Contact mechanics of microscopically rough surfaces with graded elasticity

The well-known Greenwood and Williamson contact theory for microscopically homogeneous rough surfaces is generalized by considering functionally graded elastic rough surfaces. In particular, two distinct cases giving rise to a non-constant Young's modulus with depth are considered: (I) an initially plane layered (or graded) solid which is non-uniformly eroded, so that the final product is a rough surface with asperities having an elastic modulus depending on the height; (II) an initially homogeneous rough surface which receives a surface treatment or a chemical degradation which modify the elastic properties of the asperities as a function of the depth from the exposed surface. These Functionally Graded Surfaces (FGS) can be observed both in biological systems and in mechanical components. The effects of graded elasticity on the relationship between real contact area versus applied load, and on the plasticity index are quantified and illustrated with numerical examples. It will be shown that the contact response may differ up to one order of magnitude with respect to that of a homogeneous surface. Comparison between Case I and Case II also shows that, for special surface properties, the two types of grading can provide the same mechanical response.