Stress singularities of a crack terminating at the frictional interface of a monoclinic bimaterial composite

In this analysis, the order of stress singularities at the tip of an inclined crack terminating at the frictional interface of a monoclinic bimaterial composite is investigated. The expressions for stresses and displacements are obtained by using the Stroh formalism. The stresses at the crack tip are expressed in the form σij=r−kFij(θ), where k is the crack-tip singularity. In the formulation, the problem is visualized as two wedges created by a crack, pressing on a half-plane. Both the cases of the two wedges slipping in opposite directions and the case of the two wedges slipping in the same direction are considered. The characteristic equation to determine k which incorporates the effects of the interface, the crack faces and the relative slip directions of the two wedges is derived, in terms of the generalized Dundurs constants α and β, and the complex parameters p1 and p2 of both materials. For the special case when the crack is perpendicular to the interface of an orthotropic composite and the two wedges slip in opposite directions, the characteristic equation is reduced to two equations corresponding to mode I and mode II cracks. In the numerical calculations, a bimaterial graphite/epoxy composite with different fiber orientations is considered and the singularities are graphically presented.