New plastic collapse moment equations of defect-free and throughwall circumferentially cracked elbows subjected to combined internal pressure and in-plane bending moment

Abstract

Closed-form plastic collapse moments (PCM) equations were earlier proposed for throughwall circumferentially cracked (TCC) elbow subjected to pure in-plane bending moment. However, an elbow is often subjected to combined internal pressure and bending moment in actual service condition. Therefore, the present study investigates the effect of internal pressure on the in-plane PCM of a TCC elbow. The PCM of a cracked elbow is usually expressed as a product of two parameters: PCM of a defect-free elbow multiplied by a weakening factor due to the crack. Therefore, the present study also includes analysis of defect-free elbows. Elastic–plastic finite element analysis is employed for the present analysis. A total of 396 cases of elbows with various sizes of circumferential cracks (2 θ = 0–150°), different wall thickness ( R/ t = 5–20), different levels of normalized internal pressure ( p = PR/( tσ y) = 0–1), different elbow bend radii ( R b/ R = 2,3) and two different bending modes, namely closing and opening are considered in the analysis. Elastic–perfectly plastic stress–strain response of material is assumed. The load in the elbows is split in two components: a constant internal pressure applied initially followed by in-plane bending moment monotonically increasing in definite steps. PCM are evaluated from moment—end rotation curves by twice-elastic slope method. From these results, closed-form equations are proposed to evaluate PCM of TCC and defect-free elbows subjected to combined internal pressure and in-plane closing/opening bending moment. Attempt has been made to compare the predictions of the proposed equations with the available experimental/numerical results and to rationally explain the behaviour where no experimental/numerical data is available for comparison.