Adhesive contact of sectionally smooth-ended punches on elastic half-spaces: theory and experiment

Abstract

Attractive molecular forces give rise to singular tensile stresses and to a discontinuity of displacement at the edge of contacts. These boundary conditions are those of fracture mechanics and correspond to adding a rigid body displacement to the classical elastic solution. The adhesive contact of sectionally smooth-ended punches (sphere or cone) is studied. Stress distribution, shape of the deformed surface, and relation between load and penetration are given either for equilibrium or kinetic conditions. For a flat-ended sphere, the adherence of a flat punch and the JKR theory for sphere are obtained as particular cases; for zero surface energy systems, the solution reduces to that of Ejike. The case of a sphere with a spherical cap of different radius and that of a rounded cone are also examined. Experimental verification has been performed with a glass ball (R=2.19 mm and flats between 100 and 240 mu m radius) on polyurethane. Radii of contact, penetration and kinetics of detachment agree with the theory within 2%.