Stress intensity factors in yielding materials by the method of caustics

Abstract

The method of caustics, as it has been developed by the author, was applied up to now to evaluate the stress-intensity factors in cracked plates under conditions of generalized elastic plane stress [1]. According to this method the partially reflected light beam either on the front or on the rear face of a polished cracked plate was deviated at the vicinity of the crack-tip because of the large constraint at this area, due to the Poisson effect and created a caustic. It was shown that the dimensions of the caustic are directly and intimately related to the values of the stress-intensity factor components. In this paper the theory developed for the elastic case of loading was extended to incorporate the case of a yielding material at the vicinity of the crack-tip, which can be represented by the Dugdale-Barenblatt cohesive force model, and presents a stress-strain curve resembling an elastic perfectly-plastic material. The equations for the initial curve engendering the caustic and the generalized epicycloid, which represents the caustic, were established. It was shown that at the early stage of yielding, at the vicinity of the crack-tip, the typical shape of a quasi-circular caustic appears, which later on, in a higher step of loading, evolutes to the well-known shape of the plastic wedge-shaped zone. Experimental evidence with steel and plastic specimens corroborated the theoretical results.