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COMPOSITE FOAMS Introduction Foams or cellular materials are materials that have a regular arrangement of cells and solid struts as shown in the schematic in Figure 1. Composite polymer foams are materials defined as a polymer phase with voids and an additional solid or hollow phase distributed throughout the polymer. They can be thought of as conventional single-phase polymer foams with an additional dispersed solid phase. Thus, the term composite foam excludes conventional, single-phase foams made by expanding polymers such as polystyrene, polyurethane, or polypropylene (see CELLULAR MATERIALS; MICROCELLULAR PLASTICS). Also excluded are structures with single-phase core materials and covered with a solid skin because the second phase, the skin, is not dispersed throughout the polymer phase. The fact that voids are engineered into the material results in the most attractive feature of foams, namely low density leading to high specific properties. Composite foams can be categorized as follws: syntactic foam, particlereinforced foam, and fiber-reinforced foam. The additional solid constituents are incorporated to enhance certain properties important to the function of the composite foam part such as stiffness, strength, electrical or thermal conductivity, etc. Examples of foams containing particles or fibers are shown in Figures 2a and 2b. Figure 2a shows tungsten particles in polystyrene foam (1), while Figure 2b shows Kevlar fibers in a poly(vinyl chloride) foam (2). A syntactic foam is a special type of particle-reinforced foam where the reinforcing particle is hollow. In this case, the additional dispersed solid phase also contains void. Figure 3 is a photograph of Lockheed’s Deep Quest submarine, which shows extensive use of a composite foam; a syntactic foam material made from micrometer-sized, hollow glass microballoons (MB) in an epoxy matrix (3). The deep submersible vehicle Deep Quest was designed, built, and operated by Lockheed Missiles & Space Co. Its broad program of research was available to both commercial activities and the U.S. Navy. Deep Quest was launched in June 1967, and it operated from Lockheed’s laboratory in San Diego. Deep Quest held the record, for a time, of diving to 2700 m. The submersible was designed and equipped for a variety of missions, including salvage, seafloor survey and inspection, and other special assignments. Deep Quest made its last dive on 9 September 1980. In this article, we review the processing, characterization, properties, and applications of composite foams and highlight the advantages they have over traditional single-phase foams. General Characteristics of Foams. Foams, in general, and composite foams, in particular, can provide interesting combination of physical and mechanical properties. Among these are the following characteristics: (1) Very low density: the density is significantly decreased by the presence of cells containing gas (2) High specific stiffness and compressive strength, ie, stiffness and strength divided by density: these can be further improved via sandwich construction (two dense faces and a foam core) Encyclopedia of Polymer Science and Technology. Copyright John Wiley & Sons, Inc. All rights reserved.

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Fig. 1. Construction of a single cell making up a foam.

(3) Excellent energy absorption characteristics (4) Noise and vibration control

Processing and Microstructure The processing of composite foams is done in much the same way as the processing of single-phase foams and can be classified under the broad categories of (1) Introduction of a gas a. Physical blowing agent b. Chemical blowing agent c. Mixing

Fig. 2. SEM image of tungsten particle reinforced polystyrene.

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Fig. 3. The Deep Quest submersible made by Lockhead for U.S. Navy made extensive use of hollow glass microspheres/epoxy syntactic foam. Courtesy of Naval Undersea Museum, Keyport, Wash.

(2) Removal of sacrificial cell-forming material (3) Bonding together of spheres, powders, fibers, etc It is important to remember that the objective of processing a material into foam material is to intentionally introduce voids in the finished material. The size and distribution of the voids will vary depending on the process chosen, which in turn will control the material properties. Below, we provide highlights of each of the three processing methods with examples, advantages, and disadvantages. The first method is to introduce gas into the composite material while the material is solidifying or curing. In case of the starting polymer matrix material being a thermoset, one should be able to control the degree of cure, while in the case of a thermoplastic there must be careful control of the temperature during the foaming process. A physical blowing agent is a material that undergoes vaporization during processing. Examples of this are hydrochlorofluorocarbons and pentane. Also included in this category are gases such as nitrogen and carbon dioxide, which dissolve into the polymer material under high pressure. When the pressure is released, the dissolved gas comes out of the solution, blowing the polymer into a foam. Chemical blowing occurs through (1) decomposition of a chemical additive to the polymer or (2) when using a thermosetting matrix, one of the reaction products is in the gaseous phase. A well-known example is a “hydrogen-blown” polydimethylsiloxane (PDMS) reinforced with silica as shown in Figure 4, and the simplified chemistry of which is shown in Figure 5. The actual chemistry involved in making the foams is very complex and involves several molecular weight PDMS reactants in addition to cross-linking agents and tin octoate catalyst. Another example of a chemically blown foam

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Fig. 4. (a) TEM micrograph showing the silica reinforcement in a PDMS matrix; (b) SEM micrograph of the structure obtained from a silica-reinforced PDMS hydrogen-blown foam.

occurs in the polyurethane material which can generate CO2 as a product of the curing reaction. Another interesting chemically blown material occurs in manufacturing hollow phenolic microspheres, a material extensively used as a component in syntactic foams. The patent (4) identifies many examples of chemical blowing agents that decompose and blow individual polymer droplets into hollow structures. Included are carbonates, sulfites, nitrates, and bicarbonates. When a chemical blowing agent evolves from a cross-linking reaction, careful control is required of the rheological properties of the polymer and kinetics of the reaction generating the blowing agent. If the gas evolves and the resin does not have a high enough viscosity, the foam will be overblown and collapse. The interplay among the reinforcement, viscosity, and gas generation also has direct effect on the cell size in the finished structure.

Fig. 5. Chemical reaction illustrating the chemistry involved in a hydrogen-blown PDMS foam.

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Mechanical mixing or stirring is another way of introducing voids into a material. It is easy to achieve, but very difficult to control, the type, size, distribution, and volume fraction of voids. The procedure involves vigorously stirring the polymer melt, thus entraining air. Removal of sacrificial material is an excellent method of ensuring cell size uniformity; however, in order that the method be suitable for manufacturing, a very high volume of sacrificial material must be introduced into the material so that the porosity approaches 100% open-celled. This allows for removal of the sacrificial material in a reasonable time period. A common foam prepared by this method is silica-reinforced PDMS. The PDMS in this case starts out as a gum (high viscosity polymer), and urea prills with dimensions of the desired cell size are introduced by milling. Once a high enough loading of the urea prills is achieved to ensure an open cell structure, the material is molded into the desirable geometry and cured. At this point the composite foam contains the cross-linked PDMS polymer matrix, silica reinforcement, and the sacrificial urea prills. Urea, being soluble in water, is then leached out by placing the part in a water bath. The leaching process can be accelerated if the bath is agitated. A drawback of this method is that the leaching process is efficient only for thin cross sections. Figure 6 shows a silica/PDMS foam from which the urea particles have been leached out. The last category is the bonding together of spheres, powders, and fibers. This is a broad category that encompasses syntactic foams and frit-type material.

Fig. 6. TEM micrograph showing a silica/PDMS foam from which the urea particles have been leached out.

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Fig. 7. Schematic structures of different syntactic foams: (a) two-phase foam, (b) threephase foam, and (c) four-phase foam.

Syntactic foams consisting of hollow spheres distributed in a matrix have become quite important. The word syntactic comes from Greek, meaning “to arrange parts together in a unit.” Typically, the resin matrix phase in syntactic foam has a large amount of open, interstitial voids. Strictly speaking, the matrix can be a polymer, metal, or ceramic. The polymer matrix can be epoxy, phenolic, ester cyanate, bismalemide (BMI), etc. Hollow spheres range in size from hundreds of nanometers to a few millimeters. When the hollow spheres are in the micrometer-size range, they are commonly referred to as microballoons. They may consist of glass, carbon, metal, polymer, or ceramic materials, although most commonly hollow glass microspheres (20–200 µm) are used. The microballoons can be mixed in a polymer either in a liquid or in a solid powder form. By far, the most common syntactic foam is the glass microballoon/epoxy matrix material. Syntactic foams can be further subdivided into two-, three- or four-phase foams. The microstructure of a two-phase foam has only the polymer binder and hollow microspheres (see Fig. 7a). Note that there is enough binder phase to fill the volume between microspheres. In contrast, in a three-phase material there is not enough binder volume to fill the spaces between microspheres (Fig. 7b). The voids in the binder constitute the third phases. Of course, fibers can be added to make the fourth constituent in the composite foam (Fig. 7c). A schematic of the processing of a syntactic foam by mixing carbon microballoons in a BMI polymer binder is shown in Figure 8. Short fibers can be added along with the microspheres. The addition of fibers can lead to an increase in mechanical properties, but good dispersion in the binder can be difficult (5–13). Figure 9a shows an optical micrograph of syntactic foam consisting of carbon microballoons and a small amount of BMI resin, while Figure 9b shows a higher magnification SEM micrograph wherein individual microballoons can be distinguished. The volume fraction of resin in this syntactic foam is about 8%. Syntactic foams are an attractive design option because they are relatively simple to make. Since the microballoons are hollow, the voids are inherently present and all that is required is to mix the microballoons into the desired polymer matrix. Phenolic microballoons, produced by Asia Pacific Microspheres, and Glass

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Fig. 8. Schematic of the construction of a three-phase syntactic foam (14).

Microbubbles, produced by 3M, are examples of microballoons that are readily available commercially. Cell Size. The cell size is an important microstructural parameter. Properties of composite foam depend on the cell size. Typically, one examines the cell structure in two-dimensional micrographs. The average diameter of a circular segment, d, can be obtained by taking the average of nominal cell diameters in a given micrograph. It is important to recognize that the average spherical diameter D is greater than the average circular segment diameter d obtained from a

Fig. 9. (a) Low magnification optical micrograph showing bulk structure; (b) SEM micrograph showing individual carbon microballoons/BMI syntactic foam (14).

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two-dimensional micrograph. This is because the cells are randomly truncated along the depth. The ASTM standard D3576 gives the following expression relating d to D: D=

4d π

It should be pointed out that three-dimensional images can be obtained by computer-tomography technique, which provides cell size and distribution in three dimensions.

Properties Some foam characteristics are present in both a single-phase foam and a composite foam. For example, both can be classified as either closed-celled or open-celled. If there is material forming the cell wall then it is classified as a closed-cell foam, while an open-celled foam has a discontinuous cell face as shown in Figure 1. They can be rigid or flexible and come in a wide range of densities. Density. The density of a composite foam material, ρ f , can be related to the density of the constituents and the void volume fraction by a simple rule of mixtures equation: ρf =

m1 + m2 + m3 + · · · + mi Vf

where m is the mass of constituent 1, 2, 3 . . . i, respectively, and V f is the bulk volume of foam that can usually be measured directly or calculated by the following equation: Vf = Vv + V1 + V2 + V3 + · · · + Vi where the subscript “v” indicates void and the other symbols are as indicated above. Because, in a syntactic foam, the reinforcing microballoons can have a wall thickness that varies from batch-to-batch, one can achieve a fixed density foam with various volume fractions of microballoons. The tap density of microballoons that have been made from the same material is an indirect measure of the wall thickness. Assuming that the particles arrange into the same packing factor (settle to the same volume fraction), the wall thickness increases as the tap density increases. Additionally, average dimension of microballoons and ratios of wall thickness to radius can be inferred. Despite the comparative nature of the tap density test, it is an important technique to characterize microballoons and using it can provide an extra degree of freedom in designing syntactic foams. It is the authors’ observation that phenolic microballoon manufacturers can control the tap density to ±0.002 g/cm3 . Relative Density. One very important parameter in regard to any kind of foam is its relative density ρ r , which is defined as the ratio of the foam density ρ f

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to the theoretical density of the solid material, ρ s : ρr =

ρf ρs

As the relative density ρ r of the foam increases, its cell walls become thicker. According to Gibson and Ashby (15), above a relative density of about 0.3, there occurs a transition from an open-cell foam to a closed-cell foam. In engineering practice, the parameter relative density, ρ r , becomes very useful because it is easy to determine: ρr =

ρf t =C ρs D

where ρ f is the density of the foam, ρ s is the density of cell wall material, C is a constant, t is the cell wall thickness, and D is the cell diameter. Almost all properties of foam are affected by and are a function of its relative density. Typically, the stiffness and strength increase with increasing relative density. In the case of a syntactic foam, at a constant volume of fraction of microballoons, a higher relative density implies a higher aspect ratio (wall thickness/diameter) of the microsphere. Dielectric Constant. The dielectric constant of a syntactic foam generally decreases linearly with decreasing relative density. Some silica microspheres have very low dissipation factors, which makes them suitable for low loss syntactic foams suitable for applications in radomes. Radomes require minimum absorption of electromagnetic energy (16). Elastic Constants. A number of expressions are available in the literature giving the elastic constants of the foam in terms of the elastic constants and volume fractions of the constituents. Following expressions are due to Nielsen (17): Shear modulus of the foam,  GF =

1 + ABφ2 G1 1 − Bψφ2

where GH  −1 (1 − φ2 ) (7 − 5ν1 ) G1 ψ≈1 + B=  A= φ2 2 GH (8 − 10ν1 ) φM +A G1 

In these expressions, G is shear modulus, a and b are respectively the inner and outer radii of the microballoon, ν is Poisson’s ratio, φ m is the maximum packing factor that can be achieved, and φ 2 is the volume fraction of microballoons. The maximum packing factor, φ m , is about 62.5% (18). The subscript H, S, F, and 1 indicate the hollow sphere, the solid sphere, the foam, and the polymer matrix, respectively. The shear modulus can be converted to Young’s modulus by

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the following equation valid for isotropic materials: E = 2G (1 − ν) In general, such equations due to Nielsen or others show a decrease in the modulus or stiffness of the foam with increasing amount of microspheres, assuming a constant wall thickness of the microspheres. The above analytical model will give a reasonable approximation when designing a syntactic foam material. There are examples of more complicated numerical models available throughout literature if more detailed analysis is desired. We refer the reader to Gibson and Ashby (15) for analytical relationships for elastic properties for both open- and closed-celled foam that are based on the properties of the unfoamed material and relative density of the foam. Stress–Strain Behavior in Compression. A representative schematic of the compressive stress–strain behavior of an elastic–plastic foam under uniaxial compression is shown in Figure 10. The curve shows a series of regimes. The first regime occurs at small strains and is characterized by elastic bending of struts. The long plateau region at medium strains is plastic yielding of the material. The final regime is densification, where the slope of the stress-strain curve increases rapidly. In this region, cells are collapsing, ie the top of the cell is touching the bottom. In this type of foam (eg polyurethane) full densification can occur and the slope of the stress–strain curve will approach the modulus of the unfoamed material. In practice, mechanical response of such a part in service depends on the amount of compression the part undergoes when installed. When a brittle composite foam is deformed in compression, the following common features are observed: (1) Density changes when a cellular material is deformed. (2) Plastic deformation occurs, which involves successive collapse of cells in localized bands.

Fig. 10. Generalized compressive response of an elastic–plastic foam.

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Fig. 11. Compressive behavior of a crushable carbon microballoons/BMI syntactic foam (14).

(3) Stress drops and becomes almost constant when only few noncollapsed cells are left. An example of crushable syntactic three-phase foam (microballoons undergo crushing) compressive stress versus apparent strain of a carbon microballoon/BMI, is shown in Figure 11. After an initial elastic compression, the microspheres in the foam start fracturing and the stress–strain curve starts to decrease and shows characteristic dips corresponding to isolated crushing of microballoons. Eventually, enough microballoons are broken along a section so that exfoliation or spalling occurs, which is indicated by the large dip in the curve. Continued loading in compression leads to a gradual decrease in the curve and loading of the fractured material that formed the walls of the microballoons. The behavior of the same syntactic three-phase foam as above under compressive cyclic loading is shown in Figure 12. In the elastic regime, the loading and unloading curves coincide, as expected, and no permanent set or damage results. This figure also shows that when unloaded after attaining the crushing strength

Fig. 12. Mechanical response of a crushable syntactic foam under compressive cyclic loading showing permanent damage on (——) cycle 1,770 MPa; ( ) cycle 6,700 Mpa; ( ) cycle 11,626 MPa; ( ) cycle 13,612 MPa; ( ) cycle 17,597 MPa.

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of some microballoons, there results a permanent damage. The magnitude of this permanent damage stabilizes with continued cycling. The strength of two-phase syntactic foam composites will decrease with decreasing content of hollow microspheres. This is due to two factors: a decreased load bearing cross-sectional area and a stress concentration effect of the microporosity. One can combine these effects in the following form (19): σ1 = k · σm (1 − Vv )

(1)

where σ 1 is the strength of the foam, σ m is the strength of the matrix, V v is the volume fraction of the porosity or voids, and 1/k is the stress concentration factor. This expression should give a reasonable approximation when the strength of the microballoon is negligible compared to the matrix surrounding it and applies to two-constituent syntactic foams. The reinforcing effect of these microballoons can be expressed as σ2 = (Vmb − Vv )σmb

(2)

where σ 2 is the strength contribution due to the microballoons, V mb is the volume fraction of the material that forms the microballoons, V v in the volume fraction of the voids, σ mb is the strength contributed by the material that forms the microballoons. Combining equations 1 and 2, we can write σc = σ1 + σ2 = k · σm (1 − Vv ) + (Vmb − Vv )σmb σc /σm = k(1 − Vv ) + (Vmb − Vv )σmb /σm = k − (k − Vmb σmb /σm )Vv This expression indicates the expected trend of decreasing strength with increasing void volume fraction in the composite foam. Okuno and Woodhams observed reasonably good agreement with experimental results when an appropriate choice was made of the stress concentration factor k. In three-phase composite foams, shown in Figure 9b, the compressive strength and modulus increase with increasing content of microballoons. In three-phase syntactic foams, where very little polymer binder is present, the strength of the microballoon can contribute to the syntactic foam strength. This is in contrast to a two-phase syntactic foam, where increasing microballoon content results in a decrease in density by the addition of microballoons. Unlike the twophase foam, in a three-phase syntactic foam an increase in the volume fraction of microballoons will result in a decrease in the interstitial voids and increase in mass because of the increase in total cell walls. Flammability, Smoke Density, and Toxicity. Along with the conventional mechanical and physical characteristics (stiffness, strength, toughness, density, thermal conductivity, etc), one needs to consider flammability, smoke density, and toxicity of the foam. This set of characteristics is commonly referred to as FST. By far, one of the most important applications of syntactic foams is for building material in deep-sea vehicles (see Fig. 3). Before the introduction of syntactic foams in subsea applications, liquid paraffins lighter than water, such as gasoline, were used to provide the needed buoyancy. Fire hazards, poor

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compressive strength, and thermal contraction are the main disadvantages of such materials (20). Today, using syntactic foams can result in significant improvement in mechanical performance while retaining FST properties comparable to conventional polyurethane foam.

Applications An important point to recognize is that in most cellular materials, there is always a trade-off between the requirement of a low density and strength required to bear a certain load. This is particularly true for applications involving buoyancy where syntactic foams have been in use since the 1970s. With increasing depth in water, the hydrostatic pressure increases. This requires a syntactic foam with higher strength. The additional strength is obtained by increasing the density of the foam, which means a loss in buoyancy. Below, we give some examples of applications of composite foams. Buoyancy-Related Subsea Applications. Offshore exploration of oil and gas requires insulated pipelines in order to prevent formation of waxes and hydrates (21). If the temperature of the pipeline drops too low, the heavy fractions in the crude oil can turn waxy. Natural gas can form hydrates. Both of these products can result in the clogging of the pipeline. Syntactic foams are suitable insulating materials for such buoyancy-related applications in deep water because of their higher compressive strength compared to that of conventional foam. Examples of such applications include buoys and floats, and submarine void filler for encapsulating instruments. Two characteristics that make syntactic foam an efficient buoyancy material are high compressive strength and low density. The low density of the syntactic foam allows buoyant lift to be designed into the insulation system. As an example, Cuming Microwave Corporation makes a series of syntactic foams (low loss dielectric as well as treated lossy materials), which are ultralight and high strength and can be adjusted to specifications. These materials are available in different forms: uncured, pack-in-place, cured sheet, and molded to shape. The pack-in-place variety has the consistency of a snowball, which can be readily packed into complex shapes. Elastic Compression. Any syntactic foam under hydrostatic pressure will undergo some elastic compressive strain. This will result in a loss of some of its buoyancy. We can write the following relationship from the theory of elasticity:

σp = K

V V

where σ p is the hydrostatic pressure, K is the bulk modulus, and V/V is the change in volume per unit volume, ie the volumetric strain of the material (in the present case, it is the syntactic foam). For an isotropic material, there exists the following relationship among the bulk modulus K, Young’s modulus E, and

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Poisson’s ratio ν: E = K/[3(1 − 2ν)] A typical value of Poisson’s ratio for a syntactic foam is 0.15, which would give the Young’s modulus to be about 2K, or K is about E/2. Typically, the upper limit on volumetric strain under service conditions is between 1 and 2%, which corresponds to about 65–70% of the critical stress corresponding to the onset of collapse or crushing of foam. This loss of buoyancy will be instantaneous upon the application of hydrostatic pressure. Water Absorption. Typically, the surface of syntactic foam has microscopic cracks and voids. When immersed in water, they will absorb water because of hydrostatic pressure. Of course, even ambient moisture will get absorbed. The weight gain due to moisture absorption will result in a long-term loss of buoyancy. Typical damage to syntactic foam material is similar to that in fiber-reinforced polymers composites: swelling and debonding accompanied by a degradation in mechanical properties (11,22). Insulation. Micrometer-sized pores in composite foams, together with their extremely low density, minimize conductive heat transfer. Addition of a small amount of fibers provides some rigidity to the foam. It is easy to visualize that a structure containing billions of cells will block convection and reflect heat energy back to its source. Excellent thermal insulating properties make such composite foams very useful in civil construction as well as in refractory applications. EMI Shielding. Syntactic foams based on carbon microballoons or silvercoated ceramic microballoons can be used for shielding against electromagnetic interference (EMI) (23). Such syntactic foams can provide the requisite electrical conductivity at very low density, thus avoiding the weight penalty imposed by conventional EMI shielding techniques. Biomedical Applications. Although applications of composite foams in biomedical area are not commercialized as yet, there is very active research into these materials as porous bioresorbable composite foams for applications as scaffolds in tissue engineering. A thermally induced phase separation technique was used to prepare foams of poly(lactide-co-glycolide) (PLGA) that contained up to 50 wt% bioactive glass particles. These composite foams showed well-defined, oriented, and interconnected porosity. An interesting result of this work was that they could control the in vitro degradation behavior of PLGA foam composite scaffolds by tailoring the concentration of bioactive glass (24).

Conclusions (1) Composite foams, a whole new class of materials, are natural extensions of conventional foams. (2) Additional constituents are incorporated in the formulation of composite foams to improve their overall performance/properties. (3) Syntactic foams with appropriate control of the size, morphology, and distribution of microballoons can provide a wide range of properties.

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(4) Addition of particles or fibers (long or short) provides another microstructural parameter to improve strength and damage tolerance of composite foams. (5) Composite foams find a wide range of applications: offshore exploration of oil and gas, shielding against electromagnetic interference (EMI), thermal and acoustic insulation, damping, cores in sandwich construction, etc.

BIBLIOGRAPHY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

W. Steckle and A. Nobile, Fusion Sci. Technol. 43, 301–306 (2003). L. Vaikhanski and S. Nutt, Comp. Part A, Appl. Sci. Manuf. 34A, 1245–1253 (2003). J. J. A. DeRuntz, J. Appl. Mech. 23–29 (Mar. 1971). U.S. Pat. (1957), to F. Veatch and R. W. Burhans. C. Karthikeyan, Kishore, and S. Sankaran, J. Reinforced Plast. Comp. 19, 732–742 (2000). N. Gupta, C. Karthikeyan, S. Sankaran, and Kishore, Mater. Characterization 43, 271–277 (1999). C. Karthikeyan, S. Sankaran, and Kishore, Mater. Lett. 58, 995–999 (2004). E. Papa, A. Corigliano, and E. Rizzi, Struct. Eng. Mech. 12(2), 169–188 (2001). C. Karthikeyan and Kishore, 58th Annual Technical Conference of the Society of Plastics Engineers, Technomic Publishing Co., Inc., Orlando, Fla, 2000. C. Karthikeyan, Kishore, and S. Sankaran, J. Reinforced Plast. Comp. 20, 982–993 (2001). A. Corigliano, E. Rizzi, and E. Papa, Comp. Sci. Technol. 60, 2169–2180 (2000). M. Palumbo and E. Tempesti, Appl. Comp. Mater. 8, 343–359 (2001). H. Kim and C. Mtichell, J. Appl. Polym. Sci. 89, 2306–2310 (2003). K. Carlisle and co-workers, in 14th International Conference on Composite Materials, San Diego, Calif., 2003. L. J. Gibson and M. F. Ashby, Cellular Solids: Structure and Properties, 2nd ed., Cambridge University Press, Cambridge, 1997. M. Puterman, M. Narkis, and S. Kenig, J. Cellul. Plast. 223–229 (July/Aug. 1980). L. E. Neilson, J. Polym. Sci.: Polym. Phys. Ed. 21, 1567–1568 (1983). R. K. McKeary, J. Am. Ceram. Soc. 44(10), 513–522 (1961). K. Okuno and R. T. Woodhams, Cellul. Plast. 237–244 (Sept./Oct. 1974). A. Winer, Cellul. Plast. 2, 157 (1966). T. Fine, H. Sautereau, and V. Sauvant-Moynot, J. Mater. Sci. 38, 2709–2716 (2003). V. A. Kochetkov and R. D. Maksimov, Mech. Comp. Mater. 32(1), 61–70 (1996). D. W. Radford and B. C. Chang, SAMPE Q. 24(4), 54–61 (1993). A. Boccaccini, I. Notingher, V. Maquet, and R. Jerome, J. Mater. Sci.: Mater. Med. 14, 443–450 (2003).

GARY M. GLADYSZ Los Alamos National Laboratory K. K. CHAWLA University of Alabama at Birmingham