###### Abstract  
Hot deformation is one of the main technological stages of products made from metallic materials. It is strictly required to decrease the costs of developing optimized technologies at this stage without a significant decrease in the products' quality. The present investigation offers an algorithm to unite three different models to predict the hot deformation behavior, fracture, and microstructure evolution. The hot compression and tension tests of the AISI 316 Ti steel were conducted using the thermomechanical simulator Gleeble 3800 for the models' construction. The strain-compensated constitutive model and the Johnson-Mehl-Avrami-Kolmogorov (JMAK)-type model of the grain structure evolution show a satisfactory accuracy of 4.38% and 6.9%, respectively. The critical values of the modified Rice and Tracy fracture criteria were determined using the experimental values of the relative cross-section reduction and finite element calculation of the stress triaxiality. The developed models were approved for the stainless AISI 316 Ti steel by the hot torsion with tension test. ostitutive model; hot deformation; fracture; Rice and Tracy model; JMAK model; stainless steel; AISI 316 Ti; microstructure evolution; united approach Article  
United Approach to Modelling of the Hot Deformation Behavior, Fracture, and Microstructure Evolution of Austenitic Stainless AISI 316 Ti steel  
[PERSON], [PERSON], M. M.  
microstructural characteristics of the steel. As a result, it is required to create a constitutive model for each considered steel to increase the accuracy and predictability. The second step of the united model development is a mathematical description of the fracture conditions during the ductile materials' deformation at high temperatures. By now, the fracture process can be described in two ways: using models of nucleation and the growth of pores and cracks [13; 14; 15] and phenomenological models of the relationship between the fracture criterion and the processing parameters. The first approach involves complex models of pore formation and evolution at the microstructural level. The second approach does not imply modelling the material flow at the microlevel, considering only the effect of deformation conditions on macroscopic fracture. Even though the first type of model has a greater physical justification, the second has simple regularities and a significantly smaller number of unknown parameters, making it more attractive for practical application. One of the first phenomenological models was the Johnson-Cook model [16], which describes the dependence of critical strain \(\varepsilon_{f}\) on stress triaxiality (\(\sigma^{*}\)), strain rate (\(\dot{\varepsilon},\ s^{-1}\)) and deformation temperature (\(T\), \(K\)):  
\[\varepsilon_{f}=\left[D_{1}+D_{2}e^{D_{3}\sigma^{*}}\right]\left[1+D_{4}ln \frac{\dot{\varepsilon}}{\varepsilon_{0}}\right]\left[1+D_{5}\frac{T-298}{T_{ m}-298}\right] \tag{1}\]  
where \(D_{1}\)-\(D_{5}\) are material's constants, \(\dot{\varepsilon}_{0}\) (s\({}^{-1}\)) and \(T_{m}\)(K) are reference strain rate and temperature, respectively. Stress triaxiality may be determined as:  
\[\sigma^{*}=\frac{\sigma_{m}}{\overline{\sigma}} \tag{2}\]  
where hydrostatic stress \(\sigma_{m}\) (MPa) and equivalent stress \(\overline{\sigma}\) (MPa) are calculated by the following formulas:  
\[\sigma_{m}=1/3(\sigma_{1}+\sigma_{2}+\sigma_{3}) \tag{3}\]  
\[\overline{\sigma}=\sqrt{\frac{\left(\sigma_{1}-\sigma_{2}\right)^{2}+\left( \sigma_{2}-\sigma_{3}\right)^{2}+\left(\sigma_{3}-\sigma_{1}\right)^{2}}{2}} \tag{4}\]  
where \(\sigma_{1},\sigma_{2},\sigma_{3}\) are the principal stresses, MPa. However, the Johnson-Cook model demonstrates a low accuracy at small and negative stress triaxiality values [17; 18; 19], and the scientists have supposed another fracture criterion.