Effects of elastic–plastic behaviour on the axial crush response of square tubes

• New set of analytical equations is presented for mean crush force in axial crush.
• New equations are presented for predicting max crush force and efficiency.
• Optimization strategy is presented for selecting material for crashworthiness.
• Materials exhibiting little hardening capabilities have lower crash performance.
• Low yield and high hardening materials meet crashworthiness constraints the best.

Axial crushing of square tubes is widely studied for their energy absorption characteristics that are similar to automotive structural components. In this paper, the effects of the elastic–plastic behaviour of lightweight alloys on the steady state crush force, peak crush force, energy absorption and crush efficiency response of the axial crushing of square tubes are studied. Axial crush simulations are performed on square crush tubes where the yield stress and strain, ultimate tensile strength, hardening rate, and failure strain of the material are varied. New definitions and analytical equations for crush efficiency and energy absorption are developed and calibrated with the axial crush simulations to develop a framework for optimal material selection for axial crush. This work shows that the yield stress increases the energy absorption, peak crush force and steady state crush force, while tending to decrease the crush efficiency. After sufficient increase in the hardening capabilities, positive gains are obtained in the crush efficiency when increasing the yield stress. The ultimate tensile strength, hardening rate and the yield stress of the material have a strong effect on improved energy absorption. Lightweight alloys with a low yield stress that have significant work hardening capabilities outperform materials with a high yield stress and very little work hardening in terms of energy absorption when a constraint is imposed on the peak crushing force.