Square aluminum tubes subjected to oblique loading

doi:10.1016/S0734-743X(03)00045-9

International Journal of Impact Engineering

Volume 28, Issue 10, November 2003, Pages 1077-1106

https://doi.org/10.1016/S0734-743X(03)00045-9 Get rights and content

Abstract

The behavior and energy-absorbing capability of obliquely loaded square thin-walled aluminum columns in alloy AA6060 were studied through quasi-static experiments and FEM-analyses with LS-DYNA. The specimens were clamped at one end and oblique loading conditions were realized by applying a force with different angles to the centerline of the column. The primary variables were load angle, wall thickness and heat treatment of the alloy. The experimental results were compared with the numerical results, and the capacity was compared with Eurocode 9. LS-DYNA was able to predict peak loads with very good accuracy, while the mean loads were conservative compared to the experimental results. Furthermore, the study showed that Eurocode 9 is conservative, and that the moment capacity can be increased for temper T4 and cross-section class 1 and 2. The initial and subsequent failure loci are constructed from experimental and numerical results, and the failure loci shrink for increasing additional rotation from the initial position.

Introduction

Aluminum alloys are increasingly used in structures where low weight is important. The ecological aspect of weight savings of up to 25% compared to conventional steel structures makes aluminum an attractive material in the automotive industry. The lower weight reduces the fuel consumption and the emission of carbon dioxide. Aluminum also has the ability to be recycled, which also gives environmental advantages.

Energy absorbers are often part of the car structure to protect passengers and the structure itself during impact. One type of energy absorber is the crash box, which is connected to the bumpers, situated in the front and rear end of the body structure. The crash box is designed to absorb energy at low speed impacts. Its purpose is to control the initial kinetic energy during impact, and at the same time avoid permanent deformations in the rest of the car body by keeping the force levels sufficiently low. The absorption of energy is controlled by the plastic work in the crash box, which is given by the area below the force-displacement curve.

During a high-speed crash, a larger part of the structure will be activated in order to absorb all of the energy. After the deformation of the crash boxes, deformations and forces are consequently transferred to the front rail and then to the rest of the vehicle's structure, which may lead to both bending and axial loading of other structural parts. Pure bending and axial crushing of square thin-walled columns have been subjected to extensive studies for many years, resulting in expressions for mean forces and bending moments [1], [2], [3].

The energy absorber will seldom be subjected to either pure axial loading or pure bending during an actual crash event, but rather a combination of the two load cases. According to requirements in the automotive industry, the bumper system should endure a load applied with a 30° load angle to the longitudinal axis. In an oblique impact, the crash boxes will be subjected to both moments and axial forces. If the crash box collapses globally, the energy absorption is lowered compared to axial crushing, and both moments and axial forces will be transferred to the rest of the vehicle's structure.

Although studies in this area are limited, some investigations have been carried out numerically. Han and Park [4] have investigated thin-walled columns of mild steel subjected to oblique loading, and obtained oblique conditions by impacting the column at a declined rigid wall with no friction. The response was divided into axial collapse, bending collapse and a transition zone, and an empirical expression for the critical angle was found. Kim and Wierzbicki [5] have explored the crush behavior of thin-walled columns subjected to combined bending and compression, by prescribing both displacements and rotations at the upper end of a cantilever column. They found that the failure loci shrink for increasing deformation, and that an analytical model was able to predict the numerical results.

Introductory studies by Reyes et al. [6] of thin-walled aluminum extrusions subjected to oblique loading showed that the energy absorption drops drastically by introducing a load angle of 5°. This is due to the change in collapse mode. In order to increase the database of obliquely loaded extrusions, the behavior of square thin-walled aluminum columns subjected to oblique loading was investigated, and cross sections in classes 1, 2, 3, and 4 according to the classification in Eurocode 9 [7] were tested experimentally, with varying load angles and tempers (heat treatment) of the aluminum alloy. The main objective of this study on obliquely loaded specimens was to examine their energy absorbing capability, and the effects of thickness and heat treatment. In total, 72 quasi-static tests were carried out. Additionally, numerical simulations with other load angles than in the experiments were carried out to supplement the experimental results.

Section snippets

Terminology

As the present research was motivated by the behavior of a crash box subjected to oblique loading, square aluminum tubes were studied. The joining between crash box and bumper can vary from a hinge to full clamping, and the full clamping could produce progressive buckling also for obliquely loaded columns. As the fully clamped boundary condition at the top end for a tube subjected to oblique was challenging to realize in the experimental set-up, a column with a hinge support at the top end was

Experimental study

Quasi-static tests were conducted on square thin-walled columns with constant length and outer width, 199 and 80 mm, respectively. The wall thickness was varied, with nominal values h₁=2.0 mm, h₂=2.5 mm, h₃=3.5 mm, h₄=4.5 mm. With two different tempers, T4 and T6, the effect of heat treatment was tested. The load angles were varied between θ₁=5°, θ₂=15°, and θ₃=30°, giving 72 tests with three parallel tests for each combination of wall thickness, temper and load angle. Table 1 summarizes the test

Numerical analyses

All the experiments were analyzed in LS-DYNA [11], using the same numerical model that was used in a previous study [6]. Additionally, analyses with θ=1°, 2.5° and 90° were carried out to supplement the experimental data. In the analyses, focus was placed on the force vs. plastic displacement (F–d_p) curves, peak forces, energy absorption, and collapse modes.

Interaction curves

The capacity of square thin-walled sections subjected to axial forces and moments can be calculated in accordance with Eurocode 9 [7], which is the European design code for aluminum structures. The capacity is controlled by the following interaction equation: $N N_{d}^{1.3} + M M_{d} ⩽1.0,$ where N and M are the axial compressive force and bending moment in the cross section. N_d and M_d represent the compressive force capacity and the bending moment capacity, respectively. These are calculated based on

Concluding remarks

The crushing behavior of square thin-walled aluminum columns subjected to oblique loads has been studied experimentally and numerically, and the following conclusions can be drawn:

•
The energy absorption drops drastically when a global bending mode is initiated instead of progressive buckling, and it decreases further with increasing load angle.
•
For thin-walled columns, the load increases up to the peak load, and then falls drastically. However, when the wall thickness is increased, the shape of

Acknowledgements

The authors would like to thank Hydro Automotive Structures for their generous support of the research project that forms the basis for the present work. Thanks are also given to Mr. T. Meltzer and Mr. J.T. Sundal who has provided technical assistance in the laboratory.

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