The two-dimensional plane-strain sliding contact of a smooth rigid roller on a transverse ground rough surface is analyzed. The rough surface is idealized as an elastic half-space with periodic roughness modeled as cylindrical ridges oriented transverse to the sliding direction. The contact problem is solved using a numerical iterative method in which each asperity contact is treated as a micro-Hertz contact, and the exact treatment of asperity interaction is included. The subsurface stress field is calculated using Westergaard stress functions. The subsequent analysis compares the rough surface stress fields with the corresponding smooth Hertz contact to evaluate the influence of surface roughness and friction on the subsurface stress distributions. The results show that the real area of contact is less than the corresponding smooth surface Hertz contact area, and the magnitude of the actual localized maximum contact pressure is always greater than the corresponding smooth surface contact pressure. The asperity level subsurface effective stresses are greater in magnitude than the maximum subsurface stress due to the macro-Hertz contact for low coefficients of friction, and for high coefficients of friction the maximum effective stresses occur on the bulk material surface.

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