Idealized Strut Geometries for Open-Celled Foams
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IDEALIZED STRUT GEOMETRIES FOR OPEN-CELLED FOAMS
JOSEPH W. HAGER Wright Laboratory, WL/MLBC, Wright-Patterson AFB, OH 45433-6533
ABSTRACT Open-celled foam is modeled as a network of struts formed by the nucleation, growth and intersection of uniform spherical bubbles arranged in a regular three-dimensional array. The number of struts per unit cell and their characteristic geometry and orientations depend on the bubble-centering algorithm chosen to define the array and on the degree of bubble intersection. A foam model based on a body-centered cubic arrangement of uniform spherical bubbles is used to compare strut geometries over a range of bubble interferences. The model predictions are compared to the microstructures observed in amorphous carbon foam. The significance of these idealized foam results for graphitic carbon foams is discussed. INTRODUCTION As shown in Fig. 1, reticulated foams produced by physical or chemical blowing processes can be described as three-dimensional truss structures [1]. The behavior of a truss stucture subjected to either mechanical or thermal load depends on the local properties of the truss strut materials, the individual strut geometry and on the overall truss architecture. As processing routes are developed to create reticulated carbon foams with aligned graphitic struts, the local material properties may approach those realized in carbon fiber. The theoretical limits of the behavior of a foam with carbon fiber strut properties, subjected to a mechanical or thermal load, could be analyzed if the truss geometry were known. With a reasonable truss geometry model one could also explore the effects of processing-induced variations, such as nucleation density, strut strain, length-to-breadth ratio, etc. on the global behavior of the strut network. Microstructural evaluations [2] highlight the general features of reticulated foam, including the triangular character of the strut cross-section and the four-strut intersection points. Previous foam truss models have either ignored the actual strut arrrangement and cross-sectional character altogether [3], have assumed the the intersections to be based on non space-filling geometries [4], or have ignored the structure of the strut intersections. This paper describes the
Figure 1 A reticulated polyurethane foam (FOAMEX®) exhibiting the characteristic triangular strut network of these open-celled structures. Mat. Res. Soc. Symp. Proc. Vol. 270. @1992 Materials Research Society
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structure of a space-filling foam unit cell with idealized strut geometry, and elucidates its dependence on the blowing process used to create it. MODEL In the foam blowing process, a liquid containing dissolved gas is processed so that the liquid becomes supersaturated with the gas. Supersaturation results in the nucleation of bubbles either spontaneously [5] within the melt or on the surfaces of a finely-divided, entrained heterogeneous bubble nucleating agent [6]. A number of gas bubbles, No, are assumed to simultaneously nucleate, at time zero, on a lattice w
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