A Numerical Study on the Uniaxial Mechanical Properties of Metal Foams with Spherical Cellular Structure

Metal foams as a new class of materials with interesting properties such as high stiffness and strength to density ratios, capacity to absorb impact energy, and reproducibility, are rapidly growing their share in advanced materials market. However, due to their porous microstructure, experimental investigations of their properties are not trivial and normally need rigorous procedures and high end equipments. Accordingly, there is a growing research interest towards the numerical modeling of their cellular structure in which the following three kinds of models have been commonly employed: 1) structures based on a unit cell or a building block, (2) random Voronoi diagrams, and (3) CAD data provided by Xray micro-computed tomography. In the current study, the mesostructure of aluminum foam produced by the brazing technique is simulated as a connected assembly of spherical shells. The latest inward packing scheme from the set of constructive algorithms is incorporated to efficiently pack the spheres in space. The Gamma distribution is used to control the cell diameters. Three mean values of 3, 4, and 5 mm and two variances of 0.5 and 1.0 mm are assumed for the radii of spheres and cubic specimens of 50 mm are generated. Two assumptions of constant thickness and constant thickness to radius ratio have been applied to the spherical shells. Two relative densities of 0.05 and 0.1 have been examined in the current study. A code is written to automatically transfer these geometrical data to ABAQUS FE program. The models are then meshed in 1 mm S4R shell elements. Tie contacts are defined between neighbor spheres. Furthermore, self contact is used to prevent any probable penetrations in the models. The foaming material is assumed to be AL 3003 H12 with elastic-perfectly plastic behavior. Next, the uniaxial load is applied by means of two rigid planes and the stress-strain curves are extracted. Main attention has been paid to the elastic modulus and initial yield stress of foam. It is observed that keeping the mean value of the radius and increasing its variance lead to the generation of more small spheres within the microstructure which itself increases the number of interactions inside the foam and thus increases elastic modulus and yield stress. The results also show that, for both thickness assumptions made here, increasing the mean radius of spheres decreases the number of spheres and their interaction points and subsequently weakens their uniaxial mechanical properties. Furthermore, compared to foams generated based on the constant thickness to radius ratio assumption, the presence of thick small spheres in foams with cells of constant thickness makes them stiffer and stronger. This effect is more pronounced in foam with higher densities.