A Numerical Study on Uniaxial Behavior of Aluminum Replicated Foams with Regular Microstuctures

It is a decade that replication process has gained lots of interests in the production of open-cell metallic foams. Replication process usually involves the steps of preparing porous preform، filling the free spaces by foaming material، and removing the space-holders (usually by dissolution). Independent control of pore size، pore shape، and relative density، the possibility of producing foams with pores of few microns، nearly fault free and uniform structures critical in conducting reproducible mechanical tests، applicability to various metal and alloys، and the simplicity of producing functionally graded structures are some of the benefits making replication process quite appealing for researchers involved in the field of cellular solids. This study assumes that the space-holders are initially monomodal spheres packed in regular simple cubic (sc)، body-centered cubic (bcc)، and face-centered cubic (fcc) configurations. However، the primary shapes and structures of these assemblies undergo considerable changes in the process of compaction. Thus، the realistic numerical simulation of replicated foams is required to address this compressing stage. Accordingly، the physical processes of cold isostatic pressing and preform removal (dissolution) is simulated using nonlinear finite element method and voxel element method، respectively. A code is written to take the deformed shape of a preform (as a set of finite elements)، efficiently invert the geometry، and create the FE model of replicated structure as a set of voxel elements. Three pore sizes of 0. 1، 1، and 10 mm are assumed. The corresponding unit cells are compressed to reach the desired void volume fractions of around 5 to 25%. Assuming an aluminum alloy as the foaming material، uniaxial compressive load is applied to the samples and their elastic moduli، Poisson’s ratios، and yield stresses are extracted. In the range of preforms and pore sizes simulated، no cell size dependency of the results has been observed. The fcc structure، owing to its oblique beam-like elements، shows the most flexible behavior. On the other hand، the sc structure is found the stiffest in the group. The dependencies of elastic and yield properties to relative density increase by migrating from the sc to the bcc and next to the fcc structures. More in-depth study of the results reveals that the bcc samples of higher relative densities have inherent elastic behaviors near those of the sc specimens. From yield stress point of view، the bcc and fcc foams are found superior and inferior، respectively. The computed yield stresses are also compared to some previously reported analytical estimations from which the strength level of each structure is identified. The power law exponents of numerically calculated yield points are shown to be less than their empirical counterparts. This is attributed to the random structure of actual foams and their imperfect struts. Finally، it needs to note that، the extended application of the developed computational procedure to the random assemblies of spherical preforms is already under investigation.