Elastic–plastic contact of a rough surface with Weierstrass profile

Abstract

We analyse contact between a rigid cylindrical indenter and an elastic–perfectly plastic solid with a fractal surface roughness, which is idealized as a Weierstrass profile. A hierarchical scheme is used to calculate quantities such as the number of contact spots; their size; the true contact pressure acting on the contact spots, and the total true area of contact. In addition, we calculate critical conditions that will initiate plastic flow in the asperities, and determine the extent of this plastic flow as a function of the applied loading, the material properties of the deforming solid, and the surface roughness. An important conclusion of our study is that a perfectly fractal description of surface roughness appears to lead to unphysical predictions of the true contact size and number of contact spots, for both elastic and elastic–plastic solids. Possible approaches to resolving these difficulties are discussed.