Fractal roughness in contact problems (Q1315533)

The roughness of real polished bodies is shown to be fractal in character. A relation is found between the fractal dimension of a surface and its statistical properties. Models are constructed of the contact of fractal-rough punches and the smooth surface of a deformable half-space by a modelling Winkler medium and a rigidly plastic medium. Asymptotic power laws have been obtained which associate the force operating on the punch and the depth of indentation for different (both plastic and elastic) models of the deformed base. The relation between the power index and the fractal dimension of the surface and the print is determined.