Non-linear elastic stresses in a thin hard coating/an elastic substrate system subjected to a surface pressure distribution

A hard ceramic coating on elastic steel substrates has been increasingly used in the tribological applications in order to reduce wear rates and friction. In case a surface pressure is applied to the coating surface of a coating-substrate system, the stress and deformation states inside the coating and at the edges of the coating-substrate interface play important role in service life of the coating. In this study, the geometrically non-linear stress analysis of a thin hard coating-elastic substrate system subjected to a surface pressure was carried out using the incremental finite element method (IFEM) based on the small strain-large displacement theory (SSLD). The pressure distribution was considered for plane-strain and axisymmetric cases. The comparison of the stress distributions of an uncoated substrate determined analytically with the results of both the SSLD analysis and the small strain-small displacement (SSSD) analysis showed a good agreement. In addition, the stress analysis of a thin coating/substrate system was carried out based on the SSLD and SSSD theories. The stress distributions along the coating surface, coating-substrate interface and across the coating and substrate were investigated in detail. Both theories showed that the normal and shear stresses became critical in the coating and on the coating-substrate interface regions corresponding to the centre and ends of the surface pressure distribution. These stresses are a probable reason of the coating-substrate detachment encountered in practice. However, the SSSD theory can not predict accurately lower stress and strain variations arising at the edges of the coating and the coating-substrate interface since the SSSD theory neglects the effects of the large displacements whereas the SSLD theory found that the normal and shear stresses and strains at these critical locations had also nonlinear variations as the applied load is increased. Increasing the coating modulus resulted in higher stresses in the coating and at the edges of the coating-substrate interface. In case of a thin coating, these critical stresses occurred in the substrate whereas they spread completely inside coating regions neighboring the coating-substrate interface for relatively thicker coatings. The SSLD analysis also predicted lower and non-linear normal, shear stress and strain variations at the critical locations in the coating and on the coating-substrate interface for different modulus ratios and coating thicknesses. Since the peak stresses arising along the coating surface and the coating-substrate interface were dependent on both the coating thickness and modulus it was not possible to determine an optimum coating thickness and modulus ratio reducing all stress components causing the coating failure. However, optimum coating thickness and modulus can be searched in a large solution space using the optimization techniques. (c) 2007 Elsevier B.V. All rights reserved