Effect of Lateral Constraint on the Mechanical Properties of a Closed-Cell Al Foam: Part II. Strain-Hardening Models

Experimental results, presented in the companion article, show that the compressive deformation of a closed-cell Al foam under lateral constraint is characterized by significant strain hardening. This enhanced hardening is due to the change in stress state from uniaxial to triaxial, which additionally contributes to friction between the deforming foam and the walls of the constraining sleeve. Detailed analysis, employing two different types of deformation models, is presented in this article in order to rationalize the experimental observations. In the heterogeneous model, it is assumed that plastic deformation is similar with and without constraint and that it occurs via collective plastic collapse of cells. The bands, thus formed, elastically bear the lateral stresses and give rise to friction. In the homogeneous deformation model, it is assumed that the deformation mode is different under constraint and involves uniform densification, which leads to inherent hardening as well as additional friction. By comparing the model predictions with experimental observations, it is suggested that the plastic strain hardening of the metallic foam under constraint is due, in equal measure, to the triaxial state of stress and friction. Mechanistically, the material deforms principally by collective cell collapse, though there is some evidence of concurrent homogeneous deformation.