Performance Limits for Stiffness-Critical Graphitic Foam Structures. Part I: Comparisons with High-Modulus Foams, Refractory Alloys and Graphite-Epoxy Composites

Abstract

Graphitic foams offer exciting potential for mass savings in structures. The present investigation seeks to identify the potential mass savings and corresponding dimensional tradeoffs for application of such materials to simple, stiffness-critical structural elements, in support of an in-house materials development program. A hypothetical family of graphitic foams having ligament stiffness properties identical to those of P120 graphite fiber is considered; the stiffness properties of the hypothetical foams are viewed as realistic upper bounds for the performance of this class of materials. A representative refractory alloy, AS4/3501-6 unidirectional and [0/90], composites, and commercially available SiC and amorphous carbon foams are compared to the graphitic foams for application to plates in bending and buckling, beams in bending and buckling, and tension bars, in analogy to Gordon [1] and Ashby [2,3]. The mass and thickness ratios of the foams to the comparison materials for the chosen applications depend primarily on the Young's modulus of the foam, which is modeled according to a well-established relation due to Gibson and Ashby [4]. The hypothetical foams are found to offer stiffness properties leading to structural masses ranging from competitive to dramatically improved versus the described comparison materials. Increased structural dimensions are often associated with the savings in mass. Strength properties have not been considered in the present modeling, as processing issues still need to be resolved and the resulting defect distributions are unknown; foams of substantial promise are, however, being fabricated in small quantities.

Carbon Foam Core Composite Sandwich Beams: Flexure Response

“…Owing to the inherent brittleness of the foam, realistic structural elements incorporate foam as the core in a sandwich construction, where the face sheets bear most of the in-plane loads as well as any transverse bending stresses, while the core resists deformation perpendicular to the in-plane direction, and provides shear rigidity along the planes perpendicular to the face sheets [15]. The potential weight savings and dimensional tradeoffs of using graphitic foam were analytically identified by Hall and Hager in simple, stiffness-critical structural elements, such as plates and beams, subjected to flexure and buckling, or tension [16].…”

Elastic Properties of Foams with Tetrakaidecahedral Cells Using Finite Element Analysis

“…These tetrakaidecahedral foams have held the interest of researchers for decades. Microcellular graphitic carbon foams were first developed at the US Air Force Research Laboratory in the 1990s 3 . Clearly, it has been proven that the repeating unit cell of this foam can be approximated by a regular tetrakaidecahedron 4 .…”

Elastic Properties of Open-Cell Foams with Tetrakaidecahedral Cells Using Finite Element Analysis

“…= cross-sectional area of the strut a 1 = length of the representative volume element a 2 = width of the representative volume element a 3 = height of the representative volume element b = dimension of the top and the bottom squares of the elongated tetrakaidecahedron unit cell C = stiffness matrix of the foam d = length of the side of the equilateral triangle cross section f ij = force in direction i when displacement is applied in direction j I x , I y = moment of inertia in the X and the Y directions E i = Young's modulus along axis i E s = elastic modulus of the strut material G ij = shear modulus in direction j on the plane for which the normal is in direction i J = torsion constant L = dimension of the long edges of the elongated tetrakaidecahedron unit cell l = length of each individual edge (strut) of the equisided tetrakaidecahedron r = radius of the three-cusp hypocycloid cross section V = volume of the representative volume element u i = displacement in the i direction u i = difference in translational displacement along axis i i = difference in rotational displacement along axis i " ij = macrostrain " 0 = applied macrostrain " 1 , " 2 , " 3 = strain components in the principal X, Y, and Z directions ij = Poisson's ratio s = Poisson's ratio of the strut material s = density of the strut material = s = relative density of the foam I. Introduction C ELLULAR solids are materials made out of solid strut or thin platelike structures bridged together.…”

“…It has been accepted that packed in a body-centered cubic structure, a tetrakaidecahedron (a 14-faced polyhedron) satisfies the minimum surface energy condition for monodispersed bubbles [2]. Microcellular graphitic carbon foams were first developed at the U.S. Air Force Research Laboratory in the 1990s [3]. Clearly, it has been proven that the repeating unit cell of this foam can be approximated by a regular tetrakaidecahedron [4].…”