Effects of multi-scale roughness and frictional heating on solid body contact deformation

Solid body contact is restricted to a discrete number of randomly distributed microscopic areas resulting from the deformation of interacting surface protrusions (asperities). The deformation mode of these asperity contacts can be elastic, elastic-plastic, or fully plastic, depending on the local surface interference, asperity radius of curvature, coefficient of friction, and mechanical properties of the solid surfaces. Traditionally, the surface topography has been described by statistical models which rely on unrealistic simplifications of the shape, height, and size of the asperities. Such assumptions were avoided in contemporary contact mechanics analyses, which use fractal geometry to accomplish a surface topography description over a wide range of length scales. The main objective of this article is to provide an assessment of the role of multi-scale topography (roughness) and frictional heating in contact deformation of elastic-plastic solid bodies. Contact relationships, derived at the asperity level, which include the mechanical properties of surface layer and substrate medium, layer thickness, local surface interference, and equivalent asperity radius of curvature, are presented for different modes of deformation. These asperity-level relationships and a fractal model of the surface topography are incorporated into a numerical integration scheme to analyze multi-scale thermomechanical contact deformation over the entire real contact area of homogeneous and layered media possessing realistic surface topographies.