## 3 Numerical Model  
The commercial FE software DEFORM-2 DTM (implicit solver) has been used to simulate the orthogonal cutting process of SAE 8620 steel (61 HRC) using a plane-strain coupled thermo-mechanical analysis. An updated Lagrangian model with automatic remeshing technique is applied to achieve the mechanical and thermal steady state conditions during the simulation. Concerning the workpiece material, the isotropic hardening has been assumed and the workpiece was modeled as plastic divided into 10,000 isoparametric quadrilateral elements. The cutting tool, divided into 3500 elements, was modeled as rigid in the FE model. Moreover, a high mesh-density has been set and used for the workpiece. To simulate the thermo-mechanical behavior of the current orthogonal cutting process, under severe plastic deformation (SPD) condition, the modified hardness-based flow stress model [20] was implemented. In particular, starting from the original J-C model Equation (1) it can be written as reported in Equation (2):  
\[\sigma(\varepsilon,\,\varepsilon,\,\mathrm{T})\mathrm{=}[\mathrm{A+B\varepsilon^ {n}}]\times[1+\mathrm{C}\ln(\varepsilon/\varepsilon_{0})]\times[1\mathrm{-}( (\mathrm{T-T_{0}})/(\mathrm{T_{m}-\,T_{0}}\ ))^{m}] \tag{1}\]  
where A, B, n, C, and m are the material constants; \(\varepsilon\) is the equivalent plastic strain, \(\varepsilon\) and \(\varepsilon_{0}\) are the plastic strain rate and the reference plastic strain, respectively, \(\mathrm{T_{0}}\) is reference temperature and \(\mathrm{T_{m}}\) is the melting temperature. \[\sigma(\varepsilon,\,\varepsilon,\,\mathrm{T},\,\Delta\mathrm{HRC},\,\mathrm{d })\mathrm{=}\mathrm{B(T)}\times(\mathrm{C\varepsilon^{n}+F+G\varepsilon}) \times(1+(\log(\varepsilon)^{m}\mathrm{-A})) \tag{2}\]  
where B(T) takes into account the temperature effect, F and G consider the hardness influence, and the term \((1+(\log(\varepsilon)^{m}\mathrm{-A}))\) represents the strain rate impact. The model proposed in this work starts from Equation (2) and modifies the constant C (MPa) of the flow stress to consider i) the grain refinement on the surface and subsurface caused by dynamic recrystallization (DRX), ii) the variation of the hardness and iii) the yield stress Equation (3):  
\[\mathrm{C=a+(k/d^{\prime}0.5)} \tag{3}\]  
where d is the average grain size and a and k are two numerical constants. By this modification, the material flow stress is influenced by phase transformation (mainly thermally induced) and by dynamic events (mainly mechanically induced) that significantly modify the microstructure of the machined surface and subsurface during turning. Thus, the thermo-mechanical behavior of the SAE 8620 steel is numerically represented by the new modified J-C law Equation (4):  
\[\sigma(\varepsilon,\,\varepsilon,\,\mathrm{T},\,\Delta\mathrm{HRC},\,\mathrm{ d})\mathrm{=}\mathrm{B(T)}\times((\mathrm{a+(k/d^{\prime}0.5)\varepsilon^{n}+F+G \varepsilon})\times(1+(\log(\varepsilon)^{m}\mathrm{-A})) \tag{4}\]  
The values of the numerical constants a, k, n, m, A and of the two hardness dependent factors F, G (Table 1) were calibrated through an iterative calibration strategy (Figure 1) according to what was available in the literature relating to the mechanical behavior of the material under investigation [20; 24; 25]. The physical events influencing the mechanical properties, were predicted by implementing a user subroutine with the empirical relationships of Zener-Hollomon (Z-H) parameter for grain refinement and Hall-Petch (H-P) equation for hardness evolution [22]. In particular, all the constants related to DRX and hardness changes were calibrated for SAE 8620 steel following the calibration procedure reported in [26]. Figure 2 summarizes the FE strategy developed to properly simulate the microstructural alterations. In particular, the newly developed FE model is able to predict thermal and mechanical events during hard machining, and to show, by their single contribution, when the microstructural changes are mainly thermally or mechanically induced.