J-integral evaluation for cases involving non-proportional stressing

Calculation of J for cases where the proportional stressing condition cannot be satisfied is investigated. A modified J definition is derived and implemented into an ABAQUS post-processing program for both 2-D and axisymmetric problems. The modified J-integral is path independent for cases of proportional and non-proportional stressing. For cases with proportional stressing, the modified integral gives the same value as does the standard ABAQUS J function. It is also found that the modified J is equivalent to the stress intensity factor for a linear elastic material and provides a measure of the intensity of the crack-tip fields for non-linear elastic and elastic–plastic materials. The modified J formulation is applied to the case of a cylinder with an external circumferential crack under various load conditions.