Microstructural characterization and constitutive modeling of deformation of closed-cell foams based on in situ x-ray tomography

Polymethacrylimide (PMI) foams own the highest specific stiffness and strength of all foams. In situ x-ray micro computed tomography (CT) is used to map three-dimensional (3D) microstructures of this representative closed-cell foam under quasi-static compression. The strain fields obtained via digital volume correlation reveal divergent types (discrete or spreading) of deformation banding for the PMI foam with different densities (52 or 75 kg m(-3)). Significant cell collapse occurs in the deformation bands, leading to similar to 40% reduction of the mean cell size, and alignment of cell orientations. Microstructure-based finite element analysis confirms that elastic buckling of cell walls dominates cell collapse, and the buckling strength of walls depends highly on their thicknesses and inclination angles. An edge segmentation technique is then used to quantify the morphology and buckling strength index of cell walls. The spatial distribution of the weakest 3% cell walls correlates well with the modes of deformation banding. Based on elastic buckling of cell walls, new analytical models are developed to predict the strength-density scaling law and stress-strain curves of the PMI foam, which agree well with the experimental results.