Fracture of an Orthotropic Strip Containing a Pair of Coplanar Cracks Perpendicular to the Edges of the Strip

Abstract

The problem of an infinitely long orthotropic strip containing a pair of coplanar cracks perpendicular to the edges of the strip is studied. The surfaces of the cracks are loaded by an arbitrary pressure, while the edges of the strip are free from tractions. The solutions to the problem is written in terms of two potential functions. The mixed boundary value problem is reduced to a Fredholm integral equation of the second kind by using the techniques of Fourier transform and the finite Hilbert transform. In the special case of a uniform opening pressure, exact expressions for the stress intensity factors at the inner tips and the outer tips of the cracks as well as the shape of the deformed cracks are obtained. Numerical calculations for a fiber-reinforced composite are carried out to study the interaction between cracks, the existing stress-free edges, and the effect of the direction of the reinforcement fiber on the various quantities of interest in fracture mechanics. The cracks are either parallel or perpendicular to the reinforcement fiber.