Plastic bending of a residually stressed beam

This paper contains analysis of the bending beyond the elastic limit of an ideally elasticplastic beam which contains a through-thickness distribution of high initial stresses. This is relevant to the analysis of service behaviour of components containing high residual stresses, such as might arise from heat treatment followed by quenching, plastic deformation induced by shot-peening, cold rolling, etc. The Timoshenko analysis of plastic bending of a beam is adapted for a particular case of a parabolic residual stress distribution typical of quenching treatment in bar or plate form. Attention is focused on the shake-down of residual stress, i.e., the variation in the residual stress and strain subsequent to bending. The implications of these results in terms of the analysis of bending tests are discussed. 0 1997 Elsevier Science Ltd.