Keywords: aluminium foam, nanoindentation, identification, inelasticity, finite element method.

The paper is focused on the modeling of inelastic behavior of porous aluminium foams with closed cells. Very thin pore walls (~100µm) prevent conventional experimental techniques to be used for the estimation of the foam microlevel material parameters. Therefore, nanoindentation was employed as a key experimental technique for this task. First, elastic and inelastic parameters were identified at the level of cell walls by using sharp and spherical indenters. Sharp indenters provide information on local elastic parameters of distinct microscale phases within the cell wall whereas spherical indenters allow for estimation of plastic parameters based on analytical construction of a stress-strain diagram. In this construction, indentation strains and stresses are converted to their uniaxial counterparts. Second, the indentation process was modeled with the finite element method and material constants were obtained through the best fit of the indentation curve. Elasto-plastic model with linear isotropic hardening was assumed for both cases.

A custom optimization procedure for the estimation of parameters using the finite element method was developed. A very good agreement in terms of least square errors was achieved between the experimental and the fitted curves. Good correlations between the analytical and numerical approaches were found for the cases of elastic modulus and yield strength of the cell wall (errors <19%). Larger sensitivity was found for the hardening parameter (errors <28%) that was characterized also by increased experimental variability between the tested material locations.

Regardless the uncertainties in input parameters, the overall inelastic behavior of the foam was qualitatively captured with a simplified two-dimensional beam model. In contrast to elastic calculations, it was found that the geometry of individual beams plays an important role in capturing inelastic behavior and cannot be neglected even in the simplified two-dimensional case. The finite element model modifications consisting of an introduction of a deformation localization band in the model led to the necessary reduction of the yield point. Then, the model was able to quantitatively reproduce experimental observations.

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