On the compressive response of open-cell aluminum foams
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This study is concerned with the mechanical behavior of open-cell aluminum foams. In particular the compressive response of aluminum foams is analyzed through careful experiments and analyses. The microstructure of foams of three different cell sizes was first analyzed using X-ray tomography. This included characterization of the polyhedral geometry of cells, establishment of the cell anisotropy and statistical distribution of ligament lengths, and measurement of the ligament cross sectional area distribution. Crushing experiments were performed on various specimen sizes in the principal directions of anisotropy. The compressive response of aluminum foams is similar to that of many other cellular materials. It starts with a linearly elastic regime that terminates into a limit load followed by an extensive stress plateau. During the plateau, the deformation localizes in the form of inclined but disorganized bands. The evolution of such localization patterns was monitored using X-ray tomography. At the end of the plateau, the response turns into a second stable branch as most cells collapse and the foam is densified. The crushing experiments are simulated numerically using several levels of modeling. The ligaments are modeled as shear-deformable beam elements and the cellular microstructure is mainly represented using the 14-sided Kelvin cell in periodic domains of various sizes. Other geometries considered include the perturbed Kelvin cell, and foams with random microstructures generated by the Surface Evolver software. All microstructures are assigned geometric characteristics that derive directly from the measurements. Unlike elastic foams, for elastic-plastic foams the prevalent instability is a limit load. The limit load can be captured using one fully periodic characteristic cell. The predicted limit stresses agree with the measured initiation stresses very well. This very good performance coupled with its simplicity make the characteristic cell model a powerful tool in metal foam mechanics. The subsequent crushing events, the stress plateau and desification were successfully reproduced using models with larger, finite size domains involving several characteristic cells. Results indicate that accurate representation of the ligament bending rigidity and the base material inelastic properties are essential whereas the randomness of the actual foam microstructure appears to play a secondary role.