A theoretical model for general cross section wires stress state evaluation during non-linear bending

Non-linear bending of thin wires is the main or one of the fundamental topics in several applications, especially when the plastic behaviour is widely involved. Tyre manufacturing and helical spring design are some of the most classical examples, but continuous improvement is also required in designing spectacle frames and shape memory wires. In this paper, a new analytical model is proposed, to foresee the final curvature obtained after non-linear bending of wires with nonsymmetric cross sections, once the loading parameters are known. Obviously both elastic springback after unloading and material behavioural non-linearities have been considered in the model. From an engineering point of view, negligible errors are committed if Bernoulli–Navier’s hypothesis is guaranteed. The wire stress state can be evaluated by means of the model and enables the low cycle fatigue resistance verification.