Size effects in ductile cellular solids. Part II: experimental results

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Abstract

There is increasing interest in the use of metallic foams in a variety of applications, including lightweight structural sandwich panels and energy absorption devices. In such applications, the mechanical response of the foams is of critical importance. In this study, we have investigated the effect of specimen size (relative to the cell size) on selected mechanical properties of aluminum foams. Models, described in the companion paper, provide a physical basis for understanding size effects in metallic foams. The models give a good description of size effects in metallic foams.

Introduction

Metallic foams have existed for over 40 years [1]. The development of a number of less costly processing techniques have led to increasing interest in their use in a variety of applications, including lightweight structural sandwich panels and energy absorption devices. The mechanical response of these newer metallic foams, of critical importance in such applications, is currently being evaluated [2], [3], [4], [5], [6], [7], [8], [9], [10]. An important issue in mechanical testing of foams is the effect of the specimen size, relative to the cell size, on the measured properties. The size effect is also important in design, as some components may have dimensions of only a few cell diameters (typically, d∼2–6 mm). In the previous companion paper, we analyzed the effect of the ratio of specimen size to cell size, L/d, on the uniaxial, shear and indentation response of regular, hexagonal honeycombs. The Young's modulus and uniaxial strength were found to increase with increasing values of L/d, up to a plateau level, corresponding to the bulk properties. The reduced stiffness and strength at lower values of L/d arose from the reduced constraint of cell walls at the free surface as well as from the increasing area fraction of stress-free cell walls. The model for the shear modulus and strength examined the role of a rigid boundary on two parallel faces. The shear moduli and strength decrease with increasing L/d, this time due to the increased constraint of the cell walls at the boundary. The indentation load of a honeycomb is the sum of that required to crush the honeycomb beneath the indenter and that required to yield, and then tear, cell walls at the perimeter of the indenter, allowing it to move through the honeycomb. The indentation strength varies with the inverse of the indenter width. The results for honeycombs were extended to foams by modelling the mechanisms responsible for the size effects.

In this paper, we describe measurements of the effect of specimen size (relative to the cell size) on the mechanical properties (Young's modulus, uniaxial compression strength, shear strength and indentation strength) of aluminum foams. The data are compared with models, derived in the companion paper [14], which provide a physical basis for understanding size effects in metallic foams.

Section snippets

Materials

A nominally 7% dense, 20 pore per inch, open-cell aluminum (6101-T6) foam (trade name Duocel; ERG, Oakland, CA) and a nominally 8% dense, closed-cell aluminum foam (trade name Alporas; Shinko Wire, Amagasaki, Japan) were used for the mechanical testing. Their microstructure and mechanical properties have been investigated in a number of studies [3], [6], [7], [8], [11]. The open-cell foam has cells which are elongated in one direction. The cell size was measured using calipers on 6 mm diameter,

Results

Typical compressive stress–strain curves for the open- and closed-cell foams, illustrating the unloading response and the initial peak stress, or the plastic collapse stress, are shown in Fig. 1. For the closed-cell foam (Alporas), the slope of the loading curve is less steep than that of the unloading curve, indicating that plastic deformations occur even at stresses well below the plastic collapse strength; this observation is consistent with those of other studies [2], [3], [6]. Young's

Uniaxial compression

The effect of the ratio of specimen size to cell size on the Young's modulus of a honeycomb was analyzed in the previous companion paper by considering two contributions: the decreased constraint at the free surface of the foam, giving a less stiff boundary layer, and the area fraction of cut cell walls at the boundary which remain stress-free. For a foam, both effects give (Eq. (35) of the previous, companion paper) [14]EEbulk=1−2ndL−2pdL2+4nmdL1−2ndL−2pdL+4n2m2dL2,where m is the reduced

Conclusions

The Young's modulus and plastic collapse strength of both the closed-cell Alporas and the open-cell Duocel foams increased to a plateau level as the ratio of specimen size to cell size increased. The plateau values were reached at L/d=6 for the Young's modulus for both foams and at L/d=8 and 5 for the compressive strength of the open- and closed-cell foams, respectively. The modulus and strength of the open-cell foam decreased more rapidly with decreasing L/d than those of the closed-cell foam

Acknowledgements

We are grateful for financial support of ARPA (Contract number N00014-96-1-1028). Some of the tests on the effect of specimen size on the compressive modulus and strength of the open-cell foam were performed by Dr. A.E. Simone, whose assistance is appreciated. The research of Dr. P. Onck has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The assistance of Prof. J.W. Hutchinson is highly appreciated. Fig. 2, Fig. 4, Fig. 5 appear with permission, from

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