Shear of two half planes pressed to each other and containing a surface groove. Part 2. Incomplete contact

Abstract

We consider the elastic problem of contact of two half planes made of identical materials with regard for the presence of an intercontact gap caused by a surface groove in the case of successive loading with normal and shear forces. By using the Kolosov-Muskhelishvili complex potentials, the problem is reduced to a sequence of singular integral equations the first of which is solved analytically and the second numerically. According to the procedure of numerical analysis, we separate the root singularity and represent the regular part in the form of expansion in Chebyshev polynomials of the first kind with unknown coefficients. The coefficients are determined by the collocation method. We analyze the dependences of the length of the gap and the size of the slip region on the external load and the distributions of tangential and normal stresses over the contact surface.