Approximate J-estimation methods for pipes with circumferential surface cracks in welds

Approximate J-estimation methods including the effects of weld mis-match, for a circumferentially surface-cracked pipe with an internal, constant-depth and finite-length surface flaw in pure bending are developed. The methods are based on principles described by Rahman and Brust. Closed-form J-solutions in terms of elementary functions are derived from classical beam theory combined with an equivalence criterion. Several numerical examples of welded joints are presented to verify the proposed methods.