Kinetics of adherence of a rigid truncated cone on an elastic half-space (unfilled natural rubber)

The equilibrium contact of a rigid flat-ended cone, applied against the flat and smooth surface of a soft elastomer sample (unfilled natural rubber), is studied with the help of fracture mechanics concepts, which can be easily introduced in this class of problems by using Sneddon's solution (Int. J. Eng. Sci. 3 (1965) 47) of Boussinesq's problem extended to all axisymmetric adhesive punches with a convex profile. The kinetics of adherence is measured when an imposed tensile force is applied in order to disturb the size of the contact area. Variations of the strain energy release rate G and of the associated dissipation function Φ=(G?w)/w, where w is the Dupré energy of adhesion, are studied as a function of the crack propagation speed V at the interface between a truncated cone made of PMMA and the rubber sample (the limit of the contact is considered as a crack tip). As expected, a master curve Φ(V) is found, confirming the variation of Φ as the 0.55 power function of V, as recently established by Barquins et al. in adherence of a perfect cone and flat-ended spheres in pull-off/push-on tests, adherence and rolling of cylinders experiments and rebound of balls tests, with the same elastic rubber-like material.