Unified Solution of Burst Pressure for Defect Free Thin Walled Elbows

Abstract

In order to study the mechanical properties of defectfree thin walled elbows (TWE), and evaluate impacts of the intermediate principal stress effect, tension/compression ratio, and strainhardening of materials into logical consideration, this research, in the framework of finite deformation theory, derived the computational formula of burst pressure for defectfree TWE according to unified strength theory (UST). In addition, influences of various factors on burst pressure were analyzed, which include strength disparity (SD) effect of materials, intermediate principal stress, curvature influence coefficient, strainhardening exponent, yield to tensile (Y/T) and thickness/radius ratio. The results show that the greater the tension/compression ratio is, the higher the burst pressure is. The influence of the SD effect of materials is more obvious with the increase of elbow curvature and intermediate principal stress. The intermediate principal stress effect can bring the selfbearing capacities and strength potential of materials into a full play, which can achieve certain economic benefits for projects. Moreover, the burst pressure of defectfree TWE increases with the growth of yield ratio and thickness/radius ratio, while decreases with the rise of curvature influence coefficient and strainhardening exponent. It is also concluded that the Trescabased and Mohr–Coulombbased solutions of TWE are the lower bounds of the burst pressure, the twin shear stress (TSS)based solution is the upper bound of the burst pressure, and the solutions based on the other yield criteria are between the above two. The unified solution in this paper is suitable for all kinds of isotropous materials which have the SD effect and intermediate principal stress effect. As the deduced formula has unified various burst pressure expressions proposed on the basis of different yield criteria for elbows of any curvature (including straight pipelines), and has established the quantitative relationships among them, its applicability is broader. Therefore, the unified solution is of great significance in security design and integrity assessment of defectfree TWE.