Adhesion, slip, cohesive zones and energy fluxes for elastic spheres in contact

Abstract

The energy fluxes upon shrinkage of the contact area are calculated for a pair of spheres in adhesion. Various notions of energy release rate are introduced and analyzed for correlating the external work parameters and the work of adhesion. Decomposition of the energy release rate into reversible and irreversible parts shows that the reversible part is the work of adhesion and it can be described by the cohesive response purely at the contact zone-edge. This result justifies the use of local zone-edge quantities for modeling the interaction of adhesion and friction. For specific quantitative analysis, adhesion is represented by the Dugdale model, uniform cohesive traction up to a limited separation, as an approximation to more exact inter-surface forces. Exact results are given for the entirely reversible energy release rate to the edge of the contact and the energy release rate to the cohesive zone. The latter is named the strain energy release rate and found to depend on the path in loading parameter space, while the reversible energy release rate is independent of the loading path. The solution for shear of the contact is given as well. Energy released reversibly to be converted into surface energy is identified in contrast to energy released due to slip which will be partially or totally dissipated as heat. The relevance of the results for friction is discussed and contrasted with their significance for the mixed mode fracture of a circular joint.