## 3 Numerical Results and Analysis
### Analysis of J-C Damage Parameters on the Formation of Serrated Chip  
The J-C damage parameter is an important factor governing material deformation and failure. To perform a detailed examination of the mechanism of the J-C damage parameters on the formation of serrated chips during the cutting simulation of Ti6 Al4V, the Johnson-Cook damage parameter (\(D_{1}\), \(D_{2}\), \(D_{3}\), \(D_{4}\), and \(D_{5}\)) is increased by +50%, +100%, and decreased by 50% and 100% based on the original parameters. The original J-C damage parameters are listed in Table 4.  
Figure 15 presents the micro-cutting simulation results of the Ti6 Al4V under different J-C damage parameters; the J-C damage parameters apparently affect the serrated chip morphology under different gradient damage models. Specifically, when the \(D_{2}\) damage parameter increases from \(-\)100% to 100% of the original parameter, the serrated chip morphology of Ti6 Al4V changes from the sawtooth to band morphology. Figure 16 indicates that the exponent factor \(D_{2}\) mostly affects the sensitivity of the serrated chip morphology. The serrated chip increases with increases in the \(D_{2}\) parameter; the sensitivity coefficient increases from \(-\)80% to +20%. Given that \(D_{2}\) is the factor that maximally affects the sensitivity of the serrated chips, the equivalent plastic strain is sampled along the middle of the serrated chip morphology. As shown in Figure 17, the equivalent plastic strain strength decreases with increases in \(D_{2}\). The chip serration intensity \(C.S.I.\) corresponds to 1.1 when \(D_{2}\) increases to 100% of the initial value; the chip serration intensity \(C.S.I.\) corresponds to 8 when the material damage parameter \(D_{2}\) decreases to the original parameter above 50%. The results also indicate that the frequency of the serrated chip segmentation changes significantly. When the material damage parameter \(D_{2}\) decreases, the peak value of the equivalent plastic strain adjacent to each other gradually increases, and the number of segments decreases. When the material damage parameter \(D_{2}\) corresponds to \(-\)100% of the original parameter, the Ti6 Al4V serrated chip division frequency corresponds to 60 unit/mm; the Ti6 Al4V serrated chip division frequency corresponds to 35 unit/mm when the material damage parameter \(D_{2}\) decreases to 100% of the original parameter. Therefore, the material damage parameters cannot be ignored for high-precision micro-cutting simulation models. Figure 14: Analysis of average cutting force on serrated chips for cutting speed of 3 m/s. (**a**) Variation of cutting force in the formation of serrated chips; (**b**) comparison of average cutting force under different J-C constitutive parameters (A, B, n, C, m), I, II, III, and IV correspond to variation of the original J-C constitutive parameters (\(-\)30%, \(-\)10%, +10%, and +30%, respectively). Figure 16: Sensitivity analysis of the serrated chip under different variations of the original J-C damage parameters. Figure 15: Serrated chip formation under different J-C damage parameters for a 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 damage parameters (\(-100\%\), \(-50\%\), \(+50\%\), and \(+100\%\), respectively). Figure 18 presents the temperature value sampled along the middle of the Ti6 Al4V serrated chip under different J-C damage parameters. As shown in the figure, the temperatures of the adiabatic shear band I, II, and III exceed the temperatures on both sides. The temperature from the adiabatic shear band I to III gradually decreases because the chips are no longer deformed by compression. When the material damage parameter \(D_{2}\) increases from the original parameter to +100%, the temperature region of the serrated chip is stable, and evident wave peaks or valleys are not observed.