## 3 Numerical Results and Analysis
### Analysis of J-C Constitutive Parameters on Chip Morphology  
To reveal the dependence of J-C parameters on serrated chip morphology, J-C constitutive models with different gradients were designed. The J-C constitutive parameters proposed by [PERSON] et al. (2017) are as original parameters, and the original J-C constitutive parameters are listed in Table 1. The gradients are obtained as \(-10\%\), \(-20\%\), \(-30\), \(+10\%\), \(+20\%\), and \(+30\%\) of the original parameter values. The variation of Johnson-Cook constitutive parameters for Ti6 Al4V is shown in Table 5. The cutting speed, depth, and width correspond to 3 m/s, 20 \(\upmu\)m, and 0.2 mm, respectively. [PERSON] (2017) proposed a coefficient to express the degree of the serrated chip \(G_{\mathrm{s}}\). In the study, to compare the effect of different constitutive parameters on the serrated chip, the sensitivity coefficient \(S_{i}\) is expressed as follows:  
\[G_{\mathrm{s}}=\frac{H-h}{h} \tag{12}\]  
\[S_{i}=\frac{G_{\mathrm{s}}-G_{original}}{G_{original}}\times 100\% \tag{13}\]  
where \(H\) denotes the height of the tooth top of the serrated chip and \(h\) denotes the root height of the serrated chip. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Range** & **A** & **B** & **n** & **C** & **m** \\ \hline
1 & \(+30\%\) & 1297.27 & 849.03 & 0.585 & 0.02574 & 0.91 \\
2 & \(+20\%\) & 1197.48 & 783.72 & 0.54 & 0.02376 & 0.84 \\
3 & \(+10\%\) & 1097.69 & 718.41 & 0.495 & 0.02178 & 0.77 \\
4 & [PERSON] et al. (2017) & 997.9 & 653.1 & 0.45 & 0.0198 & 0.7 \\
5 & \(-10\%\) & 898.11 & 587.79 & 0.405 & 0.01782 & 0.63 \\
6 & \(-20\%\) & 798.32 & 522.48 & 0.36 & 0.01584 & 0.56 \\
7 & \(-30\%\) & 698.53 & 457.17 & 0.315 & 0.01386 & 0.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The variation of Johnson-Cook constitutive parameters for Ti6 Al4V. Figure 6 presents the distribution of equivalent plastic strain (PEEQ) of the serrated chip of Ti6 Al4V under different J-C constitutive model parameters. The Ti6 Al4V chip apparently exhibits significant differences when various J-C constitutive parameters are changed under the same cutting parameters. When the strain rate sensitivity coefficient \(C\) increased from \(-30\%\) to \(+30\%\), the chip morphology changed from band chips to serrated chips, and the serrated sensitivity parameter \(S_{i}\) gradually increased from a negative to a positive value. Thus, when the initial yield stress \(A\) gradually increases, more energy is required when the same plastic deformation occurs. In the primary deformation area of the chip, the heat converted by plastic deformation increases, making the degree of jaggedness more apparent, further confirming the indications by [PERSON] et al. [54]. However, the micro-cutting simulation of the study indicates that the hardening modulus \(B\) is not similar to that described by [PERSON] et al. As shown in Figure 6, the serrated sensitivity coefficient increases with increasing strain rate sensitivity coefficient \(C\), which indicates the effect is the same as the initial yield stress \(A\). Figure 6: The result of serrated chip formation 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). Conversely, the serrated sensitivity parameter \(S_{i}\) exhibits decrease with increasing hardening modulus \(B\), strain rate dependency coefficient \(n\), and thermal softening coefficient \(m\). When the J-C parameters \(B\), \(n\), and \(m\) increase from \(-30\) to \(+30\%\) of the original parameters, the serrated sensitive parameters \(S_{i}\) a decrease from positive to negative values. This result is mainly due to the increase in the J-C parameters (\(B,n,m\)), leading to increased hardening capacity of the material.