A comparison of the various K based procedures for characterizing the failure of an elastic softening solid

Abstract

With regard to the behaviour of an elastic-softening solid for which a cohesive zone description is appropriate, the paper quantifies the differences between the maximum load K F, K T and K E values. K F is the stress intensity due to the applied loadings at the actual crack tip, K T is the stress intensity referred to the initial crack tip and K E is the stress intensity defined with regard to the tip of an effective elastic crack. General relations are provided for the maximum load K values, these relations being applicable for all geometries and all softening behaviours, though subject to the restriction that the solid's characteristic dimension is large in relation to the softening zone size; when D → ∞ the three maximum load K values are all identical. Underpinning is provided by direct analysis of two specific models for the idealised case where the stress remains constant within the softening zone: (a) an isolated crack in a uniformly stressed infinite solid and (b) an infinite solid containing two symmetrically situated deep cracks and with tension of the small remaining ligament.