## 2 Finite Element Modeling of Micro-Textured Tool for Cutting GH4169
### Material Constitutive Model  
In response to the high-thermoplastic, creep, thermal stability, and stress-strengthening characteristics of GH4169, this paper adopts the Johnson-Cook material constitutive model, whose mathematical expression is as follows [23]:  
\[\sigma=[A+B\varepsilon^{n}]\left[1+C\ln\frac{\dot{\varepsilon}}{\dot{\varepsilon }_{0}}\right]\left[1-\left(\frac{T-T_{r}}{T_{m}-T_{r}}\right)^{m}\right] \tag{1}\]  
where \(A\) is the yield strength (Mpa) of the material; \(B\) is the hardening modulus (Mpa) of the material; \(C\) is the strain rate strength coefficient; \(M\) is the thermal softening coefficient; \(N\) is the strain-strengthening coefficient; \(\varepsilon\) is equivalent plastic strain; \(\overline{\varepsilon}\) is the equivalent plastic strain rate; \(\overline{\varepsilon_{0}}\) is the quasi-static strain rate; \(T_{r}\) is the melting point temperature of the material; and \(T_{0}\) is the ambient temperature. Meanwhile, the plastic parameters \(A\), \(B\), \(n\), \(c\), and \(m\) of the material can be obtained from the SHPB split Hopkinson bar experiment and  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Tool Material** & **Density** & **Young’s Modulus** & **Poisson’s Ratio** & **Linear** & **Specific Heat** & **Thermal** \\  & **(g/cm\({}^{3}\))** & **(Gpa)** & & **(m/m\({}^{\circ}\)C)** & **(J/kg\({}^{\circ}\)C)** & **(J/m\({}^{2}\)K)** \\ \hline Carbide & 14.6 & 640 & 0.22 & \(4.5\times 10^{-7}\) & 220 & 75.4 \\ \hline \end{tabular}
\end{table}
Table 1: Material properties of cutting tools.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Tool Number** & \(A/\upmu\)**m** & \(B/\upmu\)m & \(C\) **(c1, c2, C1, C2)/\(\upmu\)m** \\ \hline T1 & 120 & 90 & 40 \\ T2 & 120 & 70 & 80, 40 \\ T3 & 120 & 70 & \(50,450\) \\ T4 & 120 & 70 & \(450,50\) \\ T5 & 120 & 30 & \(120,240,300,600\) \\ \hline \end{tabular}
\end{table}
Table 2: Micro-texture size parameters of different morphologies.  
quasi-static experiment of smooth specimens, and the equivalent strain rate can be obtained by fitting the average values of the compression bar, tension, and torsion experiments.  
Johnson-Cook constitutive model parameters of GH4169 are shown in Table 3.  
Johnson-Cook shear failure criterion was adopted as the failure criterion. The values of parameters defined in the Johnson-Cook dynamic failure model are shown in Table 4[24].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Failure Criterion** & \(\mathbf{d_{1}}\) & \(\mathbf{d_{2}}\) & \(\mathbf{d_{3}}\) & \(\mathbf{d_{4}}\) & \(\mathbf{d_{5}}\) \\ \hline Value & \(0.11\) & \(0.75\) & \(-1.45\) & \(0.04\) & \(0.89\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: J–C failure parameters of GH4169.  
Figure 1: Schematic diagram of micro-texture shapes and parameters: (**a**) micro-pit; (**b**) micro-pyramids; (**c**) micro-groove-parallel; (**d**) micro-groove-vertical; (**e**) micro-elliptical.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Materials** & \(\mathbf{A/Mpa}\) & \(\mathbf{B/Mpa}\) & \(\mathbf{m}\) & \(\mathbf{c}\) & \(\mathbf{n}\) & \(\mathbf{T_{m}}^{\prime}\)C \\ \hline GH4169 & 860 & 683 & 1 & 0.01 & 0.47 & 1260 \\ \hline \hline \end{tabular}
\end{table}
Table 3: J–C constitutive model parameters of GH4169.