FRACTAL MODELS OF ELASTIC PERFECTLY PLASTIC CONTACT OF ROUGH SURFACES BASED ON THE CANTOR SET

The objective of this study was to formulate discrete and continuous models to describe the elastic-perfectly plastic deformation of two rough surfaces in contact. The two surfaces in contact are assumed to exhibit fractal behavior and are modeled as an effective fractal surface compressed into a smooth rigid substrate. The rough self-affine fractal structure of the effective surface is approximated using a Canter set representation. Both of the proposed models admit analytical solutions for the cases when the plastic deformation is volume conserving or not. Results are presented that illustrate the effects that volume conservation and initial surface structure have on the elastic-perfectly plastic deformation process. The results from the continuous model are compared with the results obtained from the discrete model, and also with existing experimental load displacement results for the deformation of a ground steel surface.