![b) shows the IPF and GOS maps of the CHTed specimens. In the IPF map, the grains of the cold-rolled specimen showed strong < 100 > //ND and < 112 > //ND textures, while the recrystallized grains exhibited a texture of < 111 > //ND. The recrystallized grains are colored blue on the GOS map. Analogous to the asreceived specimen, the CHT800 in Fig. 2 (b) still shows heavily deformed grains. The recrystallization of IF steel is known to initiate between 500 °C and 600 °C [45-47] . In this study, owing to the low annealing time (11 s), recrystallization hardly occurred during CHT at 800 °C. New grains nucleate and grow in CHT with T max = 850, 870, and 900 °C. Particularly, the IPF and GOS maps of the CHT900 show that recrystallization occurred throughout the material and new equiaxed grains developed. In contrast, the microstructure of the ECTed specimens showed significantly enhanced recrystallization. During the ECT, the higher the j, the faster the temperature increases. Hence, we focused on the ECT with j = 210 A/mm 2 as the athermal effect, in this case, is expected to be the strongest among the others (40, 50, 70, and 140 A/mm 2 ). Fig. 2 (c) shows the IPF and GOS maps of specimens ECTed with j = 210 A/mm 2 . As in the CHTed specimens, the recrystallized area in the ECTed specimens increased with T max . Importantly, the ECTed specimens were recrystallized even at T max ≤ 800 °C. For the ECT700, the IPF map is similar to that of the as-received specimen, and recrystallization rarely occurs, as evidenced by the GOS map. For the ECT760, the IPF and GOS maps clearly indicate new grains nucleating at the expense of deformed grains. Furthermore, for the ECT800, recrystallization occurred throughout the material, similar to the CHT900. The grain size of ECT860 was larger than that of CHT900, indicating that the grain growth occurred during that short ECT. The recrystallization fraction evaluated from the GOS map distinctly shows enhanced recrystallization by the electric current (red curves in Fig. 2 (d)). The recrystallization fraction of ECT increases with T max , analogous to that of CHT; however, it starts to increase at lower temperatures. Additionally, we measured the Vickers hardness of the CHTed and ECTed specimens, which is another indicator of recrystallization (black curves in Fig. 2 (d)). In both the CHTed and ECTed specimens, the Vickers hardness decreased with T max as the deformed grains disappeared by recrystallization. The hardness of the ECTed specimen started to decrease at lower temperatures than that of the CHTed specimen. The recrystallization occurring during ECT at lower temperatures and shorter times than CHT implies that both the athermal and thermal effects coexist when the electric current is applied, as previously reported [ 24 , 35 , 48 ].](https://www.researchgate.net/profile/Kyeongjae-Jeong/publication/359830238/figure/fig3/AS:1150501764771842@1651312404449/b-shows-the-IPF-and-GOS-maps-of-the-CHTed-specimens-In-the-IPF-map-the-grains-of-the_Q320.jpg)
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Acta Materialia 232 (2022) 117925
Contents lists available at ScienceDirect
Acta Materialia
journal homepage: www.elsevier.com/locate/actamat
Full length article
Athermally enhanced recrystallization kinetics of ultra-low carbon
steel via electric current treatment
Kyeongjae Jeong
a , 1
, Sung-Woo Jin
a , 1
, Sung-Gyu Kang
a
, Ju-Won Park
a
, Hye-Jin Jeong
a
,
Sung-Tae Hong
b
, Seung Hyun Cho
c
, Moon-Jo Kim
d , ∗, Heung Nam Han
a , ∗
a
Department of Materials Science and Engineering and Research Institute of Advanced Materials, Seoul National University, Seoul 08826, Republic of Korea
b
School of Mechanical Engineering, University of Ulsan, Ulsan 44610, Republ ic of Korea
c
Safety Measurement Center, Korea Research Institute of Standards and Science, Daejeon 34113 Republic of Korea
d
Smart Liquid Processing R&D Department, Kore a Institute of Industrial Technology, Incheon 21999, Repub lic of Korea
a r t i c l e i n f o
Article history:
Received 20 January 2022
Revised 29 March 2022
Accepted 4 April 2022
Available online 8 April 2022
Keywo rds:
Electric current treatment
Recrystallization kinetics
Non-isothermal
Athermal effect
Annealing
a b s t r a c t
The direct application of electric current as well as heat treatment can be used to recrystallize metallic
materials. Electric current enhances the recrystallization kinetics, making the process time- and energy-
saving. The enhanced recrystallization kinetics observed during electric current treatment cannot be ex-
plained by Joule heating alone, and its quantitative analysis is yet to be conducted. This study system-
atically investigates the athermal effect of electric current on the recrystallization kinetics of ultra-low
carbon steel. Specimens were subjected to electric current at various current densities to reach the target
temperatures, and the resulting recrystallization kinetics were analyzed. A comparison with the speci-
mens heat-treated at comparable target temperatures clearly shows that electric current treatment en-
hances the degree of recrystallization, and the recrystallization kinetics have a unique tendency to de-
crease and then increase as the electric current density increases. From the recrystallization fraction dif-
ference between the electric current-treated and heat-treated specimens, we deduce the athermal effect
of the electric current on recrystallization and describe the athermally enhanced recrystallization kinet-
ics using the Johnson-Mehl-Avrami-Kolmogorov equation considering the effective activation energy and
temperature. The calculated recrystallization fraction implies that the athermal effect of the electric cur-
rent becomes more pronounced with increasing electric current density. This study suggests that the
athermal effect of electric current in the material fabrication process can be evaluated and predicted.
©2022 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Thermally activated recrystallization is a process in which new
strain-free grains nucleate and grow at the expense of the sur-
rounding deformed grains. Industrially, recrystallization is essential
for softening cold-worked metallic materials and can be achieved
by annealing the material at elevated temperatures. Many stud-
ies have been conducted using conventional heat treatment (CHT)
to explore the degree of recrystallization and the correspond-
ing changes in microstructures and mechanical properties under
various temperature and time conditions [1–3] . However, CHT is
an energy- and time-consuming process that may cause thermal
degradation and surface oxidation.
∗Corresponding authors.
E-mail addresses: moonjokim@kitech.re.kr (M.-J. Kim), hnhan@snu.ac.kr (H.N.
Han)
.
1 These authors contributed equally to this work.
The direct application of electric current can be an effective al-
ternative to CHT, as the deformed material can be annealed with
a significantly reduced processing time and energy [4] . Electric
current induces changes in the mechanical properties and mi-
crostructure of metallic materials. Numerous researchers have re-
ported electroplasticity, in which the mechanical properties related
to plastic deformation are altered by the electric current [5–9] . Mi-
crostructure tailoring, such as texture evolution [10] , phase trans-
formation [11] , precipitation [12–14] , and self-healing [15] , can be
effectively controlled using electropulsing treatment (EPT) even
without deformation. The electric current can accelerate the re-
crystallization kinetics of various metal-based materials, such as
aluminum [16] , magnesium [ 17 , 18 ], and titanium alloys [19] . Park
et al. [20] conducted an EPT on metal sheets and revealed the
athermal effect of the electric current on the recrystallization be-
havior. They showed that EPT required a shorter time and lower
temperature than CHT owing to the athermally enhanced recrys-
tallization kinetics.
https://doi.org/10.1016/j.actamat.2022.117925
1359-6454/© 2022 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
K. Jeong, S.-W. Jin, S.-G. Kan g et al. Acta Materialia 232 (2022) 117925
The thermal and athermal effects of the electric current in-
duce changes in metal-based materials. Although several studies
have suggested that the electric current-induced plasticity or mi-
crostructure of metallic materials is attributed to a thermal ef-
fect, namely Joule heating [21–23] , recent studies have reported
the evidence of the athermal effect [ 15 , 24–28 ]. To substantiate the
athermal effect, electron wind [ 29 , 30 ], pinch effect [31] , and mag-
netic effect [32] have been proposed. First, in the electron wind
theory, linking to electromigration, momentum transfer from the
drift electrons directly enhances the dislocation mobility. When the
electric current density (j) exceeds 10
3 A/mm
2 [ 29 , 33 ], the dislo-
cation movement by momentum transfer becomes effective. How-
ever, as shown in previous studies [ 5 , 6 , 20 , 34–36 ], the athermal ef-
fect can occur even at j = 10
1-2 A/mm
2
, denoting that the elec-
tron wind theory cannot fully account for the athermal effect. Sec-
ond, in the pinch effect theory, when a pulsed current is applied,
a compressive stress is generated by the pressure created by the
intrinsic magnetic field. The associated effect with current puls-
ing, however, has been found to be negligible and concluded to
be the only secondary factor in the athermal effect [ 29 , 31 ]. Third,
according to the magnetic effect theory, the plastic behavior is af-
fected by the facilitation of dislocation depinning induced by the
current-induced magnetic field. However, it requires the presence
of impurity atoms and forest dislocations. As a result, the magnetic
effect theory can only describe the electroplastic phenomenon in
restricted cases [ 32 , 37 , 38 ].
Recently, Kim et al. [39] elucidated that the origin of elec-
troplasticity is because of the weakening of atomic bonding near
defects owing to the charge imbalance under the applied elec-
tric current. Zhao et al. [26] demonstrated that defect reconfigura-
tion is the origin of macroscopic electroplasticity, which cannot be
achieved by simple Joule heating. They showed that the dislocation
pattern can be changed from planar to wavy slip during the elec-
troplastic deformation of a Ti-7Al alloy. Rudolf et al. [27] proposed
that dislocation scattering by thermal phonons and electrons can
be a mechanism of electroplasticity, supporting that neither elec-
tron wind nor local Joule heating, which is another possible mech-
anism of electroplasticity [40] , can adequately explain the electro-
plasticity effect. Despite effort s to better understand the athermal
effect, no studies have been conducted to comprehensively quan-
tify the athermal effect of the electric current in a specific and
elaborate manner, considering the mechanism of the electric cur-
rent effect. This is because Joule heating occurs in conjunction with
the application of the electric current, making it difficult to isolate
the athermal effect from the thermal effect.
Here, we investigate and quantify the athermal effect of electric
current in the recrystallization of ultra-low carbon steel. By apply-
ing electric current with various jvalues and durations, we could
precisely control the peak temperature (T
max
). A comparison of the
microstructure and mechanical properties of specimens annealed
by electric current treatment (ECT) and CHT enables the evalua-
tion of the athermal effect of electric current. The athermally en-
hanced recrystallization of ultra-low carbon steel can be described
by the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation consid-
ering the effective activation energy and temperature.
2. Materials and methods
2.1. Materials and experimental setup
Ultra-low carbon interstitial free (IF) steel (Fe-0.005C-0.08Mn-
0.06Al-0.05Si-0.04Ti-0.011P in wt.%) was used in this study. It was
cold-rolled to 0.6 mm thickness with an 80% reduction ratio. Spec-
imens for annealing and microstructural analysis were prepared
from the cold-rolled sheet to dimensions of 10 ×40 ×0.6 mm
3
in the transverse direction (TD), rolling direction (RD), and nor-
mal direction (ND), respectively. Fig. 1 (a) depicts the device used
for providing electric current to the specimen, which is designed
such that one holder could move along the lubricant rail to off-
set the thermal expansion caused by the application of the elec-
tric current. Fig. 1 (b) shows the schematics of the experimental
parameters related to ECT. The electric current was applied par-
allel to the RD of the specimen using direct current (DC) power
supplies (for electric current ≤400 A: Weltech, Republic of Ko-
rea; for ≥400 A: Vadal SP-10 0 0U, Hyosung, Republic of Korea). For
the ECTed specimen, j= 40, 50, 70, 140, and 210 A/mm
2
, and the
duration was adjusted to reach T
max = 70 0, 760, 80 0, and 860 °C,
as shown in Fig. 1 (c) (temperature history of ECTs with j= 40,
50, 70, and 140 A/mm
2 are shown in Fig. S1). The ECTed speci-
mens with T
max
= 70 0, 760, 80 0, and 860 °C are labeled as ECT700,
ECT760, ECT800, and ECT860, respectively. An infrared thermal
camera (FLIR T430, FLIR Systems, Sweden) was used to measure
the temperature of the specimens. The specimens were coated
with black thermal paint to correct the emissivity. After apply-
ing electric current, the specimens were air-cooled to 25 °C. CHTed
specimens were annealed in a preheated (1200 °C) box furnace
(Lindberg/Blue M, Thermo Electron, USA) until T
max = 800, 850,
870, and 900 °C were reached for comparison, as shown in Fig. 1 (d).
The CHTed specimens with T
max
= 800, 850, 870, and 900 °C are la-
beled as CHT800, CHT850, CHT870, and CHT900, respectively. The
temperature of the specimens during CHT was measured in real
time using a K-type thermocouple attached to the center of the
specimen surface. The specimens were then air-cooled to 25 °C af-
ter the heat treatment.
The uniformity of the temperature across the specimens in ECT
and CHT can be ensured by Fig. S2 showing the measured and cal-
culated temperature distribution and history. In the case of ECT
specimen, the infrared thermal camera can capture the temper-
ature distribution in real time during the measurement process.
Fig. S2(a) shows the uniform temperature distribution across the
ECT860 specimen presented in Fig. 1 (c), measured at T
max
. The
temperature history curves calculated through numerical simula-
tions (using commercial software ABAQUS) based on the finite el-
ement method for ECT860 in Fig. 1 (c) and CHT900 in Fig. 1 (d) fol-
low the experimental ones, as illustrated in Fig. S2(b, c). The insets
display the calculated temperature distribution of the specimens
when the T
max is reached. The temperature deviation ( T) in the
specimen at T
max is very small ( T ∼10 °C in ECT860 and T ∼
8 °C in CHT900), and there is no deviation in the temperature his-
tory at the center (actual measurement location) and the edge of
the surface with the greatest T. In addition, T around the center
of the specimen surface is ∼5 °C in both cases, and the thickness
of the specimen is sufficiently small so that there is no T in the
thickness direction. Therefore, we can confirm that the tempera-
ture distribution is uniform throughout the specimen in both ECT
and CHT. The electrical and thermal properties used in the finite
element simulations are listed in Table S1.
2.2. Microstructure characterization
Specimens for microstructure characterization were prepared
by standard mechanical grinding, polishing, and electropolishing
(10% perchloric acid and 90% ethanol solution at 20 V). An elec-
tron backscatter diffraction (EBSD) system (EDAX/TSL, Hikari, USA)
coupled with field emission scanning electron microscopy (FE-
SEM, SU70, Hitachi, Japan) was used to observe the microstruc-
ture. The acceleration voltage, working distance, and tilting an-
gle were 15 kV, 15 mm, and 70 °, respectively. Post-processing
was performed using the TSL OIM Analysis 7 software. The crit-
ical misorientation angle for grain identification was set to 15 °.
The grain size and kernel average misorientation (KAM) were mea-
sured to investigate the effect of jon the grain growth and dis-
2
K. Jeong, S.-W. Jin, S.-G. Kan g et al. Acta Materialia 232 (2022) 117925
Fig. 1. Instrumental setup and temperature history. (a) Instrumental setup for ECT. (b) Schematic illustration of the ECT conditions with va rious jval ues and durations. (c,
d) Measured temperature history of specimens (c) ECTed with j= 210 A/mm
2
and (d) CHTed in the furnace.
location recovery during ECT. KAM is an indicator of the local
grain misorientation and the density of geometrically necessary
dislocations for non-recrystallized pixels [41] . The recrystallized
grains were identified by grain orientation spread (GOS) (grains
with GOS < 2 °were classified as recrystallized grains). In addi-
tion to the microstructural analysis, we investigated the recrystal-
lization behavior by conducting a hardness test of the annealed
specimens using a Vickers hardness tester (430SVD, Wolpert group,
Germany). A force of 5 kgf was applied for 10 s, and the measure-
ment was repeated five times per specimen to obtain an average
value.
2.3. Measurement of elastic modulus using ultrasonic technique
We measured the athermal effect of the electric current from
the change in the elastic modulus. A laser-based ultrasonic tech-
nique capable of capturing the elastic modulus with high accuracy
was utilized to measure the elastic modulus under the application
of electric current. For the measurement, rod-shaped specimens
with a square cross-section (1 ×1 ×200 mm
3
) were obtained
from cold-rolled steel sheets (Fe-0.001C-0.2 Mn in wt.%) with a
grain size of 3 μm. The electric current was generated using a
DC power supply (NEO-500PS, Hyundai, South Korea). jwas set to
100, 150, 20 0, 225, 250, 275, 30 0, and 325 A/mm
2
, and the pulse
duration was 0.1 s. A Q-switched Nd:YAG pulse laser (Brilliant b,
Quantel, France) and focusing system were used to generate ultra-
sonic waves. A laser doppler vibrometer system (OFV-505, Polytec,
Germany) was used to measure the transmitted ultrasonic waves.
The reproducibility of the longitudinal wave velocity in the speci-
men was tested, and the precision error was less than ±0.1%. The
electric current reached the target value after 1 ms. To measure
the elastic modulus while minimizing the thermal effect, the wave
velocity was detected 5 ms after the electric current was applied.
To accurately detect the propagating laser ultrasonic wave while
eliminating the effect of thermal expansion caused by Joule heat-
ing, one end of the specimen was maintained free. Further details
are described in a previous study [39] .
3. Computational details
The temperature history induced by ECT ( Fig. 1 (b, c)) implies
that the annealing process in this study is the anisothermal pro-
cess. To predict the recrystallization fraction in this process, the
rule of additivity [42] must be satisfied. According to Scheil [42] ,
the onset of recrystallization under anisothermal annealing can be
identified by considering the time taken at a specific temperature
( t
i
) divided by the incubation time ( τi
). This represents the frac-
tion of the total nucleation time required. When the sum of these
fractions reaches unity, recrystallization begins:
n
i =1
t
i
τi
= 1 or
t
t
0
dt
τ(
T
)
= 1 (1)
t
t
0
dt
τX
(
T
)
=
T
T
0
1
τX
(
T
)
dt
dT
dT = 1 (2)
The additivity rule can be extended to include the entire range
of recrystallized fractions from 0 to 1 beyond the initiation of re-
crystallization as follows [43] : from the given isothermal trans-
formation diagram, the time τX
(T ) to reach a certain recrystal-
lized volume fraction, X, can be calculated. Thereafter, the frac-
tional completion on continuous annealing occurs when the inte-
gral reaches unity, as follows:
The general form of Eq. (2) considering s number of stages in
the continuous annealing cycle (see Fig. S3) is as follows [44] :
t
s
t
0
dt
τX
(
T
)
=
t
1
t
0
dt
τ+
t
2
t
1
dt
τ+ ···+
t
s
t
s −1
dt
τ
=
T
1
T
0
1
τ
dt
dT
d T +
t
2
t
1
d t
τ+
T
2
T
1
1
τ
d t
d T
d T +
t
4
t
3
d t
τ+ ···
=
s
i =1
T
i
T
i −1
1
τ
dt
dT
d T +
d t
τT
i
(3)
3
K. Jeong, S.-W. Jin, S.-G. Kan g et al. Acta Materialia 232 (2022) 117925
Fig. 2. Microstructure analysis of CHTed and ECTed specimens. (a) IPF map of the as-received specimen. (b, c) IPF (upper) and GOS (lower) maps of (b) CHTed specimens
with T
max = 800, 850, 870, and 900 °C and (c) ECTed specimens with j= 210 A/mm
2 and T
max = 70 0, 760, 80 0, and 860 °C. (d) Measured recrystallization fractions and
corresponding Vickers hardness values of CHTed and ECTed specimens. Note. RX is an abbreviation for recrystallization and was used only in the axis labels and legends of
graphs to improve readability.
Therefore, for a multi-stage annealing cycle of ( s ) anisothermal
and isothermal stages each, Eq. (2) can be modified as follows:
s
i =1
T
i
T
i −1
1
γi
τdT +
dt
τT
i
= 1 (4)
where γi ( = d T /d t ) is the rate of temperature change (negative
for cooling and positive for heating) of the i th anisothermal stage,
and T
i
the isothermal holding stage following the i th anisothermal
stage.
The isothermal recrystallization kinetics of materials is de-
scribed by the JMAK equation:
X = 1 −exp
{
−k
(
T
)
t
n
} (5)
where k (T ) is a term incorporating both grain nucleation and
growth rates; tis the holding time, and n the Avra mi (or JMAK)
exponent. From Eq. (5) , the time at which the recrystallization has
reached a certain fractional completion X
V is given as:
τX
V
(
T
)
=
1
k
(
T
)
ln
1
1 −X
V
1 / n
(6)
By substituting Eq. (6) into Eq. (4) and rearranging the terms,
the equation predicting the recrystallized fraction during continu-
ous annealing can be expressed as [44] :
X
V = 1 −exp
−
s
i =1
T
i
T
i −1
k
(
T
)
1 /n
γi
dT +
k
(
T
)
1 /n
dt
T
i
n
(7)
In this study, there was no applicable isothermal annealing
stage during ECT. Accordingly, the isothermal holding time interval,
dt, is zero, and thereby,
∫
k (T )
1 /n
dt at temperature T
i
in Eq. (1) be-
comes zero. By applying k (T ) = Aexp( −Q/RT ) , where A , Q, and R
are the pre-exponential factor, apparent activation energy, and gas
constant, respectively, Eq. (7) can be rewritten as:
X
V = 1 −exp
−A
s
i =1
T
i
T
i −1
(
exp
(
−Q/ RT
) )
1 /n
γi
dT
n
(8)
Finally, the recrystallization kinetics during continuous anneal-
ing can be predicted using Eq. (8) . The variables s , T
i −1
, T
i
, and γi
are obtained as input data from the measured temperature history
curves, and the optimal parameters, A , n , and Qcan be determined
based on the genetic algorithm (GA) and the least-squares method
using MATLAB.
4. Results and discussion
4.1. Microstructure analysis
The recrystallization of the cold-rolled IF steel is enhanced by
the electric current. It can be confirmed from the microstruc-
tural analysis of the CHTed and ECTed specimens. Fig. 2 (a) shows
the inverse pole figure (IPF) of the as-received specimen with a
severely deformed microstructure during the cold-rolling process.
4
K. Jeong, S.-W. Jin, S.-G. Kan g et al. Acta Materialia 232 (2022) 117925
Fig. 3. Microstructure analysis of ECTed specimens with various j. (a) IPF and GOS maps of the ECTed specimens with j= 40, 50, 70, 14 0, and 210 A/mm
2
, and T
max
= 760 °C.
(b) Recrystallization fractions of the ECTed specimens with five different j, and T
max
= 70 0, 760, 800, and 860 °C.
Fig. 2 (b) shows the IPF and GOS maps of the CHTed specimens.
In the IPF map, the grains of the cold-rolled specimen showed
strong < 10 0 > //ND and < 11 2 > //ND textures, while the recrystal-
lized grains exhibited a texture of < 111 > //ND. The recrystallized
grains are colored blue on the GOS map. Analogous to the as-
received specimen, the CHT800 in Fig. 2 (b) still shows heavily de-
formed grains. The recrystallization of IF steel is known to initiate
between 500 °C and 600 °C [45–47] . In this study, owing to the low
annealing time (11 s), recrystallization hardly occurred during CHT
at 800 °C. New grains nucleate and grow in CHT with T
max = 850,
870, and 900 °C. Particularly, the IPF and GOS maps of the CHT900
show that recrystallization occurred throughout the material and
new equiaxed grains developed. In contrast, the microstructure of
the ECTed specimens showed significantly enhanced recrystalliza-
tion. During the ECT, the higher the j, the faster the temperature
increases. Hence, we focused on the ECT with j= 210 A/mm
2 as
the athermal effect, in this case, is expected to be the strongest
among the others (40, 50, 70, and 140 A/mm
2
). Fig. 2 (c) shows
the IPF and GOS maps of specimens ECTed with j = 210 A/mm
2
.
As in the CHTed specimens, the recrystallized area in the ECTed
specimens increased with T
max
. Importantly, the ECTed specimens
were recrystallized even at T
max ≤800 °C. For the ECT700, the IPF
map is similar to that of the as-received specimen, and recrys-
tallization rarely occurs, as evidenced by the GOS map. For the
ECT760, the IPF and GOS maps clearly indicate new grains nu-
cleating at the expense of deformed grains. Furthermore, for the
ECT800, recrystallization occurred throughout the material, simi-
lar to the CHT900. The grain size of ECT860 was larger than that
of CHT900, indicating that the grain growth occurred during that
short ECT. The recrystallization fraction evaluated from the GOS
map distinctly shows enhanced recrystallization by the electric
current (red curves in Fig. 2 (d)). The recrystallization fraction of
ECT increases with T
max
, analogous to that of CHT; however, it
starts to increase at lower temperatures. Additionally, we measured
the Vickers hardness of the CHTed and ECTed specimens, which
is another indicator of recrystallization (black curves in Fig. 2 (d)).
In both the CHTed and ECTed specimens, the Vickers hardness de-
creased with T
max
as the deformed grains disappeared by recrystal-
lization. The hardness of the ECTed specimen started to decrease at
lower temperatures than that of the CHTed specimen. The recrys-
tallization occurring during ECT at lower temperatures and shorter
times than CHT implies that both the athermal and thermal effects
coexist when the electric current is applied, as previously reported
[ 24 , 35 , 48 ].
Recrystallization by ECT shows a unique dependence on j.
We investigated the microstructural changes of ECT700, ECT760,
ECT800, and ECT860 with lower jvalues (40, 50, 70, and
140 A/mm
2
). As the ECT time required to reach T
max
increases with
decreasing j, the increased thermal effect (by Joule heating) of the
ECT is expected at a lower j. However, the IPF and GOS maps of
ECT760 with various jvalues shown in Fig. 3 (a) (microstructures of
specimens ECTed to other T
max values can be found in Fig. S4) re-
veal that the recrystallized area does not simply increase with de-
creasing j, and the smallest area is recrystallized at j= 70 A/mm
2
.
This is consistent with other ECTs with different T
max
(Fig. S4). The
recrystallization fraction as a function of jin Fig. 3 (b) (combined
with the ECT results at j= 210 A/mm
2
) clearly shows a V-shaped
trend. For ECT700 and ECT860, the recrystallization fractions were
measured to be approximately 15% and 95%, respectively, for ev-
ery jcondition. This indicates that recrystallization was minimal
at T
max = 700 °C but nearly complete at T
max = 860 °C irrespective
of j. For ECT760 and ECT800, the recrystallization fraction clearly
decreased with the increasing jwhen j≤70 A/mm
2
. Conversely,
when the j≥70 A/mm
2
, it increased with the increasing j.
The Vickers hardness implies a similar recrystallization ten-
dency with j. Fig. 4 (a, b) show the Vickers hardness and recrys-
tallization fraction of ECT760 and ECT800, respectively. The hard-
ness shows an inverse trend to the recrystallization fraction, with
the highest Vickers hardness (138 and 88 Hv for T
max = 760 and
800 °C, respectively) at j= 70 A/mm
2
. Additionally, we measured
the average grain size for recrystallized grains and KAM for non-
recrystallized grains. The average grain size of recrystallized grains
as a function of jis plotted as a V-shaped curve, with the lowest
value at j= 70 A/mm
2
, as shown in Fig. 4 (c). This apparently indi-
cates that the growth of newly formed grains as well as recrystal-
lization are dependent on j, thus implying that the annealing pro-
cess by ECT is affected by j. Fig. 4 (d) shows the change in the value
of KAM of non-recrystallized grains. In both ECT760 and ECT800,
the KAM value increased until 70 A/mm
2 and then decreased with
the increasing j, indicating that the degree of dislocation recov-
ery was the smallest at j= 70 A/mm
2
. However, even ECT with
j=70 A/mm
2 enhanced the recrystallization kinetics. The recrys-
tallization fractions of ECT760 and ECT800 with j= 70 A/mm
2
are comparable to those of CHT850 and CHT870 ( Fig. 5 ). Hence,
the mixture of thermal and athermal effects of the electric cur-
rent makes the ECT outperform the CHT in the recrystallization of
heavily deformed material and provides a unique dependence of
recrystallization on the j.
5
K. Jeong, S.-W. Jin, S.-G. Kan g et al. Acta Materialia 232 (2022) 117925
Fig. 4. Recrystallization fraction and Vickers hardness for the ECTed specimens with five different jand T
max
= (a) 760 °C and (b) 800 °C. (c) Average size of recrystallized
grains in ECTed specimens. (d) KAM of non-recrystallized grains in ECTed specimens with T
max
= 76 0 and 800 °C.
Fig. 5. Comparison of T
max
between the CHTed and ECTed specimens with compa-
rable recrystallization fraction.
4.2. Thermal effect of the electric current on recrystallization kinetics
The expected recrystallization fraction, considering the thermal
effect of ECT, was markedly lower than the actual fraction. The re-
crystallization fractions were calculated using Eq. (8) , considering
only the temperature history of the ECT. To this end, we first deter-
mined parameters A , Q, and n in Eq. (8) through the GA optimiza-
tion, minimizing the squares of the deviations between the experi-
mentally measured and calculated recrystallization fractions of the
CHTed specimens. Considering the reported initiation temperature
of recrystallization of ultra-low carbon steels [45–47] , we set the
initial temperature in Eq. (8) to 200 °C. The optimum parameters
determined using the temperature histories of the CHTed speci-
mens ( Fig. 1 (d)) are A = 8.65 ×10
11 s
−1
, Q= 258.64 kJ/mol, and
n = 0.87, respectively. For cold-rolled steel, the recrystallization ac-
tivation energy is 150–400 kJ/mol [ 49 , 50 ]. Additionally, the average
Avrami exponent was found to be close to 1 in conventional steel
systems [51] . Therefore, the values determined in this study were
reasonable. The measured and calculated recrystallization fractions
of the CHTed specimens show a good agreement ( Fig. 6 (a)) but
a large discrepancy for the ECTed specimens. Fig. 6 (b) shows the
measured and calculated recrystallization fractions of the ECT760
and ECT800 with the determined parameters and temperature his-
tories (Fig. S4(b)) as a function of j. All of the calculated values
are significantly smaller than the measured values, suggesting that
the thermal effect of conventional Joule heating alone cannot ex-
plain the recrystallization kinetics during ECT. Hence, the quantita-
tive analysis and evaluation of the athermal effect are required to
precisely describe and further predict the recrystallization kinetics
under electric current.
4.3. Athermal effect of the electric current on recrystallization kinetics
The electric current athermally affects interatomic bonding. Ac-
cording to Kim et al. [39] , the electric current weakens the inter-
atomic bonding strength near the defects, inducing electroplastic-
ity. Specifically, the charge imbalance near the defects induced by
the electric current decreases the phonon frequency of the local-
ized optical vibration mode related to the bonding strength. This
means that we can capture the athermal effect of the electric cur-
rent from the elastic modulus, which is a measure of the inter-
atomic bonding strength. We measured the elastic modulus of IF
steel by applying an electric current of 100 ≤j≤325 A/mm
2
.
Fig. 7 shows the measured temperature, measured elastic modu-
lus (denoted as E
thermal + athermal
), and estimated elastic modulus
(denoted as E
thermal
) considering the temperature dependence of
the elastic modulus (Fig. S5). The increase in temperature with the
increase in jresults in a reduction in E
thermal
( Fig. 7 ). The exper-
imentally measured E
thermal + athermal
is lower than E
thermal
, which
is consistent with previous studies on aluminum and magnesium
alloys [39] . This implies the existence of an athermal effect, i.e., an
additional weakening of the atomic bonding strength.
The athermal effect of the electric current can be evaluated,
and the enhanced recrystallization kinetics can be accurately de-
scribed. During the recrystallization process, the athermally weak-
ened bonding strength can be regarded as a reduction in the acti-
6
K. Jeong, S.-W. Jin, S.-G. Kan g et al. Acta Materialia 232 (2022) 117925
Fig. 6. Calculation of recrystallization fraction with the established JMAK equation considering thermal effect. (a) Com parison between the measured and calculated recrystal-
lization fractions of CHTed specimens. For the calculation,
Eq. (8) was used with optimized parameters. (b) Comparison between the measured and calculated recrystallization
fractions of ECTed specimens with five different jand T
max
= 76 0 and 800 °C.
Fig. 7. Change in the elastic modulus of IF steel by electric current. Measured (E
thermal + athermal
) and estimated (E
thermal
) elastic modulus (upper graph) and measured temper-
ature (lower graph).
vation energy barrier or a virtual increase in the material temper-
ature distinct from Joule heating. The athermally induced changes
in the activation energy and material temperature can be reflected
in Eq. (8) by introducing the effective activation energy ( Q
ef f
) and
effective tem perature ( T
ef f
) as follows:
Q
ef f
= Q −Q
ath
(9)
T
ef f
= T + T
ath
(10)
where Q
ath
and T
ath
represent the magnitude of the activation
energy and temperature change due to the athermal effect, respec-
tively. The negative sign in Eq. (9) indicates that the athermal ef-
fect reduces the activation energy ( Fig. 8 (a)), while the positive
sign in Eq. (10) indicates that the athermal effect increases the
material temperature ( Fig. 8 (b)). In this study, we assumed that
Q
ath
and T
ath
are only dependent on jand are time constant.
Additionally, it is assumed that the athermal effect is only effec-
tive when the electric current is applied. The recrystallization frac-
tion of the ECTed specimen can be calculated by dividing the term
inside the square bracket of Eq. (8) into two parts: the first part
with Q
ath
and T
ath
represents the heating caused by ECT, and
the second part represents the following air cooling, as described
in Eq. (11) .
X
V = 1 −exp
−A
p
i =1
T
i
T
i −1
(
exp
(
−(
Q −αQ
ath
)
/R
(
T + βT
ath
) ) )
1 /n
γi
dT
+
f−1
i = p
T
i +1
T
i
(
exp
(
−Q/ RT
) )
1 /n
γi +1
dT
n
(11)
where fand pindicate the final and peak points, respectively, and
αand βare logical numbers. When the concept of Q
ef f
is adopted,
αand βare 0 and 1, respectively, and vice versa when T
ef f
is
adopted. From the experimentally measured recrystallization frac-
tion ( X
V
) of the ECT760 and ECT800, we evaluated the athermal
effect of the electric current, i.e., Q
ef f
and T
ef f
. Fig. 8 (c, d) show
the measured and calculated recrystallization fractions with Q
ef f
and T
ef f
, respectively. The calculated fraction well follows the mea-
sured fraction, implying that Q
ef f
and T
ef f
reflect the athermal ef-
fect delicately.
Fig. 9 (a) shows the estimated magnitude of the activation en-
ergy reduction and temperature increase as a function of j. As j
increases, both the activation energy reduction and the tempera-
7
K. Jeong, S.-W. Jin, S.-G. Kan g et al. Acta Materialia 232 (2022) 117925
Fig. 8. Calculation of recrystallization fraction with the established JMAK equation considering both thermal and athermal effects. Schematic illustrations for the concept of
(a) effective activation energy and (b) effective temperature reflected during ECT. (c, d) Comparison between the measured and calculated recrystallization fractions of ECTed
specimens with five different jand T
max
= 76 0 and 800 °C by adopting the concept of (c) effective activation energy and (d) effective temperature, respectively.
Fig. 9. Athe rmal effect of electric current in recrystallization kinetics. (a) Amount of activation energy reduction (orange) and temperature increment (red) with five different
jand fitted curves (dash lines). (b) Schematic diagram showing the change in the thermal and athermal effects with j. (For interpretation of the references to colour in this
figure legend, the reader is referred to the web version of this article.)
ture increment increase. The data-fitted curve in Fig. 9 (a) aids to
approximate the change in the activation energy and temperature
of the material by the athermal effect. As a function of j, Q
ath
and T
ath
can be expressed as in Eqs. (12) and (13) , implying that
the athermal effect of the electric current on recrystallization ki-
netics increases with j.
Q
ath
= 4 . 96
j (12)
T
ath
= 22 . 82
j (13)
With the evaluated athermal effect of the electric current, the j
dependence (V-shape trend) of recrystallization is comprehensible.
Fig. 9 (b) schematically shows the change in thermal and athermal
effects depending on j. Because the specimen is air-cooled after
removing the electric current in the ECT, jhas no effect on the
cooling rate. The thermal effect decreases with the increasing j
as the heating rate increases proportionately with j. Conversely,
the athermal effect increases with the increasing jaccording to
Eqs. (12) and (13) . Recrystallization by ECT is affected by both ther-
mal and athermal effects, hence the recrystallization fraction de-
creases and then increases with the increasing j. The quantitative
approach to the athermal effect of the electric current in this study
allows the design of optimal ECT processing conditions for the de-
sired microstructure and mechanical properties of materials.
5. Conclusions
We investigated and evaluated the athermal effect of the elec-
tric current on the recrystallization kinetics by conducting ECT
and CHT on ultra-low carbon steel. The ECTed specimens clearly
show enhanced recrystallization behavior compared to the CHTed
specimens. Furthermore, the recrystallization kinetics of ECTed
specimens show a jdependency (V-shape trend), with the de-
gree of recrystallization and grain growth decreasing when j<
70 A/mm
2 and increasing when j≥70 A/mm
2
. From the elas-
8
K. Jeong, S.-W. Jin, S.-G. Kan g et al. Acta Materialia 232 (2022) 117925
tic modulus measurements, we confirmed that the electric cur-
rent athermally weakened the interatomic bonding. By introduc-
ing the j-dependent effective activation energy and temperature
reflecting the weakened bonding to the established JMAK equation,
we deconvoluted and quantified the athermal effect from the elec-
tric current-enhanced recrystallization kinetics. An increase in the
athermal effect and decrease in the thermal effect with an increase
in jled to the tendency of the V-shape of the plot of the recrys-
tallization fraction as a function of jduring ECT. Using the quan-
titative approach in this study, optimal post-processing using the
electric current for metallic materials can be predicted and pro-
posed. Finally, this study facilitates the selection of an appropriate
method, Q
ef f
or T
ef f
, for quantitative analysis of the athermal ef-
fect induced by the electric current of metallic materials depend-
ing on the given conditions. We believe that the novel approach
presented in this study can be extended to other electric current-
induced phenomena in metallic materials, including electroplastic-
ity and EPT effects.
Declaration of Competing Interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Acknowledgments
H. N. Han was supported by the National Research Founda-
tion of Korea (NRF) grant funded by the Korea government (MSIT)
(No. NRF-2020R1A5A6017701 , NRF-2021R1A2C3005096 , and NRF-
2019M3D1A1079215 ). S.-T. Hong was supported by the National
Research Foundation of Korea (NRF) grant funded by the Korea
government (MSIT) (No. NRF-2019R1A2C2009939). M.-J. Kim was
supported by the Industrial Strategic Technology Development Pro-
gram (No. 20 0 03937) funded by the Ministry of Trade, Industry
& Energy (MOTIE, Korea). The Institute of Engineering Research at
Seoul National University provided research facilities for this work.
Supplementary materials
Supplementary material associated with this article can be
found, in the online version, at doi:10.1016/j.actamat.2022.117925 .
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