The load–compression behavior of a foam reflects its geometric structure and the physical properties of the matrix polymer. Quantitative relations between these parameters have been established in the present study. Based on both theoretical analyses and experimental data obtained on a flexible polyurethane foam, it is shown that the compressive stress can be factored into the product of two terms: (1) a dimensionless function of the compressive strain, ψ(ε), calculated from experimental load–compression data and reflecting the buckling of the foam matrix; and (2) a factor, εEf, where Ef is the apparent Young's modulus of the foam (which is a function primarily of the modulus of the base polymer E0 and of the volume fraction of polymer, φ). Thus the compressive stress behavior of a foamed polymer is determined by E0, φ, and the matrix geometry, the latter described by the function ψ(ε). Using these established relations, it now is possible to delineate precisely the structural features a foam must possess—density, cell shape and size distribution, and modulus of the base polymer—to meet a given load–compression specification.

SynopsisQuantitative relationships between the load-compression behavior and the physical characteristics of the foam matrix, previously reported for flexible systems, have now been extended to brittle foams. The shape of the compression curve is expressed in terms of fi(~), a dimensionless function of the compressive strain, while the stiffness, or load-bearing capacity, is defined by El, the apparent Young's modulus. Because the brittle matrix breaks-rather than flexes-when compressed, a brittle foam exhibits a flatter and wider plateau in the load-compression curve than a rigid (but ductile) foam of equivalent density, cell geometry, and Ej. These differences are expressed quantitatively by + ( t ) . It is important to distinguish between brittle foams and rigid, but ductile, foams. Since both types may exhibit the same stiffness, this distinction, particularly significant in energy absorbing applications, often is not considered in designing foam structures. Using the relationships established in this report, it is now possible to delineate precisely the characteristics a brittle foam must possess to meet a given load-compression specification.

synopsisThe energy-absorbing characteristics of a foam are determined by its load-compression response, and hence reflect the geometric structure and physical properties of the matrix material. In this report, the energy-absorbihg characteristics are expressed in terms of three dimensionless quantities: (1) K , the energy-absorbing efficiency, (2) I , the impact energy per unit volume divided by E,, and (3) I / K , the maximum decelerating force per unit area divided by E,, where E l is the apparent Young's modulus. Using the calculation procedures described in this report, it is now possible to delineate the geometric structure and physical properties a foam matrix must possess to meet a given energy absorption specification. This approach shows that: (1) the energy-absorbing characteristics of a brittle foam are superior to those of a ductile foam, ( 2 ) the optimum energy-absorbing foam has a large cell size, a narrow cell size distribution, and a minimum number of reinforcing membranes between the cells, (3) foam composites offer no significant advantage over a single foam, arid (4) the optimum energy-absorbing region obtains over a tenfold change in impact vebi5ty and can be extended in a given system only if the foam stiffness increases while the impact velocity is increased, as in a fluidfilled foam.

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Open-cell foams show abnormally large mechanical damping due to the energy dissipated in forcing air in and out of the foam during a deformation cycle. This pneumatic damping has recently been treated theoretically and experimentally. The dependence upon the test-piece dimensions, the frequency of deformation and the viscosity of the fluid has been shown to be in good agreement with the theoretical predictions. The dominant property of the foam structure is its permeability to fluids. This has also been measured for a number of different foams and related to their structural features by means of a simple model. A review is given of these developments.