A revised theoretical model for external inversion process over a circular die



As an ideal impact energy absorber, the external inversion process of thin-walled metal tubes over circular dies has been studied theoretically since 1960s. However, in the most existing theoretical models, the curvature in the deformation area is a constant and only the steady inversion force is studied. Limited research has been conducted on the whole inversion process. In this study, from experimental and numerical results, the curvature is found to be varying and the whole inversion process can be divided into two stages by three states. Then a modified geometric model is proposed and the force displacement curves is derived. Next, it has been observed that current theoretical results exhibit greater conformity with experimental and numerical results. Finally, the effects of the tube wall thickness, tube average radius and die radius on crashworthiness indicators are studied theoretically by the verified theoretical model. These outcomes offer valuable reference for further research on tube inversion forming and energy absorption characteristics of external inversion mode.