## 2 Finite Element Modeling Procedures  
A thermo-elastic-plastic three-dimensional numerical model for oblique cutting was established using finite element codes to simulate the turning process, as shown in Figure 1. The workpiece dimensions were \(2\times 1\times 1\) mm\({}^{3}\). In order to accurately predict the edge defects, a finer mesh was adopted in the large deformation zones by defining a high-density mesh to cover the entire chip zone, the tool-chip contact zone, and the cut-out zone, and a low-density mesh to cover the other zones of the workpiece. The units of the modeling process were: mm, MPa, N, s, mm/s. Since new cutting tools were adopted during all the turning experiments, the polycrystalline diamond (PCD) tools in simulation were defined as rigid bodies for the sake of reducing the computational time with no loss in calculation accuracy. The workpiece material was modeled as elastic-plastic and the material properties of 17 vol.% SiC\({}_{\text{p}}\)/2009 Al composites and PCD tool are listed in Table 1[24; 25]. The improved Johnson-Cook constitute model considering the coupling effects of plastic strain, strain rate, and temperature was used for 17 vol.% SiC\({}_{\text{p}}\)/2009 Al composites, of which the material constants were identified using dynamic Split Hopkinson Pressure Bar experiments under different strain rates and temperatures [26]:  
\[ \begin{split}\sigma=[A+B_{1}[1-&\exp\bigl{(}-B_{2} \varepsilon_{\text{p}}\bigr{)}][1-(T^{*})^{n1}]]\\ &[1+(1-T^{*})^{n2}\bigl{(}\dot{\varepsilon}/D\bigr{)}^{1/m}][(1- W)\exp\bigl{[}-G(T^{*})^{n3}]+W],\end{split}  \tag{1}\]  
\[T^{*}=\left\{ \begin{array}{c}0;T<T_{\text{ref}}\\ (T-T_{\text{ref}})/(T_{\text{melt}}-T_{\text{ref}});\ T_{\text{ref}}\leq T\ \ \leq T_{\text{melt}},\\ 1;T_{\text{melt}}<T\end{array} \right. \tag{2}\]  
where \(\varepsilon_{\text{p}}\), \(\dot{\varepsilon}\), and \(T\) are plastic strain, strain rate, and temperature; \(A\) is yield strength, \(B_{1}\) and \(B_{2}\) are strain hardening coefficients, \(W\) is a weighting coefficient, \(n1\), \(n2\), and \(n3\) are thermal softening coefficients; and \(m\) and \(D\) are material constants. The constitutive material constants of 17 vol.% SiC\({}_{\text{p}}\)/2009 Al composites were determined according to [26]. The shear damage criterion was adopted to describe the damage caused by shear localization, and has the following expressions [27]:  
\[\varepsilon_{\text{p}}^{\text{S}}\Bigl{(}\theta_{s},\dot{\bar{\varepsilon}}_{ \text{p}}\Bigr{)} \tag{3}\]  
and  
\[\theta_{s}=\frac{(q+k_{\text{s}}p)}{\tau_{\text{max}}}, \tag{4}\] \begin{table}
\begin{tabular}{c c c} \hline
**Material Parameters** & **PCD Tools** & **17 vol.\% SiC\({}_{\text{p}}\)/2009 Al Composites** \\ \hline \(\varrho\), Density (kg/m\({}^{3}\)) & 3520 & 2940 \\ E, Elastic modulus (GPa) & 1147 & 258 \\ \(\
u\), Poisson’s ratio & 0.07 & 0.2 \\ \(\kappa\), Thermal conductivity (W/m:K) & 2100 & 235 \\ C\({}_{\text{p}}\), Specific heat capacity (J/kg:K) & 525 & 850 \\ \hline \end{tabular}
\end{table} 
Table 1: Material properties of 17 vol.% SiC\({}_{\text{p}}\)/2009 Al composites and polycrystalline diamond (PCD) tool [24; 25]. Figure 1: Finite element model of SiC\({}_{\text{p}}\)/Al composites. where \(\varepsilon_{\text{p}}^{\text{S}}\) is the effective plastic strain at damage initiation, \(k_{\text{s}}\) is a material parameter, and \(q\) is the effective shear stress. A scalar-valued damage factor \(\omega\) for the shear criterion was used to determine the damage initiation:  
\[\omega=\int\frac{\text{d}\varepsilon_{\text{p}}\text{s}\left(\theta_{s},\hat{ \varepsilon}_{\text{p}}\right)}{\varepsilon_{\text{p}}^{\text{S}}\left(\theta_ {s},\hat{\varepsilon}_{\text{p}}\right)}=1, \tag{5}\]  
where the onset of damage will initiate when the damage factor \(\omega\) arrives at 1.