3.1. Thermal Stress Response Behavior
True stress–true strain curves of the studied 22MnB5 boron steel at various strain rates and temperatures are shown in
Figure 2. Visibly, the flow stress behavior is strongly affected by deformation temperature and applied strain rate. Except for that at the strain rate of 0.01 s
−1 and temperature of 500 °C, the flow stress increases gradually with the increase in applied strain, then tends to be saturated after reaching its peak, and finally decreases until fracture. The deformation in the early stage is predominated by strain hardening, leading to a rapid increase in flow stress. With the increase in applied strain, DRV and DRX occur successively, resulting in an increased dynamic softening. The dynamic softening affects the rate of increase in flow stress and the evolution behavior with applied strain lower than that of the peak stress, which then completely counteracts the strain hardening with further increase in applied strain. Therefore, the flow stress exhibits dynamic saturation after reaching the peak. In addition, the flow stress decreases with the increase in deformation temperature. Visibly, the effect of temperature on flow stress increases with the reduction of deformation temperature. As the deformation temperature decreases from 650 to 500 °C, the flow stress increases significantly. This is because the deformation temperature of 500 °C is in the bainite transformation range, and the bainite generated during thermal tension significantly increases the flow stress [
21]. It is widely known that the increased deformation temperature leads to an increase in the kinetic energy obtained by atoms, which finally facilitates the DRV and DRX [
22,
23]. Furthermore, the strain required for dynamic softening decreases with increasing deformation temperature. Therefore, the strain required for dynamic equilibrium between strain hardening and dynamic softening reduces. In other word, the strain corresponding to the peak stress of the studied steel decreases with increasing the deformation temperature.
Except for that at the strain rate of 0.01 s
−1 and temperature of 500 °C, the flow stress of the studied 22MnB5 boron steel increases with the increase in applied strain rate, exhibiting apparent positive strain rate dependence, as shown in
Figure 3. As reported, the increase in applied strain rate can effectively suppress dynamic softening and grain growth of metal materials by reducing response time for DRV and DRX [
24,
25], which can help to understand the positive strain rate dependence. In addition, an inflection point is detected when stretched at the strain rate of 0.01 s
−1 and temperature of 500 °C at which the slope of stress–strain curve exhibits a rapid increase. As a result, its peak stress reaches or even exceeds that at the strain rates of 0.1 and 1 s
−1. It is reported that, at low deformation temperature, the relatively low strain rate tension is beneficial to phase transition from supercooled austenite to bainite, and thus the steel is strengthened [
11]. Therefore, the flow stress of the studied 22MnB5 boron steel shows a sharp increase when stretched at the temperature of 500 °C and strain rate of 0.01 s
−1 (
Figure 3a).
The relationship between strain rate and peak stress at various deformation temperatures is shown in
Figure 4. It can be observed that the peak stress decreases with increasing deformation temperature, which is attributed to dynamic softening resulted from the decreased interatomic force as well as the increased DRV and DRX. In addition, the peak stress increases with increasing applied strain rate when the deformation temperature is higher than 500 °C. It has been reported that, as the applied strain rate increases, the decreased response time weakens the DRV and DRX of materials [
25], thereby resulting in an increase in peak stress. However, when stretched at 500 °C, the peak stress is characterized by decrease followed by continuous increase with increasing applied strain rate.
The relationship between strain hardening rate (SHR) and true strain under various deformation conditions is obtained by differentiating the curves of true stress–true strain, as shown in
Figure 5. At the same applied strain rate, the higher the deformation temperature, the lower the SHR. Additionally, the SHR at the same deformation temperature increases roughly with increasing applied strain rate. As reported, low applied strain rate facilitates phase transition from supercooled austenite to bainite as deformation temperature is in the bainite transition zone [
26,
27]. When stretched at the strain rate of 0.01 s
−1, the SHR shows a rapid decrease followed by an increase, and then it decreases again. The slope at the increasing stage drops apparently with the increase in deformation temperature. At the deformation temperatures of 500, 650 and 700 °C, a visible increase in SHR is detected, which is related to bainite transition because the deformation temperature is in the bainite transition zone. When the applied strain rate is higher than or equal to 0.1 s
−1, the SHR of the studied 22MnB5 boron steel shows a sharp decrease at initial deformation stage, and then shows a decrease with the increase in applied strain. The relatively low SHR in the middle and later deformation stages is related to DRV and DRX, leading to an increased dynamic softening with the increase in applied strain. Finally, a dynamic equilibrium is reached between dynamic softening and strain hardening. For 22MnB5 boron steel, 500 °C is in the bainite transformation zone, and the transformation amount of bainite generated during thermal tensile process is positively related with the deformation duration [
21]. Even if the cooling rate is higher than the critical quenching rate of 22MnB5 boron steel, the low strain rate prolongs the deformation time, which is conducive to the transformation of supercooled austenite into bainite, thereby promoting a sudden increase in the deformation resistance of the studied steel [
21]. In contrast, at high strain rate, the austenite does not have time to transform. Therefore, at the deformation temperature of 500 °C, the peak stress first decreases and then increases with the increase in strain rate due to the influence of bainite transformation.
3.4. Constitutive Modeling
As shown in
Figure 6, the bainite transition occurs when deformed at 500 °C with strain rate of 0.01 s
−1; therefore, only the stress–strain data at strain rates of 0.1, 1 and 10 s
−1 are selected for constitutive modeling. It is well known that the deformation at high temperature is a thermal activation process, and the dynamic equilibrium between strain hardening and thermal softening induced by DRV and DRX strongly affects the stress response behavior [
33]. As shown in
Figure 2 and
Figure 3, the stress response behavior of the studied 22MnB5 boron steel is apparently influenced by the applied strain rate and temperature. In present study, a modified Arrhenius model based on hyperbolic sine correction function is selected to describe the thermally activated deformation behavior of the studied 22MnB5 boron steel. This model contains the Zener-Hollomon parameter [
34]; therefore, the flow stress is a function of deformation activation energy, deformation temperature and applied strain rate [
35]. The expression is as follows:
where
is the strain rate (s
−1),
A is the structural factor,
B is the stress multiplier,
σ is the flow stress,
n is the stress exponent,
Q is the thermal deformation activation energy (kJ·mol
−1),
R is the gas constant (J·mol
−1·K
−1),
T is the deformation temperature (K) and
Z is the Zener-Hollomon parameter. Based on Equation (1), the following expression can be deduced:
where
F(
σ) is the stress function, and can be expressed using the following formula.
Equation (1) can be derived using Taylor series expansion. According to Taylor series expansion, Equation (1) can be simplified to a power function relationship when the flow stress is low (
Bσ < 0.8), as shown in Equation (4), and can be simplified to an exponential function relationship when the flow stress is high (
Bσ < 1.2) [
36,
37]. These expressions are shown in Equations (4) and Equation (5), respectively. Accordingly, Equation (4) is used to describe the creep process of metals, and Equation (5) can better depict the deformation of materials under high strain rate load.
where
and
are material parameters that satisfy the following relationship with
B.
By combining Equations (1) and (4) and Equations (1) and (5), the following equations can be achieved.
The curves of
and
are plotted based on Equations (7) and (8). Thereby, the parameter
B can be determined by solving the slope of the curves. Treating the deformation activation energy
Q as a parameter that is unaffected by other conditions, the following equation can be built by combining Equations (4) and (5) followed by the natural logarithm.
On this basis, the relationship curves of as functions of and are plotted, and the stress exponent n and the structural factor A are calculated by fitting the linear regression equations.
Taking the experimental data at strain of 0.08 with temperature ranging from 500 °C to 950 °C as an example, the curves of
and
are drawn as shown in
Figure 13. Clearly, each curve is basically linear with a similar slope. The slope and the correlation coefficient of regression analysis are listed in
Table 4. By averaging the slope of each curve, the 1/
m1 and 1/
m2 are obtained with values of 0.0721 and 20.640. Finally, the parameter
B is calculated to be 0.0038 based on Equation (6).
The curves of
at various deformation temperatures are drawn and shown in
Figure 14. Clearly, the
is approximately linear with
. The correlation coefficients of linear fitting at 500, 650, 700, 800, 900 and 950 °C are 0.996, 0.981, 0.997, 0.996, 0.995 and 0.991, respectively. The value of
at the strain of 0.08 is obtained by averaging the slope of each curve, so the parameter
n can be evaluated to be 9.666.
Equation (9) can be expressed as follows:
Based on Equation (10), the relationship between
and
is drawn and shown in
Figure 15. As can be seen, although a slight hyperbolic sine function relationship is shown, linear relationship is more consistent. Slope
k, intercept
h and their correlation coefficient
R of linear fitting are obtained and listed in
Table 5. Substituting them into Equations (11) and (12), the deformation activation energy
Q and
lnA are calculated as 196,778.5 kJ/mol and 19.894 s
−1, respectively.
According to the above solving method, the
m1,
m2,
B,
n,
Q and
lnA at the strains of 0.02, 0.04, 0.06, 0.10 and 0.12 are calculated and listed in
Table 6. Thereby, the regression equations are obtained by polynomial fitting, as shown in Equations (13)~(18). The fitting correlation coefficients are between 0.9954 and 0.9999, as shown in
Table 7.
Both sides of Equation (10) are taken logarithmically, and then simplified as follows:
Based on Equations (15)~(19), above, the flow stress constitutive equation of the studied 22MnB5 boron steel under isothermal deformation condition can be achieved. The comparison between constitutive fitted and experimental flow stresses is shown in
Figure 16. Clearly, the constitutive fitting results are in good agreement with the experimental results, indicating that the constructed constitutive equation can accurately describe the thermal deformation behavior of the studied 22MnB5 boron steel. To more precisely characterize the fitting accuracy of the constitutive model, the experimental and fitting stresses at specific strains of 0.2, 0.4, 0.6…1.6 under different deformation conditions are selected for comparison. The results are shown in
Figure 17. It is obvious that almost all the points are distributed within the error range of −5~5%, indicating that the established model has a high prediction performance in wide ranges of deformation temperature (500 °C to 950 °C) and strain rate (0.01 s
−1 to 10 s
−1).