A theoretical study of the expansion metal tubes

• Based on energy conservation, a theoretical model is proposed for expansion metal tubes.
• Deformation mechanism adopted considers energy dissipated by bending along axial direction.
• The predictions of steady compressional force and the tube radius after expansion are obtained.
• Predictions by current model agree well with finite element simulations and experimental data.

As an important type of energy absorption devices, the expansion of metal tubes over a mandrel conical die are investigated by proposing a theoretical model, in which the deformation mechanism enlightened by finite element simulation is adopted. Different to the previous theoretical analysis that base on the momentum equations, the present model starts from the energy conservation point of view. That is, in the steady stage deformation of an expansion tube, the external work done by the compressional force should be dissipated by expansion in circumferential direction, bending in meridional direction, and friction.The theoretical model provides the predictions of steady compressional force and the tube radius after expansion, for rigid, perfectly plastic (R-PP) material, with or without strain hardening effect. Compared with the existing experimental data, and also the corresponding finite element simulations, the steady compressional force predicted by current theoretical analysis are both quite accurate.