Adhesive contacts of rough elliptical punches

We numerically study adhesive contact between an elastic half-space and a rigid punch with elliptic shape and superimposed roughness. Simulation is carried out using the Fast Fourier Transform-assisted Boundary Element Method for JKR-type adhesive contact. Both regular roughness (in form of a two-dimensional wave) and random fractal roughness are studied. It is confirmed that the main governing parameter determining different modes of adhesion is the Johnson parameter. For under-critical values of the Johnson parameter (large enough amplitude of roughness), the adhesive force increases with the normal force during compression stage, until it reaches a plateau. The evolution of the contact area during the pull-off shows different configurations depending on the roughness and the pre-loading. For large Johnson parameters the detachment begins from the ends of the major axis of the ellipse and propagates to the center of the contact. In a narrow interval near the critical Johnson parameter, the detachment can also start from the center of ellipse or from the ends of minor axis, if the pre loading is not too large (so that the complete compact contact is not established). The maximum pull-off force (force of adhesion) is also a function of the Johnson parameter. Enhanced adhesion is observed when the maximum pull-off force is larger than that for a flat-ended punch. In experiment, steel flat indenters with different elliptical shapes are indented into soft rubber sheets. It is observed that the detachment begins from the edge of minor axis of ellipse in all cases, contrary to the results of numerical simulation and analytical theory.

Automated summary

We numerically study adhesive contact between an elastic half-space and a rigid punch with elliptic shape and superimposed roughness. The main governing parameter of different adhesion modes is the Johnson parameter. The adhesive force increases with the normal force during compression until it reaches a plateau. The evolution of the contact area during pull-off depends on the roughness and pre-loading. Experimental results differ from numerical simulation and analytical theory.