## 2 Finite Element Model  
### J-C Constitutive Model  
The J-C constitutive model [23; 24; 25] chosen for this research links the hardening, strengthening and thermal softening effects and affects the flow stress of the cladding layer material. It can better reflect the mechanical change behavior of Ti6 Al4V titanium alloy materials under the milling model; the expression is as follows [26; 27]:  
\[\sigma_{JC}=\big{[}A+B\epsilon^{n}\big{]}\bigg{[}1+C\ln\bigg{(}\frac{\dot{ \epsilon}}{\dot{\epsilon}_{0}}\bigg{)}\bigg{]}\bigg{[}1-\bigg{(}\frac{T-T_{r}} {T_{m}-T_{r}}\bigg{)}^{m}\bigg{]} \tag{1}\]  
where \(A\) is the initial yield stress; \(B\) is the strain hardening parameter; \(C\) represents the strain rate hardening parameter; \(n\) is the hardening index; \(m\) is the thermal softening index; \(\dot{\epsilon}\) is the equivalent plastic strain rate; \(\dot{\epsilon}_{0}\) indicates the reference strain rate, the value used in this study is 0.001/s; \(T_{\rm r}\) = 20 \({}^{\circ}\)C; \(T_{\rm m}\) = 1668 \({}^{\circ}\)C. \(A\), \(B\), \(C\), \(m\) and \(n\) are undetermined material parameters, which need to be determined according to the experimental curves of stress-strain relationship under different strain rates and different temperatures. The process of determining the parameters of the J-C model is generally as follows. First, the complete stress-strain curve of the material is obtained through the quasi-static compression experiment, and the first parameter of the J-C model is determined by data fitting number \(A\), \(B\), \(n\):  
\[\sigma_{JC}=A+B\epsilon^{n} \tag{2}\]  
Then, the current temperature is taken as the reference temperature (room temperature), namely \(T=T_{\rm r}\), and it is brought into Equation (1):  
\[\sigma_{JC}=\big{[}A+B\epsilon^{n}\big{]}+\bigg{[}1+C\ln\bigg{(}\frac{\dot{ \epsilon}}{\dot{\epsilon}_{0}}\bigg{)}\bigg{]} \tag{3}\]  
Then,  
\[C=\frac{\sigma_{JC}-\big{[}A+B\epsilon^{n}\big{]}}{\big{[}A+B\epsilon^{n} \big{]}\Big{[}\ln\Big{(}\frac{\dot{\epsilon}}{\dot{\epsilon}_{0}}\Big{)} \bigg{]}} \tag{4}\]  
The stress-strain curve of titanium alloy is obtained through the Hopkinson bar experiment at room temperature and different strain rate, and the parameter C is obtained by the data fitting method. In the same way, under the condition of the determined first two parameters of the J-C mode, the movable terms of Equation (1) are combined as follows:  
\[m=\frac{\ln\Bigg{[}1-\frac{\sigma_{JC}}{(A+B\epsilon^{n})\left(1+C\ln\bigg{(} \frac{\dot{\epsilon}}{\dot{\epsilon}_{0}}\bigg{)}\right)}\Bigg{]}}{\ln\Big{(} \frac{T-T_{\rm r}}{T_{\rm m}-T_{\rm r}}\bigg{)}^{m}} \tag{5}\]  
The stress-strain curve of titanium alloy can be obtained through the Hopkinson bar experiment under different temperature and constant strain rate conditions, and the coefficient \(m\) is obtained by the data fitting method. The specific parameters of Ti6 Al4V titanium alloy in this paper are obtained in accordance with reference [26] and are shown in Table 1. In addition, the material properties of Ti6 Al4V alloy are listed in Table 2. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Material** & \(A\)**(MPa)** & \(B\)**(MPa)** & \(n\) & \(m\) & \(C\) \\ \hline Ti6 Al4V & 1000 & 780 & 0.47 & 1.02 & 0.033 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Johnson-Cook constitutive model parameters of Ti6 Al4V titanium alloy. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Chemical Element** & **Al** & **Si** & **Fe** & **V** & **C** & **O** & **N** & **Ti** \\ \hline wt\% & 5.4 & 0.15 & 0.30 & 3.41 & 11.0 & 0.15 & 0.15 & Bal \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Chemical composition of Ti6 Al4V titanium alloy (mass fraction, wt%). The geometric structure design of the tool includes the basic dimensions of the tool and the basic sectional design. The basic sectional design of the tool mainly includes the parameters of the tool's rake angle, rear angle, helix angle, and so on.