Approximate methods for predicting J-integral of a circumferentially surface-cracked pipe subject to bending

This study proposes two new methods to estimate the energy release rate of a circumferentially cracked pipe with an internal, constant-depth, finite-length surface flaw subjected to pure bending loads. The methods are based on the deformation theory of plasticity, constitutive law characterized by Ramberg–Osgood model, and an equivalence criterion incorporating reduced thickness analogy for simulating system compliance due to the presence of a crack. Closed-form solutions were developed in terms of elementary functions for an approximate evaluation of J-integral. They are general and can be applied in the complete range between elastic and fully plastic conditions. Several numerical examples are presented to illustrate the proposed methods. The comparisons with the results of elastic–plastic finite element analysis showed satisfactory prediction of J-integral by one of the proposed methods.