A Comparison of J Estimating Procedures for a Solid Subjected to Bending Loads

Zahoor and Kanninen have recently developed a simple procedure for estimating the magnitude of the J-integral for through-wall cracks in pipes subjected to bending loads. This paper gives consideration to their procedure, but to check its predictions against available numerical results, it is explored in detail for the case of a crack in a solid deforming under plane-strain bending conditions. In this case, an implicit assumption in the procedure is that the plastic rotation depends on the ligament size, and not on any other geometrical dimension. This assumption is strictly valid only for deep cracks, and this paper shows the degree of inaccuracy obtained when it is applied to shallow cracks. The assumption is also shown to correlate with the existence of a unique relation, independent of geometrical parameters, between the ligament net-section stress and the J-integral, and also with the existence of Turner’s plastic η factors.