This paper presents plastic limit loads and approximate J estimates for axial through-wall cracked pipe bends under internal pressure and in-plane bending. These loads and estimates are based on small strain finite element limit analyses using elastic-perfectly plastic materials. Geometric variables associated with the crack and pipe bend are systematically varied, and three possible crack locations (intrados, crown and extrados) are considered. Effects of the bend and crack geometries on plastic limit loads are quantified, and closed-form limit load solutions are given. Based on the proposed limit load solutions, a reference stress based the J estimation scheme for axial through-wall cracked pipe bends under internal pressure and in-plane bending is proposed.
EYoung's modulus E =E/(1 − ν 2 ) for plane strain; =E for plane stress J , J e J -integral and its elastically calculated value K Linear elastic stress intensity factor M, M L In-plane moment and limit moment of a cracked pipe bend, respectively M o , M s o Limit in-plane moment of an un-cracked pipe bend and straight pipe, respectively n Strain hardening index (1 ≤ n < ∞) for the Ramberg-Osgood model, Eq. 18 P , P L Internal pressure and limit pressure of a cracked pipe bend P o , P s o