The local yield maps for the identification of the yield initiation positions of hard coating on three-dimensional (3D) elastic half space under sliding contact were developed. In this study, the semi-analytical method (SAM), which is based on the conjugate gradient method (CGM) and the discrete convolution and fast Fourier transform (DC-FFT) technique, was employed to analyze the contact problem. By using this method, the von Mises stress distributions for various combinations of coating thicknesses, friction coefficients, and elastic moduli of the coating and substrate were calculated. Then, the positions of yield initiation were found with the calculated results by comparing the critical maximum contact pressure P max,c for von Mises yielding at or in the different positions (surface, coating, interface, and substrate), and the 3D-local yield maps were introduced in relation to the yield strength ratio of the coating to the substrate (Y f /Y b ) and the ratio of the coating thickness to the Hertzian contact radius (t/a 0 ). Finally, the effect of critical friction coefficient on the transition of yielding positions was discussed.

The evolution of the maximum contact stresses in amorphous carbon coated silicon during sliding wear against a Si3N4 ball was investigated. Amorphous carbon coating was prepared on a silicon substrate by the electron cyclotron resonance (ECR) plasma sputtering method. Surface morphologies of the coating and counterpart were measured by an atomic force microscope (AFM). The friction and wear behavior of the coating was studied by a ball-on-disk tribometer. The cross-sections of the wear tracks at different wear stages were observed with a scanning electron microscope (SEM). Maximum contact stresses with different coating thicknesses were calculated by the three-dimensional semi-analytical method (SAM). The results demonstrated that when taking surface asperities into consideration, maximum shear stress at the bonding interface and adjacent substrate showed a dramatic increase during wear and should be responsible for the initiation and propagation of the cracks observed at the final stage of sliding.