Rotationally Symmetric Limit Surface for Hard Isotropic Foams

Hard foams are materials with micro-heterogeneous properties depending on cell morphology, local micromechanical behaviour and defects. As a part of the component, hard foams are subjected to multiaxial loads, which must be limited by strength criteria in the design process. The phenomenological strength criteria define the limit surfaces in the principal stress space. For hard foams, the limit surfaces are closed. Schleicher criterion as second order ellipsoid is the basic standard for hard foams. Nowadays, it is not sufficient to properly approximate the measured data of hard foams to make reasonable extrapolations. By decomposing into linear factors, Schleicher criterion is reformulated as a function of two hydrostatic nodes which determine the strength at hydrostatic tension and hydrostatic compression. By weighting these nodes appropriately, resulting in two additional parameters for any polynomial series, measured data can be well approximated. Using this decomposition, a unified I1-substitution is derived to extend the pressure-insensitive criteria. The criterion parameters are fitted to the measured data. Although superimposed tension-torsion and compression-torsion tests are often performed, this data alone cannot be reliably extrapolated to the hydrostatic tension and hydrostatic compression strengths. Therefore, conservative fitting is recommended. The simplest objective functions are proposed to compare the optimal fitting variants. Ratios, analogous to the elastic Poisson’s ratios at tension and compression, as well as the strength ratio for the torsion bar, are introduced to characterise the limit surface. The suggested procedure is demonstrated by analysing the series of measurements carried out on open-cell aluminium foams. We discuss five series with different data sets and present the best fitting results in Burzyński-plane. The relevant values and ratios are summarised in tables for easy comparison.