Effective mechanical properties of layered rough surfaces

In contact mechanics of layered rough surfaces, found in various systems such as magnetic storage devices and micro/nanoelectromechanical systems, it is of interest to calculate effective elastic modulus and hardness so as to obtain contact parameters using simple analyses for homogeneous surfaces. In this study, effective elastic modulus and hardness of layered rough surfaces are defined on the basis of real area of contact. A numerical model developed by the first author to simulate the contact of layered rough surfaces is used to derive these equations. Completely nondimensionalized empirical equations for these effective mechanical properties are presented. Separate equations are developed for the contact of a single conical asperity on a flat surface, a single spherical asperity on a flat surface, and for multiple asperity contact between two rough surfaces. These equations establish the dependence of effective mechanical properties on indentation depth, layer thickness, hardness and elastic modulus ratios of layer and substrate and surface roughness/asperity geometry. Comparisons of values predicted by the equations with experimentally obtained results are presented. Contact stress contours obtained from this model are analyzed to get a better understanding of the mechanics of contact.