An Analysis of the Plastic Bending of Wide Plate, and the Effect of Stretching on Transverse Residual Stresses

Abstract

Part I of this analysis is devoted to solving the problem of bending a wide beam of ideally plastic material, under substantially plane strain conditions. A geometric method of solution, in which the stress and strain paths during the deformation are determined in the stress plane, is compared with the well-known analytical solution. Curves are given which will allow the rapid estimation of bending moments and ‘spring-back’ for plates of an aluminium alloy conforming to B.S. 1476:HE 15W†. The system of residual stresses induced is determined and compared with that for a narrow beam. In Part II the geometric method mentioned above is used to estimate the effectiveness of stretching in reducing residual stresses which are transverse to the direction of stretching. This is a problem of some technological interest in that residual stresses arising from operations such as heat treatment and quenching are usually complex, lying in all directions within the plane of the plate. It is shown that stretching in a direction transverse to the major residual stresses is almost as effective in their reduction as stretching in a parallel direction.