Single-Edge and Double-Edge Cracks in a Fully Anisotropic Strip

Abstract

The mode I and II stress intensity factors in a fully anisotropic infinite strip with a single-edge or double-edge crack configuration are obtained from an approach based on the continuous dislocation technique. The elastic solution of a single dislocation in an anisotropic half plane is used in conjunction with an array of dislocations along the boundary of the infinite strip, which is supposed to be traction-free, to provide the solution of a single dislocation in an anisotropic infinite strip. The dislocation densities of the dislocation array are determined in such a way that the traction forces generated by the dislocation array cancel the residual tractions along the boundary due to the single dislocation in the half plane. The stress field of a single dislocation in the infinite strip is thus a superposition of that of the single dislocation and the dislocation array in the half plane. This solution is then applied to calculate the mixed mode I and II stress intensity factors for a single-edge and a double-edge crack in the anisotropic strip, by replacing the cracks with a series of dislocations and satisfying the crack surface traction-free conditions. To illustrate the results, typical material data for graphite/epoxy were used in a unidirectional construction with the fiber orientation, θ, measured from the load direction (perpendicular to the crack direction), varying between 0 and 90 degrees. It is found that the effect of anisotropy on the mode I stress intensity factor is significant between 30 and 60 degrees and depends strongly on the relative crack length, being larger for cracks of relative larger length. The mode mixity, defined such that it is zero for pure mode I and 90 degrees for pure mode II, is significant between 40 and 70 degrees, and is in general between zero and 20 degrees.