An adhesive detachment paradox: Does the substrate thickness matter?

A normal adhesive contact between a flat-ended cylindrical punch with elliptical cross-section and the surface of an elastic substrate, which can be regarded as an elastic layer of finite thickness, is considered. The experimental evidence published elsewhere indicates that the initiation of detachment can occur at the ends of the minor axis of the elliptical contact area, which eventually comes into contradiction with the surface energy theory developed so far. This paradox of adhesive detachment is examined in the framework of the JKR-type model formulated in terms of the stress intensity factor (SIF) of the contact normal stress. Based on the asymptotic model for a relatively thick elastic layer, the contact SIFs at the ends of the minor axis are shown to grow with decreasing the relative layer thickness faster than those at the ends of the major axis of the initial contact area. A plausible explanation for the observed inconsistency between experiment and state-of-the-art theory is found in the effect of the nonuniform elastic deformations on the square root singularity of the contact pressure at the punch edge.