## 3 Numerical Results and Analysis
### Analysis of J-C Constitutive Parameters on Chip Morphology
Ultimately, the degree of serrated chips decreases. As shown in Figure 7, the initial yield stress \(A\) and the thermal softening coefficient \(m\) have the greatest effect on the sensitivity coefficient of the serrated chip. When the initial yield stress \(A\) decreases from \(-30\) to \(+30\%\) based on the original value, the serrated sensitivity coefficient \(S_{A}\) increases from \(-63\) to \(+69\%\). The thermal softening coefficient \(m\) is within the same range and the serrated chip sensitivity coefficient \(S_{m}\) decreases from \(+60\) to \(-17\%\). Figure 8a presents a micro-cutting simulation model without considering temperature, and Figure 8b presents a micro-cutting simulation model considering the temperature. The constitutive parameters and cutting parameters are identical. The micro-cutting simulation model considering temperature exhibits apparent adiabatic shear bands and serrated chips, while the cutting simulation model that does not consider temperature effects does not exhibit the serrated chips. This further illustrates that the plastic deformation in the shear zone generates a significant amount of heat and the adiabatic shear zone undergoes softening. Figure 8: Comparison of simulation results with and without thermal factors. (**a**) chip morphology without thermal factors; (**b**) chip morphology with thermal factors. Figure 7: Sensitivity analysis of serrated chip under different variations of the original J-C constitutive parameters (\(A\), \(B\), \(n\), \(C\), \(m\)). To further examine the frequency of the serrated chip and the chip serration intensity (_C.S.I._) of the titanium alloy Ti6 Al4V, an equivalent plastic strain was sampled along the middle of the chip. The specific path is shown in Figure 9a with the equivalent plastic strain curve. In this section, the _C.S.I._ proposed by [PERSON] et al. [53] is used to represent the compression deformation of the serrated chip and is expressed as follows in Equation (14):  
\[CSI=\frac{\epsilon_{p.peak-\epsilon_{p.valley}}}{\epsilon_{p.valley}} \tag{14}\]  
where \(\epsilon_{p.peak}\) denotes the equivalent plastic strain at the top of the tooth and \(\epsilon_{p.valley}\) denotes the equivalent plastic strain at the root of the tooth. The serrated frequency refers to the number of serrated chip units per unit time or length. [PERSON] et al. calculated the serrated frequency by measuring the length and speed of a single serrated chip. The formation of the serrated chips is usually accompanied by the appearance of adiabatic shear bands. Therefore, the peaks of the adiabatic shear bands are used as the dividing line. The expression used to calculate the frequency of the serrated chips is presented by Equation (15) as follows:  
\[f_{chip}=1000\frac{I_{sample}}{N} \tag{15}\]  
Figure 9b presents the equivalent plastic strain sampled along the middle design path of the sawtooth. There are apparent differences in the _C.S.I._, shear band spacing \(L_{s}\), and frequency of the serrated chips \(f_{chip}\) under different parameters. Among them, the equivalent plastic strain value and distance \(L_{s}\) of the hardening module \(B\) are uniform, thereby indicating that the material constitutive parameter \(B\) exhibits a small effect on the frequency and _C.S.I._ of the sawtooth chip. Other constitutive parameters (\(A\), \(C\), \(n\), \(m\)) affect the evident change in the equivalent plastic strain spacing \(L_{s}\) and _C.S.I._  
Figure 10a presents the _C.S.I._ variation parameters under different constitutive parameters. The _C.S.I._ increases when the constitutive parameters (\(A\), \(C\)) increase. Conversely, _C.S.I._ decreases when the constitutive parameters (\(B\), \(n\), \(m\)) increase. Among them, the hardening modulus \(B\) exhibits the smallest effect on _C.S.I._, and the initial yield stress \(A\) exhibits the largest effect. When the initial yield stress \(A\) increases from \(-30\%\) to \(+30\%\) of the original parameter, _C.S.I._ increases from 1.2 to 14, which is a 10.6-fold increase.