Quantitative relationships between cellular structure parameters and the elastic modulus of aluminum foam

The accurate prediction of the elastic modulus of aluminum foam is important for the application in high-tech fields, e.g. in aerospace industry. However, the scaling law based on the Gibson-Ashby model did not achieve the precise prediction of elastic modulus, in absence of complex porous structural features. In this study, we extended the scaling law by introducing the topological and morphological parameters into the multivariate equation. The 3D numerical images of aluminum foam specimens were obtained by X-ray tomography method, and the nine structural parameters were calculated and analyzed. The results show that as the porosity increases from 77% to 91%, the highest frequency of sphericity and solid material thickness of the cellular structure remains practically constant, although the distribution of cell size becomes more dispersed. The edges connections and the Inter-Branches Angle (IBA) of aluminum foam remain unchanged for all the specimens. Seven structural parameters were introduced into the extended scaling law to predict the elastic modulus with a higher residual value R2 of 0.932, in contrast to the R2 of 0.702 for the conventional scaling law. Through a stepwise linear regression method, the extended scale method was simplified by removing redundant parameters, and still achieved the elastic modulus predictions with a residual value R2 of 0.929. The remaining structural parameters in the extended scaling law, i.e. relative density, solid material thickness, and sphericity, were supposed to independently influence the elastic modulus, according to the covariance analysis. The three independent parameters offer the possibility to accurately predict and regulate the mechanical properties of aluminum foam.