3.3. Description of DRX Behaviors
It is well-accepted that the resistance heating isothermal compression can be summarized as an electrical-thermal-mechanical multi-field issue [
28,
29]. In order to describe the evolution of DRX behaviors in the hot compression process of SAE 5137H steel, the obtained true stress–strain data and established DRX kinetics models were programed into finite element codes, and then the FE model was developed on the DEFORM-3D platform. In this FE model, the workpiece was simplified as a cylindrical specimen with 10 mm in diameter and 12 mm in height. The workpiece was defined as a plastic body without elastic deformation, and the two anvils were set as rigid bodies. The friction between workpiece and anvils was assumed as shear type, and the friction coefficient was taken as 0.3. The heat transfer coefficient between workpiece and anvils was set as 0.033. The initial grain size of workpiece was set as 64.8 μm. The velocity of compressing anvil can be calculated from Equation (17) [
28]. Based on the developed FE model, the hot compression processes in agreement with the experimental conditions were simulated, and the DRX behaviors were discussed:
where
is the velocity of compressing anvil;
is the proposed strain rate;
t is time;
l0 is the initial height of workpiece.
When the specimen deformed at 1303 K and 0.1 s
−1, the distributions of DRX volume fraction at different true strains were demonstrated in
Figure 14, in which the true strains of 0.105, 0.223, 0.357, 0.511, 0.693, and 0.916 correspond to height reductions of 10%, 20%, 30%, 40%, 50%, and 60%, respectively. In
Figure 14, it can be observed that, when the true strain increases from 0.105 to 0.511 (point A to point D), DRX volume fraction increases appreciably. When the true strain exceeds 0.511 (point D to point F), DRX occurs completely, DRX volume fraction is changed insignificantly with the continuous increase of true strain. Moreover, it can also be noted that the distribution of DRX volume fraction is not uniform. At the center of a deformed specimen, DRX volume fraction is the maximum, while it is relatively small at the center of upper and lower end-surfaces of the specimen. This is owing to the fact that the nonlinearly interactions of temperature field, strain rate field, and strain field are distributed non-homogeneously, which directly affects the microstructure evolution in the hot deformation process of materials [
5,
29].
Figure 15 exhibits the DRX volume fraction distributions of the specimens isothermally compressed to different true strains of 0.223, 0.511, and 0.916 under the constant strain rate of 0.1 s
−1 and different deformation temperatures of 1123K, 1213 K, 1303 K, 1393 K, and 1483 K. It is evident that, for a fixed true strain, the distribution of DRX volume fraction at any given temperature is similar to each other. From the center region to the outer edge, DRX volume fraction gradually decreases, and its maximum value appears at the center region of the deformed specimen. As true strain increases from 0.223 to 0.916, the DRX volume fraction in all region of specimen increases. By comparing the distribution of DRX volume fraction under different temperatures, it is shown that the volume fraction of DRX grains increases with increasing temperature. In addition, it is worth noting that, at higher temperature, DRX volume fraction at the center region of specimen has reached the maximal value at a relatively small true strain. This is owing to the fact that higher temperature can provide more activation energy for the nucleation of DRX grains. Hence, DRX occurs more easily and more completely at elevated temperature. The distributions of grain size at the end of hot compression (the true strain of 0.916) under the constant strain rate of 0.1 s
−1 and different temperatures of 1123K, 1213 K, 1303 K, 1393 K, and 1483 K were demonstrated in
Figure 16a–e, respectively. It is noticed that the distribution of grain size shows an opposite variation tendency with DRX volume fraction distribution. From the center region to the outer edge, grain size gradually increases. At the center region of the deformed specimen, grain size reaches the minimum value, while its maximum value appears at the center of the upper and lower end-surfaces. An obvious feature can be observed from
Figure 16a–e is that the distributions of grain size are not uniform in the deformed specimens under different temperatures. The standard deviation (SD) of grain size distribution gradually increases as the temperature increases. It indicates that the inhomogeneous degree of grain size increases with temperature increasing. Under the temperatures of 1123 K, 1213 K, 1303 K, 1393 K, and 1483 K, the values of average grain size (denoted as “Avg.” in
Figure 16) are calculated as 14.8 μm, 24.1 μm, 38.0 μm, 69.3 μm, and 74.3 μm, respectively. It reveals that grain size increases with the increase of temperature. The reasons accounting for this phenomenon are as follows. As we all know, grain size is determined by the comprehensive action of grain refinement induced by DRX and grain coarsening resulted from grain growth [
9,
29]. At higher temperatures, the occurrence of DRX can be significantly promoted, resulting in the increase of DRX volume fraction—while, at the same time, the grain boundary migration rate is higher at elevated temperatures. The mechanism of grain growth plays a dominant role in the evolution of grain size, thus provoking grain coarsening. From the simulation results in
Figure 15 and
Figure 16, it can be concluded that DRX volume fraction and grain size increase with temperature increasing.
Figure 17 illustrates the distributions of DRX volume fraction of the specimens compressed to different true strains of 0.223, 0.511, and 0.916 under the constant temperature of 1303 K and different strain rates of 0.01 s
−1, 0.1 s
−1, 1 s
−1, and 10 s
−1. Comparing
Figure 17 with
Figure 15, it can be seen clearly that, for a constant true strain, DRX volume fraction exhibits the similar distribution under diverse temperatures and strain rates. The distributions of DRX volume fraction at different strain rates are also inhomogeneous in the deformed specimens. At the true strain of 0.223, a significant difference on the distributions of DRX volume fraction can be observed under the strain rates of 0.01 s
−1 and 10 s
−1. Especially, for the center region of specimen, the DRX volume fraction at the strain rate of 0.01 s
−1 is much higher than that in the strain rate of 10 s
−1. In addition, this difference is decreased when the true strain exceeds 0.511, since DRX occurs completely with the continuous increase of strain. The comparisons of the distributions of DRX volume fraction under different strain rates indicate that DRX volume fraction increases with strain rate decreasing, and, meanwhile, for a fixed true strain, the center region of specimen with relatively high DRX volume fraction also increases as well. This attributes to the fact that the lower strain rate can provide enough time for the DRX process, and then DRX occurs more completely.
Figure 18a–d display the distributions of grain size at the end of hot compression under the constant temperature of 1303 K and different strain rates of 0.01 s
−1, 0.1 s
−1, 1 s
−1, and 10 s
−1, respectively. It is noted that the distributions of grain size in the deformed specimens exhibit the similar tendency under different strain rates, and all distributions are inhomogeneous. The standard deviation (SD) of grain size distribution increases as the strain rate increases, which implies that the degree of deformation inhomogeneity increases with the strain rate increasing. Under the strain rate of 0.01 s
−1, 0.1 s
−1, 1 s
−1, and 10 s
−1, the values of average grain size (denoted as “Avg.” in
Figure 18) are calculated as 46.9 μm, 38.0 μm, 30.6 μm, and 25.9 μm, respectively. It indicates that grain size becomes finer with strain rate increasing. On the one hand, the dislocation generation rate and dislocation density increase with the increase of strain rate. There are more deformation energies stored in the deformed SAE 5137H steel, which promotes the nucleation of DRX grains. On the other hand, there is no sufficient time for grain growth, resulting in finer grain size at a higher strain rate. Based on the simulation results in
Figure 17 and
Figure 18, it can be summarized that DRX volume fraction and grain size increase with the strain rate decreasing:
In order to examine the predictive ability of the multi-field and multi-scale coupling FE model embedded with DRX kinetics models, for the center of specimens marked “X” in
Figure 3, the values of grain size were computed from simulation results. The comparisons of grain size between experimental results and predicted ones were performed, as shown in
Figure 19. The mean relative error is calculated as 6.5%, which indicates a good agreement between the predicted and experimental results. It strongly confirms that the established DRX kinetics models can be successfully incorporated into the FE model to describe the DRX behaviors of SAE 5137H steel in the hot deformation process.