Elastic-plastic analysis of an elbow with a through-wall axial 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 under in-plane bending moment are not available in open literature. This paper presents the J-integral results for 90°, long radius elbows subjected to in-plane opening bending moment based on a large number of finite element analyses covering a wide range of standard geometries. The non-linear elastic-plastic finite element analyses were performed using WARP3D software. Both geometric and material non-linearity were considered in the study. The geometry considered were for Rm/t = 5, 6, 7.5, 9, 12, 15, 20 and 25 with crack angles of 9°, 18°, 27° and 36° and strain hardening exponent, 'n' varied for 2, 3, 5, 7 and 10.