## 3 Numerical Results and Analysis
### Analysis of J-C Constitutive Parameters on Chip Morphology
Owing to increasing in the initial yield stress \(A\) increase the amount of heat generated,  
Figure 9: Dependency of the equivalent plastic strain evolution on initial yield stress \(A\). (**a**) Design path along the middle thickness of the chip; (**b**) comparison of the equivalent plastic strain under different variation of the initial yield stress \(A\) (\(-30\%\), original, \(+30\%\), respectively). and equivalent plastic stress increases after compression in the shear zone after thermal softening. Figure 10b indicates that the frequency of the serrated chip increases as the constitutive parameter (\(A\), \(C\)) increases; conversely, it decreases when the constitutive parameters (\(B\), \(n\), \(m\)) of the material increase. The frequency of the serrated chips is inversely proportional to the _C.S.I._ The results indicate that the decreases in the serrated frequency result in increased _C.S.I._ Although the number of serrations per unit length decreases, the damage to a single serration increases damage to the tool. Therefore, it is recommended to decrease the _C.S.I._ to a certain serrated frequency, which is conducive to reducing tool wear. The dependence of the J-C parameter on the shear field temperature and cutting force is analyzed to further examine the effect of the constitutive parameters of Ti6 Al4V on the formation mechanism of the serrated chip. Figure 11 presents the temperature field in the primary shear zone under different constitutive parameters. The temperature of the primary shear zone gradually increases when the initial yield stress \(A\), the hardening modulus \(B\), the strain rate dependency coefficient \(C\), and the thermal softening coefficient \(m\) increase from \(-30\) to \(+30\%\) based on the original value. This is mainly due to the constitutive parameter (\(A\), \(B\), \(C\), and \(m\)) affecting the strength of the bond inside the material and increasing the energy required for the micro-cutting process, thereby increasing the amount of heat in the cutting zone. Conversely, an increase in the hardening parameter \(n\) decreases the temperature in the adiabatic shear zone. The serrated chips become less apparent with a decrease in temperature. This further proves that an increase in the hardening index decreases the serrated sensitivity coefficient. Figure 12a presents the temperature of the chip sampled along the middle of the serrated chip. As shown in Figure 12a, the highest temperature in the second shear zone is due to friction between the tool and chips; thus, a significant amount of heat is generated on the rake face. The temperature of the adiabatic shear band (A.S.B.) exceeds the temperature on both sides of the adiabatic shear zone, which is mainly due to the plastic deformation in the adiabatic shear zone and low thermal conductivity of Ti6 Al4V. Hence, heat in the shear zone is not transferred. Figure 10: (**a**) Comparison of chip serration intensity (_C.S.I._) under different J-C constitutive parameters (\(A\), \(B\), \(n\), \(C\), \(m\)); (**b**) comparison of the frequency of serrated chip under different J-C constitutive parameters (\(A\), \(B\), \(n\), \(C\), \(m\)); I, II, and III correspond to variations of the original J-C constitutive parameters (\(-30\%\), \(0\), and \(+30\%\), respectively). Figure 11: Temperature field under different J-C parameters for cutting speed of 3 m/s. _A:_ initial yield stress, _B:_ hardening modulus, _n:_ strain rate dependency coefficient, _C:_ strain rate sensitivity coefficient, _m:_ thermal softening coefficient; _I, II, III, and IV correspond to variation of the original J-C constitutive parameters (\(-\)30%, \(-\)10%, +10%, and +30%, respectively). Figure 12: Temperature field during chip formation. (**a**) the design path along the middle thickness of the chip; (**b**) comparison of the temperature under different variations of the initial yield stress \(A\) (\(-\)30%, \(-\)10%, +10%, +30%, respectively). As shown in Figure 12b, the temperature of ASB I is the highest, and that of ASB III is the lowest.