A model to represent the effect of cold-bending wide sheet on subsequent behaviour under uniaxial stressing

The effect of cold-bending wide sheet to a circular profile to form a component such as a light-gauge structural member is considered. The residual stresses created by this process followed by spring-back are known to influence subsequent behaviour of such a load-bearing member. A four-element model is described to portray the essential nature of a moderately cold-bent member which is then subjected to uniform uniaxial strain in the longitudinal direction. An ideally elastic-plastic material response is assumed for each element with Tresca's yield criterion and associated flow rule being employed during axial loading. Following forming and spring-back, the individual loading history of each element is traced under controlled strain conditions. A gross stress-strain curve is then computed to reveal the effects of cold-bending subject to the usual equilibrium and Euler-Bernoulli requirements. Significant lowering of the proportional limit compared with the full load capacity based on the original yield stress is recovered but only after significant plastic straining of all elements. Finally, the effect of unloading such a member is shown to eliminate all the residual stresses induced by forming.