Contact mechanics for layered materials: Rubber film on hard substrate

Abstract

I consider the contact mechanics for a layered material, consisting of an elastically soft film glued to a hard substrate. I calculate the area of real contact for surfaces with fractal-like roughness and for surfaces with roughness in narrow length scale regions. For the fractal-like surfaces, when the product q0d of the film thickness d and the low cut-off wavenumber q0 of the surface roughness power spectrum satisfy q0d < 0.1, the effective modulus becomes very large. This results in large contact stresses, which can induce plastic deformation or wear, in particular during sliding contact. I also calculate the probability distributions of the normal and tangential stresses at the film–substrate interface. If the tangential (shear) stress is too high, the adhesive bond between the film and the substrate will break. I compare the thin-film contact mechanics problem with the Gent solution for a thin elastic sheet confined between two flat solid surfaces, and discuss the origin of the difference in effective elastic modulus.