Article,
Limit analysis of flaws in pressurized pipes and cylindrical vessels. Part II: Circumferential defects
Engineering Fracture Mechanics, 97 (1): 314--333 (January 2013)
DOI: 10.1016/j.engfracmech.2012.05.017
Abstract
Upper and lower bound theorems of limit analyses have been presented in part I of the paper. Part II starts with the finite element discretization of these theorems and demonstrates how both can be combined in a primal–dual optimization problem. This recently proposed numerical method is used to guide the development of a new class of closed-form limit loads for circumferential defects, which show that only large defects contribute to plastic collapse with a rapid loss of strength with increasing crack sizes. The formulae are compared with primal–dual FEM limit analyses and with burst tests. Even closer predictions are obtained with iterative limit load solutions for the von Mises yield function and for the Tresca yield function. Pressure loading of the faces of interior cracks in thick pipes reduces the collapse load of circumferential defects more than for axial flaws. Axial defects have been treated in part I of the paper. ► This paper presents plastic limit loads for cracked thick-walled pipes for von Mises yield function and for Tresca yield function. ► Limit loads are given for the whole parameter range: from shallow to penetrating cracks, from short to fully-circumferential defects. ► Limit loads are derived for exterior cracks and for interior surface flaws with and without pressure on crack faces. ► All limit loads are compared with direct primal–dual FEM limit analyses and with burst tests.
