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The role of carbon on the kinetics of bainite transformation in steels D. Quidort a, Y. Br�eechet b,* a IRSID-USINOR, Carbon Steels Metallurgy, Flat Products Center, BP 30320 Voie Romaine, 57283 Maizi�eeres-l�ees-Metz, France b LTCPM-ENSEEG, Institut National Polytechnique de Grenoble, BP 75 Domaine Universitaire, 38 402 St-Martin-d’H�eeres, France Abstract The roles of carbon, cementite precipitation and substitutional alloying elements are discussed with respect to their effects on the bainite transformation kinetics. Our description of the nucleation and growth steps has allowed the derivation of a kinetic model for the overall transformation. � 2002 Published by Elsevier Science Ltd. on behalf of Acta Materialia Inc. Keywords: Phase transformation; Bainite; Kinetics; Physical model 1. Introduction Among all austenite decomposition reactions, bainite transformation remains the least clearly understood. Bainite plays a key role among solid– solid phase transformations because it exhibits features of both diffusive and displacive transfor- mation. A number of morphological features and similarities with martensite as far as stress or strain effects on the bainite transformation have led some authors to develop a ‘‘displacive approach’’ to bainite (see Refs. [1,2] for a recent review of this viewpoint). On the opposite, the kinetic similarities with Widmanst€aatten ferrite have led other authors to develop a ‘‘diffusive approach’’ to bainite [3,4]. It is worth noticing that, when bainite and pearlite coexist at a given temperature, as illus- trated in Fig. 1, the scales of the ferrite differ by one order of magnitude, and the ferrite in bai- nite consists of leaves or different misorientation whereas the ferrite in pearlite is a single crystal [5]: this simple remark points to the difference between pearlite and bainite as a difference between a pla- nar front growth and a needle like growth. With this respect, bainite appears to be closer to Wid- manst€aatten ferrite or lath martensite than to pear- lite. This is in contrast with what is supported in ref. [6]. The issues raised are twofold: (i) what is the atomistic mechanism for the transformation of the crystal lattice from an FCC to a BCC structure? (ii) what are the kinetically limiting mechanisms? In the present contribution, we will focus on the second point only. With this respect, the key point of the controversies on the nature of bainite is related to the carbon content of ferrite just after the transformation front has swept the mother Scripta Materialia 47 (2002) 151–156 www.actamat-journals.com *Corresponding author. Tel.: +33-4-7682-6610; fax: +33-4- 7682-6644. E-mail address: yves.brechet@agora.ltpcm.inpg.fr (Y. Br�eechet). 1359-6462/02/$ - see front matter � 2002 Published by Elsevier Science Ltd. on behalf of Acta Materialia Inc. PII: S1359-6462 (02 )00121-5 phase. Since this question would require a ‘‘local in situ investigation’’, coupled with chemical analy- sis, at transformation rates of the order of sev- eral micrometers per second, direct experimental evidence for either theories is difficult to obtain. Therefore, one is left with indirect evidence from experimental investigation of transformation ki- netics. This contribution focuses on the respective roles of carbon diffusion and carbides precipitation on the transformation kinetics to draw some ideas on the limiting kinetic factors of upper bainite. 2. Measuring growth kinetics: deconvoluting nucle- ation and growth The overall transformation kinetics, as they are measured using classical dilatometry, convolute the nucleation and growth kinetics. Since the transformation mechanisms may differ for these two aspects, it is necessary to decouple the mea- surements of growth and nucleation. In order to do so, a two step heat treatment was performed, allowing the nucleation ferrite at high temperature of grain boundary allotriomorphic ferrite, which act as seeds for the further growth of bainite laths at lower temperatures. In the series of 0.5%C steels we have investigated [7], a cooling rate of about 200 �C was sufficient to prevent transformation of the specimen during cooling between the ferritic and the bainitic steps. Measuring optically the lengthening of bainite lath allow a direct evalua- tion of growth kinetics. The analysis implicitly assumes that the macroscopic growth velocity is constant as it has been verified several times in the literature using in situ techniques [8–11]. Knowing the growth rate and the overall trans- formation kinetics allows to evaluate the nucle- ation rate, without the difficult and almost impossible task of measuring a nucleation rate by optical metallography after short heat treat- ments. The analysis is based on the observation that isothermal transformation kinetics (volume fraction of bainite after a given time) in the up- per bainite temperature range usually follows a Johnson–Mehl–Avrami kinetics with a con- stant Avrami approximately equal to 2. This value is compatible with a constant one-dimensional growth rate of bainite plate and a constant nu- cleation rate. Details of the procedure used to deduce the nucleation kinetics from the overall and the growth kinetics can be found in Ref. [12]. Fig. 2 shows the growth rate and the nucleation rate at various temperatures for 0.5%C steels. These re- sults are discussed in the following sections. 3. Interpretation of the effect of carbon diffusion on growth kinetics Fig. 3 is a metallographic observation of a typical aggregate of bainitic laths in a silicon alloy of composition Fe–0.5C–5Ni–1.5Si. The specimen has been partially transformed into bainite at 400 �C and quenched to room temperature. A special etchant, prepared by mixing 2 g of Na2S2O5 with 100 ml of a saturated aqueous solution of Na2S2O3, reveals residual austenite as a light- etching constituent. It shows clearly a layer of stabilised austenite close to the bainitic front: this indicates that carbon enrichment >1%, very loca- lised at the reaction interface, has taken place. From these observations, we have derived a model for the growth kinetics based on the diffu- sion of carbon away from the reaction front as a limiting step, the details of which can be found in [7]. A model for the transformation kinetics Fig. 1. Coexisting pearlite and bainite in a Fe–0.5C–5Ni steels transformed at 450 �C: the scales of the ferrite constituent differ by one order of magnitude. 152 D. Quidort, Y. Br�eechet / Scripta Materialia 47 (2002) 151–156 should be able to account for (i) the temperature effect, (ii) the carbon content and (iii) the solute element content. In order to do so, the ingredients are (i) thermodynamic data for the driving force, (ii) transport equation for carbon and (iii) an ap- propriate choice of interfacial conditions. About the latter, investigation of the ternary Fe–Ni–C phase diagram using Thermo-Calc indicates that, at the transformation temperature, local equilib- rium would require Ni partitioning (Fig. 4). This would lead to very low values for the growth rates that are not observed experimentally. Therefore, we have chosen the paraequilibrium condition at the interface. The transport kinetics of carbon away from the interface is described using a Trivedi model for parabolic growth [13]. This analysis leads to an estimate of the maximum growth rate. Fig. 5 shows that this model describes accurately, without any adjustable parameters, the depen- dence of the growth kinetics both with tem- perature and carbon content. The agreement with Fig. 2. (a) Growth rate and (b) nucleation rate in different steels as a function of the temperature. The y-abscissa on the latter graph actually represents a scalar which exhibits the same temperature dependence as the nucleation rate [12]. Fig. 4. Comparison betweenexperimental data for Fe–6Ni–C alloys measured by Yada and Ooka [11] and model calculations (solid lines): the effect of both the temperature and the carbon content is correctly captured. Fig. 3. Optical metallography revealing the local stabilisation of the austenite close to the bainitic reaction front in a Fe–0.5C– 5Ni–1.5Si steel reacted at 400 �C. A narrow austenite layer (white) is clearly visible around each laths of bainitic ferrite (dark gray). The matrix in light gray is martensite. D. Quidort, Y. Br�eechet / Scripta Materialia 47 (2002) 151–156 153 absolute values is easy to get via an adjustable parameter which would describe the tip curvature of the needle, but the important information here is that the variations with %C and T are satisfac- torily described. Irrespectively of the details of the FCC/BCC transformation for Fe atoms, the phe- nomenon limiting the growth kinetics of bainite lath seems to be the carbon diffusion from the in- terface into the austenite. 4. Interpretation of the nucleation mechanism From the previous analysis, one can deduce the nucleation rates shown in Fig. 2b. The salient feature of this figure is that the nucleation rate decreases with decreasing temperature: this is in- consistent with a displacive interpretation of the nucleation rate [1]. Indeed, according to the iso- thermal martensite nucleation theory [14,15], the activation energy for nucleation would be taken as a linear function of driving force for the trans- formation without composition change which in- creases with decreasing the temperature. Contrary to the present observation, the nucleation rate would then increase as the temperature is lowered. Therefore we have analysed the thermal de- pendence via the classical nucleation theory in the regime where the temperature dependence is con- trolled by the diffusion coefficient and not by the driving force. The activation energy obtained from this analysis is compatible with a nucleation step being limited by carbon diffusion along the auste- nite grain boundaries [12]. There seems to be no controversy for the oc- currence of carbon partitioning during the forma- tion of the nucleus. Bhadeshia [1] already pointed out the linear correlation found in a large number of steels between the apparent Bs temperature and the driving force for diffusional nucleation of ferrite allowing carbon partition between the nu- cleus and the matrix. The correlation is not as satisfactory when any other driving force, and particularly that for martensitic nucleation (no composition change), are considered. This empir- ical result emphasises the important role played by carbon redistribution during the formation of a nucleus. 5. Effect of carbide precipitation When the silicon concentration is high enough to delay carbide precipitation, the description of the growth kinetics of bainitic laths could only focus on the diffusion of carbon away from the tip interface. However, when the silicon content is reduced, carbide precipitation accompanies the de- velopment of bainitic ferrite laths as a secondary process and provides new sinks for the flow of carbon in excess in the austenite. This can be ac- counted for by an additional flux of carbon to- ward precipitates. The quantitative formulation of this effect requires a model for carbide nucle- ation, which is difficult to validate. However, this interpretation allows to understand qualitatively why the removal of silicon and the concurrent precipitation of carbides leads to an accelerating multiplicative factor on the kinetics of bainitic growth (Figs. 2a and 5). 6. Effect of alloying elements The present model can be used to evaluate the effect of both temperature and carbon content on the bainite kinetics. The presence of alloying ele- ments is also taken into account only through their effect on the paraequilibrium concentrations and Fig. 5. Dilatometric signal recorded during the bainite trans- formation at 400 �C in a series of Fe–0.5C–5Ni–Si alloys showing the effect of the presence of cementite precipitates (Si < 1%) on the overall kinetics. 154 D. Quidort, Y. Br�eechet / Scripta Materialia 47 (2002) 151–156 the driving forces. However, comparing experi- mental data for the growth velocity of bainite laths in a series of Fe–0.5C–Ni alloys with the present model, we have demonstrated that the slowing down effect of Ni addition is larger than predicted by a pure thermodynamic effect [7]. This suggests that some interaction between Ni atoms and the moving interface induces a possible solute drag effect [16,17]. In addition, one of the important kinetic fea- tures of bainite reaction is the incomplete trans- formation: the transformation stops before the volume fraction of ferrite reaches the value ex- pected from the lever rule between ferrite and austenite. It is observed in high silicon or alu- minium alloys which produce carbide free bainite but also in alloys with strong carbide formers such as Mo and Cr. The measurements, presented in Fig. 6, of the overall kinetics in a series of alloys with increasing Cr concentrations show that the maximum volume fraction of bainite that forms during isothermal holding is very sensitive to the content in substitutional element [18]. Again, this result strongly supports the occurrence of a spe- cial interaction of the growing interface with the solute elements. The effect of Cr observed here is more important than the corresponding displace- ment of any equilibrium limit. Particularly, it weakens the opinion based on the T0 equilibrium limit commonly invoked to explain the incomplete reaction phenomenon [1]. 7. Conclusions Our current understanding of the bainite trans- formation kinetics is the following: • the nucleation rate is controlled by carbon diffu- sion at the austenite grain boundaries and can be described by classical nucleation kinetics; • the growth rate is controlled by carbon diffusion from the bainite/austenite front. This diffusion is ensured by transport in the austenite, the in- terfacial conditions for carbon concentration being given by paraequilibrium; • carbide precipitation provide extra sinks for carbon and the additional flux accelerate the transformation. A quantitative description of this effect is still lacking; • The effects of substitutional alloying elements via the thermodynamics (i.e. their effect on the paraequilibrium conditions for carbon) is min- ute compared to the experimentally observed ones, pointing toward an important contribu- tion of solute drag. A coherent self consistent description of the interplay between solute drag, interfacial conditions and growth kinetics, with- in the framework of a mixed mode analysis is still to be developed. This interpretation of both nucleation and growth bainite transformation kinetics has al- lowed to develop a complete model [12] with a minimal number of adjustable parameters, able to describe accurately the influence of carbon content and temperature for isothermal kinetics (Fig. 7a). The physical meaning of the model parameters allows a direct extension toward non-isothermal kinetics, as shown in Fig. 7b for continuous cool- ing at various cooling rates. The agreement is satisfactory. However, at higher cooling rates, the model overestimates the maximum fraction of bainite obtained after cooling. The reason for this discrepancy is not straightforward. It might come from a transition from upper bainite, with the presence of carbides at the austenite–ferrite Fig. 6. Effect of Cr on the isothermal decomposition at 480 �C into bainite of a series of Fe–0.2C–1.5Mn–Cr alloys. [18]. D. Quidort, Y. Br�eechet / Scripta Materialia 47 (2002) 151–156 155 interface acting as carbon sinks, to lower bainite where carbides precipitate inside the ferrite and cannot absorb the carbon rejected at thelath tips. Accordingly, the transformation kinetics into lower bainite are expected to be slower than the extrapolated transformation kinetics into upper bainite at the same temperature, and the final volume fraction of bainite is overestimated by the model. Acknowledgements The authors wish to thank Profs. Gary Pury and Gerhard Inden for fruitful discussions con- cerning the work presented here. References [1] Bhadeshia HKDH. Bainite in steels. second ed. London: The Institute of Materials; 2000. [2] Ohmori Y, Maki T. Mater Trans JIM 1991;32:631. [3] Aaronson HI, Reynolds WT, Shiflet GJ, Spanos G. Metall Trans A 1990;21:1343. [4] Hillert M. ISIJ Int 1995;35:1134. [5] Hillert M. In: Zackay VF, Aaronson HI, editors. Decom- position of austenite by diffusional processes. New York: Wiley Interscience; 1962. [6] Lee HJ, Spanos G, Shiflet GJ, Aaronson HI. Acta Metall 1988;36:1129. [7] Quidort D, Br�eechet Y. Acta Mater 2001;49:4161. [8] Goodenow RH, Matas SJ, Hehemann RF. Trans AIME 1963;227:651. [9] Rao MM, Winchell PG. Trans Met Soc AIME 1967;239: 956. [10] Oblak JM, Hehemann RF. Transformations and hardena- bility in steels, Climax Moly. Ann Arbor, MI, 1967. p. 15. [11] Yada H, Ooka T. J Jpn Inst Met 1967;31:766. [12] Quidort D, Br�eechet Y. ISIJ Int, in press. [13] Bosze WP, Trivedi R. Metall Trans 1974;5:511. [14] Pati SR, Cohen M. Acta Metall 1969;17:189. [15] Olson GB, Cohen M. Metall Trans A 1976;7:1897. [16] Purdy GR, Br�eechet YJM. Acta Metall 1995;43:3743. [17] Oi K, Lux C, Purdy GR. Acta Mater 2000;48:2147. [18] Desch�eere D, Quidort D. unpublished results. Fig. 7. Comparison between experimental kinetics in a Fe–0.5C–0.8Mn–0.3Cr alloy and the overall kinetics model: (a) isothermal conditions and (b) continuous cooling, same set of parameters [12]. 156 D. Quidort, Y. Br�eechet / Scripta Materialia 47 (2002) 151–156 The role of carbon on the kinetics of bainite transformation in steels Introduction Measuring growth kinetics: deconvoluting nucleation and growth Interpretation of the effect of carbon diffusion on growth kinetics Interpretation of the nucleation mechanism Effect of carbide precipitation Effect of alloying elements Conclusions Acknowledgements References
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