Simplified Equations for Predicting Secondary Stress Around Pipe’s Circumference

Abstract

This paper examines the magnitude and location of the maximum residual stress induced in pipes after the process of bending, reverse-bending and straightening. Dimensional analysis is used to establish generalized equations relating the maximum residual stress magnitude and location to the pipe geometry, maximum bending curvature and pipe material’s yield stress. 64 design cases based on an analytical solution assuming elastic-perfectly-plastic material behavior have been conducted. Regression analysis has revealed that the magnitude of the maximum residual stress can be conservatively approximated by a simplified quadratic equation involving the maximum axial bending strain, whereas the location of the maximum residual stress can be approximated by a linear function based on the same. Both equations are expected to be valid and conservative for X65 and X70 grade steel pipes under global maximum axial strain between 1% and 3%. Non-linear finite element analysis based on a realistic design example with isotropic hardening material is used to validate the prediction results based on the simplified equations.