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The article considers the contact problem of indentation of an absolutely rigid stamp with dry friction into one of the edges of an interfacial finite crack located in a piecewise homogeneous elastic plane. The governing system of equations for the problem is derived in the form of a system of three singular integral equations with respect to the normal contact pressure under the stamp and dislocation components of the displacements of the crack edge points. The exact solution is constructed. The behavior of contact stresses near the end points of a crack is studied depending on the ratio of the elastic characteristics of heterogeneous materials of half-planes that formed a piecewise-homogeneous plane.

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