Effects of strain field on light in crack opening interferometry

Crack opening interferometry is a standard technique used to measure the normal opening displacement profile of a crack in a transparent material. This paper calculates how much an incident light ray deflects from a nominally straight line path due to strain induced changes in the index of refraction. It is shown that an incident plane wavefront of light that propagates toward a plane strain crack is split into two linearly polarized light rays : one polarized in a direction parallel to the crack front ; the other polarized in the plane perpendicular to the crack front. Assuming linear, elastic mechanical behavior and linear optical behavior in a homogeneous, isotropic medium, the index of refraction of both wavefronts is derived for a Mode I crack in the K-hield region. In general, the index of refraction is anisotropic and inhomogeneous. Four new material parameters are identified which characterize crack opening interferometry; values are tabulated for three materials. Using geometrical optics, the paths of both light rays are calculated analytically for a special set of initial conditions and an expression for the total light deflection at the crack flank is obtained. The results show that for some materials and specimen geometries, the absolute deflection of each light ray is large enough to be measured, but the relative deflection (i.e. the difference in deflection between the two light rays) is too small to be measured. The main effect that this phenomenon has on crack opening interferometry is to cause a shift in the apparent position of the crack tip. It is shown that this shift will not affect the interpretation of the interference fringes in terms of crack opening displacement. © 1997 Elsevier Science Ltd.