The reflected-shadow method for the study of the constrained zones in cracked birefringent media

Abstract

An optical method has been developed for the study of the constrained zones embedded at the crack tips in birefringent materials. Deviation of the partially reflected light beam from the back surface of a thin transparent plate made of a birefringent material, which contained a crack, formed a caustic which defined the constrained zone around the crack tip. The shape of the constrained zone, limited by the caustic, depended on the thickness variation of the plate, as well as on the double refraction of the impinging light beam. It is shown that for an elastically strained birefringent material with a birefringent constant ξ the caustic has the shape of a curve depending on ξ, which for ξ ↑ 0 degenerates to a circle. This curve, when projected on a screen, forms a generalized epicycloid created by the tips of the resultant vector, which represents the reflected and optically deviated light rays. The characteristic properties of the epicycloids are discussed and their connection with the stress intensity factor KI, which is related to the opening mode of fracture, is established. Experimental examples with transversely cracked plates made of birefringent materials are given.