Microstructural characterization of metal foams: An examination of the applicability of the theoretical models for modeling foams

Establishing the geometry of foam cells is useful in developing microstructure-based acoustic and structural models. Since experimental data on the geometry of the foam cells are limited, most modeling efforts use an idealized three-dimensional, space-filling Kelvin tetrakaidecahedron. The validity of this assumption is investigated in the present paper. Several FeCrAlY foams with relative densities varying between 3 and 15% and cells per mm (c.p.mm.) varying between 0.2 and 3.9 c.p.mm. were microstructurally evaluated. The number of edges per face for each foam specimen was counted by approximating the cell faces by regular polygons, where the number of cell faces measured varied between 207 and 745. The present observations revealed that 50–57% of the cell faces were pentagonal while 24–28% were quadrilateral and 15–22% were hexagonal. The present measurements are shown to be in excellent agreement with literature data. It is demonstrated that the Kelvin model, as well as other proposed theoretical models, cannot accurately describe the FeCrAlY foam cell structure. Instead, it is suggested that the ideal foam cell geometry consists of 11 faces with 3 quadrilateral, 6 pentagonal faces and 2 hexagonal faces consistent with the 3–6–2 Matzke cell.

Research highlights
► Over 50% of the cell faces of FeCrAlY foam microstructures are pentagonal.
► The Coxeter equations were used to determine cell characteristics.
► The Kelvin model does not agree with 90 years of compiled experimental data.
► Residual stresses in the could partly account for this discrepancy.
► The 3–6–2 Matzke cell is consistent with the FeCrAlY foam cell topology.