Friction in an adhesive tangential contact in the Coulomb-Dugdale approximation

We study the problem of tangential frictional contact in the presence of adhesion. The model can be considered as a generalization of the theory by Cattaneo and Mindlin to the case where there are "long range adhesive interactions" between the contacting surfaces, which exert an additional pressure on the surfaces even in the absence of an external normal force. The adhesion forces are described by the Dugdale model and the tangential forces in the contact by Coulomb's law of dry friction. These approximations allow obtaining an analytical solution for the tangential contact problem of a rigid parabolic indenter and a half-space. As in the case of nonadhesive contact, application of an arbitrarily small tangential force leads to slip in the narrow ring-shaped area near the contact boundary. Further increase in tangential load leads to a decrease in the radius of the stick region until sliding expands to the entire contact region. The obtained analytical solution shows that the main governing parameter of the problem is the parameter lambda introduced by Maugis for the normal adhesive contact problem.