A three-dimensional model of circular tube under quasi-static external free inversion

Abstract The free inversion of a metal tube can be applied in energy absorbing devices. The existing two-dimensional theoretical predictions on the knuckle radius and the steady load all displayed large discrepancy from the experimental observations. In this paper, with the rigid, perfectly plastic simplification, a three-dimensional analytical model is proposed based on the assumption of volume conservation and von Mises yield criteria, for quasi-static free inversion of circular tubes. A two-stage assumption on the thickness change is adopted, and the strain variation along the thickness direction is also considered. In order to validate the theoretical model, static inversion experiments are performed for aluminum tubes, and finite element calculations are also carried out for the elastic, perfectly plastic material. Compared with the experimental data and corresponding FE simulations, the current 3D model provides a better prediction on the steady inversion load than the previous 2D models.