James R. Barber

Cattaneo and Mindlin showed that if a Hertzian contact is loaded first by a normal force and then by a monotonically increasing tangential force, the resulting shear tractions can be expressed as a simple superpositon, provided we assume that the frictional tractions in the slip zone are everywhere aligned with the applied force—a result which is strictly true only in the special case where Poisson’s ratio is zero. Ciavarella later showed that with this assumption, a similar superposition applies to any uncoupled three-dimensional contact problem for the half space. Here we relax this assumption and develop a general solution for the case where the tangential force is relatively small, so that the slip annulus is thin compared with other dimensions of the contact area. The local conditions are then characterized by the mode II and III stress-intensity factors in the corresponding adhesive problem. We show that the slip direction depends only on a dimensionless coordinate, so that all points in the slip zone pass through scaled versions of the same expressions as the applied shear force increases. The results show a surprisingly large deviation in slip direction, particularly for incompressible materials.