Comparison between the adherence of a rigid axisymmetrical cone and a truncated one, in adhesive contact on an elastic half-space

Abstract

We compare the equilibrium contacts and the kinetics of adherence of an axisymmetrical rigid cone and a flat-ended one with the same angle, applied against the flat and smooth surface of a soft elastomer sample (unfilled vulcanized natural rubber, cured with dicumyl peroxide), with the help of fracture mechanics concepts which can easily be introduced in this class of problems by using Sneddon's solution (1965) of Boussinesq's problem extended to all axisymmetric adhesive punches with a convex profile. The kinetics of adherence are 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 | =(G m w)/w, where w is the Dupré energy of adhesion, are studied as a function of the parameter, a T ± V, in which V is the crack propagation speed at the interface between a cone and a truncated one made of glossy Plexiglass®, and the rubber sample (the limit of the contact is considered as a crack tip), and a T , is the shift factor of the Williams-Landel-Ferry transformation. As expected, a master curve | (V) is found, confirming the variation of | as the power function V 0.55 , at fixed temperature, as recently established by Barquins et al. in adherence of a flat ended sphere and cone in pull-off/push-on tests, adherence and rolling of cylinders experiments and rebound of balls tests, with the same elastomer. Present results lead to propose one to write | =k ± (a T ± V) 0.55 , k=2520 and V being valued using S.I. units, for the reference temperature θ=25°C, with a quite good accuracy in the order of 1%.