The representation of J in terms of eta factors and energy integrals for an elastic softening solid

Abstract

With a knowledge of the opening displacement at the initial crack tip, and J as determined from measurements using specimens with different initial crack sizes, Li and Ward have been able to obtain the complete softening p (stress)− v (relative displacement) curve of an elastic softening material displaying cohesive zone characteristics. The present paper investigates whether J can be determined using a single specimen, i.e. one initial crack size, via load and load-point displacement measurements and thereby energy and complementary energy integrals, coupled with the use of appropriate eta factors. However, in contrast with the behaviour of a metallic-type material where the plastic deformation characteristics are not associated with a length dimension, with an elastic softening material that exhibits cohesive zone characteristics, there is an extra length dimension associated with the softening. This means that, unlike the case of a metal, J cannot be determined for all loading levels using a single specimen. Nevertheless it is shown that, with an elastic softening material, the single specimen procedure can in principle be used at small loading levels, i.e. where the cohesive zone is only partially developed, so as to give the initial portion of the p− v softening curve.