A two-scale micromechanical model for aluminium foam based on results from nanoindentation

• Using a bottom-up approach for prediction of effective properties via a multi-scale model.
• Employing several advanced methods (e.g. nanoindentation, FFT-based homogenization) for the analysis.
• Application of the methodology to the microscopically inhomogeneous and highly porous material.
• Reduction of the foam geometrical complexity in the model.
• Verification of the proposed model by experiments.

The main aim of this paper is to develop and verify simple but effective model for elastic properties of a porous aluminium foam system and to compare results received from experimental micromechanics with solutions given by analytical or more advanced numerical methods. The material is characterized by a closed pore system with very thin but microscopically inhomogeneous pore walls (∼0.1 mm) and large air pores (∼2.9 mm). Therefore, two material levels can be distinguished. The lower level of the proposed model contains inhomogeneous solid matter of the foam cell walls produced from an aluminium melted with admixtures. Elastic parameters as well as volume fractions of microstructural material phases at this level are assessed with nanoindentation and effective properties computed via analytical and numerical homogenization schemes. The effective Young’s modulus of the cell walls was found close to 70 GPa irrespective to the used homogenization procedure.The higher model scale contains homogenized cell walls and a significant volume fraction of air voids (91.4%). Since analytical schemes fail to predict effective properties of this highly porous structure, numerical homogenization based on a simple two dimensional finite element model is utilized. The model geometry is based on foam optical images from which an equivalent beam structure is produced using Voronoi tessellation. Effective foam Young’s modulus was found to be 1.36–1.38 GPa which is in relation with ∼1.45 GPa obtained from uniaxial compression experiments.