## 3 Results
### Dynamic Recrystallization Model  
The DRX kinetics parameters of the AISI 316 Ti steel were determined using true stress-true strain curves from the maximum stress to steady-state mode. The volume fraction of the DRX grains was assumed from the additive contributions of the deformed and recrystallized grains to overall stress value:  
\[X_{DRX}=\frac{\sigma_{p}-\sigma}{\sigma_{p}-\sigma_{\rm ss}}, \tag{34}\]  
where \(\sigma_{p}\) is the peak stress which corresponds to the stress of the deformed grains, \(\sigma_{\rm ss}\) is the steady-state stress characterizing the deformation resistance of the recrystallized grains, and \(\sigma\) is the current stress value. Examples of the fittings using the JMAK model (14) and Equation (34) are shown in Figure 7a. The k\({}_{\rm d}\) parameter has a value of about 1.7 for all compression tests conducted at the temperatures of 1373, 1423, and 1473 K and the strain rates of 0.1, 1, and 10 s\({}^{-1}\). This value approximately correspondent to the ones obtained earlier [(36; 58)].  
The dependences of the \(\varepsilon_{p}\) and \(\varepsilon_{0.5}\) from the Zener-Hollomon parameter are presented in Figure 7b. We can see good accordance of the \(\varepsilon_{p}\) and \(\varepsilon_{0.5}\) experimental values with the  
Figure 6: The dependence of the critical values of the modified Rice and Tracy criteria on the Zener–Hollomon parameter.  
Figure 7: Kinetics of the dynamic recrystallization of the AISI 316 Ti steel during compression at 0.1 s\({}^{-1}\) (**a**) and plots \(\ln(\,|\,\varepsilon_{p}\,|\,)\)\(\ln(\,|\,\varepsilon_{0.5}\,|\,)\) vs. InZ (**b**).  
Equations (16)-(19). The values of both effective activation energies of recrystallization at the beginning and in the middle of the DRX are significantly larger than the values for the effective activation energy of the deformation. It may be described by the significant influence of the dynamic recovery on the microstructural changes due to high SFE value. Some of the dislocations annihilate before new grains' nucleation, and the energetic barrier of the DRX increases.  
The microstructures of the AISI 316 Ti steel after hot plastic deformation are shown in Figure 8. The average grain size is in the range of 7-30 \(\mu\)m. Its value is significantly dependent on the deformation conditions and decreases with increasing the strain rate and decreasing the temperature. The experimental grain size values were used for the determination of the unknown material's constants in Equations (20) and (21). The dependence \(\ln(\mathrm{d}_{\mathrm{DRX}})\) vs. \(\ln(\mathrm{Z}_{\mathrm{d}})\) is shown in Figure 9a. The effective activation energy \(\mathrm{Q}_{\mathrm{d}}\) = 922 kJ-mol (steady stage) has a value almost equal to a value of \(\mathrm{Q}_{0.5}\) = 915 kJ-mol (middle of the DRX process) and higher than the value at the beginning of the DRX (\(\mathrm{Q}_{\mathrm{P}}\) = 722 kJ-mol). It means that the new grains' growth in the deformed matrix is the limiting process of dynamic recrystallization. The comparison of the calculated and experimental grain size values is shown in Figure 9b. The average absolute relative error was 6.9%, comparable with the mean grain size value's measurement error. This fact allows us to include the constructed model in the united scheme of modelling the hot deformation behavior, fracture, and microstructure evolution.  
Figure 8: The microstructure of the AISI 316 Ti steel after hot deformation.  
Figure 9: Dependence of \(\ln(\mathrm{d}_{\mathrm{DRX}})\) on \(\ln Z\) (**a**) and (**b**) a comparison of the experimental and calculated grain size after hot deformation of the AISI 316 Ti steel.