A Study of the Contact of an Elastic Layer–Substrate System Indented by a Long Rigid Cylinder Incorporating Surface Effects

Abstract

Contact problem of a layer–substrate system comprising of an elastic layer and an elastic substrate perfectly bonded to each other with surface effects based on Gurtin–Murdoch (GM) model indented by a long rigid cylinder is solved. The requisite Green's function relating surface displacement to surface load is obtained semianalytically through the combination of the Airy stress function and Fourier transforms under the planestrain condition. The contact solution is analyzed to study the influence of layer thickness, modulus mismatch between the layer and substrate, and surface parameters on contact size and contact pressure during indentation of a layer–substrate system. A map is presented which indicates whether during indentation by a rigid cylinder, a layer–substrate system is required or a homogeneous system based on layer properties is enough for a given shear modulus mismatch ratio and layer thickness. The map and the related analysis clearly indicate that whenever the contact size or layer thickness approaches intrinsic length scale based on the ratio of surface parameter and bulk elastic properties, surface effects should be considered.