kinetics of the simultaneous decomposition of austenite into several

mater.Vol. 45, No. 7, pp.2911-2920,19970 1997ActaMetalhmzicaInc.4!!!!!9Pergamon Pu~lishedbyElsevierSci&e LtdPII: S1359-6454(96)00392-8 Printedin GreatBritain.Allrightsreserved

1359-6454/97$17.00+ 0.00

KINETICS OF THE SIMULTANEOUS DECOMPOSITION OFAUSTENITE INTO SEVERAL TRANSFORMATION

PRODUCTS

S. J. JONES and H. K. D. H. BHADESHIAUniversityof Cambridge,Department of Materials Scienceand Metallurgy,PembrokeStreet, Cambridge

CB2 3QZ, U.K.

(Received 25 September 1996)

Abstract-Transformations in steels rarely occur in isolation. This paper describes a modification ofthe Avrami overall transformation kinetics theory as adapted by Cahn, for grain boundarynucleated phases. The modification deals with the simultaneous occurrence of two or moretransformations. The method is demonstrated to faithfully reproduce published data on the volumefractions of allotriomorphic,Widmanstatten ferrite and pearlite as a function of chemical composition,austenite grain size and heat treatment (isothermalor continuouscoolingtransformation). ~ 1997ActaMetallurgic Inc.

INTRODUCTIONAlmost all commercial steels are produced usingheat-treatments in which the austenite coolscontinuously through the transformation tempera-ture range. This usually leads to a final microstruc-ture which is a mixture of many transformationproducts, because the high-temperature austenitecan decompose into a large variety of ferritictransformation products, each of which can formby a different mechanism. These reactions mayoverlap and interact with each other, either byhard-impingement in which adjacent particlestouch, or by soft-impingement where theirdiffusion or thermal fields overlap [1]. The inter-actions are known to be important in determiningthefinal microstructure.

It follows that in order to model the develop-ment of microstructure, it is necessary to develop atheory capable of handling simultaneous, interact-ing precipitation reactions. The evolution of volumefraction during solid-state transformation is usuallydescribed using the classical JohnsonMehlAvramitheory, which has been reviewed thoroughly byChristian [1].The present work deals with a generalextension of this theory to multiple reactions, whichis then applied to explain published data on steels.In particular, structural steels frequently havea microstructure consisting of allotriomorphicferrite, Widmanstatten ferrite and pearlite.Although a great deal is known about allotriomor-phic ferrite and pearlite, kinetic theory for Wid-manstatten ferrite is rather limited. Anunderstanding of Widmanstatten ferrite is import-ant because it is a phase which greatly influencesthe mechanical properties of steels. There are

2911

many investigations which suggest that Wid-manstatten ferrite can be detrimental to toughness[2]. It tends to grow in packets of parallel platesacross which cracks tend to propagate withoutmuch deviation.

Watson and McDougall [3]demonstrated that thegrowth of Widmanstatten ferrite leads to a change inthe shape of the transformed region. This shapedeformation is an invariant-plane strain (IPS) with alarge shear component, which is characteristic ofdisplacivetransformation. Carbon neverthelesshas topartition into the austenite during the growth ofWidmanstatten ferrite. The transformation is there-fore a paraequilibriumdisplacivetransformation withthe growth rate controlled by the diffusionof carbonin the austenite ahead of the plate tip, with anappropriate allowancemade for the strain energydueto the IPS shape change [4]. The nucleationmechanismof Widmanstatten ferrite is understood tothe extent that it is possible to calculate thetransformation start temperature (JVS)and the rate asa function of undercookingbelow Ws [5,6]. It shouldtherefore be possible to estimate the overalltransformation kinetics as a function of the steelcomposition and heat treatment.

It is emphasised that Widmanstatten ferriterarely occurs in isolation. It is usually preceded bythe formation of allotriomorphic ferrite at theaustenite grain surfaces and there may be othertransformations such as pearlite which compete foruntransformed austenite [7]. To deal with thiscomplexity, we begin with a brief introduction tothe classical JohnsonMehlAvramimodel, in orderto set the scene for the modificationsmade to allowfor simultaneous reactions.

2912 JONES and BHADESHIA: KINETICS OF SIMULTANEOUSDECOMPOSITION

OVERALLTRANSFORMATIONKINETICS

A given precipitate particle of the phase ~effectively forms after an incubation period z.Assuminggrowth at a constant rate G, the volume w.of a spherical particle is given by

w,= (47r/3)G3(t Z)3 (t > t) (1)with w,= O for (t < r) where tis the time definedfrom the instant the sample reaches the isothermaltransformation temperature.

Particles nucleated at different locations mayeventually touch; this problem of hard impingementis neglected at first, by allowing particles to growthrough each other and by permitting nucleation tohappen even in regions which have already trans-formed. The calculated volume of the ~ phase isthereforean extended volume. The changein extendedvolume due to particles nucleated in a time intervalt = z to t= T+ dz is, therefore,

Jf~ = (47cv/3) G3Z(t T)d~ (2),=0where Zis the nucleation rate per unit volume and Vis the total sample volume.

Only those parts of the change in extendedvolumewhich lie in untransformed regions of the parentphase can contribute to the change in real volume of~. If nucleation occurs randomly in the parentmaterial then the probability that any change inextended volume lies in the untransformed parentphase is proportional to the fraction of untrans-formed material at that instant. It follows that theactual change in volume in the time interval t tot+ dt is

so that

and

-ln(l-~)=(4z3)G3.rz(t-)3d3)For a constant nucleation rate, integration ofequation (3) gives the familiar JohnsonMehlAvrami equation:

~= # = 1 exp(-+czt)4)where CBis the volume fraction of /3.

This approach is limited to the precipitation of asingle phase; it can be applied to cases where more

than one decomposition reaction occurs, if theindividualreactions occur over differenttemperatureranges, i.e. they occur successively and largelyindependently[8,9]. This is not the case in practice.The adaptation of the JohnsonMehlAvrami ap-proach to deal with many reactions occurringsimultaneously is illustrated with a simple examplebelow.

SIMPLE SIMULTANEOUSREACTIONS:RANDOMDISTRIBUTIONOF NUCLEATIONSITES

The principles involved are first illustrated with asimplifiedexamplein whicha and Bprecipitate at thesame time from the parent phase which is designatedy. It is assumed that the nucleation and growth ratesdo not change with time and that the particles growisotropically.

The increase in the extended volume due toparticles nucleated in a time interval t = ~ tot= T+ d~ is, therefore, given by

dn = ;rcG:(t z)3ZrVd~and

d~ = ;zG;(t T)3ZflV d~ (5)whereG., Gfl,Z.and Iflare the growth and nucleationrates of a and ~, respectively, all of which areassumedhere to be independentof time. Vis the totalvolumeof the system.For each phase, the increaseinextended volume will consist of three separate parts.Thus, for a the parts are:

(a) a which forms in untransformed y;(b) a which forms in existing a;(c) a which forms in existing /?.

Only a formed in untransformed y will contribute tothe real volume of a. On average, a fraction[1 (V. + V8)/Vl of the extended volume will be inthe previously untransformed material. It followsthat the increase in real volume of a in the timeinterval tto t+ dt is given by

Va=k+)dnand similarly for ~,

v=(--)d~In general, V. will be some complex function of V~and it is not possible to analytically integrate theseexpressionsto find the relationship between the realand extended volumes,although they can, of course,be integrated numerically. However,in certain simplecasesit is possibleto relate V. to Vflby multiplicationwith a suitable constant, K, in which case VI = KV.and analytical integration becomes possible.

JONES and BHADESHIA: KINETICS OF SIMULTANEOUSDECOMPOSITION 2913

The equations relating the increment in the realvolume to that of the extendedvolume can thereforebe written as

( )dVa= 1- K+VKVd~and

( )v~+KVPdJ,7e.dVb = 1 ~V (6)They may then be integrated to find an analyticalsolution relating the extended and real volumesanalogous to that for single-phaseprecipitation:

n 1[

In 1 $(1 + K)7l+K 1and ;==+[1-%+317)The total extendedvolume fraction is found for eachphase by integrating equation (5) with respect to z.This gives:

a=(M1-exp[-~(1+mzGza41=(~)(-exp[-:(~)G41))These equations resemble the well-known Avramiequation for single-phase precipitation with extrafactors to account for the presence of a secondprecipitate phase. When the volume fraction of bothprecipitating phases is very small the equationsapproximate to the expressions for each phaseprecipitating alone. This is because nearly all of theextended volume then lies in previously untrans-formed material and contributes to the real volume.As simultaneousprecipitation proceeds,the predictedvolume fraction of each phase becomeslessthan thatpredicted if the phases were precipitating alone. Thisis expected, because additional phases reduce thefraction of the extended volume which lies inpreviously untransformed material.

Since the nucleation and growth rates wereassumed to be constant, it is possible to calculateexplicitly the value of K, which is given by

K = Vf/V. = (Z8G;)/(ZaG;).An example calculation for the case of linear (i.e.constant) growth is presented in Fig. 1, for the casewhere the growth rate of /3is set to be twice that ofa (with identical nucleation rates). The final volumefraction of the I!Iphase is eight times that of the aphase because volume fraction is a function of thegrowth rate cubed.

Whereas the analytical method is more satisfying,numericalmethods are more amenable to changesinthe boundary conditions during transformation, asdescribed below.

COMPLEXSIMULTANEOUSREACTIONS

The analytical expressions discussed above forsimultaneous reactions rely on the assumptions ofconstant nucleation and growth rates, which are notappropriate for the present purposes. The nucleationand growth rate of allotriomorphic ferrite, Wid-manstatten ferrite and pearlite may change with theprogressof the transformation as the composition ofthe austenite and/or the temperature changes whilstthe nucleation sites are grain surfaces.

There are two applications of the Avrami extendedspace idea for grain boundary nucleated reactions,the first applying to the gradual elimination of freegrain boundary area and the second to the gradualelimination of volume of untransformed material[10].If we consider a boundary of area O, (which isequal to the total grain boundary area of the sample)in a systemwith n precipitating phases, where Oi,Yisthe total real area intersected by the ith phase on aplane parallel to the boundary but at a distance ynormal to that boundary at the time t, we have forthe jth phase,

.

Ao=(l-%?10)where AOjwis the change in the real area intersectedwith the plane at y by the phase j, during the smalltime interval t to t + At. AO~Yis similarly,the changein extendedarea of intersection with the same planeat y. This may have a contribution from particlesnucleated throughout the period t = O to t= m At,where m is an integer such that m At is the current

o 75 1s0 2i5 300Time

Fig. 1. Simultaneous precipitation of ~ and a. Identicalnucleation rates but with # particles growing at twice the

rate of the a particles.


time, so that

whereAj,kJ.k the rate of change of area OfinterSeCtiOnon plane yof a particle of the phasej whichnucleatedat z = k Az at the current time t = m At. ~,k is thenucleation rate per unit area of the phasej during thetime interval t = k AT to t = k AT+ Az. Note thatAt and At are taken to be numericallyidentical andthe number of extended particles nucleated in thistime interval is therefore O& AT.AOjNis then usedto update the total real area of intersection of thephase j with the same plane at y at the time t + Atby writing

O1a,,+~,= OjY,l+ AOj,Yfor j = 1 . . . n.To obtain a change in the extended volume of the

phase j on one side of the boundary, it is necessaryto integra@as follows:

where the integrand dOja is equivalent to AOj,Yand%~axis the maximum extended size of a particle ofphase j in a direction normal to the grain boundaryplane. Thus the change in the extendedvolumeof thephase j on one side of the boundary in the timeinterval tto t + At may be numericallyevaluated as

A~ = Ay ~ AOj,Y (11)~=o

where Ay is a small interval in y. Therefore, thecorresponding change in real volume after allowingfor imping~mentwith particlesoriginatingfrom otherboundaries is

n

Afi=(-%2)where V,isthe real volumeof the ith phase at the timet.The instantaneous value of AVj, together withcorresponding changes in the volumes of the othern 1 phases, can be used to calculate the totalvolumeof each phase at the time t + At in a computerimplemented numerical procedure by writing

fi,,+,i,= V,,+ Au for j = 1.. . nso that a plot of the fraction of each phase can beobtained as a function of time. The growth andnucleation rates can also be updated during this step,should they have changed because of soluteenrichment in the untransformed parent material orbecause there is a change in temperature duringcontinuous cooling transfonnation.

The next section explains how these equationsapply to allotriomorphic ferrite, Widmanstattenferrite and pearlite. These phases are henceforthidentifiedby setting the phase index as j = 1, 2 or 3,respectively; these subscripts are also used inidentifying the nucleation and growth rates of thephases concerned.

ALLOTRIOMORPHICFERRITE

Classical nucleation theory is used to model thenucleation of allotriomorphic ferrite, with the grainboundary nucleation rate per unit area given by:

=ca~exp{-~le13)where h is the Planck constant, k is the Boltzmannconstant, C. = 1.214x 1012m-z is a fitted constant[11],R is the universalgas constant and Q = 200kJ/mol is a constant activation energy representing thebarrier to the transfer of atoms across the interface.The activation energyfor nucleation, G* = C,O/AG=,where a = 0.022J/m* represents the interracialenergy per unit area, Cb = 5.58 is another fittedconstant and AG is the maximum chemical freeenergy change per unit volume available fornucleation [12].The second exponential term relatesto the achievementof a steady-state nucleation rate;7* = n~h(4a.kT)-] exp{Q/RT}, where n, is thenumber of atoms in the critical nucleus and a, is thenumber of atoms in the critical nucleus which are atthe interface [1].

The nucleation and growth of allotriomorphicferrite has been described by modelling the allotri-omorphs as discs having their faces parallel to thenucleating grain boundary plane [13].The discs areassumed to grow on both sides of the parentboundary under paraequilibrium conditions, so thatthe half-thickness ql of each disc during isothermalgrowth is given by:

,. s

ql = L(t 7)1/2 (14)where( is the one-dimensionalparabolic thickeningrate constant. The growth rate slows down as theconcentration gradient ahead of the movinginterfacedecreases to accommodate the carbon that ispartitioned into the austenite. The growth rateparallel to the grain boundary plane is taken to bethree times that normal to it, givinga constant aspectratio ~, of 3.o, so that the disc radius is qlql [14].

For non-isothermalgrowth the change in thicknessduring a time interval dt is given by differentiatingequation (14):

dql =;((t7)-/2 dt.Therefore,,for a particle nucleated at z = k ATthehalf thickness at the time (m+ 1)At is evaluatednumerically as:

ql,(m+ l)At = ql,mAf + ;~(m At ~ AT)-]2 At.


The rate of change of area of intersection on a planey of a disc of phase 1 (allotriomorphic ferrite)nucleated at z = k Az at the time m At is:

41,,,,= rrq?c (ql,(m+1)A(> y)AM,,= nq?9;,(tn+,)A,/At (9M~+1)A,= Y)A,,~,Y= O (ql>(~+1)M< ~).

Sincethe ferrite allotriomorphs can growinto both ofthe adjacent austenite grains, it followsfrom equation(11) that

(15)

The parabolic rate constant is obtained by solvingthe equation [1]:

2(9Q=exp{$}erfc{*lwith

-&-~Q=x~xay

and where XYand xv are the paraequilibrium carbonconcentrations in austenite and ferrite, respectively,at the interface (obtained using a calculatedmulticomponent phase diagram), i is the averagecarbon concentration in the alloy and@ is a weightedaverage diffusivity[15]of carbon in austenite, givenby:

where D is the diffusivityof carbon in austenite at aparticular concentration of carbon.

WIDMANST~TTENFERRITE

There is fine detail in TTT (timAemperature-transformation) diagrams, but they consistessentiallyof two C-curves (Fig. 2). One of these representsreconstructive transformations at elevated tempera-tures where atoms are mobilewithin the time scaleofthe usual experiments on steels. The lower tempera-ture C-curve represents displacive transformationssuch as Widmanstatten ferrite and bainite.

The lower C-curve has a flat top; the temperaturecorresponding to this flat top is identifiedas Th, thehighest temperature at which displacive transform-ation occurs during isothermal heat-treatment. Thiseither the Widmanstatten ferrite start (Ws) orbainite-start (Bs) temperature depending on thedriving force available at Tb for the steel concerned.

Figure 3 shows two plots; the first is a calculationof the driving force for the paraequilibriumnucleation of ferrite at Th, allowing carbon topartition between the austenite and ferrite. The

-------------------------------

cReamstmctive------------

Displacive

Thne Fig. 2. SchematicTTTdiagram illustratingthe two C-curves

and the ~h temperature.

secondis the casewherethere is no partitioning at allduring the nucleation of ferrite.

It is evident that the nucleation of Widmanstattenferrite or bainite cannot in general occur withoutthe partitioning of carbon. The second interestingpoint is that the curveillustrated in Fig. 3(a) is linear.This straight line, which represents all steels, ishenceforth called the universal GNfunction and is

o - -------------------------

-.300 n.,, t : l

-600 n n Impl.-9cm n

~ m

10 I 1 ISoo 6rm 700

+n

_~ ~

400 500 m 7W

Temperature/C

Fig. 3. Curvesrepresentingthe free energychangenecessaryin order to obtain a detectable degree of transformation toWidmanstatten ferrite or bainite [5].Note that each pointrepresents a different steel. (a) The free energy changeassuming paraequilibrium nucleation. (b) The free energy

change assumingpartitionless nucleation.


Table 1. Chemical composition (wt%)c Si Mn Cu v0.18 0.18 1.15 0.09


Table 2. Details of the data plotted in Fig. 4. a and ct. represent the allotriomorphic ferrite and Widmanstatten ferritefractions, respectively.The measured fractions are due to Bodnar and Hansen

y grain size Cooling rate E c! u. % Pearlite(yin) Pearlite(K/rein) measured calculated measured calculated measured calculated30 101 0.46 0.7230

0.23 0.07 0.3159

0.210.525 0.74

300.174 0.05 0.301

300.21

0.645 0.78 0.056 0.0130 16

0.298 0.210,717 0.75 0 0.02 0.283

30 110.23

0.73 0.78 0 0.01 0.26955 99

0.210.285 0.17 0.403 0.65

55 590.311 0.18

0.336 0.36 0.362 0.4555 30

0.301 0.190.417 0.27 0.292 0.5

55 160.291 0.23

0.523 0.7 0.189 0.155 11

0.287 0.20.568 0.77 0.147 0.04

100 1010.285 0.19

0.165 0.12 0.523 0.71100

0.31259

0,170.196 0.16 0.499 0.69

1000.305

300.15

0.244 0.23100

0.462 0.57 0.29316

0.20.301 0.27 0.412 0.51 0.286

100 110.22

0.355 0.34 0.361 0.45 0.283 0.21

is givenby g~= VZ(tt) during unhindered isother-mal growth. For non-isothermal transformation,

qz,(~+l)Af = q2,mAf + V2 At.The rate of change of area of intersection on a planeat a distance y from the austenite grain boundary istherefore:

A2,~,J= 2q2~(m At k AT) (q2,(m+ l)At > Y)A,,k,,= qzq:,,~+,,~,/At (qZ>(*+l)Af= y)A*,~,y= O (qZ,(m+ l)At < ~)

where qj is the ratio of the length to the thickness ofthe Widmanstatten ferrite plate, taken to be 0.02.Since the plates grow by displacive transformation,they can only grow into one of the adjacent austenitegrains, so that the change in the extended volume(Afi) is given directly by equation (11).

PEARLITE

The nucleation of pearlite is treated as forallotriomorphic ferrite but with a nucleation ratewhich is two orders of magnitude smaller. This isachieved by reducing the number density ofnucleation sites.

The growth of pearlite was approximated to occurby a paraequilibriummechanism,although it neverinpractice growsin this way. It is also assumedthat themajority of diffusion occurs in the austenite justahead of the transformation front. In thesecircumstances, the growth rate is given by [19]

where Orepresents cementite, a the ferrite within thepearlite and y the austenite. g is a geometric factorequal to 0.72 in plain carbon steels, s is theinterlamellar spacing, whose critical value at whichgrowth stops is sc and s., so are the respective

thicknessof ferrite and cementitelamellae.The valuesof s and SCare estimated empirically [20]and it isassumed that s adopts a value consistent with themaximum rate of growth.

Like allotriomorphicferrite, pearlite growth occursby a reconstructive mechanism and is not restrictedby the presence of a grain boundary. The shape ofpearlite colony is taken to be that of a disc (aspectratio qj = 1) of half-thickness

q = V(t ~) with qs,(~+I)A,= q,rn&+ V3At.The rate of change of area of intersection on atest-plane located at a distance y is given by

A3,,,Y= 2rr~:V@ At k Az) (q3,(m+ l)At > y)A3,w = rdd,(tn+ ,)At/At (93,(m+ 1)AI = Y)

,43,&y = o (q,@+ I)A, < ~).

Since pearlite nodules nucleate at an austenitegrain boundary and can grow into either of theadjacent austenite grains, A~ is given by equation(15).

RESULTSANDDISCUSSION

There have been many studies about the occur-rence of Widmanstatten ferrite in steelsas a functionof the chemicalcomposition, austenite grain sizeandcooling rate during continuous cooling transform-ation [e.g. 7, 2123]. It is consequently wellestablishedthat Widmanstatten ferrite is favoured inaustenite with a large grain structure. This isprobably because Widmanstatten ferrite is rarelyfound in isolationbut often forms as secondaryplatesgrowing from allotriomorphic ferrite layers. Theprior formation of allotriomorphic ferrite, which isfavoured by a small grain size, enriches theuntransformed residual austenite with carbon andreduces the volume fraction of residual austenitewhich can subsequently transform into Wid-manstatten ferrite, so it is not surprisingthat a small

JONES and 13HADESBHA:KINIYFW!S:@F=ULTANEOWD~OM~S~ION2918

1.o-

.

4 ::.~

a$ 0.4

0.2

0.0

DPaiiite@ w~El Allotrilxwphic1010c!#E4n

580 620 660 700 740Temperature/C

0.8I

0.2

0.0 -r..-580 620 660 700 740

Temperature/C

1.0

0.8.s

! 06# 04g ,

0.2

nn.

600 640 680 720 760Tsmpcr@ure/C

1.0

0.8

! 06if 0.4

0.2

An.

600 640 680 720 760Temperature/C

Fig.5. Calculatedevolutionofmicrostructureasa fimetionof the austenitegrainsizeand ooohngrate.

auat.enitegrain size suppresses Widmanstatten ferrite.Fqr @Matne reasons, an increase in the cooling ratewill Wtd to favour the formation of Widmanstattenfufiitl?.

These and other concepts are implicitly built intothe model presented here. This is because allotri-amorphic fkrrite, Widmanstatten ferrite and pearliteare allowed to grow together assuming thatthermodytmmicand kinetic conditions are satisfied.Their interactions are all taken into account duringthe course of transformation. It followsthat it shouldbe possible to reproduce the excellent quantitativedata recently published by Bodnar and Hansen [7].The presertt analysis is restricted to Fe-Si-Mn--Csteel rather than the microalloyed steels also studiedby Bodnar and Hansen.

The chemical composition of the steel is given inTable 1.Theyused heat-treatments whichled to threedilferent austenite grain sizes of 30, 55 and 100pm.In addition,, samples were cooled at five differentrates; 11, 16, 30, 59 and 100C/min.

Widmanstatten ferrite can nucleate directly fromthe austenite grain surfaces or indirectly fromallotriomorphic fernte-austenite interfaces. The pre-sent model includes both of these scenarios becauseof an approximation made in the formulation ofextended area in equation (10). It is strictly notpossible to separate out the contributions AOJfromeach phase (for all valuesof y) when the phases growat different rates. The result of the approximation isthereforeto allowWidmanstatten ferrite to form evenif the @ire austenite grain surface is decorated withallotrknnorphic ferrite. This is approximately equiv-alent to the secondary nucleation of Widmanstattenferrite and pearlite on allotriomorphic ferrite.

The reasonable overall levelof agreementbetweenexperiment and theory is illustrated in Fig. 4, for allof the data from Ref. [7];the quantitative data plottedin Fig. 4 are also included in Table 2 since thecompletedetails cannot be includedin the plot. In allcases where the allotriomorphic ferrite content isunderestimated, the Widmanstatten ferrite content isoverestimated. This is expected both beeause thecomposition of the austenite changes when allotri-omorphic ferrite forms and because its formationchanges the amount of austenite that is free totransform to Widmanstatten ferrite.

MICROSTRUCTUREMAPS

Figure 5 showcalculationswhichillustrate how themodel can be used to study the evolution ofmicrostructure as the sample cools. The calculationsare for the steel composition stated in Table 2.

All of the generally recognised trends arereproduced. The amount of Widmanstatten ferriteclearly increases with the austenite grain size, andwith the cooling rate within the range considered.Bodnarand Hansen[7]suggestedthat the effectofcoolingrateon theamountofWidmanstattenferrite


1.0

0.8ge~ 0.6A?j 04s>

0.2

on---

580 620 660 700 740 0.0

1.0

0.8gs8 0.6&$04z+

0.2

0.0

Temperature /C

3n PearliteWidmanstattenq Allotriommphic30pm101OC/min2.0wt%Mn

580 620 660 700 740

1.0

0.8n3# 0.6~ 0.4~

0.2

0.0

Temperature/C

I IW Pcadite

560 600 640 680 720 560 600 640 680 720Temperature/C Temperature /C

Fig. 6. Calculated evolution of microstructure as a function of the austenite grain size and the coolingrate. The steel composition is as given in Table 2, but with the carbon or manganese concentrations

increased as indicated,

was smaller than that of the austenite grain size (forthe values considered).This is also evident in Fig. 5.

The model also correctly predicts the influenceofalloying elements such as carbon or manganese. Atlarge cooling rates, Fig. 6 shows that an increase inthe carbon concentration reduces the amount ofWidmanstatten ferrite; this is because of thereduction in the temperature at which the Wid-manstatten ferrite first nucleates and also bysuppressing its growth rate.t The suppression oftransformation temperatures also reducesthe concen-tration of carbon in the residual austenite at whichthe formation of pearlite begins,sincethe y/y + @hasa positive slope on a plot of temperature vs carbonconcentration. The fraction of pearlite is thereforeincreased in the microstructure.

The effect of carbon at the slower cooling rate ismainly to suppress the formation of allotriomorphicferrite and hence to increase the proportion of

tFor an austenite grain size of 30pm, a cooling rate of101K/rein, Widmanstatten ferrite formation is sup-pressedto 693C(from 725C)with the increasein carbonconcentration. Similarly, the growth rate of Wid-manstatten ferrite at 675Cis reduced approximatelybya factor of four with the increasein carbon concentration.

pearlite (Fig. 6). At the austenite grain size of 30~mand a cooling rate of 11C/min, Widmanstattenferrite is essentially absent at both the carbonconcentrations studied.

An increase in the concentration of manganese to2 wt% (Fig. 6) has a differenteffectbecausethe effecton the pearlite transformation is less pronouncedthan carbon. Thus, the suppression of allotriomor-phic ferrite permits a greater degree of transform-ation to occur to Widmanstatten ferrite.

SUMMARY

The classical JohnsonMehlAvrami theory foroverall transformation kinetics has been successfullyadapted to deal with the simultaneous formation ofallotriomorphic ferrite, Widmanstatten ferrite andpearlite. A comparison with published experimentaldata has shown that the model developed isreasonable both quantitatively and with respect towell-establishedtrends. The model can now be usedto study theoreticallythe evolution of microstructureas a function of the alloy composition, the austenitegrain size and the cooling conditions. Further workis neededto includeother phases such as bainite, andto deal with microalloyingadditions. It would also be


interesting to incorporate nucleation sites other thanaustenite grain surfaces.

Ac/rnowledgemerrts-Weare grateful to the EngineeringandPhysicalSciencesResearchCouncil,and BritishSteelplc. forsupporting this work. It is a pleasure to acknowledgesomeveryhelpfuldiscussionswith Dr Graham Thewlis.HKDHBisgratefulto the RoyalSocietyfor a LeverhulmeTrust SeniorResearch Fellowship.

1

2

3

4,

5

6.

7.

8.

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kinetics of the simultaneous decomposition of austenite into several

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