# Effect of Residual Stress in Surface Layer on Plastic Yield Inception
## 5 Conclusions  
In this study, the effect of residual stress in the surface layer on the plastic yield inception of the surface layer/substrate system during contact is calculated using FEM. The critical load and locations for yield inception with different residual stress levels and different surface layer thicknesses were acquired. The results were discussed, and the following conclusions can be drawn:  
1. The residual stress in the surface layer has little influence on the stress field in the substrate during contact. The residual stress mainly influences the normal stress in the plane parallel to the contact surface and only has a minor influence on the other stress components in the surface layer. The influence of the residual stress on the critical yield load is mainly due to variations in the stress field in surface layer.
2. For all the surface layer thicknesses, as the dimensionless residual stress (\(\sigma_{r}/\gamma_{l}\)) varies from \(-1\) to \(1\), the critical yield load increases firstly to a peak value or is leveled to a plateau value, and subsequently decreases. Generally, a moderate compressive residual stress in the surface layer results in higher critical yield load than that without residual stress or with tensile residual stress. An optimal value of \(\sigma_{r}/\gamma_{l}=-0.6\) is found to maximize the critical yield load of the contact system with the surface layer.
3. The surface layer thickness and residual stress in the surface layer co-determines the yield inception location of the contact system, thereby influencing the critical yield load of the contact system jointly. For relatively small surface layer thickness, the yield inception can both happen in the surface layer or substrate, while for large surface layer thickness, the yield inception can only happen in the surface layer. The critical yield load is leveled to a plateau value on the change of residual stress when the yield happens in the substrate. Residual stress can affect the critical yield load only when the yield happens in the surface layer.  
The results can be applied in the contact of systems with a surface layer, especially in the area of mechanical engineering, such as mechanical parts with a film or coating, or with a hardened or stressed top layer after machining or heat treatment. The results may also provide some insight for the contact of systems in other areas of expertise with similar layered structures, such as roads with stressed concrete surface, layered rocks, etc.  
Conceptualization, S.Z. and X.H.; methodology, S.Z., X.H. and W.W.; writing--original draft preparation, S.Z.; writing--review and editing, S.Z., X.H., W.W. and Y.Y.; supervision, S.Z.; funding acquisition, S.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant number 51905535), the Fundamental Research Funds for the Central Universities (grant number 2020 YQJD03) and the Tribology Science Fund of State Key Laboratory of Tribology (grant number SKLTKF18B06).  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.