Contents lists available at ScienceDirect Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws Full length article Parametric study of the cross-section shape of aluminium tubes in dynamic three-point bending David Bilston a , Dong Ruan a , Artur Candido b , Yvonne Durandet a, ⁎ a Swinburne University of Technology, Faculty of Science, Engineering and Technology, Department of Mechanical and Product Design Engineering, Hawthorn, Victoria 3122, Australia b GM Holden Ltd., 191 Salmon St, Port Melbourne, Victoria 3207, Australia ARTICLEINFO Keywords: Plastic deformation Finite element analysis (FEA) Energy absorption Cross-section shape Three-point bending ABSTRACT Square and circular tubes were tested experimentally and numerically in quasi-static three-point bending. A fnite element model with failure criterion was developed that correlated well with the experimental results and provided accurate simulation of top surface failure of the tubes. The model was used to conduct a parametric study of the efects of common cross-section shapes, with or without rib reinforcements, on dynamic bending performance. Results showed the reinforced shapes had higher specifc energy absorption (SEA). The highest SEA was obtained for a square tube with internal parabolic shaped rib, but this was the only shape that sufered catastrophic failure. 1. Introduction With motor vehicles making a signifcant contribution to green- house gas emissions and global warming, governments of the world are setting increasingly strict limits on vehicle emissions. While powertrain improvements such as electric propulsion or alternative fuels can ofer signifcant benefts, vehicle inertia will continue to play a key role in determining energy consumption and emissions. The desire for light- weighting has spurred research of advanced or alternative materials in motor vehicles [1], such as high strength steels [2–5], magnesium al- loys [6–9], aluminium alloys [10,11], and carbon fbre reinforced plastics [12–18]. Hybrid tubular structures using metal / polymer foam can have considerably higher specifc energy absorption (SEA, energy absorption per unit mass) than their empty steel counterparts when subjected to plastic bending [19–26]. However, choosing lightweight materials is only part of the solu- tion. The design of structural members must consider vehicle crash- worthiness requirements while minimising mass. Energy must be ab- sorbedinacontrolledmanner,limitingforcesexertedonoccupantsand avoiding unstable behaviours such as buckling or catastrophic failures. Duarte et al. developed a manufacturing process for an in-situ foam flled tube, with the foam formation occurring inside the tube at ele- vated temperatures, providing a good bond between the foam and in- terior wall of the tube and an increase in ductility. The results de- monstrated predictable deformation without formation of cracks under compression [27] and bending [28]. It was also demonstrated that the level of energy absorption and structure weight could be adjusted si- multaneously by varying the tube wall thickness [29]. It has been shown that further optimisation of hybrid structures in bending can be achieved by varying topological features. For instance, Li and Lu [22] showed that a square hybrid tube had signifcantly higher energy absorption (EA) than a circular hybrid tube. An et al. [30] found that the performance in bending could be optimised by varyingthewallthicknesswithinthecross-sectionofasquaretube.Sun et al. [31] varied the wall thickness of a circular tube longitudinally, and reported an increase in SEA compared with a tube of uniform wall thickness. Ma and You [32] conducted a numerical simulation of a thin walled automotive bumper beam with origami pattern. The pattern was predicted to induce new collapse modes in bending, leading to a 24% increase in SEA compared with a uniform profle. Zhang et al. [33] studied an empty square tube with an internal semi-elliptical rib and reported a 57% increase in SEA compared with the empty tube without the rib. Ab Ghani et al. [34] looked at the efect of the size and posi- tioningofsquareshapedindentationsonthetopandbottomsurfacesof empty square tubes, concluding that the SEA could be increased. Nia [35] investigated the efect of section shape on energy absorp- tion for tubes undergoing axial crush (circular, square, rectangular, hexagonal, triangular, pyramidal and conical shapes) and concluded that the circular shape had the highest energy absorption. The research on the efect of section shape on SEA in bending is https://doi.org/10.1016/j.tws.2018.12.032 Received 15 July 2018; Received in revised form 14 December 2018; Accepted 27 December 2018 ⁎ Corresponding author. E-mail addresses: dbilston@swin.edu.au (D.Bilston), druan@swin.edu.au (D.Ruan), artur.candido@gm.com (A.Candido), ydurandet@swin.edu.au (Y.Durandet). Thin-Walled Structures 136 (2019) 315–322 Available online 07 January 2019 0263-8231/ © 2018 Elsevier Ltd. All rights reserved. T