Experimental and numerical studies of foam-filled sections

https://doi.org/10.1016/S0734-743X(99)00036-6Get rights and content

Abstract

A comprehensive experimental and numerical studies of the crush behavior of aluminum foam-filled sections undergoing axial compressive loading is performed. Non-linear dynamic finite element analyses are carried out to simulate quasi-static test conditions. The predicted crushing force and fold formation are found to be in good agreement with the experimental results. Based on the numerical simulations, simple closed-form solution is developed to calculate the mean crushing force of the foam-filled sections. It is found that the increase of mean crushing force of a filled column has a linear dependence with the foam compressive resistance and cross-sectional area of the column. The proposed solution is within 8% of the experimental data for wide range of column geometries, materials and foam strengths.

Introduction

Recent developments of cost-effective processes for the production of low-density metallic cellular material, such as aluminum foam, have cleared the way for using it in light-weight structural members. This is due to the unique characteristics of the cellular material which can undergo large strain deformation while maintaining its low stress level before the densification, which occurs at the densification strain in the range of 60–90%. One potential application of this type of material is to reinforce thin-walled prismatic columns in space frame structures. It has been shown through numerical studies that the crushing characteristics of a thin-walled column are improved dramatically by filling it with aluminum foam [1].

A comprehensive experimental study on the effect of filling thin-walled columns with aluminum foam was done by Hanssen et al. [2], [3]. They investigated the axial crushing behavior of the foam-filled aluminum extrusion under quasi-static loading condition. They found that significant increases of crushing force were obtained from the direct compressive strength of the foam and from the interaction between the foam and wall column. The interaction at the foam–wall interface decreases the folding length, and therefore increases the crushing force. For a typical column with a length to width ratio of 3, the non-filled extrusion formed 5 lobes, while the foam-filled sections formed as many as 9 lobes. Similar experimental results were obtained by Seitzberger et al. [4], on the axially compressed steel tubes filled with aluminum foam. The experimental results on the folding mode of aluminum foam filling method agreed qualitatively with earlier results on the low-density polyurethane foam filling reported by Thornton [5], Lampinen and Jeryan [6], and Reid et al. [7]. However, Thornton et al. [8] summarized the effect of polyurethane foam by concluding that even though a considerable increase of collapse load was achieved, thickening of the column wall was still more weight efficient than polyurethane foam filling.

Numerical investigations on the effect of aluminum foam filling of thin-walled prismatic columns undergoing axial crushing were recently carried out by Santosa and Wierzbicki [9]. In terms of energy absorption per unit total mass, aluminum foam filling was found to be preferable to thickening of the column wall. Therefore, the energy absorption characteristics of thin-walled columns can be improved significantly with aluminum foam filling. This is due to the prevention of the inward fold formations of the thin-walled column by the presence of the foam filler, leading to large plastic membrane deformation and, accordingly, increased energy dissipation. Santosa and Wierzbicki have also expanded their numerical analysis to the case of torsion and bending with cross-sectional crushing [10], [11]. In both cases, numerical analyses showed that aluminum foam filling reduced the amount of sectional collapse, resulting in the increase of the energy absorption of the filled columns.

The objective of this paper is to validate the numerical prediction of the crushing behavior of aluminum foam-filled columns using available experimental data. Of interests in the study are the instantaneous crushing force, the mean crushing force, and the deformation mode of the aluminum foam-filled columns. The numerical study was conducted at the Impact and Crashworthiness Laboratory, MIT, while the experimental study was conducted at the Norwegian University of Science and Technology. Both studies involve aluminum extrusion and HYDRO aluminum foam filler. Furthermore, experimental validation is also conducted for the case of steel column with MEPURA aluminum foam, in which the data was obtained from Ref. [4]. Simple closed-form solutions for the mean crushing load are constructed based on the analytical and numerical results and compared to the experiments.

Section snippets

Theoretical prediction

The energy dissipation of foam-filled columns undergoing a crushing process depends on the membrane and bending energy of the empty column, crushing energy of the foam, and the interaction between these two mechanisms. The existence of the coupling between the foam and the column in the deformed geometrical parameters posses a complex analytical problem. Abramowicz and Wierzbicki [12] developed an approximate solution to the problem of axial crushing of foam-filled columns. The interaction was

Test program

Fig. 2 shows the test matrix designed for the present experimental investigation. The influence of three parameters on the energy absorbing behavior was studied, i.e. the density of the foam, the wall thickness of the extrusion and bonding between the foam and extrusion by applying adhesive.

A typical factorial design approach was selected for this investigation [18]. Three different densities of foam were investigated in addition to empty extrusions. For each density of foam, the wall thickness

Finite element modeling

The explicit dynamics non-linear finite element code PAM CRASH 97 was used to numerically simulate the axial crushing process of foam-filed columns. The finite model was created by mesh generator program HYPERMESH 2.1. The column wall was modeled with a Belytschko-Tsay-4-node thin shell element, while the foam core was modeled with an 8–node solid element. Since the foam core can undergo a large strain deformation, solid element using selective reduced integration rule was chosen to avoid

Thin-walled prismatic column

The constitutive behavior of the thin shell element for the column material was based on the elastic–plastic material model with Von Mises's isotropic plasticity algorithm. The transverse shear effect was considered by this material model. Plastic hardening was based on the polygonal curve definition, in which pairs of the plastic tangent modulus and the plastic stress were specified.

The aluminum extrusion AA 6060 T4 mechanical properties are: Young's modulus E=6.82104N/mm2, initial yield

Quasi-static simulation

The explicit solution method is a true dynamic procedure originally developed to model high-speed impact events in which inertia plays a dominant role in the solution. Therefore, in a quasi-static analysis, the goal is to model the process in the shortest time period in which inertial forces remain insignificant.

Two ways of achieving a quasi-static process by using the explicit dynamics procedure are presented in this section. The first is scaling down the mass of the material so that the

Numerical and experimental analyses

Two groups of simulations were investigated on the foam-filled sections. First, the simulation was conducted on the square box column made of mild steel RSt37 with the cross section width b=40mm and thickness t=1.4mm used by Seitzberger et al. [4]. The thin-walled steel column was filled with MEPURA aluminum foam, which has base material AlMg 0.6Si 0.3Ti, and the mass density of 0.52g/cm3. From uniaxial compression test [4], this foam has the crushing resistance of σf=8.2 MPa. The numerical

Discussion and conclusion

The finite element modeling developed in the present work has shown to correctly predict the crush behavior of foam-filled column. The numerical simulation has indicated that the overall behavior of the progressive crushing process follows the actual test condition. The main points of the present numerical and experimental studies can be summarized as follows:

  • 1.

    The numerical model predicted very well the instantaneous crushing force, mean crushing force, fold formation, and folding length. Based

Acknowledgements

The present work was supported by the Joint MIT/Industry Consortium on Ultralight Metal Body Structures and by Norks HYDRO ASA . The financial support from both sources are gratefully acknowledged. The author would like to thank to Mr. Seitzberger of the Technical University of Vienna for providing the experimental data and fruitful discussion. Words of appreciation are also directed to Dr. E. Haug of ESI Paris, Dr. A. Tanavde of ESI US, and Mr. G. Christ of Altair Computing for their

References (22)

  • W. Abramowicz et al.

    Axial crushing of foam filled columns

    Int J Mech Sci

    (1988)
  • T.Y. Reddy et al.

    Axial compression of foam-filled thin-walled circular tubes

    Int J Impact Engng

    (1988)
  • S.P. Santosa et al.

    On the modelling of crush behavior of closed-cell aluminum foam structure

    J Mech Phys Solids

    (1998)
  • Santosa SP. Results of MIT pilot studies on weight efficient crashworthy components. Presented at the Meeting of the...
  • Hanssen AG, Langseth M. Development in aluminium based crash absorption components. Presented to the Norwegian-French...
  • Hanssen AG, Langseth M, Hopperstad OS. Static crushing of square aluminium extrusions with aluminium foam filler. Int J...
  • M. Seitzberger et al.

    Crushing of axially compressed steel tubes filled with aluminium foam

    Acta Mech

    (1997)
  • Thornton PH. Energy absorption by foam filled structures. SAE paper 800081,...
  • Lampinen BH, Jeryan JA. Effectiveness of polyurethane foam in energy absorbing structures. SAE paper 820494,...
  • S.R. Reid et al.

    Static and dynamic axial crushing of foam-filled sheet metal tubes

    Int J Mech Sci

    (1986)
  • Thorton PM, Mahmood HF, Magee CL. Energy absorption by structural collapse. Jones N, Wierzbicki T. editors. Structural...
  • Cited by (0)

    View full text