# Performance Investigation of Coated Carbide Tools in
## 3 Results
### Tool Performance Estimation Using FEA
#### 3.2.1 Fatigue Endurance Strength Determination  
A 2D FE model was utilized using the ANSYS 2024 R2 software to analyze the coated surface response under quasi-static loads, which was based on [26]. The model, along with the boundary conditions and finite element discretization, is depicted in the left part of Figure 8a. To mesh the 2D geometry of the carbide ball, coating, and substrate, plane elements were selected, resulting in approximately 27,000 elements. In addition, contact elements were utilized to define the interface between the ball indenter and the coating, where the contact elements can be used in the simulation such that no penetration could take place between the indenter and the examined coating. Hence, the nodes on the contact surfaces will be prevented from unrealistic penetration into the volume of the target surface, as well as ensuring proper load transmission. In addition, the adhesion properties of the coating and substrate interface could also be simulated through the implementation of appropriate contact elements. However, it must be noted that in the case of the perpendicular impact test, the adhesion between the coating and its substrate does not affect its performance [26]. Moreover, a \(Y\)-axis constraint was imposed on the nodes at the bottom surface of the substrate. The deformation induced in the coating \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Algorithm** & **Exper. No.** & **Vc** & **ae** & **fz** & **MSE/MAE** & **Prediction** & **Measured** & **Error \%** \\ \hline \multirow{4}{*}{SVR} & 1 & 125 & 8 & 0.40 & & 28.62 & 26.53 & 7.89 \\  & 2 & 150 & 5 & 0.25 & & 22.67 & 21.58 & 5.07 \\  & 3 & 175 & 11 & 0.90 & \(1.502/\) & 17.78 & 16.25 & 9.45 \\  & 4 & 225 & 2 & 0.15 & \(1.070\) & 9.92 & 10.54 & 5.92 \\  & 5 & 250 & 17 & 0.60 & & 11.63 & 12.40 & 6.18 \\  & 6 & 275 & 15 & 0.80 & & 6.56 & 6.87 & 4.49 \\ \hline \multirow{4}{*}{KNN} & 1 & 125 & 8 & 0.40 & & 28.02 & 26.53 & 5.62 \\  & 2 & 150 & 5 & 0.25 & & 22.88 & 21.58 & 6.01 \\  & 3 & 175 & 11 & 0.90 & \(2.499/\) & 19.18 & 16.25 & 18.01 \\  & 4 & 225 & 2 & 0.15 & \(1.371\) & 11.40 & 10.54 & 8.19 \\  & 5 & 250 & 17 & 0.60 & & 12.03 & 12.40 & 2.98 \\  & 6 & 275 & 15 & 0.80 & & 8.15 & 6.87 & 18.59 \\ \hline \multirow{4}{*}{ANN} & 1 & 125 & 8 & 0.40 & & 27.93 & 26.53 & 5.28 \\  & 2 & 150 & 5 & 0.25 & & 22.30 & 21.58 & 3.35 \\ \cline{1-1}  & 3 & 175 & 11 & 0.90 & \(0.865/\) & 17.43 & 16.25 & 7.28 \\ \cline{1-1}  & 4 & 225 & 2 & 0.15 & \(0.810\) & 9.44 & 10.54 & 10.36 \\ \cline{1-1}  & 5 & 250 & 17 & 0.60 & & 12.07 & 12.40 & 2.63 \\ \cline{1-1}  & 6 & 275 & 15 & 0.80 & & 6.72 & 6.87 & 2.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Outcomes and metrics of the developed ML models on the test set. and substrate by the slow penetration of the carbide ball into the film was evaluated at predefined indentation depths. Using this FE model, both maximum indentation depth and remaining imprint depth (RID) after coating relaxation were determined as functions of the reaction force amplitude, leading to an equivalent resulting pressure, which deforms the investigated coated tool, as presented in the middle part of Figure 8a. Taking into account that at the maximum impact force Fmax, which corresponds to the fatigue threshold force of 950 N (see Figure 4), the correlated maximum equivalent stress in the coating during its loading is equal to 3.95 GPa, and the remaining one due to the substrate plastic deformation is 1.10 GPa. Utilizing these data, the Smith-like diagram exhibited in the right part of Figure 8b was constructed [19]. This diagram enables the determination of the coating fatigue endurance stress under cyclic loading, where the load varies from zero to a specified maximum value. Based on the obtained values, the Woehler-like diagram was also created, as depicted in the left part of Figure 8b. This diagram is essential for understanding how materials respond to repeated loading and predicting their fatigue life.