Shear of Two Half Planes Pressed to Each Other and Containing a Surface Groove. Part 1. Full Contact

We consider a plane problem of shear of two half planes preliminarily pressed to each other. One of these planes contains a shallow surface groove. By using the Kolosov-Muskhelishvili complex-valued potentials, the problem is reduced to a singular integral equation. This equation is analytically solved for a special form of the groove. We discovered three ranges of external tangential loads in which the contact couple exhibits qualitatively different types of behavior: perfect adhesion of the bodies, local sliding of points of the surface, and global sliding of the bodies relative to each other. The behavior of the system under the conditions of local sliding is analyzed in detail.