# Effect of Residual Stress in Surface Layer on Plastic Yield Inception
## 1 Introduction
[PERSON] [22] studied the effect of internal stress on the micro/nano mechanical properties of a thin CNx film during a nanoindentation test using the finite element method (FEM). The results showed that the film with compressive stress has a larger hardness and modulus than that with tensile stress. [PERSON] [23] studied the effect of residual stress on the behavior of aluminum alloy 8009 during elastic-plastic indentation using FEM. An equi-biaxial residual stress was applied by applying stress around the circumference of the specimen. The results showed that the pileup around the indentation was promoted by compressive stress and diminished by tensile stress, which influenced the measurement of the contact areas and the derivation of hardness. [PERSON] [24] evaluated the influence of equi-biaxial residual stress on the unloading behavior of nanoindentation on elastic-plastic strain-hardening materials using FEM. An equi-biaxial residual stress was applied by prescribing a radial displacement along the outer surface of the specimen prior to indentation. The results showed that both the true contact area and elastic recovery increased with the increase in the compressive stress and decreased with the increase in the tensile stress. [PERSON] [25] studied the effect of pre-existing stress on the interpretation of the nanoindentation data of gold using molecular dynamics simulations. It was found that compressive pre-stress resulted in a higher mean pressure, whereas tensile pre-stress resulted in a lower mean pressure. [PERSON] [26] studied the effect of residual stress on plastic yield inception in single-crystal copper thin films under nanoindentation using molecular dynamics simulations. It was found that the indentation hardness decreased with the tensile residual stress but increased with moderate compressive residual stress; it decreased again under higher compressive residual stress. Although these simulation results provided important insights for understanding the effect of residual stress on the contact behavior, they did not consider the interaction between the surface layer and substrate. Mechanisms on the effect of residual stress in surface layer on contact have been proposed. The most commonly mentioned mechanism was that the compressive residual stress inhibits crack initiation, growth, and propagation [14; 15; 17]. An atomic-level mechanism was proposed that would allow residual stress to change the average distance between atoms in the lattice from their equilibrium position, therefore changing the response of the material [17; 27]. For a surface layer/substrate system, the critical load of the yield inception is important because it determines the load-bearing capacity of the system. A mechanism in terms of critical yield load has not been discussed. Studies on the plastic yield inception of coating/substrate systems have been reported [28,29]; however, the influence of residual stress was not considered. A study on the effect of residual stress in surface layer on plastic yield inception has not been seen. The location of the yield inception is also important because it is usually related to the failure modes [30,31]. The effect of residual stress in surface layer on the location of the yield inception has not been investigated. In this study, FEM was used to study the effect of residual stress in the surface layer on the contact behavior of layered solids. The critical load and locations of the yield inception with different residual stress levels and different surface layer thicknesses were studied. An optimal value of residual stress to increase the critical yield load was found. The influence mechanism of the residual stress on the contact behavior was discussed by analyzing the stress field in the surface layer/substrate system.