Stress Singularity Analysis of a Crack Terminating at the Interface of an Anisotropic Layered Composite

The order of stress singularities at the tip of an inclined crack terminating at the interface of an anisotropic layered composite is investigated. Both fully bonded and frictional interfaces are considered. 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. The singularity k is obtained by solving a characteristic equation which incorporates the effects of the interface and the crack faces. The problem can be visualized as two wedges created by a crack, pressing on a half-plane. For the frictional interface, depending on the relative slip directions of the two wedges, both the case of the two wedges slipping in opposite directions and the case of the two wedges slipping in the same direction are treated. In the numerical calculation of the singularities, a high modulus graphite/ epoxy layered composite is used and the effect of the crack inclination on the stress singularity k is graphically presented. In general, there are three roots of k for the fully bonded interface, while there are only two roots of k for the slipping interface.