Path of light in near crack tip region in anisotropic medium and under mixed-mode loading

Abstract

The theory governing the propagation of light in the region near a plane strain crack tip is extended to optically anisotropic media. As for the case of isotropic media, an incident wavefront of light is split into two independent wavefronts. The planes of polarization of the two wavefronts lie in planes parallel and perpendicular to the crack front only for specific crystal orientations relative to the crack front. The general functional forms for the index of refraction of both the parallel and perpendicular wavefronts are given in terms of the principal indices of refraction, orientation of the index ellipsoid, and the direction of propagation of the wavefront. It is demonstrated how the principal indices of refraction and the orientation of the index ellipsoid can be calculated from the results of a finite element analysis and the coefficients of the elasto-optic tensor for a specific case. The characteristic equations which govern the propagation of light in anisotropic media are solved for a specific case to calculate the path of light relative to a crack tip in a bicrystal specimen. We also report the path of light rays approaching a mixed Mode I and Mode II crack tip in a material that is optically isotropic in its unstrained state.