# Effect of Residual Stress in Surface Layer on Plastic Yield Inception
## 1 Introduction  
Residual stress is the stress that remains in a solid material after the original cause has been removed. Residual stress often exists in the surface layer of solids [1; 2; 3; 4; 5]. The surface layer can be a deposited film/coating or can be a hardened or stressed top layer. Several processes can lead to the generation of residual stress in the surface layer, for example, after surface heat treatment processes such as quenching, or after machining processes such as turning or grinding, or after the deposition of coatings or films on a substrate surface. Residual stress may originate in the surface layer through various mechanisms, including thermal mismatch, structural (phase) change, and inelastic (plastic) deformation [6]. When two solids come into contact, stress and deformation are produced. The characterization of the contact behavior of solids is not only highly crucial for analyzing tribological problems such as friction, wear, and lubrication [7; 8; 9], but also for other technological problems such as thermal and electrical contact resistance [10; 11; 12]. When solids with residual stress are in contact, the residual stress in the surface layer is superimposed on the stress generated by the contact, changing the critical load of yield inception and strengthening or weakening the surface layer/substrate system. The effect of residual stress on the contact behavior of surface layers has been previously investigated. [PERSON] [13] studied rolling/sliding contact fatigue behaviors of induction remelted Ni-based coating and the results showed that residual stress in the coating played an important role in interfacial delamination. [PERSON] [14] treated 17 Cr2 Ni2 MoVNb steel using shot peening and found that the treated samples with compressive residual stresshad better wear resistance. [PERSON] [15] studied the tribological fracture behavior of TiN, DLC, and MoS\({}_{2}\)-coated surfaces, and concluded that higher compressive residual stresses corresponded with increased fracture toughness. [PERSON] [16] isolated the effect of residual stresses on coating wear from microstructure, and results showed that larger compressive residual stress reduced wear. [PERSON] [17] studied the effect of residual stress on the bonding strength of a SiN thin film using nanoscratch tests. The results showed that the decrease in the residual compressive stress and increase in the tensile stress accelerated the interfacial failure in the nanoscratch tests. [PERSON] [18] studied the effects of residual stress on the wear properties of DLC coatings, and found that higher compressive residual stress showed more serious wear in nanowear tests. [PERSON] [19] studied effect of residual stress on the wear behavior of several PVD thin coatings and found that the coating containing moderate compressive residual stress had a better wear behavior compared to the coating with higher compressive residual stress. [PERSON] [20] studied roles of residual stress on the damage resistance of nanocomposite TiSiN coatings on steels and found that coatings with intermediate compressive residual stress reached a combination of high damage resistance and good adhesion strength. [PERSON] [21] studied the effect of residual stress on the tribological properties of TiN coatings on 304 stainless steel and concluded that intermediate residual stress was crucial for achieving better performance. Although existing experimental studies indicated that the residual stress in the surface layer had a significant influence on the mechanical properties and contact behavior of the surface layer, owing to the difficulty in acquiring the required residual stress value in experiments, it is difficult to explore the effect of residual stress in full range from compression to tension, and the mechanism is difficult to study in depth. However, numerical methods have been widely used in this regard.