The determination of thru-thickness residual bending stresses

Abstract

In order to understand the fatigue behavior of dents in pressurized pipelines it is necessary to understand the residual stresses that result from cyclic plastic bending. Three approaches are taken here in studying a beam cross section: a discrete model, an exact solution, and a finite element solution. The residual stress distributions that are studied are those that arise from yielding an initially stress free cross section in bending and those which arise from reyielding a residually stressed cross section. A method by which an exact solution may be obtained is presented in addition to several conclusions. The exact solution provides specific information about the residual stress distribution. Also, residual stresses are shown to alter the yield point and the post yield stiffness of a bending cross section. Simple relationships are given to predict the residual stress distributions that are produced by certain types of sequences of applied and released moments.