Contact Problem for a Piecewise Homogeneous Plane with a Finite Crack Under the Static Friction

The plane stress state of a piecewise homogeneous space consisting of two dissimilar half-spaces with an interphase finite tunnel crack into one of the edges of which is pressed into an absolutely rigid punch with a flat base is considered. It is assumed that, there are also static shear contact stresses under the punch, which are related to normal pressure by the generalized law of dry friction, the coefficient of which is directly proportional to the coordinates of the contacting points of the contacting surfaces. The governing system of equations for the problem was derived in the form of a system of singular integral equations with variable coefficients, the solutions of which were constructed using the numerical-analytical method of mechanical quadratures. The patterns of changes in contact stresses and crack opening were studied depending on the maximum value of the friction coefficient and the physical and mechanical characteristics of heterogeneous half-spaces.