Investigation of Basic Assumption for Contact Between Spheric Asperities in Rough Surface

Accurate analyses of contact problems for rough surfaces are important but complicated. Some assumptions, namely that all asperities can be approximated by a hemisphere with the same radius and assuming a Gaussian distribution of the asperity heights, are convenient but may lead to less accurate results. The purpose of this work is to investigate these assumptions and analyze the conditions under which they are valid. The finite element method is used to construct spherical asperity contact models with different radii and materials. The validity of the assumptions is assessed by comparatively analyzing the results of four models in terms of contact loads, contact radii, and average contact pressures under different yield strengths. The results show that these assumptions are fully applicable under elastic deformation. For plastic cases, the lower yield strength of the two contacting bodies is the dominant factor affecting the contact results. Assuming the same lower yield strength, the ratio of the yield strengths of two spheres has an influence on contact characteristics in the range from 1.2 to 3, but a negligible influence when the ratio is greater than 3. With an equivalent yield strength and yield ratio, the plastic contact of asperities can be analyzed in detail, which be conducive to clarifying the application scope of the above assumption. The work reported in this study provides some theoretical basis for an accurate contact model of rough surfaces.