Energy absorption of expansion tubes using a conical-cylindrical die: Theoretical model

摘要

Previous experimental and numerical investigations have shown that expansion tubes under axial compression by a conical-cylindrical die had stable and efficient energy absorption characteristics [1]. In order to further understand the energy absorption mechanisms of such a tube expansion process, a theoretical analysis is given in this paper. The tube material is assumed to be rigid, linear hardening and the die is rigid. When the die is gradually pushed in, the tube expands. Both the radial deflection of the tube wall and the required driving force vary with the stroke of the die and their expressions are obtained theoretically. The final radius of the tube and the driving force in the steady-state are estimated. The theoretical analysis explains three deformation modes observed in the experiments [1]: tube tip-conical surface contact mode (T-C mode), tube wall-conical surface contact mode (W-C mode), tube wall-conical and cylindrical surface contact mode (W-CC mode), depending on the values of geometrical parameters of the tube and the die, such as the ratio of tube thickness to radius h/R-0 and the semi-angle of the die gamma. Deformation characteristics in each mode are discussed and a map of phases in the h-gamma plane is given theoretically. The theoretical results are compared with the experimental data, with a reasonably good agreement. In addition, an analysis of the early deformation stage using elastic, linear hardening tube material model demonstrates that the elastic deformation of the tube is negligible.