## 5 Results and Discussion  
The simulation results show that the load of the indenter was significantly affected by the presence of tensile residual stress. The presence of tensile residual stress resulted in a decrease in the load of the indenter. The larger the residual tensile stress was, the smaller the load of the indenter would be. On the contrary, the greater the compressive residual stress was, the greater the head load would be. This phenomenon could be explained by elastoplastic theory. The residual stress that existed on the surface of the material was parallel to the surface, while the stress that the indenter exerts on the matrix is the compressive stress perpendicular to the machined surface. When tensile stress was present in the workpiece, the plastic deformation capacity of the material was increased, resulting in a reduction in the required indenter load at the same penetration depth. When \(E^{*}/Y=245\), the normalized mean contact pressure is affected by the normalized indentation depth, as shown in Figure 7. For different residual stresses, the mean contact pressure has the same variation trend in the elastoplastic zone. With an increase in the normalized indentation depth, the normalized average contact pressure will first show a gradual increasing trend, and then, gradually stabilize, which means that the material has reached a completely plastic state. The critical value of the indentation depth at which the normalized average contact pressure does not change with an increase in the normalized indentation depth is called the critical depth. Different materials have different critical depths, which are related to the physical and mechanical properties of the materials. When the normalized indentation depth reaches the critical depth, the normalized mean contact pressure reaches the maximum value, indicating that the workpiece surface has reached a fully plastic state. When \(\sigma_{R}/Y=0\), there is no residual stress on the machined surface of the workpiece, and its curve is the curve of contact pressure and indentation depth under ideal conditions. When \(\sigma_{R}/Y<0\), the material hardness increases with an increase in the compressive residual stress, and the indentation transforms the completely plastic state in advance. The normalized critical indentation depth of the \(\sigma_{R}/Y=-0.8\) curve is about 0.052, while the normalized critical indentation depth of the \(\sigma_{R}/Y=-0.2\) curve is about 0.10. It can be seen that when there is residual compressive stress on the workpiece surface, the greater the compressive residual stress is, the earlier the indentation will transform the fully plastic state. When \(\sigma_{R}/Y>0\), the material hardness decreases with an increase in the tensile residual stress, and deeper indentation is needed to achieve complete plasticity. The normalized critical indentation depth of the curve \(\sigma_{R}/Y=0.2\) is about 0.15, while the normalized critical indentation depth of the curve \(\sigma_{R}/Y=0.8\) is about 0.23. It can be seen that when there is residual tensile stress on the workpiece surface, the greater the residual tensile stress is, the later the indentation will transform the complete plastic state. Comparing the curve \(\sigma_{R}/Y<0\) with the curve \(\sigma_{R}/Y>0\), it can be found that the curve  
Figure 6: Experimental and testing devices: (**a**) Vickers Hardness Tester; (**b**) X-ray diffraction residual stress tester. \(\sigma_{R}/Y>0\) has a larger trend change and contains a wider indentation depth, which also proves that tensile residual stress has a greater influence on indentation than compressive residual stress. Figure 8 shows the relationship between the simulated normalized hardness difference and residual stress. The relationship curve between the normalized hardness difference and residual stress was obtained by fitting the normalized hardness difference and residual stress data in Figure 8. It can be seen that the curve of normalized hardness difference and residual stress was consistent with Equation (8).