Adhesive contact of elastic–plastic spheres

Abstract

We examine the process of decohesion of two adhering elastic–plastic spheres following mutual indentation beyond their elastic limit. In the first instance, it is assumed that during unloading to the point of pull-off, the deformation is predominantly elastic. First, elastic–plastic loading is modelled by a fine grid finite element analysis revealing that, for elastic–perfectly plastic materials, the contact pressure at the end of loading p o is approximately uniform. Next, the contact size and pressure distribution during elastic unloading from a uniform pressure, in the absence of adhesion, is found by the method of rigid punch decomposition. The pressure distribution approaches that of Hertz as the contact size approaches zero. The distribution of adhesive traction has been found in two ways. First, using the singular traction distribution of linear elastic fracture mechanics, and second, using a step cohesive law, whereby a constant adhesive stress σ o acts between surfaces separated by less than δ o , while the surfaces separated by more than δ o , are traction-free. The cohesive zone solution depends on two non-dimensional parameters, while the asymptotic singular solution depends on one non-dimensional parameter only. The limit where the singular model provides a good approximation for the more accurate cohesive zone solution is defined. Finally, a decohesion map is deduced, which divides the parameter space into the regions where decohesion process is governed by different physical mechanisms. The deduced mechanisms are compared with the existing experimental data.