_𝛾=𝐴× Δ𝑤_𝑐𝛾 (2)

with𝐴=0.033∀∕wt.%[31].

UsingEq.(2)andconsideringthattheaustenite hasthenominal carboncontentofthesteel,wc0𝛾(Table1),oncetheaustenitizationis

completed,themeancarboncontentintheaustenite(wc𝛾)canbe esti-matedatanymomentofthetransformationusingthevariationoflattice parameteraftersubtractionofthermalcontributionΔa_𝛾:

𝑤𝛾 𝑐=

Δ𝑎_𝛾

𝐴 +𝑤𝑐0𝛾 (3)

TheresultofsuchestimationisgiveninFig.8forferrite-pearlite andtemperedmartensiteinitialmicrostructuresandfordiﬀerent heat-ingrates.

Whatevertheconsideredinitialmicrostructureandheatingrate,a continuousdecreaseinthemeancarboncontentinausteniteisobserved untiltheendoftheaustenitization,whenthecarboncontentstabilizes andremainsconstantduringfurtherheating.Thecarboncontentinthe

first 3wt.% ofaustenite(“initial” austenitemeancarbon content)is equalto0.59wt.%fortheinitialferrite-pearlitemicrostructureandthe lowestheatingrateof0.25°C/s.Anincreaseintheheatingrateleads toanincreaseinA_C1temperatureandtoadecreasein“initial” mean carboncontentinfreshaustenite(0.54wt.%for10°C/sand0.44wt.% for100°C/s).Asimilarbehaviorisobservedfortheinitial microstruc-ture of temperedmartensite(Fig.8(b))with lessdifferencebetween the“initial” meancarboncontentinausteniteforthedifferentheating rates.

Marking theend ofcementitedissolution, diﬀerentstagescan be outlined(Fig.8):aﬁrstonewithasharpdecreaseincarboncontentin austenitebetweenthebeginningofthetransformationandthecomplete dissolutionofcementiteandasecondonewithasmootherdecrease cor-respondingtotheremainingferritedissolution.Oncetheaustenitization iscompleted,thecarboncontentinausteniteremainsconstantandequal tothemeancarboncontentofthestudiedsteel.

Whentheheatingrateincreases,thecementitedissolutionﬁnishes athighertemperaturesandthecorrespondingmeancarboncontentin austenitedecreasessinceahigherferriteamounttransformsinaustenite beforecompletecementitedissolution[15].

The mean carbon contentevolution in austenite during thetwo stagesoftheaustenitizationintheferrite-pearliteinitialmicrostructure

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Fig. 8. Meancarboncontentinausteniteandaustenitefractionversustemperatureduringaustenitizationfordiﬀerentheatingratesandtwoinitialmicrostructures: (a) ferrite-pearliteand(b)temperedmartensite.

Fig. 9. Meancarboncontentinausteniteandaustenitefractiononheating dur-ingaustenitizationofinitialbainiticmicrostructurefordiﬀerentheatingrates.

heatedat0.25°C/scanbefurtheranalyzed.FromresultsshowninFig.8, thecarboncontentinausteniteattheendofpearlite(i.e.,cementite) dis-solutionisabout0.45wt.%correspondingtothemeancarboncontent intheinitialpearlite.Indeed,thepearlitefractionestimatedbyimage analysisfromimagesacquiredonScanningElectronMicroscope(SEM, Fig.1(a))wasfoundtobe80%.Consideringthatthereisnocarbonin ferrite,themeancarboncontentinpearlitecanberoughlyestimatedas

0.356

0.8 =0.445wt.%,whichagreeswellwith0.45wt.%estimatedfromin situexperimentasdiscussedabove.

FromFig.8,weconcludethatforthelowestheatingrateof0.25°C/s, theﬁrstformedaustenitehasahighercarboncontent(0.59wt.%)than themeancarboncontentin theinitialpearlite (0.44wt.%).As tem-peratureandaustenitefractionincrease,themeancarboncontentin austenitedecreasesuntilreachingthemeancarboncontentofthe ini-tialpearliteattheendoftheﬁrststageofthetransformation.During thesecondstageofthetransformation,thedissolutionoftheremaining 20%offreeferritewithnegligiblecarboncontentoccursandthemean carboncontentinaustenitedecreasesmoresmoothly.

Inthecase ofbainiticmicrostructure, adecreasein meancarbon contentinausteniteisalsoobservedduringthetransformation. How-ever,theinitialcarboncontentinausteniteincreaseswiththeheating rate(Fig.9).Such aresult,diﬀerentfromthoseobtainedforthetwo

otherinitialmicrostructuresshouldbeexplainedusingthe microstruc-turaldiﬀerencesindiﬀerentinitialstatesofthestudiedsteel.Indeed, asmallamountofretainedaustenitewasfoundintheinitialbainitic microstructureunliketheferrite-pearliteandthetemperedmartensite microstrutures.Fortheheatingrateof0.25°C/s,theretained austen-itecompletelytransformsintoferriteandcementitebetween240and 410°C.Fortheheatingratesof10°C/sand100°C/s,theretained austen-ite(initialfractionof3wt.%)isnotcompletelytransformedwhen reach-ingAC1temperatureandthetransformedaustenitefractiondecreases

with increasein heatingrate(about0.7 wt.%at745 °Cfor 10 °C/s and2wt.% for100 °C/s).Keepingthe assumptionthat theinternal stressesarerelaxedinausteniteatthosetemperatures,thehighercarbon contentintheaustenitewhenreachingA_C1temperatureforincreased heatingratemayberelatedtothecarbonenrichmentoftheretained austeniteduringthebainitictransformation[35].Apartial transforma-tionoftheretainedausteniteinferriteandcementite(heatingrateof 10°C/s)couldthusleadtoaglobalincreaseinthecarboncontentin austeniteattheﬁrstmomentofaustenitization(for3wt.%ofaustenite) (Fig.9).OncetheAC1temperatureisreachedandaustenitefraction

in-creases,themeancarboncontentinaustenitestartstodecreasedueto ferrite+cementite→austenitetransformationasfortheother microstruc-tures.

Inadditiontothemeancarboncontentinaustenite,itschemical ho-mogeneitycanbeestimatedusingtheFWHM(full-widthheightmiddle) ofdiﬀractionpeaksrecordedduringinsituexperiments.Accordingto Caglioti’sequation,FWHMvarieswiththediﬀractionangle𝜃[36]:

FWHM=

√₍

𝑈× tan2₍_𝜃₎₊_𝑉_{× tan}₍_𝜃₎₊_𝑊) ₍₅₎ whereU,V,Warethehalf-widthparametersthatcanbeobtainedby Rietveldreﬁnement.

First,thediﬀractiondiagramswiththe(111)_𝛾and(200)_𝛾peaksare giveninFig.10forthreeaustenitefractionsandferrite-pearliteinitial microstructureheatedat0.25°C/s.TheyillustratethelargerFWHMat thebeginningofthetransformation(6wt.%ofaustenite).

TheFWHMevolutionfor(111)_𝛾and(200)_𝛾peakscalculatedusing theCaglioti’sEq.(5)areplottedversus temperatureinFig.11.2 _For

easeofcomparison,themeancarboncontentinaustenitepreviously discussedisalsoreported.AstrongcontinuousdecreaseintheFWHMof

2 _As_the_same_evolutions_of_FWHM_for_diﬀerent_{microstructures}_with_increase inheatingrateswereobserved,Fig.11reportsthedataforthreemicrostructures andthreediﬀerentheatingrates.

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Fig. 10. Austenitediffractionpeaks(111)and(200)correspondingto differ-entstagesofausteniteformationonheatingwiththeheatingrateof0.25°C/s ininitialferrite-pearlitemicrostructure:6wt.%(beginning),66wt.%(endof cementitedissolution)andfullyaustenitic(endoftheaustenitization). (111)_𝛾and(200)_𝛾peaksisobservedduringthefirststageofthe austen-iteformationfollowedbyaplateauduringthesecondstage(remaining freeferritedissolution)andlateronceausteniteformationiscompleted. Anenlargementindiffractionpeaksmaybeduetoseveralfactors: smallsize of diffractingdomains, heterogeneities(chemical,internal

stresses,localtemperature).ThedecreaseinFWHMcanbemainly as-sociatedwithahomogenizationofcarboncompositionoftheaustenite becausestressandthermalgradientduringausteniteformationas dis-cussedearliercanbeconsiderednegligible.Indeed,gradientsincarbon contentarepresentduringthetransformation.Thechemical homoge-nizationbeingcontrolledbydiﬀusion,isacceleratedwithtemperature. TheFWHMofaustenitediﬀractionpeaksisthusmaximalatthe begin-ningofthetransformationduetoamaximumchemicalheterogeneity. Moreover,itisworthnotingthatthemaximumFWHMincreasesasthe heatingratesincreasesuggestingincreaseinchemicalheterogeneities inaustenite.

5. Discussion

Sinceanydataforthechemicalcompositionofdifferentphasesin differentinitialmicrostructureswerenotavailable,severalassumptions arerequiredforfurtherdiscussion.Threeinitialmicrostructureswere obtainedatdifferenttemperaturesandfordifferentdurations:625°C - 1hforferrite-pearlite,425°C-30minforbainiteand500°C-1h fortemperedmartensite.Thesethreetemperaturesandcorresponding durationsseemtobedisadvantageousforasignificantdiffusiondistance ofthesubstitutionalelements(Si,Mn,Ni,Cr,MoandCu).Indeed,the estimationofthebulkdiffusionlengthsinaustenitefortheseelementsat thehighesttemperatureof625°Cfor1hannealing,indicatethatitdoes notexceed10nmforthefastdiffusingelementslikeCrandMn[37]. However,thecementiteinpearlitecanbesignificantlyenrichedinMn eventhoughthepearliteformationtakesplaceatlowtemperaturesdue toacceleratedMndiffusionalongtheinterfaces[38,39].Nevertheless,

Fig. 11. FWHMof(111)_𝛾and(200)_𝛾diﬀractionpeaksofaustenitecomparedtothemeancarboncontentevolutionduringausteniteformationfordiﬀerentinitial microstructuresandheatingrates:(a)ferrite-pearliteat0.25°C/s,(b)bainiteat10°C/s,(c)temperedmartensiteat100°C/s.

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Table 5

Austenitestarttemperature(AC1)andmeancarboncontentinausteniteatthebeginningofaustenitization(C0𝛾)(3wt.%offormedaustenite)fordiﬀerentheating

ratesandinitialmicrostructures.

Heatingrate(°C/s) Ferrite-pearlite Temperedmartensite Bainite

AC1(°C) C0𝛾(wt.%) AC1(°C) C0𝛾(wt.%) AC1(°C) C0𝛾(wt.%)

0.25 740 0.594 736 0.593 736 0.585

10 761 0.543 742 0.586 – –

100 781 0.442 753 0.554 – –

Fig. 12. Isoplethphasediagramforthe37MnCr4-3steelforﬁxedcontentof substitutionalelementsandvaryingcarboncontent(attheexpenseofiron) ob-tainedusingThermo-CalcsoftwareandTCFE9database.Mncontentwastaken 1.285wt.%(blacklines)andcorrespondingto5,10and20wt.%(dashed col-oredlines)ofMnincementiteinequilibriumwithaustenitetotakeintoaccount eventualMnenrichmentincementiteduringpearliteformation.Initialcarbon contentinausteniteobtainedexperimentally(points)iscomparedwiththemean carboncontentinaustenite,whichisinthermodynamicequilibriumwith fer-riteandcementitehavingthesamecontentofsubstitutionalelements(dotted greenline).(Forinterpretationofthereferencestocolorinthisﬁgurelegend, thereaderisreferredtothewebversionofthisarticle.)

diﬀusionofsubstitutionalelementsduringtheformationoftempered martensiteandbainiteshouldbesuﬃcientlylimitedtobeneglected.

Therefore,onecan expectthesame contentofsubstitutional ele-ments(thesameu-fraction)inferriteinbainiteandtempered marten-sitemicrostructureswhilesomeMnpartitioningcouldtakeplaceduring thepearliteformationleadingtocementiteenrichedbyMn.Duringthe austenitization,Mn partitioningcanoccuraswell whichdepends on initialMncontentinferriteandcementite[40,41].

Wenowcananalyzetheformationoffreshausteniteusingan iso-plethphasediagramobtainedforthefixedcontentofthesubstitutional elements(accordingtoTable1),exceptthatofMn,andvaryingcarbon content(attheexpenseofiron)usingThermo-CalcsoftwareandTCFE9 database(Fig.12).Inordertotakeintoaccountpossiblecementite en-richmentbyMnduringpearliteformationorduringslowheatingrate ofthethreeinitial microstructures,Mncontentincementitein ther-modynamicequilibriumwithaustenitewasbeingvariedwhenplotting isoplethdiagram.However,onecanobservethatdifferentMncontent incementite(from5to20wt.%)inequilibriumwithaustenitedoes notchangesignificantlyaustenite/cementiteequilibriumascompared toglobalcontentofMnof1.285wt.%(Fig.12).Therefore,the discus-sioncanbelimitedtothenominalMncontentinthestudiedsteelof 1.285wt.%.

Theisoplethphasediagramfor1.285wt.%ofMn(blacklines)gives carboncontentintheausteniteinequilibriumwithcementitec_𝛾/𝜃and

ferritec_𝛾/𝛼havingthesamecontentofsubstitutionalelementsasthatin

austenite.

Plottingtheinitialmeancarboncontentinausteniteobtainedfrom theinsituexperiments(pointsinFig.12),weobservethatforthe heat-ingrateof0.25°C/s(thelowestaustenitestarttemperature),the austen-itemeancarboncontent,atthestartofaustenitization,isclosetothe eutectoidcomposition,butnearertothecompositionoftheausteniteat equilibriumwithcementite.Thecarboncontentoffreshausteniteclose tothatofeutectoidcompositionwerereportedin[4,40,42]and sug-gestedrecentlyin[15]whereausteniteformationisstartingcontrolled bycarbondiﬀusion[40,41,43–47].

Fordiﬀerentheatingratesandferrite-pearliteandtempered marten-sitemicrostructures,adecreaseofthemeaninitial carboncontentin austeniteisobservedwhenheatingrate(andthus theaustenitization starttemperature(AC1))increases(Table5).

Whenwereportallexperimentalvaluesofinitialcarboncontentin austeniteontheisoplethphasediagram,weobservethatincreasingthe heatingrate,theinitialmeancarboncontentinaustenitevaries accord-ingtotheaveragevalue(c_𝛾/𝛼+c𝛾/𝜃)/2(Fig.12).Sucharesultsuggestsa

lineargradientforcarboncontentintheﬁrstausteniteformedbetween ferriteandcementite[48].

Inthecaseoftheferrite-pearliteinitialmicrostructureandtherate of100°C/s,adeviationfromtheaveragevalue(c_𝛾_/_𝛼+c_𝛾_/_𝜃)/2is ob-served.Eventual partitioningof Mnduringaustenitization andwhen forminginitialferrite-pearlitemicrostructureshouldbecarefully exam-inedforfastheatingrate.Theassumptionofnon-linearcarbonproﬁlein austenitecanbesupposed.Experimentally,itrequiresadditional anal-ysisofchemicalcompositionofphasesininitialmicrostructuresbefore austenitization.

6. Conclusion

Theinﬂuenceofheatingrateandinitialmicrostructureonthemean latticeparametersofferrite,cementiteand,especially,thatofaustenite duringaustenitizationwasinvestigatedbyinsituHE-XRDina 0.36C-1.3Mn-0.7Cr-0.07Mowt.%steel.Themainresultsaresummarized be-low:

(1) Ferriteandcementiteareundercompressionattheendoftheir transformationintoaustenite;

(2) Duringtheaustenitization,themeanlatticeparameterof austen-itedecreases;thisdecreaseismainlyassociatedtoachangein themeancarboncontent;

(3) Assumingthattheelasticstrainsinaustenitearenegligible,the variationsinmeancarboncontentinaustenitearecalculated us-ingmeanaustenitelatticeparameterforeachtransformation con-dition.Theﬁrstformedaustenitehasthehighestmeancarbon content;itdecreasesrapidlydue tothesimultaneous transfor-mationofferriteandcementiteintoaustenite.Oncecementite isdissolved,duringtheferritetransformation,themeancarbon contentinaustenitedecreasesmoreslowly;

(4) Theinitial meancarbon contentin austeniteat thebeginning oftheausteniteformationisdependent ontheheatingrate:it decreasesasheatingrateincreases(asclearlyshownfor ferrite-pearliteandtemperedmartensiteinitialmicrostructures).Forthe lowestheatingrate,thecarboncontentintheﬁrst3wt.%formed austeniteisnearthecalculatedeutectoidcompositionobtained byThermo-CalcandTCFE9database;

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(5) Valuesofinitialcarboncontentintheﬁrstausteniteformedarein goodagreementwiththermodynamiccalculationswithor with-outpartitioningofMnininitialcementite.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompetingﬁnancial interestsorpersonalrelationshipsthatcouldhaveappearedtoinﬂuence theworkreportedinthispaper.

Acknowledgements

Authors gratefully acknowledge the Deutsches Elektronen-Synchrotron (DESY, Hamburg, Germany) and staﬀ of the P07 line atPETRAIII, especially,Andreas Starkfor theassistancewithX-ray diﬀraction experiments. Financial support of the National Research Agency (ANR) (research grant No. ANR-2010-RMNP-011-06) is gratefullyacknowledged.

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