The Interaction of Frictional Slip and Adhesion for a Stiff Sphere on a Compliant Substrate

Abstract

How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson–Kendall–Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A simple model for the interaction of friction and adhesion is utilized, in which some of the work done against frictional resistance is assumed to be stored reversibly. This behavior is considered to arise from surface microstructures associated with frictional slip such as interface dislocations, where these microstructures store some elastic strain energy in a reversible manner. When it is assumed that a fixed fraction of the work done against friction is stored reversibly, we obtain good agreement with data.