## 3 Results
### Hot Deformation Behavior Modelling  
The hot deformation of the steel in the austenitic phase range proceeds in two main stages. At the first stage, two main structural changes are strain hardening (SH) and dynamic recovery (DRV). During this stage, the stress increases with a strain and achieves saturation. At the second stage of the deformation, dynamic recrystallization (DRX) is added to the SH and DRV processes. This stage appears by the maximum on the stress-strain curve when the increase of the SH's stress is compensated by softening from the annihilation of the dislocations (DRV) and nucleation of new undeformed grains (DRX). However, it is known that the DRX process begins at the strain, which is lower than the peak strain at the deformation curve. Usually, the critical strain may be determined as a minimum on the d\(\theta\)/d\(\sigma\) vs. \(\sigma\) graph where \(\theta\) = d\(\sigma\)/d\(\varepsilon\) is a strain hardening coefficient [51]. As shown in Figure 3, the stage of the DRX in the AISI 316 Ti may be achieved only at high temperatures in the range of 1373-1473 K due to high stacking fault energy (SFE). The calculated SFE value accordingly [52] is about 49 mJ\(\cdot\)m\({}^{-2}\) which is higher than for the AISI 304 (19 mJ\(\cdot\)m\({}^{-2}\)) [53] and AISI 301 (6.7 mJ\(\cdot\)m\({}^{-2}\)) [54] austenitic steels. The high value of the SFE makes the dissociation of the dislocations in the slip plane difficult. The dislocations cross-slip proceeds more easily, leading to the annihilation of the dislocations without nucleation of new grains. Figure 2: Phase composition of the investigated steel accordingly thermodynamic calculations (**a**) and experimental DTA-curve (**b**). The Zener-Hollomon parameter-based constitutive model was constructed using the experimental data. The universal hyperbolic sine law was used to describe stress dependence on the strain rate (\(\dot{\epsilon}\)\(s^{-1}\)) and temperature (T, K):  
\[\text{Z}=A_{HS}[\sinh(\alpha\sigma)]^{n_{HS}} \tag{22}\]  
where Z is the Zener-Hollomon parameter:  
\[\text{Z}=\dot{\epsilon}e^{\frac{Q_{HS}}{\text{Z}t}} \tag{23}\]  
where \(A_{HS}\), \(n_{HS}\) and \(\alpha\) are experimentally determined parameters, \(Q_{HS}\) is the effective activation energy of the hot deformation, J/mol, R is the universal gas constant (8.314 J\(\cdot\)mol\({}^{-1}\cdot\)K\({}^{-1}\)). However, the description of special cases of the constitutive models is required to determine the \(\alpha\) parameter's value. The power-law form of the constitutive model is applicable for low stresses:  
\[\text{Z}=\text{A}_{P}\sigma^{n_{P}} \tag{24}\]  
The exponential form is usually used for a high level of stress:  
\[\text{Z}=\text{A}_{\text{E}}\text{e}^{\beta\sigma} \tag{25}\]  
where A\({}_{P}\), n\({}_{P}\), A\({}_{\text{E}}\), and \(\beta\) are experimentally determined parameters. Figure 3: True stress vs. true strain curves for hot deformation of the AISI 316 Ti steel at a strain rate of (**a**) 0.1 s\({}^{-1}\), (**b**) 1 s\({}^{-1}\), and (**c**) 10 s\({}^{-1}\). The comparison between the predicted and the experimental values of the flow stress (**d**). Parameter \(\alpha\) may be approximately determined as:  
\[\alpha\approx\frac{\beta}{\mathrm{n}_{p}} \tag{26}\]  
It is known that the materials constants' values are dependent on the strain [55; 56].