Materials Science and Engineering A 420 (2006) 87–99 Elastic and electric properties of closed-cell aluminum foams Cross-property connection Igor Sevostianov a,∗ , Jaroslav Kov´ aˇ cik b , Frantiˇ sek Simanˇ c´ ık b a Department of Mechanical Engineering, New Mexico State University, Las Cruces, NM 88001, USA b Institute of Materials, Machine Mechanics, Slovak Academy of Sciences, Racianska 75, Bratislava 3, SK-831 02, Slovak Republic Received 26 September 2005; accepted 17 January 2006 Abstract Foamed aluminum (AlMg1Si0.6) in the porosity range 0.45–0.85 produced by the powder metallurgy method is analyzed with regard to its elastic and electric properties. Various predictive models for the electrical conductivity and Young’s modulus of closed-cell metal foam are assessed based on the experimental measurements. It is shown that the differential scheme provides the best predictions of the electrical conductivity in the porosity range 0.7–0.85, while Mori–Tanaka’s scheme gives the best results for the Young’s modulus. Comparing the two sets of the experimental data, cross-property coefficient that connects changes in the Young’s modulus and electrical conductivity of a material due to pores was determined. A non-trivial finding is that the best prediction of the cross-property coefficient is obtained in the framework of non-interaction approximation. © 2006 Elsevier B.V. All rights reserved. Keywords: Cross-property connection; Metal foams; Effective properties; Elasticity; Conductivity 1. Introduction Metal foams are highly porous materials with cellular struc- ture. Due to this, they possess an excellent combination of mechanical properties (strength and stiffness) at the low weight, absorb high impact energies regardless of the impact direction, are electrically and thermally conductive, and are highly efficient in electromagnetic shielding and vibration damping. As men- tioned by Grenestedt [1] aluminum foams seem to have a poten- tial to greatly outperform the polymer foams (due to mechanical properties) and honeycomb structures (due to environmental properties). Structure and properties of metal foams (and cel- lular solids, in general) are discussed in detail in books [2,3]. A number of theoretical and experimental papers have been published on macroscopic behavior of the metal foams during last decade. Various constitutive laws have been suggested for the characterization and modeling of the macroscopic properties of the metal foams as functions of porosity p. Most of them, how- ever, contain fitting parameters (see review [4]), which indicates that the derivation of the microstructure-property relationships for open or closed-cell foams is still not an accomplished issue. ∗ Corresponding author. Tel.: +1 505 646 3322; fax: +1 505 646 6111. E-mail address: igor@me.nmsu.edu (I. Sevostianov). Semi-empirical modeling is usually based on percolation the- ory [5]. There, the effective property K behaves as a power of 1 - p: K = K 0 (1 - p) t (1.1) where K 0 is the corresponding property of the cell wall mate- rial. Experimentally measured properties of the foam can be fitted to (1.1) and the exponent t can be determined (see, for example [6]). The main disadvantage of this approach is that the exponent may be different for different properties and its micromechanical meaning is unclear (and, therefore, cannot be strictly predicted from microstructural parameters like shape and size of the pores). In Section 3, however, we show that for the electrical conductivity exponent t has very clear micromechan- ical sense and can be evaluated from the foam morphology. For elastic properties, such evaluation can be done approximately (see Section 4). Semi-numerical model was proposed [7,8] in the context of calculation of the Young’s modulus and the yield stress of closed- cell foams. In these papers, however, the material is idealized as a perfectly periodic structure and the influence of the perturbation of periodicity is not discussed. Several micromechanical models for the overall elastic mod- uli of the closed-cell foams were analyzed in [1]. Substantial 0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.01.064