Cellular ceramics constitute a class of materials where the properties may be optimized against the weight. These materials may be potentially useful in both structural and non-structural applications. In order to broaden the utilization of the currently- available materials, the mechanical properties must be improved. The objective of this paper is to review several recent studies on the strength and toughness of open cell brittle materials. The work was aimed at understanding the mechanisms involved in the failure of these materials and the relationship between the properties and the microstructure.

Cellular materials are increasingly used in engineering. Proper design requires an understanding of the response of the materials to stress; and, in real engineering design, the stress state is often a complex one. In this paper we model the elastic buckling, plastic yield, and brittle fracture of cellular solids under multiaxial stresses to develop equations describing their failure surfaces. Comparison of the analysis with data shows that the models describe the main features of the multiaxial behavior of foams well.

The mechanical behavior of microcellular open-cell foams prepared by a thermally induced phase separation process are investigated. The foams studied were prepared from isotactic polystyrene, polyacrylonitrile, and poly(4-methyl-1-pentene) (rigid foams), and polyurethane and Lycra (elastomeric foams). Their densities were in the range 0.04–0.27 g/cm3. Conventional polystyrene foams were used for comparison. The moduli and collapse stresses of these foams were measured in compression and compared with the current constitutive laws which relate mechanical properties to densities. A reinforcement technique based on the in-situ precipitation of silica was used to improve the mechanical properties.

High energy physics applications at the Department of Energy National Laboratories require unique low-density foams of demanding homogeneity specifications (cell sizes on the order of 10 μm or smaller). These delicate and fragile foams are machined and shaped into specimens to exacting tolerances. In this work, the mechanical properties of a variety of these low density microcellular foams are reported as functions of foam density and morphology.

Specimens of heated alumina foams were thermally shocked by immersion in water or oil. Two distinct temperature profiles were found to exist during liquid quenching: a macroscopic gradient due to heating of the fluid during infiltration into the foam and a microscopic gradient across each individual strut. Thermal stresses were calculated using a semi-empirical, finite element model. The peak thermal stresses were coupled with the two-parameter Weibull distribution of the strut strengths to calculate the probability of crack extension on a strut for eight cellular geometries. Experimentally, the thermal shock resistance increased with increasing relative density and increasing cell size. The predicted critical temperature differences were in fair agreement with measured values.

The failure behavior and stress distribution of a novel ceramic sandwich system was investigated. A highly porous, open-cell A12O3 was used as the core material with relative densities ranging from 9% to 20%. The faceplates were dense A12O3 of varying thickness. The composites were tested in flexure and failure loads of the cellular core were shown to compare favorably to those predicted by theory when Weibull statistics were incorporated. Stresses in the tensile faceplates were also measured. For composites with relatively thick faces and low modulus cores, the stress distribution was significantly altered by a local bending effect. These stresses were predicted using a refined model.

An experimental study was carried out on the indentation of cellular materials under quasi-static conditions. The study concentrated on a closed cell rigid polyurethane foam, but other cellular materials were tested. Load (F) - penetration depth (x) curves were obtained for various types of indenters which fall into two main types: sharp indenters (e.g. normal nails) and blunt indenters (e.g. flat ended nails). The F(x) curves are similar for the two types with an initial high slope region followed by a lower slope region in which F increases linearly with x. Nevertheless, the mechanisms of indentation are completely different, with a blunt indenter pushing the material under it and a sharp indenter pushing it radially as it penetrates. The effect of dimensions and shape of the indenters on the F(x) curves was investigated and scaling relations could be derived. Penetration-removal cycles clarify the differences between the two types of indenters, and give additional information on the mechanics of indentation. The experiments were complemented with scanning microscope observations of sections of the indented material. Two approaches are advanced for modelling indentation: a discrete approach in which the cellular structure is taken into account and a continuum approach.

Although its morphology is complex, the mechanical properties of the flesh of apples can be understood qualitatively in terms of the way the cells are assembled. There is no quantitative model for structures of turgescent cells which are not totally adherent.

The texture of apple flesh is important in assessing its eating qualities. The texture in turn is related to the structure of the parenchyma. The parenchyma cells of the fruit are arranged in radial quasi-columnar form with radial spaces in between. This anisotropy has a marked effect on the fracture properties such that it is much easier to drive a crack between the columns (radially) than to drive it across them (tangentially). The fracture tests used were simple crack-opening tests under tension or using a wedge. This difference was also detected by a taste panel. The radial spaces ease the passage of cracks travelling along them, and act as crack stoppers for cracks travelling at right angles to them. They also allow the cells to deform more in one orientation more giving the structure ductility and making the apple tougher in that orientation. It is possible to increase this effect by controlled damage such as slow freezing which causes the intercellular spaces to expand increasing the crack-stopping mechanisms and increasing the ductility, therefore increasing the fracture toughness. Toughness first increases, then decreases with increasing damage. This effect can be mimicked with brittle paper: fracture toughness of tracing paper initially increases if holes are punched randomly in it.

Contrary to existing models, strengths need not be a strong function of porosity for intermediate density, brittle materials. Flaw sizes can remain small (<50μm) if the void space is distributed uniformly in minimum dimension pores. For RBSN, fracture toughness decreases linearly with porosity for 0< porosity <40%. Strains to failure and specific strengths of these materials are higher than fully dense counterparts.

Composites of trinitrotoluene and cyclotrimethylene trinitramine have been studied in uniaxial compression and in triaxial confined compression. Failure by crack propagation and fracture was observed in all uniaxial studies while failure by yield and plastic flow was found for all triaxial confined compression work. The yield strength is approximately a factor of 2 greater than the uniaxial compressive fracture strength. The relationships between the fracture and yield strengths and Young's modulus indicate that all three decrease with increasing porosity. Based on this porosity interpretation, the compressive strength, the yield strength and Young's Modulus may be increased significantly by reducing the porosity.

This paper addresses the question of representing the dependence of the elastic coefficients in the anisotropic form of Hooke's law upon the microstructure of a material. The concern is with textured material symmetries, that is to say materials such as natural and man-made composites whose material symmetry is determined by microstructural organization. The approach is to relate the anisotropic elastic coefficients to local geometric or stereological measures of the microstructure. The predictions of micromechanical models and continuum mechanical models are compared and are found to be consistent with each other.

Using a digital-image-based representation of a continuum composite, we apply computer simulation techniques to obtain the elastic moduli of a matrix containing randomly-centered circular voids. As the area fraction of the voids increases, the elastic moduli of the composite decrease until they eventually vanish at the percolation threshold. We compare our results with an effective medium theory, which predicts that Poisson ratio tends to a fixed value as the percolation threshold is approached, independent of the values of the elastic moduli in the pure system. Our results are also compared with recent experimental results.

Randomly intercalated layered alloys are excellent models for two-dimensional microporous systems. We have studied the nonlinear gallery expansion and the gallery height fluctuations by constructing a double layer model that describes the layer rigidity and the size and stiffness of the intercalant species. Exact solutions, simulations and an effective-medium theory (EMT) results are compared. Applications of the results to ternary intercalation compounds are discussed.

The development of a constitutive model describing the deformation response of plasma sprayed metal matrix composite (MMC) foils during hot isostatic pressing (HIP) is described. A representative volume element of the composite is chosen whose constitutive behavior, including inelastic compressibility, is analyzed for the particular case of constrained uniaxial compression. Results of this preliminary model for the case of a SCS–6/Ti–14wt%Al–21wt%Nb intermetallic matrix composite are presented in the form of a density–pressure HIP map.

Low-density, microcellular polymer foams have numerous applications as structural supports in high-energy physics experiments, in catalysis, ion exchange, and filtration, and for a variety of biomedical uses. A versatile method to prepare such foams is by thermally-induced phase separation (TIPS) of polymer solutions. Demixed solutions can be transformed into a foam by freezing the demixed solution and removing the solvent by freeze-drying. The morphology of these foams is determined by the thermodynamics and kinetics of phase separation. A model of both the early and late stage structure development for demixed polymer solutions will be presented. For semi-crystalline polymers, gels can be prepared by crystallizing the polymer from solution, either a homogeneous solution or a demixed solution. Foams can be prepared from these gels by the super-critical extraction of the solvent. By understanding and utilizing the phase separation behavior of polymer solutions, engineered microcellular foams can be prepared. To design the foams for any application one must be able to characterize their morphology. Results will be presented on the morphological characterization of these foams and the relationship of the morphology to their processing history.

A variety of cellular SiO2 materials have been synthesized using a foaming sol-gel process and their properties have been characterized. The process uses the rapid viscosity change during gelation to stabilize the structure of a foamed silica sol. It was found that the properties of these cellular materials are determined by method used. For example, the porosity and strength of these porous oxides depend on method of agitation and addition of Freon during the foaming process.

Density measurements, viscosity measurements as a function of pH, optical characterization, x-ray crystallography, ultimate compressive strength, dielectric constant measurements and thermal diffusivity were used to characterize these porous SiO2 materials. This paper will discuss the synthetic processes used to develop the porous silicas and properties of these materials.

Open porous materials of higher strength and higher porosity were produced by a hot isostatic process (HIP). A grinding wheel of fused alumina grain with powdered frit for bridge is discussed as an example. The samples were directly heated to a normal sintering temperature under HIPping conditions. The HIPped products were characterized by higher bending strength in spite of having more open porosity than the normally sintered ones.

The flexibility of chemical vapor deposition (CVD) permits the fabrication of a large number of materials in various geometric forms, one of which is the porous cellular structure. CVD fabrication of such a structure begins with the pyrolysis of a resin-impregnated thermosetting foam to obtain a reticulated carbon foam skeleton. The foam ligaments can then be coated with a variety of materials (metals, oxides, nitrides, carbides, borides, silicides, etc.), either singly or as hybrid, layered, alloyed, or graded structures. During this process, 10 to 1000 microns of the desired material(s) are deposited onto the foam ligaments by a variation of CVD known as chemical vapor infiltration (CVI). The thermomechanical properties of the resultant structure are dominated by the properties of the deposit, becoming independent of the carbon properties at very small material loadings. With precise control over the variables available, it is possible to obtain the simultaneous optimization of stiffness, strength, thermal conductivity, overall weight, and environmental resistance. This paper discusses the fabrication and properties of various CVD foam materials investigated to date.

Achieving spatially uniform and hierarchically structured microstructures during the shape-forming of colloidal ceramics depends largely on (i) the magnitude of the effective stresses (i.e., stresses that are supported by the particulate network) and (ii) plastic properties, which in turn are significantly altered by processing parameters affecting interparticle friction and adhesion. To quantify the effects of processing parameters on consolidation, we present a novel approach for analyzing sediments by gamma-ray densitometry and a fluid mechanics model. This method enables us to correlate processing parameters with spatial variations of the packing density and the local effective stress. These correlations are difficult to achieve by traditional techniques (e.g., rheometry, sedimentation kinetics modeling, soil mechanics tests), especially for the low stresses (< 1000 Pa) that are typically encountered in sediments. Aside from being destructive to samples, these techniques also tend to measure volume-averaged properties, and as a result they usually fall short of describing localized consolidation phenomena.