Elastic J-integral solution for an elbow with axial through-wall crack at crown under in-plane bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires knowledge of the J-integral. The J-integral values for axially through-wall cracked thick elbows are not available in the open literature over a certain range. This paper presents a closed form expression for elastic J-integral for 90°, long radius elbows subjected to bending moment. The expression is derived, based on the results of a large number of finite element analyses covering a wide range of standard geometries. The analyses were performed using WARP3D software. The present study enables the estimation of the elastic J-integral over a range of Rm/t from 5 to 25 (Rm/t = 5, 6, 7.5, 9, 12, 15, 20 and 25) and thus extends the range of earlier solution towards the thicker elbows used in nuclear industry. The crack angles considered were 9°, 18°, 27° and 36°.