A theoretical model of the inversion tube over a conical die

As an important impact energy absorber and a way to produce double-wall tubes, the inversion of the metal tube over a conical die is investigated in this study. Adopting the deformation profile inspired by FEM simulations, a theoretical model is proposed assuming the energy is dissipated by bending and compression in the meridional direction, and expansion in the circumferential direction. FEM simulations with a large range of geometrical parameters are used to validate the theoretical model, and results show that both the compressional force and the final circular radius of tube predicted by the theoretical model are quite accurate. Then, the energy dissipations along the axis of the tube by various mechanisms are analyzed in detail, and it is identified that the tube deformation in the thickness direction is the major reason of the current model's deviation. Besides, the influence of the die radius, the friction between die and tube, as well as the dynamic effect are discussed.