Closed form expression for plastic J-integral for an elbow with a through-wall crown crack under opening bending moment

Piping elbows under bending are vulnerable to cracking at the crown. Hence it is necessary to estimate the crack driving force. This paper presents a closed form expression for the plastic J-integral for axially through-wall cracked, long radius elbows under opening bending moment. The equation is derived, based on a large number of finite element analyses covering a wide range of geometries. The non-linear finite element analyses were performed using WARP3D software and accounted for geometric and material non-linearity. The material was assumed to follow the Ramberg-Osgood law with a wide range of strain hardening exponent (n=2,3,5,7 and 10)