## 5 Discussion and Conclusions  
In this paper, a FE model has been proposed to simulate the hard machining of SAE 8620 steel at varying cutting speed, insert geometry and flank wear. The proposed FE strategy successfully simulates both the thermal and the mechanical phenomena on the surface and subsurface leading to microstructural changes. The Zener-Hollomon parameter and the Hall-Petch relation were implemented for predicting grain size and hardness evolutions. A new modified hardness-based J-C model was implemented considering the effect of grain size on the material's behavior during the SPD process. More specifically, the influence of grain refinement, due to DRX, on the material flow stress was taken into account following the Hall-Petch equation. This aspect is of main importance considering the inverse function existing between the flow stress curve and the grain size: smaller grain size (i.e., grain refinement) results in higher material strength. The numerical results were validated by comparison with those performed by [PERSON] et al. [23] and a satisfactory agreement was found. In particular the average error was always contained around 20% for grain size and 4% for the surface hardness. Furthermore, it was found that the cutting speed, the insert geometry and the flank wear strongly influence the machined surface and subsurface integrity of SAE 8620 bearing steel. In fact, with the increase of the cutting speed a coarser grain size was observed. In fact, at higher cutting temperatures the dynamic recrystallization is contained leading to a smaller amount of grain refinement. On the contrary, higher refinement is highlighted machining with fresh cutting tools which induce higher localized strains. In particular, the developed FE model brought to observe that the hardness variation on the machined surface and subsurface is due to both mechanical and thermal contributions, showing a predominant thermal influence during hard machining. The proposed phenomenological model allows better understanding of the physical aspects of the analyzed process, showing the contribution of the mechanically-activated hardness variation for DRX events and the thermally-activated hardness variation for phase transformation phenomena to the as-received material hardness. The model highlights the influence of grain size and hardness variation on the material behavior at both macro and micro scale, directly considering the influence of microstructural changes on material flow stress also for higher strain rates and temperatures. Thus, the proposed FE strategy can be used to properly simulate the cutting process of the SAE 8620 steel, providing accurate results since it was considered the coupled effect of grain refinement and microhardness variation on the material flow stress equation. Figure 10: Hardness profile prediction: a) NH-F/V = 91m/min, b) NH-W/V = 91m/min, c) NH-F/V = 273m/min, d) NH-W/V = 273m/min (NH-W: negative rake worn insert, NH-F: negative rake fresh insert). **Author Contributions:** Conceptualization, D.U. and A.D.P. ; methodology, D.U., S.C., and G.R. ; software, S.C. and G.R. ; formal analysis, S.C.; G.R., D.U. and A.D.P. ; investigation, S.C. and G.R. ; data curation, S.C. and G.R. ; writing--original draft preparation, S.C. and G.R. ; writing--review and editing, D.U. and A.D.P. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Conflicts of Interest:** The authors declare no conflict of interest.