Axial crushing of pressurized cylindrical tubes

• Tube׳s crushing load on internal pressure and tube׳s size is studied.
• An analytical model is built to predict tube׳s crushing load.
• Crushing load of tube wall increases and then decreases with internal pressure.
• The results are explained by different deformation modes and energy partitioning.
• Critical pressure for transformation between tube’s deformation modes is estimated.

The crushing response of the pressurized cylindrical tubes under low-speed axial crushing is investigated by both numerical simulations and theoretical analysis. The internal pressure inside the tubes varies in a wide range from 0% to 80% of the tube׳s yield pressure. Numerical simulations with lower internal pressure are verified by the experiments reported in literatures. It is shown that under axial crushing the tubes with lower internal pressure deform into the mixture of symmetric mode and unsymmetrical mode. With the increase of internal pressure, the tube’s deformation under axial crushing is dominated by the symmetric mode. The total load-carrying capacity of the pressurized structure increases with the internal pressure. However, the load-carrying capacity of the tube wall itself decreases with the increase of internal pressure once the pressure is greater than 13% of the yield pressure. This behavior is very different from the foam-filled tubes, for which the load-carrying capacity of the tube wall is enhanced by the filler inside. Based on the symmetric fold׳s evolution process observed from numerical simulations, an analytical model is proposed to establish the expression of the tube wall׳s load-carrying capacity in relation to the internal pressure and the tube׳s size. It is shown that the tube wall׳s load-carrying capacity under higher internal pressure decreases with the internal pressure, while it increases with the cross-sectional area of the tube. By combining the analytical predictions obtained in the present paper under symmetric mode and that under non-symmetric mode reported in literature, the critical internal pressure for the transformation between the two deformation modes is estimated. All the analytical predictions are found to be in good agreements with the numerical simulation results.