F. HAN et al.: CELLULAR AUTOMATA SIMULATION OF THE DYNAMIC RECRYSTALLIZATION ...
717–724
CELLULAR AUTOMATA SIMULATION OF THE DYNAMIC
RECRYSTALLIZATION OF THE TC4 ALLOY DURING HOT
COMPRESSION
SIMULACIJA DINAMI^NE REKRISTALIZACIJE ZLITINE TC4
MED VRO^IM STISKANJEM NA OSNOVI CELI^NIH
AVTOMATOV
Fei Han
1*
, Yun Wang
1
, Rongquan Chen
1
,QiGao
2
, Yongqiang Wang
2
1
School of Mechanical and Materials Engineering, North China University of Technology, No. 5 Jinyuanzhuang Road,
Shijingshan District, Beijing 100144, China
2
Baoti Group Ltd, No. 88 Gaoxin Avenue, Baoji City, Shaanxi Province 721014, China
Prejem rokopisa – received: 2018-12-14; sprejem za objavo – accepted for publication: 2019-04-24
doi:10.17222/mit.2018.273
To predict and control the microstructure evolution of the TC4 alloy during hot-compression deformation, a cellular automaton
model including dynamic recrystallization (DRX-CA) was established based on dislocation-driven nucleation conditions and the
grain-growth dynamics theory. The isothermal compression tests were conducted at temperatures ranging from 1000 °C to
1200 °C at 100 °C intervals and at strain rates ranging from 0.1 s
–1
to 10.0 s
–1
. The effects of the deformation process parameters
(strain rate, deformation temperature and deformation degree) on the simulation results were analyzed, including the dynamic
recrystallization fraction, average grain size and flow stress curve. Visual simulation of the dynamic recrystallization
microstructure evolution of TC4 titanium alloy during high-temperature deformation was completed. For a single-phase area,
the simulated flow stress curve was compared with the experimentally obtained stress curve, which verified the rationality and
accuracy of the DRX-CA model.
Keywords: cellular automata, microstructural evolution, dynamic recrystallization, flow stress
Avtorji prispevka so za napoved in kontrolo razvoja mikrostrukture titanove (Ti) zlitine vrste TC4 med vro~o tla~no
deformacijo, postavili simulacijski model na osnovi celi~nih avtomatov. Ta vklju~uje dinami~no rekristalizacijo (DRX-CA), ki
temelji na z dislokacijami gnanih pogojih nukleacije in teoriji dinamike rasti zrn. Izvajali so izotermne tla~ne preizkuse v
temperaturnem obmo~ju med 1000 °C in 1200 °C v intervalih po 100 °C in hitrostih deformacije od (0,1 do 10,0) s
–1
. Analizirali
so vpliv deformacijskih procesnih parametrov (stopnja, hitrost in temperatura deformacije) na rezultate simulacij, vklju~ujo~
dele`e dinami~ne rekristalizacije, povpre~no velikost kristalnih zrn in krivulje te~enja. Izdelali so vizualno simulacijo dinami~ne
rekristalizacije razvoja mikrostrukture Ti zlitine TC4 med visokotemperaturno deformacijo. Za posamezno fazno podro~je so s
simulacijami dobljene krivulje te~enja primerjali z eksperimentalno dobljenimi, kar je potrdilo racionalnost in natan~nost
postavljenega DRX-CA modela.
Klju~ne besede: celi~ni avtomati, razvoj mikrostrukture, dinami~na rekristalizacija, napetost te~enja
1 INTRODUCTION
The TC4 alloy is a typical titanium alloy and has
many attractive properties, such as low density, high
specific strength, high temperature resistance and high
oxidation and corrosion resistance. These excellent
properties have allowed the TC4 alloy to be widely used
in aerospace, aviation, navigation, automobile and other
industries.
1–3
Normally, the manufacture of components,
for example, forging, punching and cutting, has specific
precise requirements on the mechanical and physical
properties. In addition, F. Ren et al.
4
confirmed that the
microstructure evolution of the alloy during hot deforma-
tion plays a key role in improving the mechanical pro-
perties. As known, the flow behavior of materials at
elevated temperatures is a source of essential informa-
tion, X. Shang et al.
5
and B. Li et al.
6
have shown that the
microstructure evolution during hot deformation is very
complicated and affected by a multi-physical mecha-
nism, such as work hardening, dynamic recovery and
dynamic recrystallization softening and so on. In a
macro view, the flow stress changes with the process
parameters, such as the temperature, strain rate and
deformation extent. In recent years, how to control the
microstructure and mechanical properties of products by
controlling the temperature, strain rate and deformation
degree in hot forming has become a research hotspot in
thermoforming. F. Chen et al.
7
found that dynamic re-
crystallization (DRX) is one of the most important res-
toration mechanisms during hot deformation, affecting
the final microstructure; therefore, DRX has been
increasingly used in the control of the microstructure
evolution to obtain finer grains. K. Tan et al.
8
proposed
that the recrystallization behavior of a titanium alloy
during hot deformation is an important influencing factor
that determines the microstructure and properties. The
Materiali in tehnologije / Materials and technology 53 (2019) 5, 717–724 717
UDK 548.53:669.295:66.046.8:62-965-026.565 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 53(5)717(2019)
*Corresponding author's e-mail:
hanfei@ncut.edu.cn

recrystallization evolution of steel has been the subject
of extensive previous research and a mathematical model
for predicting the microstructure and properties has been
established. However, quantitative research on the
recrystallization behavior of a titanium alloy during hot
deformation has received much less attention.
A finite-element simulation is an economical and
effective tool to simulate the material flow behavior and
optimize the forming parameters of the material. In a
finite-element simulation, the constitutive equation that
describes the correlation of the flow stress with the pro-
cessing parameters is necessary to predict the dynamic
flow behavior and optimize the deformation process of
metallic materials.
9–12
In recent years, D. K. Kim et al.,
13
Y. Zhi et al.
14
and M. H. Pourian et al.
15
have shown that
grain (CA) simulation, which takes into account the
curvature of the driving simulation, the stored energy
drive of grain-boundary migration, recrystallization and
the mesoscopic grain growth behavior, has been applied
to materials research; the prediction of the microstruc-
ture evolution of metals using CA has become a hot issue
in international frontier research. Therefore, the develop-
ment of a method to predict the evolution of the recrys-
tallization of a titanium alloy during hot deformation is
of great significance. In this paper, the combination
methods of the principles of physical metallurgy and CA
were adopted, and programming was carried out on the
platform of MATLAB. The DRX process of the hot
compression of the TC4 alloy is predicted.
In the present work, a series of hot-compression tests
were performed on the TC4 alloy in the temperature
range 1000 °C to 1200 °C and strain rate range of 0.1 s
–1
to 10.0 s
–1
. At the same time, a cellular automaton model
including dynamic recrystallization (DRX-CA) was
established based on dislocation-driven nucleation
conditions and the grain-growth dynamics theory. A
visual simulation of the dynamic recrystallization micro-
structure evolution of the TC4 titanium alloy during
high-temperature deformation was completed. Then, a
series of simulations for the DRX evolution in com-
pressions under different deformation conditions were
performed. The effects of the deformation process para-
meters (strain rate, deformation temperature and defor-
mation degree) on the simulation results were analyzed,
including the dynamic recrystallization fraction, average
grain size and flow stress curve. For the single-phase
region, the simulation results were compared with the
flow stress curves to verify the accuracy of the DRX-CA
model.
2 EXPERIMENTAL PART
The material used in this study is the TC4 alloy. The
chemical compositions are given in Table 1. Specimens
with a diameter of 10 mm and a height of 15 mm were
machined from the ingot. The following experimental
procedures were conducted according to ASTM:
E209-00. In this study, the processing route for the
isothermal hot compression test is simplified as shown in
Figure 1. First, the specimens were heated to the pre-set
temperature at a heating rate of 10 °C/s and held for
300 s to ensure a uniform temperature field and decrease
the material anisotropy. Subsequently, the isothermal
compressions were conducted on a computer-controlled,
servo-hydraulic Gleeble-3800 simulator. The deforma-
tion degree was 60 % for all the specimens. Then, the
tests were performed at 1000 °C, 1100 °C, and 1200 °C
with strain rates of 0.1 s
–1
, 1.0 s
–1
and 10.0 s
–1
, respect-
ively. To minimize the friction, tantalum foils with a
thickness of 0.2 mm were set between the specimen and
the anvils. During the compression process, the vari-
ations of the stress and strain were monitored con-
tinuously using a personal computer equipped with an
automatic data-acquisition system. The true stress and
true strain were derived from the measurement of the
nominal stress–strain relationship. The true stress-strain
curves were recorded automatically in the isothermal
compression process.
Table 1: Chemical composition of TC4 alloy (w/%)
A lVF eONCHT i
6.02 3.78 0.052 0.18 0.0062 0.008 0.0049 Balance
3 METHODOLOGY
3.1 Calculation of the activation energy for hot defor-
mation
M. H. Wang et al.
16
have shown that the activation
energy derived by constitutive analyses is normally used
as an indicator to evaluate the difficulty of the hot-defor-
mation process. It can also furnish information about the
microstructure and flow stress evolution in successive
deformation processes to determine the deformation
mechanism. During hot deformation, the potential for
atomic diffusion and the driving force for dislocation
movement depend on the deformation temperature. The
growth velocity of the dislocation densities and the
grain-boundary energy depend on the strain rate.
F. HAN et al.: CELLULAR AUTOMATA SIMULATION OF THE DYNAMIC RECRYSTALLIZATION ...
718 Materiali in tehnologije / Materials and technology 53 (2019) 5, 717–724
Figure 1: Experiment on high temperature compression

Therefore, the peak stress has conventionally been con-
sidered to depend on the deformation temperature and
strain rate. Based on the above statements, the following
constitutive model was proposed by J. J. Sellars and
C. M. Tegart
17
to calculate the activation energy for hot
deformation.
 ()e x p  =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ AF
Q
RT
(1)
where F( ) is a function of the flow stress. The function
has three forms depending on the flow-stress level.
Under low-stress conditions, the relationship between
the flow stress and strain rate can be expressed as:
 exp  =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ A
Q
RT
n
1
1
 < 0.8 (2)
Under high-stress conditions, this relationship can be
expressed as:
 exp( )exp   =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ A
Q
RT
2
 < 1.2 (3)
At any other stress level, this relationship can be ex-
pressed as:
[]  sinh( ) exp   =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ A
Q
RT
n
(4)
The deformation activation energy is calculated by
Equation (5):
[]
[] {}
QR
dl
dT
T
=⋅ ⋅
∂
∂
ln
 ln sinh( )
ln sinh( )
(/)
 

 1
(5)
where A, A
1
, and A
2
are material constants; n and n
1
are
the stress exponents;  and  are the stress level
parameters ( =  /n); and R is the molar gas constant
(J/mol·K). T is the absolute deformation temperature
(K); Q is the deformation activation energy (kJ/mol),
which shows how easily the material is hot deformed;
 is the strain rate (s
–1
); and is the flow stress (MPa) for
a given strain. According to the above formulas, the
deformation activation energy Q is 199.967 kJ/mol.
3.2 Theoretical model for DRX
Dynamic recrystallization (DRX) occurs only when
the dislocation density in a deforming matrix accumu-
lates to a critical level or the strain reaches a critical
value. The two important aspects of DRX that affect the
microstructure are nucleation and grain growth, and both
are closely related to the dislocation density. Therefore,
three theory models have been proposed by researchers
to characterize the microstructure evolution of the TC4
alloy during hot deformation. H. Kocks and U. F. Meck-
ing
18
developed the KM model to predict the variation of
the dislocation density. The model assumes that the flow
stress of the high-temperature plastic deformation of the
material is determined by dislocation density. The
relationship between dislocation density and strain is as
follows:
d
d
   =− kk
12
(6)
Based on the assumption of the KM model, the dis-
location density increases with the increase of strain. It is
generally considered that the flow stress is proportional
to the square root of the average dislocation density. The
expression is as follows:
 =
1
2
b (7)

 =−
− ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 109 1
300
.
T
T
m
(8)
where k
1
is the work-hardening coefficient and k
2
is the
softening coefficient.  is the average dislocation den-
sity, b is the Burgers vector and μ is the shear modulus.
μ
0
is the shear modulus corresponding to the material at
room temperature (300 K). T
m
is the melting point.
The average dislocation density  in a particular
region at different times is determined by the average of
the dislocation densities of all the cells in the region:
 =
==
∑
1
0
N
ij
ij
iAjB
,
,
,
(9)
where N
0
is the total number of cells in the CA simu-
lation region, i.e., N
0
= A×B ; A and B represent res-
pectively the number of cells in the i, j direction;  i,j
is
the dislocations density of the cells at coordinates (i, j).
Z. X. Guo and R. Ding
19,20
developed the nucleation
model to calculate the nucleation rate of DRX. The
model considers the relationship between the nucleation
rate, temperature and strain rate, which can be expressed
as:
 (
,)
 exp nTC
Q
RT
 =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ nucl
(10)
where C is the material constant,
 is strain rate, Q
nucl
is
the activation energy for nucleation (kJ/mol).
Dynamic recrystallization nucleation occurs when the
dislocation density reaches the critical dislocation den-
sity of dynamic recrystallization during thermal process-
ing. The critical dislocation density  c
can be calculated
from the energy required for grain nucleation.
 
 c
m
=
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 20
3
2
 blM
(11)
M
Db
kT
Q
RT
=−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟  ob b
exp (12)
 =
1
2
2
b (13)
l
b
=
10  s
(14)
F. HAN et al.: CELLULAR AUTOMATA SIMULATION OF THE DYNAMIC RECRYSTALLIZATION ...
Materiali in tehnologije / Materials and technology 53 (2019) 5, 717–724 719

where m
is the grain-boundary energy of the high-angle
boundary, M is the mobility of the grain boundary, the
line energy, l is the average free distance of dislocation.
 is the thickness of the characteristic boundary, D
ob
is
the diffusion coefficient at 0 K, k is the Boltzmann con-
stant, Q
b
is the self-diffusion activation energy. s
is the
saturated flow stress, which can be obtained from the
true stress-strain curve.
R. Roberts and B. Ahlblom
21
developed the grain-
growth kinetics model to determine the link between the
driving force and the stored strain-energy difference bet-
ween the dynamic recrystallized grains and the matrix.
After dynamic recrystallization nucleation, the essence
of recrystallized grain growth is the migration of high-
angle grain boundaries. The growth rate of a new grain
can be expressed as:
VM f
ii
= (15)
f
r
ii
i
i
=−−  
 ()
m
2 (16)
 
      i
i
ii
i
=
≥°
−
⎛ ⎝ ⎜ ⎤ ⎦ ⎥ ≤°
⎧ ⎨ ⎪ ⎩ ⎪ m
m
mm
5C
5C
1
11 ln
(17)
where  m
and  i
are the dislocation density in the ori-
ginal and recrystallized grains, respectively,  m
is the
interface energy of the i
th
grain, r
i
is the i
th
recrystallized
grain radius,  m
is the misorientation angle when the
grain boundary becomes a high-angle boundary (in this
study m
= 15°), i
is the grain boundary between the i
th
grain and its neighboring grain.
These values of the material constants used in this
study are listed in Table 2.
Table 2: Material parameters of TC4 alloy
b (nm) ì (GPa) Q
b
(KJ/mol) Q
nucl
(KJ/mol)
0.286 21.93 120 199.967
 m
(°)  D
ob
T
m
(K)
15 5.4*10
-17
1933
3.3 Cellular automata model for DRX
Based on the theory model of DRX, combined with
the CA method, the DRX model for the TC4 alloy during
hot compressive deformation was developed with two
major steps. The first step was to create the initial micro-
structure via a normal grain-growth algorithm, and the
flowchart is shown in Figure 2.
First, the cellular orientation variable in the entire
simulation area is initialized to zero, and the number of
nucleation of dynamic recrystallization is set. Cells are
randomly selected at any position in the simulation
region, and if the cellular orientation variable is zero, a
random integer is assigned between cells 1 to 180. Con-
versely, if the cellular orientation variable is not zero, the
cells at any position are reselected until the number of
dynamically recrystallized cells reaches the specified
number of nucleation. With the nucleation point as the
center, the periodic boundary conditions for growth are
adopted, and the entire simulated area is scanned. Four
random numbers are generated that correspond to the
four neighbouring cells of the central cell, and four
random numbers are compared with the nucleation prob-
ability. The central cell is transformed according to the
rules, and the initial tissue morphology is displayed by
using the MATLAB image-display function.
The CA simulation process of the dynamic recrys-
tallization process of the TC4 titanium alloy is shown in
Figure 3. The detailed steps for the CA model are as
follows:
1) Initial microstructure created in the first step;
2) Input material and process parameters;
3) Set the calculation time and steps of the model;
4) Calculate dislocation density;
5) Nucleation of recrystallization;
6) Grain growth of recrystallization.
F. HAN et al.: CELLULAR AUTOMATA SIMULATION OF THE DYNAMIC RECRYSTALLIZATION ...
720 Materiali in tehnologije / Materials and technology 53 (2019) 5, 717–724
Figure 3: Programming flowchart of the microstructure evolution
simulation with DRX-CA
Figure 2: Programming flowchart for achieving the initial microstruc-
ture with DRX-CA

4 RESULTS AND DISCUSSION
4.1 Hot-deformation flow curves
The true stress-strain curves obtained from the hot
compression tests at different deformation temperatures
and strain rates are shown in Figure 4. These curves
show the flow stress change with different process para-
meters such as temperature, strain rate and deformation
extent. It was obvious that the flow curves with different
deformation temperatures and strain rates had a similar
variation. That is, the flow stress increased quickly with
the increase in strain at the beginning. The increase
occurs because in this stage, the generation and multi-
plication of dislocations that induce working hard (WH)
develop rapidly. Meanwhile, the accompanying dynamic
recovery (DRV) caused by the annihilation of disloca-
tions due to the ease of cross slip, climb, and dislocation
unpinning at the hot-working temperatures is too weak to
overcome WH. Then, a rising trend is maintained until
the flow pressure peak is reached. Finally, the flow stress
maintains a stable value and does not change with the
increase in strain. At this stage, another softening me-
chanism, i.e., DRX, takes place, resulting in the gradual
decrease in the work-hardening rate with the increase in
the strain. When the dynamic softening (DRV and DRX)
rate is equal to the work hardening rate, the flow stress
reaches a peak value, following which the flow stress
gradually decreases due to the predominant softening
mechanism, i.e., DRX, until a steady stage.
Under the condition of the same strain rate, the flow
stress decreases with the increase in deformation tem-
perature. However, under the condition of the same
deformation temperature, the flow stress increases with
the increase of the strain rate. According to M. S. Chen
et al.
22
and A. Mohamadizadeh et al.,
23
this is mainly be-
cause a lower strain rate provides a longer time for ener-
gy accumulation and that a higher deformation tem-
perature promotes the mobility at the boundaries for the
annihilation of dislocations and the nucleation and
growth of dynamically recrystallized grains, thus re-
ducing the flow stress level.
4.2 Initial microstructures
In this study, the microstructural evolution of a TC4
alloy during DRX was simulated at various strain rates
and temperatures. The simulation lattice was set at
400×400, and periodic boundary conditions were used.
The size of one lattice represents 4 μm of the real
dimension of the material, and hence the simulation area
corresponds to 1600 μm × 1600 μm in a real sample. The
initial microstructure for the TC4 alloy is shown in
Figure 5. From the final initial microstructure simulation
F. HAN et al.: CELLULAR AUTOMATA SIMULATION OF THE DYNAMIC RECRYSTALLIZATION ...
Materiali in tehnologije / Materials and technology 53 (2019) 5, 717–724 721
Figure 5: The initial microstructure of the TC4 alloy before CA simu-
lation
Figure 4: Flow stress curves of TC4 alloy at different strain rates

diagram, we can see that most of the grains are
hexagonal in shape, and basically all the intersections are
trilateral intersections. The angle is approximately 120°.
Moreover, the growth of the crystal grains is mainly
achieved by continuously phagocytizing small crystal
grains by large crystal grains. Through the change in the
grain topological structure, the initial structure of grain
coarsening and growth is completed. According to the
above principle, a single-phase microstructure, i.e., a
cellular automaton simulation of the  phase, is con-
structed.
4.3 The effect of strain rate on DRX
Under the specified conditions, the simulation of the
microstructure evolution of the TC alloy during DRX at
a deformation temperature of 1000 °C and strain rates of
0.1 s
–1
and 1.0 s
–1
was conducted, and the results are
shown in Figure 6. The effect of different strain rates on
the volume fraction recrystallization is shown in Fig-
ure 7. The corresponding recrystallization volume frac-
tions are 4.42 % and 2.29 %, respectively, and the recrys-
tallized average grain sizes are 3.0 μm and 2.47 μm.
These results show that the time to reach the required
deformation degree is shorter with the increase in strain
rate, and the proportion of dynamic recrystallization is
less. This is because the driving force for recrystalliza-
tion is generally provided by the storage energy of the
metal. When the strain rate is low, the storage energy in
the alloy is less, which reduces the driving force of the
recrystallization. Therefore, the volume fraction of the
dynamic recrystallization decreases with the increase in
strain rate. At the same time, as the strain rate increases,
the relative time that recrystallization occurs is later, and
the recrystallization does not occur sufficiently, which
makes the recrystallized grain not grow sufficiently in
the growth cycle, and the dislocation density is increas-
ing. Therefore, the grain size of the dynamic recrys-
tallization decreases with the increase of strain rate, i.e.,
finer recrystallization grains can be obtained at a higher
strain rate, but the proportion of recrystallization that
occurs is lower. A lower strain rate is favorable for the
occurrence of dynamic recrystallization, but the micro-
structure of the recrystallized grains is coarser. These
laws are consistent with the experiments, which fully
verify the correctness of the model.
4.4 The effect of temperature on DRX
The CA simulations of the microstructure evolution
of the TC4 alloy during DRX at a strain rate of 1.0 s
–1
and two temperatures of 1000 °C and 1100 °C were con-
ducted, and the numerical results are shown in Figure 8.
The effect of different temperatures on the volume frac-
tion recrystallization can be found in Figure 9. The
corresponding recrystallization volume fractions are
2.29 % and 6.78 %, respectively, and the recrystallized
average grain size are 2.47 μm and 3.64 μm.
The results show that when the strain rate is constant,
the dynamic recrystallization percentage and the average
size of the dynamic recrystallized grains gradually in-
crease with the increase in the deformation temperature.
The higher the temperature is, the more new recrys-
tallized nuclei are formed and the migration rate of grain
boundaries is much higher. That is, the more favorable
the nucleation and grain growth of the recrystallization.
However, too high of a temperature will make the micro-
structure of the recrystallized grains become coarse.
Generally, when the strain is the same, the higher the
deformation temperature or the lower the strain rate is,
the easier the dynamic recrystallization can occur, and
F. HAN et al.: CELLULAR AUTOMATA SIMULATION OF THE DYNAMIC RECRYSTALLIZATION ...
722 Materiali in tehnologije / Materials and technology 53 (2019) 5, 717–724
Figure 7: The effect of strain rate on the volume fraction recrystalliza-
tion and recrystallized grain size
Figure 6: The effects of strain rate variation on the microstructure at
T = 1000 °C
Figure 8: The effects of temperature variation on the microstructure at
 = 1.0 s
–1

the higher the dynamic recrystallization percentage.
Dynamic recrystallization always occurs when the strain
reaches a certain critical value at a given strain rate and
deformation temperature. When the deformation tem-
perature is constant, the higher the strain rate is, the
greater the critical strain value at which dynamic
recrystallization occurs. When the strain rate is constant,
the higher the temperature is, the smaller the critical
strain value of the dynamic recrystallization.
4.5 The comparison of flow stress curve
To further verify the accuracy of the model, a com-
parison of the flow stress curves of the TC4 alloy during
hot deformation from the experiment and the CA simu-
lation is shown in Figure 10. And because the tempe-
rature is above the phase transition point, the TC4 alloy
is in the  phase region. The results show that the
variation of the flow stress curve obtained by using the
cellular automaton model at different deformation tem-
peratures is in good agreement with the flow stress curve
obtained by the thermal compression test, with the
typical characteristics of dynamic recovery rheological
curves.
Moreover, the simulated steady flow stress and peak
flow stress are slightly larger than the actual experi-
mental results. The main reason for this result is that the
DRX-CA model has assumptions and simplifications
that do not consider the two-phase particles and other
microstructure defects. And the internal dislocation
density during the actual material deformation process is
difficult to measure, and the dislocation density used in
the simulation is slightly different from the dislocation
density of the actual material.
5 CONCLUSIONS
Based on the dislocation-driven nucleation conditions
and grain-growth dynamics theory, a dynamic recrystalli-
zation model (DRX-CA) was established to visualize the
dynamic recrystallization microstructure evolution of the
TC4 titanium alloy during high-temperature deforma-
tion. The achievements of the current research are
summarized as follows:
1) The initial microstructure of the TC4 titanium
alloy and the microstructure change during the dynamic
recrystallization of high-temperature compression
deformation were simulated by using the established
DRX-CA model.
2) The effects of the deformation process parameters
(strain rate, deformation temperature and deformation
degree) on the simulation results were analyzed,
including dynamic recrystallization fraction, average
grain size and flow stress curve. The simulation results
showed that with the increase in strain, the decrease in
strain rate and the increase in deformation temperature,
the recrystallization volume fraction and recrystallization
average grain size steadily increased.
3) For a single-phase area, the simulated flow stress
curve was compared with the experimentally obtained
stress curve, which verified the rationality and accuracy
of the DRX-CA model.
F. HAN et al.: CELLULAR AUTOMATA SIMULATION OF THE DYNAMIC RECRYSTALLIZATION ...
Materiali in tehnologije / Materials and technology 53 (2019) 5, 717–724 723
Figure 10: Comparison of the flow stress curves between the test and
simulation
Figure 9: The effect of temperature on the volume fraction recrys-
tallization and recrystallized grain size

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