## 4 FE Validation and Results  
The proposed FE model was validated by comparing its output with the corresponding experimental data. Figure 3 shows that the implemented user routine gave stable and uniform data prediction in the steady-state zone. In particular, Figure 3 reports the numerical prediction for both grain refinement and affected layer at a cutting speed of V = 273 m/min and fresh insert with positive rake angle (UP-F). As reported in Figures 3-9, the results show the ability of the customized model to successfully predict the thermo-mechanical phenomena taking place during the selected processes. Figure 3: Grain size prediction: positive rake fresh insert with cutting speed (UP-F/V) = 273 m/min. Figure 2: Finite element strategy to predict the grain size and hardness variation due to thermal and mechanical events. Figure 4: Grain size prediction: overall results (NH-W: negative rake worn insert, NH-F: negative rake fresh insert, UP-W: positive rake worn insert and UP-F: positive rake fresh insert). Figure 5: Prediction of strain distribution: (**a**) UP-F/V = 273 m/min, (**b**) UP-W/V = 273 m/min (UP-W: positive rake worn insert and UP-F: positive rake fresh insert). Figure 6: Prediction of temperature distribution: (**a**) NH-W/V = 91 m/min, (**b**) NH-W/V = 273 m/min (NH-W: negative rake worn insert). Figure 8: Surface hardness prediction (NH-W: negative rake worm insert, NH-F: negative rake fresh insert). Figure 7: Hardness prediction: NH-W/V = 91 m/min (NH-W: negative rake worm insert). Figure 9: Thermal (phase transformation) and mechanical (dynamic recrystallization (DRX) event) hardness contribution to the as-received material hardness: a)–b) NH-W/V = 273m/min, c)–d) NH-F/V = 91m/min (NH-W: negative rake worm insert, NH-F: negative rake fresh insert). Figure 4 reports the numerical-experimental comparison of all the analyzed tests, showing a good agreement in the prediction of the grain size evolution. As experimentally found, the grain size range was about 100 times smaller than the bulk grain size (2 \(\upmu\)m) [23]. For all the investigated cases, higher refinement (i.e., smaller grain size) was experimentally found by using a new cutting tool as shown in Figure 4. In these cases, FE model shows that, when hard machining is performed by a new cutting tool, higher strains provide smaller grain size due to grain refinement (Figure 5). On the contrary, experiments show a grain size increase (i.e., coarser grain size) with the increase of the cutting speed (Figure 4). Thus, the FE model allows observation of increasing temperatures when the cutting speed rises, as seen in Figure 6.  
For overall results, coarser grain size was produced on the machined surface and subsurface due to higher temperatures. Figure 7 shows the hardness prediction when the cutting speed of V = 91m/min and worn insert with negative rake angle (NH-W) were used, while Figure 8 reports the comparison of surface hardness experimentally observed and numerically predicted. A very good agreement between the numerical and experimental data was verified. The numerical results confirm that machining of SAE 8620 hardened steel causes severe surface and subsurface structural changes, which are mainly thermally induced through phase transformations, as also suggested by the FE model. In fact, the proposed phenomenological model makes possible to evaluate both thermally and mechanically induced microstructural changes and to show their single contribution in the deformation zone, chip and machined surface. Hence, comparing NH-F (V = 91 m/min) and NH-W (V = 273 m/min) tests, a great difference is shown concerning grain size evolution (Figure 4), while a not evident difference is revealed concerning machined surface hardness variation (Figure 8). This is due to the different mechanical and thermal events occurring for each single test. With the increase of the cutting speed, higher temperatures are reached during machining (Figure 6), resulting in a thermally-activated hardness increase for phase transformation phenomena (quenching).