Axial compression of the empty capped-end frusta during the inversion progress

This paper introduces a new theoretical model of plastic deformation during the inversion process on the capped-end frusta using a solid cylindrical punch. Based on the theoretical deformation model, the instantaneous axial load versus the displacement during the inversion process of the capped-end frusta is predicted. In the analytical model, the inversion process is divided into two different stages including plastic deformation of the frusta bottom and inversion of the frusta wall. Also, instantaneous absorbed energy versus the axial displacement and maximum inversion load during the process are estimated using the theoretical model. Some axial inversion experiments were carried out on capped-end conical tubes with different materials and geometrical dimensions to verify the present theory. A good agreement between the theoretical predictions and the experimental results affirms precision and accuracy of the new theoretical model and the analytical formulas.