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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
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[5] Hillert M. In: Zackay VF, Aaronson HI, editors. Decom-
position of austenite by diffusional processes. New York:
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[7] Quidort D, Br�eechet Y. Acta Mater 2001;49:4161.
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[10] Oblak JM, Hehemann RF. Transformations and hardena-
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[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.
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[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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