Contact interaction of two solids with surface groove under proportional loading

The contact interaction of two elastic solids of identical materials, one of which possesses a sloping surface groove of small depth, under simultaneous application of a normal load and a proportional shear load is studied without involvement of the incremental approach. The relative tangential shift of the surfaces arises within the intercontact gap due to the action of the tangential stress. The contacting surfaces are in stick in the contact regions. The contact plane problem is reduced to a set of singular integral equations for height of intersurface gap and relative tangential shift of the boundaries. For the grooves of the specified shapes, the solutions of the contact problem are obtained in a closed form. The method of finding these solutions is generalization of the method developed in our earlier work (2005b), where the analytical solution for the groove of the simplest shape, was obtained.The analysis of contact parameters of the contacting couple due to the applied loading is carried out. Based on the classical strength criteria, the most possible crack-initial and plastic yielding zones are found.