###### Abstract
Therefore, [PERSON] and [PERSON] used a system of equations for different levels of stress triaxiality [20]:  
\[\varepsilon_{f}=A[\sigma^{*}+1/3]^{B}\text{ for }\sigma^{*}=-0.33\text{--}0 \tag{5}\]  
\[\varepsilon_{f}=C\sigma^{*2}-D\sigma^{*}+E\text{ for }\sigma^{*}=0\text{--}0.4 \tag{6}\]  
\[\varepsilon_{f}=F\sigma^{*-1}\text{ for }\sigma^{*}=0.4\text{--}0.95 \tag{7}\]  
where \(A,B,C,D,E\), and \(F\) are the material's constants. [PERSON] has developed a plastic fracture criterion that includes two coupled fracture mechanisms and has demonstrated its high accuracy in predicting ductile fracture over a wide range of stress triaxiality [21]:  
\[[\left(\frac{\sigma_{1}-\sigma_{3}}{\overline{\sigma}}\right)^{C_{1}}+\sigma ^{*}-\frac{1}{3}]^{C_{2}}\varepsilon_{f}=C_{3} \tag{8}\]  
where \(C_{1},C_{2},C_{3}\) are material's constants. In addition to models that describe the critical value of plastic deformation, accumulated energy models were also developed. Thus, [PERSON] and [PERSON] [22] have proposed a criterion defining the integral accumulation of damage during deformation:  
\[CL=\int_{0}^{\overline{\varepsilon}_{f}}\sigma_{1}d\overline{\varepsilon} \tag{9}\]  
strain rates and temperatures. Constant \(a_{1}\) has a value of about 0.83 in accordance with [PERSON] et al. [36]. The size of the dynamically recrystallized grains at the stage of steady-state flow is practically independent of the strain and is determined only by the strain rate and deformation temperature:  
\[d_{DRX}=a_{d}\cdot Z_{d}^{m_{d}} \tag{20}\]  
\[\sigma^{*}=\frac{\sigma_{m}}{\overline{\sigma}} \tag{2}\]0  
where \(a_{d}\), \(m_{d}\), \(Q_{d}\)(J-mol\({}^{-1}\)) are material constants that are determined empirically using microstructural investigations. By now, the microstructure evolution models for the different types of stainless steels were constructed. Some of such models are listed in \[\sigma^{*}=\frac{\sigma_{m}}{\overline{\sigma}} \tag{2}\]1  
Three considered stages of the technology development may be united by the finite element (FE) approach. At the current state, the finite element simulation of hot deformation and heat treatment processing is the most powerful tool providing the optimal thermo-mechanical parameters without any sufficient material expenses [40; 41; 42; 43; 44]. This approach to calculating deformation and fracture processes has been successfully applied for the conditions of cutting [45], cold [46], and hot plastic deformation [47; 48]. Despite many of the works devoted to investigating and modelling the hot deformation behavior, fracture and microstructure evolution of metallic materials, all of the models were described independently of each other. The simultaneous realization and approach of such models were not presented up to now in the literature. In the present work, the united finite element approach considering hot deformation behavior, fracture conditions, and microstructure evolution was developed and approved for the 316 Ti stainless steel. The realization of the developed united approach for different materials in semi-industrial conditions should be done as a next step of the investigation and may approve its applicability.