Deformation-assisted diffusion for the enhanced kinetics of dynamic phase transformation

Abstract

Comparison on the kinetics of two different phase transformations, including phase transformation after deformation and phase transformation during deformation (i.e. dynamic transformation, DT), reveals a new discovery that the transformation kinetics can be significantly enhanced in DT even under low driving forces. DT enables continuous generation of defects (e.g. dislocations) near the phase boundary, which can act as short-circuiting diffusion paths for atoms. The diffusivity of atoms is enhanced and the activation energy for the atom jump across the phase boundary is lowered under stress during DT, resulting in more pronounced grain growth as well as accelerated transformation kinetics.

Full text

MATER. RES. LETT.
2018, VOL. 6, NO. 11, 641–647
https://doi.org/10.1080/21663831.2018.1527787
ORIGINAL REPORT
Deformation-assisted diffusion for the enhanced kinetics of dynamic phase
transformation
Lijia Zhaoa,b, Nokeun Parka,c, Yanzhong Tiana,d,e, Akinobu Shibata a,dand Nobuhiro Tsuji a,d
aDepartment of Materials Science and Engineering, Kyoto University, Kyoto, Japan; bAdvanced Steel Processing and Products Research Center,
Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, CO, USA; cSchool of Materials Science and
Engineering, Yeungnam University, Gyeongsan, Republic of Korea; dElements Strategy Initiative for Structural Materials (ESISM), Kyoto
University, Kyoto, Japan; eShenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences,
Shenyang, People’s Republic of China
ABSTRACT
Comparison on the kinetics of two different phase transformations, including phase transformation
after deformation and phase transformation during deformation (i.e. dynamic transformation, DT),
reveals a new discovery that the transformation kinetics can be significantly enhanced in DT even
under low driving forces. DT enables continuous generation of defects (e.g. dislocations) near the
phase boundary, which can act as short-circuiting diffusion paths for atoms. The diffusivity of atoms
is enhanced and the activation energy for the atom jump across the phase boundary is lowered under
stress during DT, resulting in more pronounced grain growth as well as accelerated transformation
kinetics.
IMPACT STATEMENT
Deformation-enhanced grain growth is revealed in dynamic phase transformation, which will pro-
mote microstructure and property design of structural materials where phase transformations
occur.
ARTICLE HISTORY
Received 4 June 2018
KEYWORDS
Dynamic phase
transformation; deformation;
diffusion; kinetics; grain
growth
Solid-state phase transformation commonly exists in
materialsandplaysamajorroleincontrollingtheir
microstructures and properties [1–5]. Diusional phase
transformation generally incorporates nucleation and
grain growth. During the nucleation, a new interface
separating the product phase from the parent phase is
generated. The interface migrates into the surrounding
parent phase through jumps of atoms across the phase
boundary (growth of nuclei) [6,7]. As in a typical diu-
sional phase transformation, e.g. austenite (face-centered
cubic, FCC) to ferrite (body-centered cubic, BCC) trans-
formation in steels, interstitial carbon atoms experience
partitioning from ferrite to austenite by long-range dif-
fusion. Simultaneously, individual jumps of iron and
CONTACT Lijia Zhao zhaolj618@gmail.com Department of Materials Science and Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto
606-8501, Japan, Advanced Steel Processing and Products Research Center, Department of Metallurgical and Materials Engineering, Colorado School of Mines,
Golden, CO 80401, USA
Supplemental data for this article can be accessed here. https://doi.org/10.1080/21663831.2018.1527787
substitutional alloying elements across the interface lead
tothereconstructionoftheBCCcrystalfromtheparent
FCC austenite.
The kinetics of diusional phase transformation can
be inuenced by plastic deformation, which is often
applied during processing of materials. The diusivity of
either interstitial or substitutional atoms could be aected
by lattice defects (dislocation, vacancy, etc.) introduced
by plastic deformation, since the defects may lower the
planar density of atoms and provide extra free volumes
that can be favorable pathways for atomic diusion [8].
Basically, there are two dierent phase transformations
in high-temperature processes including plastic defor-
mation: (1) phase transformation after deformation of
© 2018 The Author(s). Published by Informa UK Limited, trading as Taylor& Francis Group.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.

642 L. ZHAO ET AL.
the parent phase (i.e. static transformation, ST) [9,10]
and (2) phase transformation during deformation (i.e.
dynamic transformation, DT) [4,5,11–15]. The deforma-
tion applied before or during transformation determines
how and where the defects are introduced, and therefore
could lead to dierent scenarios of transformation kinet-
ics aected by nucleation density and growth rate related
to atomic diusion.
In this work, the eect of plastic deformation on the
kinetics of ferritic transformation in a low-carbon steel
was compared between the route-ST (i.e. phase transfor-
mation after deformation) and the route-DT (i.e. phase
transformation during deformation). A surprising dis-
covery was found: the diusivity of atoms as well as the
transformation kinetics was signicantly enhanced even
underlowdrivingforcesintheroute-DT.Thisstudygives
a new perspective to tailor the microstructures in a wide
range of materials where phase transformations occur.
The material used in this study is an Fe–10Ni–0.1C
alloy (C: 0.111, Ni: 10.08, Mn: 0.01, P: 0.001, Si:
0.006, Al: 0.33, S: 0.0017, Fe: bal. (wt.%)). Para-
equilibrium temperature (Ap3) of the Fe–10Ni–0.1C
alloy is 583°C calculated by Thermo-Calc software
(time–temperature–transformation diagram is shown in
supplementary Figure S1). Cylindrical specimens with a
height of 12 mm and a diameter of 8 mm were machined
from a homogenized plate and used for simulating
the thermomechanical controlled process (TMCP) on
Thermecmastor-Z (Fuji Electronic Industrial Co. Ltd.).
All the specimens were austenitized at 1000°C for 300s.
In the route-ST, the austenitized specimens were cooled
to 520°C at a rate of 30°Cs−1, held for 60 s at 520°C to
homogenize the temperature in the specimens, uniaxially
compressed to a strain of 0.916 at a strain rate of 10°s−1
and then isothermally held at 520°C for dierent periods
of time followed by water quenching. In the route-DT,
the austenitized specimens were cooled to 520°C at a rate
of 30°C s−1, held for 60 s at 520°C, and then uniaxially
compressed to a strain of 0.916 at dierent strain rates
from 10° s−1to 10−3s−1followed by water quenching.
Microstructures at the sections parallel to the compres-
sion axis were characterized by optical microscopy (OM),
and a eld-emission type scanning electron microscope
(FE-SEM, FEI XL30S FEG) equipped with the electron
back-scattering diraction (EBSD) system. The point-
counting method was used for measuring the volume
fractions of ferrite on OM images. The area measured to
get the ferrite fraction in the present study was 33,232.1
(μm)2for each condition.
The comparison on transformation kinetics in dif-
ferent processing routes is summarized in Figure 1(a),
and corresponding microstructures are shown in Figure
1(b–e). More relevant microstructures can be seen in
supplementary Figures S2, S3 and S4. Here, the transfor-
mation time incorporates deformation time and isother-
mal holding time (after deformation). Compared to the
sluggish kinetics of static ferrite transformation without
deformation (indicated as ‘ST without Def.’), the kinetics
of ferrite transformation in the route-ST is signicantly
accelerated by the deformation of austenite which could
introduce a high density of defects as the nucleation sites
for the subsequent ferrite transformation [9,10]. The vol-
ume fraction of ferrite in the route-ST is 0.5% at 9 s (i.e.
1 s of deformation time and 8s of holding time after
the deformation, Figure 1(b)), and reaches 79% at 916 s
(Figure 1(c)). In the route-DT, the volume fraction of
ferrite is around 31% at a transformation time of 9 s
(corresponding to the time required for the compres-
sion deformation to a true strain of 0.916 at a strain
rate of 10−1s−1,Figure1(d)), and the fraction of fer-
rite dramatically increases to 86.2% at 916s (the time for
deformation at a strain rate of 10−3s−1,Figure1(e)). It
is of great interest that within the same transformation
time, the volume fraction of ferrite in the route-DT is
much higher than that in the route-ST, suggesting that
the kinetics is signicantly accelerated when the trans-
formation occurs during deformation compared to that
occurring after deformation.
The kinetics can be principally aected by the driving
forceforphasetransformation|Gαγ |,whichisgivenby
|Gαγ |=|Gchem
αγ |+|Gdef
γ|
−|Gdef
αγ (fα)+Gint
αγ (fα)|(1)
where Gchem
αγ (<0) is the chemical Gibbs energy dif-
ference between ferrite (α)andaustenite(γ)atthe
same temperature, Gdef
γ(<0) is the stored energy in
deformed γ,Gdef
αγ (fα)(>0)is the summation of elas-
tic and plastic mist energies between αand γat the
interface, and Gint
αγ (fα)(>0)isthefreeenergyofα/γ
interface. Gdef
αγ (fα)+Gint
αγ (fα)includes the area den-
sity of interfaces per volume and is a function of ferrite
fraction. The stored energy in austenite Gdef
γcan be cal-
culatedbythefollowingformula[16], assuming that the
stored energy is mostly due to dislocations accumulated
in the crystal during the plastic deformation,
Gdef
γ=μb2ρ(2)
where μis the shear modulus, ρis the dislocation
density, and bis the magnitude of the Burgers vector.
The relation between ow stress σof deformed austen-
ite and dislocation density follows the Bailey–Hirsch

MATER. RES. LETT. 643
Figure 1. (a) Variation in volume fraction of ferrite with transformation time at 520°C. (b–e) OM images of the corresponding microstruc-
tures obtained in the two routes (ST and DT). ‘F’ and ‘M’ indicate ferrite (light area) and martensite (dark area), respectively. Compression
axis is parallel to the vertical direction in the images.
equation [17],
σ=Mαμbρ1/2(3)
where Mis the Taylor factor of polycrystalline austenite,
and αis a numerical constant. Thus, combining Equa-
tions (2) and (3), the stored energy in austenite could be
described as
Gdef
γ=σ2/μM2α2(4)
In Equation (4), μM2α2isaconstant,sothatGdef
γis
proportional to the square of the ow stress σ2.Forthe
steel used in the present study, the values of M,μand α
are 3.08, 6.1 ×1010 Jm
−3and 0.2, respectively [18].
Figure 2(a)showsthetruestress-truestraincurves
of the specimens deformed at 520°C. The stored ener-
gies in γcalculated from Equation (4) are plotted against
the deformation time in Figure 2(b). It is clear that the
Gdef
γis lower in the route-DT than that in the route-
ST.Itshouldbenotedthatintheroute-DT,austenite

644 L. ZHAO ET AL.
Figure 2. (a) True stress-true strain curves of specimens
deformed to a strain of 0.916 in the route-ST (at a strain rate of
10° s−1) and the route-DT (at strain rates from 10−1to 10−3s−1)
at 520°C. (b) Stored energy in austenite (γ)inthetworoutes,
calculated by Equation (4).
to ferrite transformation occurred during the deforma-
tion. The transformed ferrite was further after its nucle-
ation, which means that less plastic strain than the total
strain was applied to γ. The actual stored energy in
deformed γis even less that that calculated by Equation
(4). Results of the comparison on all the parameters in
Equation (1) are summarized as follows: the chemical
driving force Gchem
αγ is equal in both routes at 520°C,
since it only depends on the temperature; the Gdef
γis
lower in the route-DT, as derived from Figure 2(b); the
term [Gdef
αγ (fα)+Gint
αγ (fα)] increases with increasing
the ferrite fraction [19], so it is higher in the route-DT
than in the route-ST according to Figure 1(a). Therefore,
the total driving force Gαγ should be smaller in the
route-DT.Thisisarathersurprisingconclusionthatthe
transformation kinetics in the route-DT is faster than that
in the route-ST even under lower driving forces.
Figure 3(a,b) shows grain average misorientation
(GAM) maps of microstructures obtained at a transfor-
mation time of 916 s in (a) the route-ST and (b) the route-
DT. The GAM map obtained by EBSD measurement can
be used to evaluate the degree of misorientation inside
each grain [20–22]. A higher GAM value (dark red color)
indicates higher misorientation within the grain. The fer-
rite statically transformed after plastic deformation in
the route-ST incorporates mostly equiaxed grains sur-
rounded by high-angle boundaries (HABs). The ferrite
dynamically transformed in the route-DT incorporates
mostly elongated coarse grains containing a large amount
of low-angle boundaries (LABs). The average GAM val-
ues of ferrite transformed in the route-ST and route-DT
are 0.34° and 0.63°, respectively (Figure 3(c)), indicat-
ing a more deformed ferrite structure in the route-DT.
Figure 3(d) shows variations of the apparent nucleation
density of ferrite in the two routes. The apparent nucle-
ation density of ferrite was calculated by dividing the
number of ferrite grains by the total area of ferrite [23,24].
As shown in Figure 3(d), the apparent nucleation den-
sity decreases with increasing the transformation time in
both routes due to the growth of nucleated ferrite. Within
the same transformation time at 520°C, the apparent
nucleation density in the route-DT is much lower than
that in the route-ST. This is reasonable since the higher
driving force (due to higher dislocation density) in the
route-ST enhanced the nucleation of ferrite. According to
Figure 1(a), the ferrite fraction in the route-DT is always
higher than that in the route-ST. Therefore, it can be
concluded that the faster transformation kinetics in the
route-DT is mainly due to the enhanced growth of ferrite
during deformation.
The dierence in ferrite grain growth behavior
between the two routes is further discussed here. In the
present study, all the experiments were conducted at
520°C, which is below the para-equilibrium temperature
(583°C) of the steel, so the substitutional element Ni can-
notfullydiuseinausteniteatthislowtemperature.Since
the transformation kinetics of static transformation with-
out deformation is slow (shown as ‘ST without Def.’ in
Figure 1(a)), carbon could be partitioned between ferrite
and austenite and its long-range diusion is considered to
dominate the growth of ferrite. It is worth noting that the
interaction between Ni and carbon or moving interfaces
is negligible due to the low binding energies between
them [25,26]. Thus, possible segregation of Ni in the
interfaceandthesolutedrageect,ifany,isexpectedto
be small in the present study.
The diusion of carbon in austenite and ferrite can be
aected by plastic deformation in terms of two aspects:
strain and stress. In the route-ST, the strain of 0.916 is
totally applied on austenite at a high strain rate of 1 s−1.
The static ferrite transformation occurs during isother-
mal holding after the deformation. In the route-DT at
lower strain rates (10−1to 10−3s−1), on the other hand,
the plastic deformation is rstly applied on austenite at

MATER. RES. LETT. 645
Figure 3. (a) and (b) are GAM maps obtained by EBSD measurements of specimens at a transformation time of 916 s in the route-ST and
route-DT, respectively. Non-ferrite phases (i.e. martensite and/or retained austenite) are painted in black. LABs with misorientation of
2–15° and HABs with misorientation above 15° are drawn in red and blue lines, respectively. C.A. indicates the compression axis. (c) and
(d) show distributions of GAM and variations in apparent nucleation density of ferrite grains transformed in two different routes (route-ST
and route-DT), respectively.
early stages and then on dual phases after the formation
of ferrite. It is, therefore, reasonable to consider that the
density of the lattice defects (dislocations, etc.) in austen-
ite, which provide potential nucleation sites for ferrite,
is higher in the route-ST. Therefore, the nucleation den-
sity of ferrite was much higher in the route-ST than in
theroute-DTasshowninFigure3(d). Figure 4schemat-
ically illustrates microstructural evolutions in the two
routes. Grain boundaries of austenite are strong obstacles
for dislocation slips due to the crystallographic discon-
tinuity. It is also expected that various slip systems are
activated near grain boundaries for satisfying compati-
bility between neighboring grains. As a result, dislocation
densities near grain boundaries of austenite are expected
to be higher than that at grain interior (Figure 4(a)). In
the route-ST, ferrite grains prefer to nucleate near grain
boundaries of austenite (and along deformation bands, if
any: Figure 4(b)), and consume dislocations accumulated
nearby the grain boundaries (Figure 4(c)). The ferrite
grains could experience early impingement due to the
higher nucleation density and thus the growth of ferrite
is suppressed near the austenite grain boundaries in the
route-ST.Thenucleatedferritegrainscouldgrowintothe
grain interior of austenite with less nucleation sites and
impingement (Figure 4(c)). In the route-DT, on the other
hand, the austenite is gradually strained at a slower strain
rate, leading to the lower density of nucleation sites for
ferrite at early stages of transformation (Figure 4(d)). The
austeniteandferritearebothdeformedatlaterstages,and
dislocations are preferentially stored near austenite grain
boundaries as well as austenite/ferrite phase boundaries
(Figure 4(e)). The dislocations can act as eective pipes
along which atoms can diuse faster [27]. Therefore, the
diusion of carbon atoms can be enhanced through the
fast routes, and thus the migration rate of austenite/ferrite
phaseboundariesisincreased.Thisistheessentialdier-
ence between DT and ST in ferrite growth, i.e. there are
more dislocations continuously generated near the mov-
ing phase boundaries during DT, and the diusion of car-
bon in ferrite and austenite can be enhanced due to these
additional ‘express-ways’, resulting in more pronounced
grain growth (Figure 4(f)).
The stress may also aect the growth of ferrite grains.
For a single atom, the atom must pass through a ther-
mally activated state with an activation energy to achieve
an eective jump over the interface. It has been simulated

646 L. ZHAO ET AL.
Figure 4. Schematic illustrations of (a–c) static ferrite transformation from deformed austenite (route-ST) and (d–f ) dynamic ferrite
transformation (route-DT). Orange and blue lines depict austenite and ferrite grains, respectively. Black lines represent defects (mainly
dislocations). The areas where atom diffusion is enhanced are highlighted by green color in (e and f).
[8] that under a compressive stress, the presence of lat-
tice defects (vacancy, etc.) near austenite/ferrite inter-
faces could reduce the planar density of atoms, provid-
ing extra free volume at moving interfaces, and thereby
lowers the extent of local rearrangement necessary to
move the interface. Dierent from the route-ST where
the transformed ferrite is almost free of defects (Figures
3(a) and 4(c)), the ferrite in the route-DT is continu-
ously deformed during transformation (Figures 3(b) and
4(f)). The introduced lattice defects could enhance the
accommodation of jumping atoms over the phase bound-
ary under stress, and then increase the migration rate of
the phase boundary (i.e. growth rate of ferrite).
In summary, our ndings reveal a signicant enhance-
ment of transformation kinetics in dynamic phase
transformation even under low driving forces. This is
attributed to the enhanced diusivity of atoms in the
migration of phase boundary (i.e. growth of ferrite)
under strain and stress applied by continuous deforma-
tion. The strain-enhanced diusivity of atoms results pri-
marily from dislocation-assisted diusion through short-
circuiting paths (pipes) near austenite/ferrite interfaces.
Stress may lower the activation energy for atoms to jump
across phase boundaries. This discovery could lead to
new strategies for tailoring required microstructures and
properties in many materials where phase transformation
occurs.
Disclosure statement
No potential conict of interest was reported by the authors.
Funding
This study was nancially supported by the Elements Strategy
Initiative for Structural Materials (ESISM) and the Grant-in-
Aid for Scientic Research (S) (No.15H05767), both through
the Ministry of Education, Culture, Sports, Science and Tech-
nology (MEXT), Japan.
ORCID
Akinobu Shibata http://orcid.org/0000-0001-8577-6411
Nobuhiro Tsuji http://orcid.org/0000-0002-2132-1327
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