Article
DOI:10.1557/s43578-025-01519-5
Dynamic recrystallization behavior of TC21 titanium alloy
Rui Deng1, Song Xue1,a), Minglong Xu1, Zenong Li1, Shaoxiang He1, Ying Zhang1,
Rongchao Li1, Qiankun Li1
1
School of Manufacture Science and Engineering, Key Laboratory of Testing Technology for Manufacturing Process, Ministry of Education, Southwest
University of Science and Technology, Mianyang 621010, China
a)
Address all correspondence to this author. e-mail: xuesong2004@126.com
Received: 12 July 2024; accepted: 2 January 2025
Vol.:(0123456789)
© The Author(s), under exclusive licence to The Materials Research Society 2025
2025
Over the past 20 years, titanium alloys have been successfully
applied to fuselage products such as aircraft, aircraft engines,
and rocket engines due to its excellent performance, contributing significantly to the structural integrity of the majority of
military aircraft [1–3]. TC21 titanium alloy is widely used in the
aerospace field due to its superior comprehensive mechanical
properties, including high strength, high toughness, low density,
high damage tolerance, and low crack growth rate. It is increasingly replacing TC4 titanium alloy and has already become one
of the key materials for manufacturing critical components of
aircraft [4, 5]. Therefore, these components require excellent
mechanical properties, which are influenced by the evolution
of the material’s microstructure. The dynamic recrystallization
occurring inside metal materials can effectively refine the grain
structure, thereby obtaining uniform and fine equiaxed structure is critical [6–8].
Mironov et al. [9] investigated microstructure evolution during warm working of Ti–6Al–4V with a colony-a microstructure
by EBSD technique, the research result indicates that changes
in strain path may be beneficial in promoting globalization
during warm working. Lin et al. [10] investigated the softening
mechanism behavior of Ti-55511 alloy during thermal compression, mainly the spheroidization of lamellar α phase and
recrystallization of β phase, the results indicate that the degree
of spheroidization of the layered α phase is closely related to the
deformation temperature and strain rate. The spheroidization
fraction of lamellar α phases begins to drop at about 700 °C as
the strain rate is higher than 0.01 ­s−1. Luo et al. [11] investigated
the microstructure evolution and rheological stress behavior of
TC17 titanium alloy in the dual-phase region, and they believed
that the spheroidization rate of the α phase would increase
slightly with the increase of strain and deformation temperature. By observing the trend of the rheological stress curve, it is
concluded that the greater the degree of spheroidization of the
α phase, the more favorable it is to reduce the rheological stress.
Ma and Zhang [12] investigated the spheroidization behavior
of cast Ti–6Al–4V alloy after rolling by spheroidization process of coupling pulsed electric, the spheroidization process
mainly formed needle-like or equiaxed α phase, significantly
improving the mechanical properties of the Ti–6Al–4V alloy. Li
et al. [13] conducted microstructural studies on TC18 titanium
Journal of Materials Research
Introduction
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This study investigated the dynamic recrystallization behavior of TC21 titanium alloy in the dual-phase
region (850–930 °C) through thermal compression tests, analyzed the softening mechanism behavior
through the stress–strain curve and microstructure, and then calculated the hot deformation activation
energy of the material. Kinetics model was established. Dynamic recrystallization simulation was
conducted using DEFORM-3D finite element software. The dynamic recrystallization of TC21 titanium
alloy occurred in the dual-phase region was revealed by combining microstructure analysis and the
value of thermal deformation activation energy. The predicted values of the dynamic recrystallization
volume fraction model show a correlation coefficient of 0.967 with experimental values. By comparing
grain size, the simulation and experimental results indicated that the grain size error is approximately
10.8%, demonstrating a certain level of reliability for kinetics model. Under the deformation conditions
of deformation temperature is 890 °C and strain rates of 0.1 and 1 ­s−1, relatively uniform and fine
microstructure can be obtained.
Article
Stress–strain curve
Figure 1 is the true strain–stress curve obtained based on the
thermal compression test data. It can be observed that the flow
stress exhibits a decreasing trend with increasing deformation
temperature across various strain rates. The main reason is that
with increasing deformation temperature, more heat energy is
obtained inside structure. The motion between atoms becomes
© The Author(s), under exclusive licence to The Materials Research Society 2025
When the deformation temperature is 850 °C, as shown in
Fig. 2(a), compared with the original structure, it was observed
that in the microstructure after thermal compression deformation, many small dynamic recrystallization (DRX) grains
appeared between equiaxed α phase, indicating that TC21 titanium alloy has started to undergo dynamic recrystallization at
850 °C. As depicted in Figs. 2, 3 and 4 that when the strain
rate is between 0.01 and 1 ­s−1, with increasing deformation temperature, number of α phase decreases firstly, part of α phases
merge and grow with each other, as shown in Fig. 2(c); overall,
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Microstructure analysis
2025
Result and discussion
unstable, and the atomic motion becomes more active, accelerating the speed of grain boundary slip and grain growth,
both of which are manifestations of dynamic recrystallization.
Therefore, the accumulation of dislocations and work hardening
generated by thermal compression will be partially offset by the
softening mechanism of dynamic recrystallization [16–18]. In
addition, as increasing deformation temperature, α phase inside
alloy gradually decreases, but β phase gradually increases due to
the proximity to the phase transformation temperature. Because
α phase belongs to hard phase, but β phase belongs to phase with
better processing plasticity [19, 20]. So, as the deformation temperature increases, the flow stress shows a decreasing trend. The
flow stress of TC21 titanium alloy first reaches a peak quickly,
then begins to decrease slowly, and gradually tends to a stable
value, this is because at the beginning of hot deformation, dislocations gradually accumulate and work hardening occurs, at
this stage, the true stress–strain curve shows a straight line rise.
When the dislocations accumulate to a certain extent, reaching the critical strain value for dynamic recrystallization, then
material begins to experience dynamic recrystallization. When
the curve reaches its peak, due to the interaction between softening mechanism and work hardening, the flow stress begins
to decline and gradually tends to dynamic equilibrium [21–23].
As depicted in Fig. 1, it is evident that the flow stress of
the alloy rises with increasing strain rate at same deformation
temperature. This phenomenon arises due to the increasing hot
deformation compression, leading to the increasing dislocation
accumulation within the structure, consequently inducing work
hardening; moreover, higher strain rates correspond to shorter
time of hot deformation. The dislocation slips and climbing
inside the structure are difficult to carry out, and the mobility
between atoms has also become difficult, therefore, there is not
enough time to undergo dynamic recovery and dynamic recrystallization, mitigating the hardening phenomenon induced by
hot compression becomes difficult. At the macro level, there is
an increase in deformation resistance and a decrease in plasticity, therefore, at same temperatures, an increasing strain rate
corresponds to a great flow stress [24, 25].
Journal of Materials Research
alloy produced by laser additive manufacturing at different hot
working temperatures, after double annealing treatment, the
degree of spheroidization of the α phase was highest when the
temperature was below 750 °C. Pu et al. [14] in order to study
the dynamic recrystallization behavior of TC4 titanium alloy
under isothermal compression test, they used the Poliak Jonas
method to obtain the critical strain value for dynamic recrystallization and then analyzed the thermal deformation behavior
of the material based on the rheological stress curve. Yi and
Pan [15] studied the dynamic recrystallization behavior of TC4
titanium alloy through thermal compression test and established
a dynamic recrystallization model, the results showed that the
grain size and volume ratio of TC4 titanium alloy increased with
increasing temperature and decreasing strain rate.
Most scholars have conducted research on the hot behavior
of metal materials, mainly including phase transitions and different softening mechanisms, the purpose is to obtain a uniform
microstructure to improve the mechanical properties of metals. The research material of this article is TC21 titanium alloy,
which is a typical dual-phase titanium alloy. Currently, there
is relatively little research on the dynamic recrystallization of
TC21 titanium alloy in the dual-phase region. Due to the crucial
role of grain size in the evolution of metal forming process, the
dynamic recrystallization model is an effective research tool;
therefore, this article mainly analyzes the dynamic recrystallization evolution of TC21 titanium alloy in the dual-phase region
through the changes of grain size.
This article studies the dynamic recrystallization evolution of TC21 titanium alloy in the dual-phase region through
a dynamic recrystallization model, mainly by grasping the
changes in grain size to study the evolution of its microstructure.
Thermal compression tests were conducted on TC21 titanium
alloy using the Gleeble-3800 thermal simulator, subsequently,
the stress–strain curve and microstructure obtained from the
test were analyzed for work hardening and softening behavior.
Dynamic recrystallization kinetics model was established based
on experimental data, we conducted thermal compression simulations using this model and analyzed the simulation results and
verified the reliability of the model by comparing experimental
and simulated values of grain size.
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Article
120
(a)
160
140
80
/MPa
/MPa
100
850℃
60
890℃
40
930℃
20
120
100
850℃
80
60
890℃
40
930℃
20
0
0.0
200
(b)
180
0.2
0.4
0.6
0.8
0
0.0
1.0
(c)
300
0.2
0.4
0.6
0.8
1.0
(d)
150
850℃
/MPa
/MPa
250
890℃
100
0
0.0
850℃
150
890℃
100
930℃
50
200
930℃
50
0.2
0.4
0.6
0.8
1.0
0
0.0
0.2
0.4
0.6
0.8
1.0
© The Author(s), under exclusive licence to The Materials Research Society 2025
2025
in Fig. 4(d). As shown in Fig. 4(b), with increasing deformation
temperature, part of α phase in microstructure is broken, and
many fine equiaxed α grains appear at the grain boundary. In
summary, the dynamic recrystallization of TC21 titanium alloy
occurred in the range of 850–930 °C, but when the strain rate is
10 ­s−1, it is mainly dynamic recovery.
At same deformation temperature, recrystallized grain size
tends to grow with decreasing strain rate, especially at deformation temperature of 850 and 890 °C and in strain rate range of
0.01–1 ­s−1, some recrystallized grains appear to aggregate and
show a chain shape at grain boundary, as shown in Fig. 3(b),
this is because there is sufficient deformation time, and the dislocations caused by plastic deformation caused by compression
are eliminated by slip and climb. Because dislocation density
determines the number of nucleation sites of recrystallized
grains, dislocation density is lower at this time, resulting in a
decrease in nucleation rate of recrystallized grains, and the driving force of dynamic recrystallization decreased; therefore, slight
recrystallized grains are easily stacked in a chain shape. When
Journal of Materials Research
the number of α phases shows a decreasing trend, while their
size increase, especially at 930 °C. This is because that the temperature approaches phase transition temperature, leading to
a greater transformation of α phase into β phase, the presence
of β phase in microstructure surpasses that of α phase. With
the rise in deformation temperature, atomic activity increases,
accelerates grain boundary migration speed, and the condition
of recrystallized grain growth is carried out by grain boundary
migration. Therefore, recrystallized grains will undergo growth,
at the same strain rate, it can be observed that the nucleation of
fine grains gradually decreases. At deformation temperature of
930 °C and strain rate of 0.01 ­s−1, grown recrystallized grains
were observed, as shown in Fig. 4(a); as strain rate is 10 ­s−1 and
deformation temperature is 930 °C, from the observation of the
metallographic structure, it was found that most of the grains
were elongated and flattened; at the same time, due to the high
strain rate, the nucleated grains did not have sufficient time to
grow, resulting in the appearance of many fine grains, which
are typical characteristics of dynamic recovery [19], as shown
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Figure 1: True stress–strain curves at various strain rates. (a) 0.01 ­s−1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1.
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Hot deformation activation energy
The deformation activation energy denotes the energy required
for atomic transition, serving as an indicator of the alloy’s
© The Author(s), under exclusive licence to The Materials Research Society 2025
2025
deformation difficulty. Typically, when the hot deformation
activation energy of a titanium alloy approaches the self-diffusion activation energy of the α phase in pure titanium, which is
242 kJ/mol, it indicates that the alloy’s softening mechanism primarily involves dynamic recovery. Conversely, if the hot deformation activation energy significantly exceeds the self-diffusion
activation energy of the α phase in pure titanium, the alloy’s
softening mechanism is predominantly attributed to dynamic
recrystallization. The former is because during the dynamic
recovery process, migration, rearrangement, and annihilation
of defects such as vacancies and dislocations in the material are
all achieved through the diffusion mechanism; so, the diffusion activation energy is similar to the self-diffusion activation
energy of α phase in pure titanium. The dynamic recrystallization of the latter is realized by nucleation and growth of grains,
which requires more energy than the vacancy diffusion, therefore, activation energy required for dynamic recrystallization
process is much larger than the self-diffusion activation energy
of α phase in pure titanium [26].
The dynamic recrystallization of alloy belongs to hot activation process, that is, with the continuous accumulation of dislocations in alloy. When reached critical strain, the alloy will
begin to undergo dynamic recrystallization. Hot deformation
Journal of Materials Research
deformation temperature is 930 °C and strain rate is in the range
of 0.01–1 ­s−1, due to the high temperature, the energy provided
for atomic diffusion increases, resulting in acceleration of atomic
migration; therefore, at this temperature, recrystallized grains
are more dispersed, and there are some broken fine equiaxed α
grains, as shown in Fig. 4(b). When strain rate is 10 ­s−1, due to
large strain rate, softening mechanism is mainly dynamic recovery and deformation time is shortened, the deformation mode
is mainly dislocation slip and climbing. However, grain growth
will be hindered due to difficulty of dislocation slips and climb
and can only participate in the compression deformation inside
structure by changing its own shape; therefore, it can be seen
that recrystallization grains are elongated and flattened. Increasing dislocation density elevates both the number of nucleation
sites and the nucleation rate of grains; however, due to short
deformation time, recrystallization grains cannot fully grow up,
so recrystallized grain size is more refined [20, 21], as shown in
Fig. 4(d).
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Figure 2: Microstructure of different strain rates at 850 °C. (a) 0.01 ­s−1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1.
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Figure 3: Microstructure of different strain rates at 890 °C. (a) 0.01 ­s−1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1.
ε̇ = A2 exp(A3 σ ) ασ ≥ 1.2,
(2)
Q
ασ for all,
ε̇ = A[sinh (ασ )]n exp −
RT
(3)
where ε̇ is the strain rate, α is the stress level constant, σ is the
peak stress, Q is the hot deformation activation energy, R is the
molar gas constant, its value is 8.314 J/(mol K), T is the deformation temperature, and A1, A2, A3, and A are constants related
to materials.
According to deformation temperature, strain rate, and
stress–strain curve data, the values of n1 and A3 were fitted to
obtain 6.486 and 0.05063, respectively.
The value of hot deformation activation energy Q can be
expressed as Eq. (4):
∂ ln ε̇
Q=R
∂ ln[sinh ασp ]
∂ ln[sinh ασp ]
.
∂(1/T)
© The Author(s), under exclusive licence to The Materials Research Society 2025
(4)
Kinetic model
Critical strain equation
When the material undergoes dynamic recrystallization, traditional concept believes that it begins at the peak of stress–strain
curve, with more and more research later, and it is found that
dynamic recrystallization of the material has occurred before the
peak strain, which is called the critical strain of the material [29,
30]. However, the true stress–strain curve cannot directly obtain
the critical strain value of material, so it is impossible to know the
degree of material deformation to which dynamic recrystallization will occur. Therefore, this paper uses method of work hardening rate [31] to process stress–strain curve, and critical strain
www.mrs.org/jmr
(1)
2025
ε̇ = A1 σ n1 ασ ≤ 0.8,
The hot activation energy Q = 395.463 kJ/mol of TC21 titanium alloy in dual-phase region was obtained by fitting the
parameters in Eq. (4), and the hot activation energy is much
larger than self-diffusion activation energy of α phase in pure
titanium 242 kJ/mol, so it can be inferred that the TC21 titanium
alloy has dynamic recrystallization in dual-phase region, and the
metallographic diagram of the microstructure can also prove the
accuracy of this inference.
Journal of Materials Research
activation energy can be described by Eqs. (1)–(3), which are
applicable to the relationship between flow stress and strain rate
at low stress level, high stress level, and so on [27, 28].
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Article
Figure 4: Microstructure of different strain rates at 930 °C. (a) 0.01 ­s−1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1.
Since work hardening rate is obtained by slope of the true
stress–strain curve, that is, θ = dσ/dε. True stress–strain curve
obtained from thermal compression test is not smooth, therefore it
is necessary to fit the stress–strain curve to obtain the fitting equation and then the derivative of the fitting equation is used to obtain
the slope of stress–strain curve under various deformation conditions, that is, work hardening rate θ, then the θ − σ curve is drawn,
and critical strain value under different deformation conditions is
determined from curves related to θ [32]. The specific method is
illustrated by deformation temperature of 930 °C and strain rate
of 0.01 ­s−1. Critical strain equation of dynamic recrystallization is
expressed by Eq. (5):
εc = kεp ,
© The Author(s), under exclusive licence to The Materials Research Society 2025
(5)
(6)
Because it is difficult to directly derive the fitting equation,
in origin software, the fitting equation can be derived by fitting
the stress–strain curve data and the value of work hardening
rate under this deformation condition can be obtained; thus,
the θ − σ curve can be drawn. Then, by taking the logarithm of
the work hardening rate θ , the ln θ − ε curve is drawn, and at
the same time, the polynomial third-order fitting of the ln θ − ε
curve is performed; the third-order fitting equation is provided
as Eq. (7):
ln θ = 14.038 − 1040.99ε + 25391.496ε2 − 191952.98ε3 .
(7)
The inflection point of ln θ − ε curve is the critical strain
value under this deformation condition. In order to obtain the
value more accurately, the data of the ln θ − ε curve are derived
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1.26 × 10−5 + 0.041ε − 1.462ε2 + 598.326ε3 + 4735.481ε4 − 1407.352ε5
.
6.59 × 10−6 + 5.714 × 10−4 ε − 0.047ε2 + 13.565ε3 + 74.209ε4 + 113.202ε5 − 86.098ε6
2025
σ =
where εc is the critical strain, k is the material-related constant,
and εp is the peak strain. By processing the data of strain–strain
curve, the fitting equation under this deformation condition was
obtained as Eq. (6).
Journal of Materials Research
of material corresponds to the curve of work hardening rate and
stress (θ − σ), ln θ − ε and ∂ ln θ/∂ε − ε.
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1.0
(a)
0.8
0.8
0.6
0.6
0.4
0.4
850℃
890℃
930℃
0.2
0.0
0.0
0.2
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0.8
1.0
1.2
0.0
0.0
1.0
(c)
0.8
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0.6
0.4
0.2
0.4
0.6
0.8
1.0
1.2
(d)
0.4
850℃
890℃
930℃
0.2
0.0
0.0
850℃
890℃
930℃
0.2
Xdrx
Xdrx
1.0
(b)
Xdrx
Xdrx
1.0
0.2
0.4
0.6
0.8
1.0
1.2
850℃
890℃
930℃
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Figure 5: Dynamic recrystallization volume fraction curves under different deformation conditions. (a) 0.01 s­ −1; (b) 0.1 ­s−1; (c) 1 ­s−1; and (d) 10 ­s−1.
εc = 0.575εp .
© The Author(s), under exclusive licence to The Materials Research Society 2025
(8)
Peak strain equation
The peak strain equation of dynamic recrystallization can be
expressed by Eq. (9):
εp = a1 ε̇m1 exp(Q1 /RT).
(10)
The peak strain under various deformation conditions is
obtained from stress–strain curve, fitting Eq. (10). The relevant
parameters of Eq. (10) are fitted to obtain m1 = 0.09117 and
Q1 = 34473.579 J/mol . The calculated m1 and Q1 are substituted into Eq. (10) to calculate the value of a1. The peak strain
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(9)
where a1, n1, and m1 are material-related constants, εp is the peak
strain, d0 is the initial grain size, Q1 is the activation energy, R is
the molar gas constant, its value is 8.314 J/(mol K), and T is the
deformation temperature.
Because the initial grain size is relatively uniform, it is
neglected, therefore, Eq. (9) can be simplified to Eq. (10):
2025
εp = a1 d0n1 ε̇m1 exp(Q1 /RT),
Journal of Materials Research
for the second time to obtain the ∂ ln θ/∂ε − ε curve, and the
critical strain value under this deformation condition can be
accurately obtained by curve of ∂ ln θ/∂ε − ε, which is 0.04406.
Similarly, the correlation curves under other deformation conditions can also be obtained; accordingly, critical strain values
under various deformation conditions can be obtained.
In the past, the correlation coefficient between critical strain
and peak strain was obtained based on experience, but this
test inevitably had errors. Therefore, the correlation coefficient
between critical strain and peak strain can be obtained more
accurately by this method, and the critical strain values of TC21
titanium alloy under various deformation conditions in the dualphase region can be obtained by above method. The peak strain
values under various deformation conditions can be obtained by
true stress–strain curve. Fitting with obtained values and peak
strain values, the critical strain equation is provided as Eq. (8):
7
1.0 (a)
1.0 (b)
0.8
0.8
Predicted data
Xdrx
Article
0.6
0.4
0.2
0.0
0.0
Experimental value
Predictive value
0.2
0.4
0.6
0.8
1.0
1.2
0.6
0.4
0.2
0.0
0.0
Data points
Fitting line
0.2
0.4
0.6
0.8
1.0
Test data
Figure 6: Under the conditions of deformation temperature of 930 °C and strain rate of 0.01 s­ −1. (a) Comparison between experimental and predicted
volume fraction values; (b) correlation between experimental and predicted values.
(11)
Dynamic recrystallization model
In the process of hot compression deformation, dynamic
recrystallization occurs under the condition of the dislocation distortion energy existing in material. When dislocations accumulate to a critical strain, dynamic recrystallization grains will nucleate and grow up at grain boundary in
microstructure with an equiaxed shape and slowly covering
the original structure, forming a new structure composed of
new equiaxed grains. Dynamic recrystallization transformation has no change in crystal structure and chemical composition, which is dynamic recrystallization; volume fraction of
dynamic recrystallization is related to critical strain, strain
rate, and deformation temperature. The Aviami equation [33]
is used to establish dynamic recrystallization volume fraction
model.
Xdrx = 1 − exp −βd
ε − εc
ε0.5
kd ,
ε0.5 = a2 d0n2 ε̇m2 exp(Q2 /RT),
(12)
(13)
where Xdrx is the dynamic recrystallization volume fraction, βd ,
kd , a2, and n2 and m2 are the material-related constants, ε is the
strain, εc is the critical strain, ε0.5 is the strain at dynamic recrystallization volume fraction of 50%, d0 is the initial grain size, Q2
is the dynamic recrystallization activation energy, and R is the
molar gas constant, its value is 8.314 J/(mol K).
The formula for calculating volume fraction of dynamic
recrystallization is provided as Eq. (14):
© The Author(s), under exclusive licence to The Materials Research Society 2025
(14)
where σsat is the saturation stress (MPa), σ is the instantaneous stress during hot compression (MPa), σss is the steady-state
stress (MPa).
σss and σsat can be obtained through the method of work
hardening rate [31], and the critical strain values [32] under
different deformation conditions have been calculated based
on the work hardening rate method.
Substituting corresponding parameters under various
deformation conditions into Eq. (14), variation of dynamic
recrystallization volume fraction curve with strain during
hot compression under various deformation conditions can
be obtained and is shown in Fig. 5.
As depicted in Fig. 5, volume fraction of dynamic recrystallization increases roughly as an S-shaped curve with
increasing hot compression strain. Due to the higher deformation temperature, the greater energy will be obtained
inside the material and the activation of material itself will
be enhanced. The dynamic energy of the atomic motion will
be increased, so that dynamic recrystallization has sufficient
driving force to occur; hence, the volume fraction of dynamic
recrystallization will also increase with increasing deformation temperature.
Due to uniform distribution of initial grain size, its impact
on this study can be ignored, therefore, in Eq. (2), n2 = 0 , so
Eq. (2) can be abbreviated as Eq. (15):
ln ε0.5 = ln a2 + m2 ln ε̇ + Q2 /RT.
(15)
According to dynamic recrystallization volume fraction
curve, the strain at a volume fraction of 50% under various
deformation conditions can be obtained, the corresponding
parameters are fitted to obtain m2 = 0 and Q2 = 20,330.94 J/
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exp(34473.579/RT).
σsat − σ
,
σsat − σss
2025
εp = 0.00147ε̇
0.09117
Xdrx =
Journal of Materials Research
equation of TC21 titanium alloy in the dual-phase region is
Eq. (11):
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Figure 7: Dynamic recrystallization grain size cloud diagram at different deformation temperatures. (a) 850 °C, 0.1 s­ −1; (b) 890 °C, 0.1 s­ −1; and (c) 930 °C,
0.1 ­s−1.
ε − εc
Xdrx = 1 − exp −0.994
ε0.5
1.687 ,
ε0.5 = 0.03594ε̇0.13 exp(20330.94/RT).
(16)
(17)
The predicted volume fraction values under various deformation conditions were calculated by dynamic recrystallization model and then compared with the experimental values of
dynamic recrystallization volume fraction, as shown in Fig. 6, and
the comparison between experimental value and predicted value
of dynamic recrystallization volume fraction at a deformation temperature of 930 °C and a strain rate of 0.01 ­s−1 was given.
From Fig. 6, it can be seen that experimental values fit well
with predicted values, with a correlation coefficient of R2 = 0.967,
fully demonstrating that the model can effectively predict the
dynamic recrystallization behavior of TC21 titanium alloy.
© The Author(s), under exclusive licence to The Materials Research Society 2025
ddrx = a3 d0h3 εn3 ε̇m3 exp (Q3 /RT) + C3 ,
(18)
where a3, h3, n3, m3, and C3 are material constants, Q3 (J/mol) is
the recrystallization activation energy, R is the molar gas constant, and T is the deformation temperature.
The parameters d0h3 and εn3 with initial grain size are regarded
as constants. Fitted the corresponding data in Eq. (18), by fitting the
slope of curve, m3 = 0.1288, similarly, Q3 = −49551.406 J/mol,
and a3 = 10985.516, and the dynamic recrystallization grain size
model is obtained as Eq. (19):
ddrx = 10985.516ε̇−0.1288 exp (−49551.406/RT).
(19)
Hot compression simulation
Import established kinetics models into DEFORM-3D finite
element software for hot compression simulation of TC21
titanium alloy; the deformation amount is 70%. The effects
of deformation temperature and strain rate on the dynamic
recrystallization grain size and volume fraction were analyzed, respectively.
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Grain size is an important characteristic parameter that characterizes dynamic recrystallization behavior. This paper uses Photoshop
(PS) and Image Pro Plus (IPP) to calculate the average recrystallization grain size in the metallographic image. The original grain
size is 38 μm and then the parameters are fitted based on dynamic
recrystallization grain size model and is shown in Eq. (18):
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Grain size model
Journal of Materials Research
mol, the values of m2 and Q2 obtained are substituted into
Eq. (15), the values of a2 under each condition are calculated,
and the average value of a2 is taken as 0.03594. Substitute
the obtained parameters into Eq. (15) for fitting and then
calculate kd and βd based on slope and intercept obtained
from the fitting curve, the values of them are 1.687 and 0.994,
respectively.
Therefore, the dynamic recrystallization kinetics model is provided as Eqs. (16) and (17):
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As depicted in Fig. 7, as strain rate is 0.1 ­s , average grain
size shows increasing trend with increasing deformation
temperature, which is 9.1, 10.6, and 11.9 μm, respectively.
This phenomenon occurs due to the increasing deformation temperature, leading to an increase in the internal hot
energy of structure, thereby facilitating the growth of recrystallized grains. Moreover, when the deformation temperature
is 890 °C, the grain size distribution of the sample is most
uniform.
As depicted in Fig. 8, grain size shows decreasing trend
with increasing strain rate; the grain sizes are 9.3, 10.6, 8.8,
and 8.2 μm, respectively. This occurs because higher deformation rates result in shorter deformation time, thus, the
nucleated recrystallized grains do not have sufficient time
to grow. Moreover, when the strain rate is 0.1 and 1 ­s−1, the
grain size of the sample is relatively uniform.
The influence of deformation parameters on volume
fraction
As depicted in Fig. 9, at a strain rate of 0.1 ­s−1, volume fraction increases with increasing deformation temperature. With
increasing temperature, atomic activity is strengthened and a
greater amount of energy is supplied for dynamic recrystallization. In order to offset the dislocation accumulation caused by
compression, leading to more complete dynamic recrystallization, so, the volume fraction increases.
© The Author(s), under exclusive licence to The Materials Research Society 2025
Figure 10 illustrates the impact of various strain rates on
volume fraction at deformation temperature of 890 °C. As the
strain rate rises, the volume fraction gradually decreased, this
phenomenon arises due to the gradual increment of dislocation
density with increasing compression. However, higher strain
rates result in shorter time for the alloy to counter dislocation
accumulation through dynamic recrystallization; therefore,
dynamic recrystallization will not be carried out sufficiently,
and the volume fraction will decrease.
Based on the above analysis, a higher volume fraction of
dynamic recrystallization does not necessarily indicate the
attainment of a fine-grained microstructure. Because with the
deformation temperature increases, the grain size also enlarges;
however, a higher volume fraction suggests that dynamic recrystallization has proceeded more thoroughly, resulting in a relatively more uniform microstructure. Combining the simulation
results of grain size, increasing the strain rate leads to slighter
recrystallized grains; however, combined with microstructure
analysis, when the strain rate is 10 ­s−1, most of the grains are
elongated and flattened, which is not conducive to the macroscopic properties of the material; therefore, a higher strain rate
does not necessarily mean that fine recrystallized grains can be
obtained.
In summary, combining microstructure morphology,
according to the experimental and simulate result, when the
hot compression deformation temperature is 890 °C and the
strain rate is 0.1 and 1 ­s−1, a relatively uniform and fine equiaxed
structure can be obtained.
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Journal of Materials Research
The influence of deformation parameters on grain size
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Figure 8: Dynamic recrystallization grain size nephogram under different strain rates. (a) 890 °C, 0.01 s­ −1; (b) 890 °C, 0.1 s­ −1; (c) 890 °C, 1 ­s−1; and (d)
890 °C, 10 ­s−1.
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Figure 9: Dynamic recrystallization volume percentage cloud diagram at different deformation temperatures. (a) 850 °C, 0.1 s­ −1; (b) 890 °C, 0.1 s­ −1; and
(c) 930 °C, 0.1 ­s−1.
Through thermal compression tests, the dynamic recrystallization behavior of TC21 titanium alloy was investigated within the
dual-phase region. The following conclusions were summarized:
1.
2.
Based on experimental data, kinetic model was established,
the correlation coefficient between experimental data and
predicted values of dynamic recrystallization model reached
0.967.
The results of the thermal compression simulations demonstrate a strong concordance with the established mode, and
the average error in grain size is approximately 10.8%.
© The Author(s), under exclusive licence to The Materials Research Society 2025
Materials and methods
The experimental material is Φ300 mm TC21 titanium alloy bar
produced by China Baotai Group, which is an eight-element
two-phase titanium alloy independently developed by Northwest Nonferrous Metals Research Institute of China. The initial
microstructure consists of equiaxed α phase and fine lamellar α
phase distributed within the β transformation matrix.
In this experiment, the thermal compression test of the
alloy was carried out by Gleeble-3800 thermal simulator, and
the size of the sample was Φ10 mm × 15 mm. The surface of
both ends of the sample was clean, parallel, and smooth, without defects, such as cracks. In order to reduce the influence
of friction on the thermal compression specimen and ensure
uniform deformation of the specimen, graphite lubrication
sheets were attached to both ends of the specimen in this
experiment. The thermal compression experimental plan is
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Conclusion
When the deformation temperature is 890 °C and the strain
is 0.1 and 1 ­s−1, more uniform and finer microstructure of
TC21 titanium alloy can be obtained.
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The grain size of the metallographic structure was measured
using IPP software, and the results under different deformation
conditions are obtained.
Comparing the simulated values of grain size with the actual
measured values, the average error is obtained to be 10.8%, so,
the established model has a certain level of reliability.
3.
Journal of Materials Research
Verification of grain size
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Figure 10: Dynamic recrystallization volume percentage cloud diagram at different strain rates. (a) 890 °C, 0.01 s­ −1; (b) 890 °C, 0.1 s­ −1; (c) 890 °C, 1 ­s−1;
and (d) 890 °C, 10 s­ −1.
as follows: deformation temperature is 850, 890, 930 °C, strain
rate is 0.01, 0.1, 1, 10 ­s−1, rate of heating is 15 °C/s, insulation
time is 2 min, compression amount is 70%, and the cooling
method after compression is water cooling. After test, specimen underwent corrosion using a solution consisting of HF,
­HNO3, and H
­ 2O in a volume ratio of 1:3:7. Subsequently, the
microstructure was observed using an optical metallographic
microscope (OLYMPUS SZ-51).
Funding
There is no funding source available.
Data availability
The data are not publicly available due to their containing
information that could compromise the privacy of research
participants.
© The Author(s), under exclusive licence to The Materials Research Society 2025
Conflict of interest The authors declare that they have no
known competing financial interests or personal relationships
that could have appeared to influence the work reported in this
paper.
Supplementary Information
The online version contains supplementary material available at https://​doi.​org/​10.​1557/​s43578-​025-​01519-5.
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Rui Deng contributed to writing—original draft, investigation, and the use of software; Song Xue contributed to resource,
writing—review and editing, conceptualization, and supervision; Minglong Xu contributed to formal analysis and validation;
Zenong Li contributed to investigation and visualization; Shaoxiang He contributed to the use of software and investigation;
Ying Zhang contributed to investigation and formal analysis;
Rongchao Li contributed to the use of software and validation;
Qiankun Li contributed to visualization and investigation.
Journal of Materials Research
Author contributions
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Declarations
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