Keywords: nanoindentation, aluminium foam, multi-scale model, homogenization, elastic properties.

This paper focuses on the assessment of the effective elastic properties of closed-cell aluminium foams by means of a two-scale micromechanical model. The commercially available aluminium foam 'Alporas' was studied. The material is characterized by a closed pore system with very thin pore walls (~60 µm) and large air pores with close to spherical shape (equivalent pore diameter ~2.9 mm).

The lower level of the proposed model contains the inhomogeneous solid matter of the foam cell walls produced from aluminium melt with admixtures. Elastic parameters as well as volume fractions of microstructural material phases at this level are assessed with nanoindentation [1,2] and the effective properties are computed using analytical and numerical homogenization schemes [3]. Analytical estimates have been further checked with numerical FFT-based scheme [4] with very good agreement (less than 4 % error).

The upper level of the proposed model contains homogenized cell wall properties and a significant volume fraction of air voids (91.4 %). Analytical tools applied on the first level were used without success. Very poor estimates were given by the Mori-Tanaka or self-consistent arising from extremely high air content in the foam.

Since analytical schemes failed to predict effective properties of this highly porous structure, numerical homogenization based on a simple two-dimensional finite element model were utilized. The polished foam cross-section was scanned in high resolution and converted to a binary image. Pore centroids were detected, Delaunay triangulation and Voronoi tessellation were applied. An equivalent two-dimensional beam structure was produced from the Voronoi cell boundaries on a large domain (106x106 mm). Kinematic boundary conditions were prescribed around the domain which was subjected to homogenous macroscopic strain in an axial direction. Microscopic strains and stresses were evaluated in a significantly smaller area (20x20 mm and 30x30 mm) inside the domain to minimize the effect of the boundary conditions and the effective stiffness was computed for this area. The resulting Young's modulus of the foam was found to be 1.11-1.21 GPa which is in relation with experimental values reported in the literature. Slightly higher stiffness (E~1.45 GPa) was obtained in our macroscopic experiments in which Alporas blocks (30x30x60 mm) were subjected to uniaxial compression. Two-dimensional approximation underestimated the overall stiffness by 20-30 % compared to experimental values. The lower stiffness obtained from the two-dimensional model is likely as a result of the inability to capture additional confinement coming from the three-dimensional material microstructure or from the insufficient RVE size.

1

J. Nemecek, V. Králík, J. Vondrejc, J. Nemecková, "Identification of Micromechanical Properties on Metal Foams using Nanoindentation", in B.H.V. Topping, Y. Tsompanakis, (Editors), "Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 125, 2011. doi:10.4203/ccp.96.125

2

J. Nemecek, V. Šmilauer, L. Kopecký, "Nanoindentation characteristics of alkali-activated aluminosilicate materials", Cement and Concrete Composites, 33(2), 163-170, 2011. doi:10.1016/j.cemconcomp.2010.10.005

3

A. Zaoui, "Continuum Micromechanics: Survey", Journal of Engineering Mechanics 128, 2002. doi:10.1061/(ASCE)0733-9399(2002)128:8(808)

4

J. Zeman, J. Vondrejc, J. Novák, I. Marek, "Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients", Journal of Computational Physics, 229(21), 8065-8071, 2010. doi:10.1016/j.jcp.2010.07.010

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £65 +P&P)