Essay About International Journal Of Impact Engineering And Experimental Results

Experimental And Numerical Studies Of Foam-“Lled Sections
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* Corresponding author. Tel.:#1-617-253-2104; fax: #1-617-253-1962.
E-mail address: [email protected] (T. Wierzbicki)
International Journal of Impact Engineering 24 (2000) 509}534
Experimental and numerical studies of foam-“lled sections
Sigit P. Santosa!, Tomasz Wierzbicki!,*, Arve G. Hanssen”, Magnus Langseth”
!Impact & Crashworthiness Laboratory, Massachusetts Institute of Technology, Room 5-218,
77 Massachusetts Avenue, Cambridge, MA-02139, USA
“Department of Structural Engineering, The Norwegian University of Science and Technology,
N-7034, Trondheim, Norway
Received 30 September 1998; received in revised form 29 June 1999
Abstract
A comprehensive experimental and numerical studies of the crush behavior of aluminum foam-“lled
sections undergoing axial compressive loading is performed. Non-linear dynamic “nite 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-“lled sections. It is found
that the increase of mean crushing force of a “lled 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. ( 2000 Elsevier Science Ltd. All
rights reserved.
Keywords: Thin-walled column; Aluminum foam; Axial crush
1. Introduction
Recent developments of cost-e!ective 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 densi”cation,
which occurs at the densi”cation 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
0734-743X/00/$ – see front matter ( 2000 Elsevier Science Ltd. All rights reserved.
PII: S 0 7 3 4 – 7 4 3 X ( 9 9 ) 0 0 0 3 6 – 6
Nomenclature
E Youngs modulus
H half-wave folding length
P instantaneous crushing force
b column width
n strain hardening exponent
t column thickness
CI foam strengthening constant
EH elastic modulus of foam material
F0, F& characteristic load of empty and “lled column
GH foam shear modulus
P. mean crushing force of empty column
P.,& mean crushing force for “lled column
P.,& mean crushing force for bonded-“lled column
*P. increase of the mean crushing force
d instantaneous shortening distance
l Poissons ratio
h rotation angle of superfolding element
eD densi”cation strain
oH foam density
os density of solid cell wall of foam
p0 plastic #ow stress
p6 ultimate strength
p: yield stress
p& crushing strength of foam
pH1- plastic collapse stress of foam
p&!*- tensile strength of adhesive
qH1- plastic shear strength of foam
q&!*- shear strength of adhesive
shown through numerical studies that the crushing characteristics of a thin-walled column are
improved dramatically by “lling it with aluminum foam [1].
A comprehensive experimental study on the e!ect of “lling thin-walled columns with aluminum
foam was done by Hanssen et al. [2,3]. They investigated the axial crushing behavior of the
foam-“lled aluminum extrusion under quasi-static loading condition. They found that signi”cant
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-“lled extrusion formed 5 lobes, while the foam-“lled sections
formed as many as 9 lobes. Similar experimental results were obtained by Seitzberger et al. [4], on
the axially compressed steel tubes “lled with aluminum foam. The experimental results on the
510 S.P. Santosa et al. / International Journal of Impact Engineering