This paper presents improvements to the LBB.ENG2 method for predicting the moment-rotation response of a circumferential through-wall cracked (TWC) pipe under combined tension and bending loads. The LBB.ENG2 method provides closed-form equations for J-integral (J) estimation using a load-displacement relationship, where the Mode I stress intensity factor (K) solution, beam differential equations, and limit load solutions are utilized for elastic and plastic displacements under a thin-shell assumption. Due to its good predictions and simplicity, LBB.ENG2 has been incorporated into the recent probabilistic fracture mechanics codes, PRO-LOCA and xLPR.

The LBB.ENG2 method, however, has a limited applicability inherited from the thin-shell assumption and the K solution. That is, it might yield an unrealistic J for a thick pipe, or very short and long cracks. In this study, improvements are made to the method, and the thin-shell assumption is revisited. First, in order to extend the applicability limit of the K solution and, hence, the limit of the LBB.ENG2 method, newly developed and more accurate K solutions are implemented in a suitable form to derive equations explicitly for prediction of the crack instability point. Second, thin-shell and thick-shell assumptions are compared and technical justification for the use of the thin-shell theory is provided. In addition, based on the LBB.ENG2 method, moment-rotation response curves of circumferential through-wall cracked pipes are generated.

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