Applicability of reference stress-based J estimates to semi-elliptical surface crack problems

This paper discusses the applicability of the reference stress method to estimate J along the semi-elliptical surface crack front. For a systematic investigation, two steps are taken in the present work. The first step involves investigation of the dependence of angular variations in normalized J (with respect to its elastic value) along the semi-elliptical surface crack front on the geometry, loading mode and loading magnitude. In the second step, the error associated with the reference stress-based J estimates is investigated. It is found that angular variations in normalized J are strongly dependent on the geometry, loading mode and loading magnitude. As the application of the reference stress approach to semi-elliptical surface cracks implies proportional increases in the normalized J, the present results pose a question on the applicability of the reference stress approach to estimate J for surface cracks. However, it is also found that the reference stress approach can still provide reasonably accurate J results from an engineering point of view, provided that the maximum J along the crack front is accurately estimated. In this respect, investigation of the error in the estimated J in the present work suggests that the reference stress approach is an effective engineering tool for estimating crack driving force along the semi-elliptical surface crack front, provided that the reference stress is properly defined.