An analytical study of collapse of locally corroded tubes under external pressure

Abstract

This paper presents a perturbative analysis of bifurcation pressure of 2D corroded rings characterized by locally thinned regions under external pressure by asymptotically analyzing the Timoshenko differential equation and parametric analysis. First, for the case of one corrosion region, we formulate regular perturbative solution separately for anti-symmetric bifurcation and symmetric bifurcation cases. Concise formulation is presented by introducing a corrosion severity parameter and perturbative solution is presented. Second, we present a detailed analysis for the case where corrosion region has small angular extent by converting it into a singular perturbative problem and conduct various asymptotic analyses to illustrate the interesting interlacing behaviors. The derived explicit formula explains some numerical observation by Fatt in literature. Third, we conduct parametric analysis for the case of two interacting corrosion regions by classifying it into two cases: symmetric corrosion case and non-symmetric corrosion case. Finally, we present asymptotical analysis to investigate the extremely corroded case and show by Prufer transformation that anti-symmetric bifurcation pressure decreases when the distance of two corrosion regions is increasing. This paper serves to enhance the understanding of the collapse pressure of subsea pipes with local thickness reduction.