The finite-element method (FEM) is used to study the influence of porosity and pore shape on the elastic properties of model porous ceramics. Young's modulus of each model is practically independent of the solid Poisson's ratio. At a sufficiently high porosity, Poisson's ratio of the porous models converges to a fixed value independent of the solid Poisson's ratio. Young's modulus of the models is in good agreement with experimental data. We provide simple formulas that can be used to predict the elastic properties of ceramics and allow the accurate interpretation of empirical property-porosity relations in terms of pore shape and structure.

Elastic Properties of Model Porous Ceramics

Carbon nanofiber (CNF), as one of the most important members of carbon fibers, has been investigated in both fundamental scientific research and practical applications. CNF composites are able to be applied as promising materials in many fields, such as electrical devices, electrode materials for batteries and supercapacitors and as sensors. In these applications, the electrical conductivity is always the first priority need to be considered. In fact, the electrical property of CNF composites largely counts on the dispersion and percolation status of CNFs in matrix materials. In this review, the electrical transport phenomenon of CNF composites is systematically summarized based on percolation theory. The effects of the aspect ratio, percolation backbone structure and fractal characteristics of CNFs and the non-universality of the percolation critical exponents on the electrical properties are systematically reviewed. Apart from the electrical property, the thermal conductivity and mechanical properties of CNF composites are briefly reviewed, as well. In addition, the preparation methods of CNFs, including catalytic chemical vapor deposition growth and electrospinning, and the preparation methods of CNF composites, including the melt mixing and solution process, are briefly introduced. Finally, their applications as sensors and electrode materials are described in this review article.

Carbon Nanofibers and Their Composites: A Review of Synthesizing, Properties and Applications

The microstructure and mechanical properties of sintered Fe–0.85Mo–Ni steels were investigated as a function of sintered density. A quantitative analysis of microstructure was correlated with tensile and fatigue behavior to understand the influence of pore size, shape, and distribution on mechanical behavior. Tensile strength, Young's modulus, strain-to-failure, and fatigue strength all increased with a decrease in porosity. The decrease in Young's modulus with increasing porosity was predicted by analytical modeling. Two-dimensional microstructure-based finite element modeling showed that the enhanced tensile and fatigue behavior of the denser steels could be attributed to smaller, more homogeneous, and more spherical porosity which resulted in more homogeneous deformation and decreased strain localization in the material. The implications of pore size, morphology, and distribution on the mechanical behavior and fracture of P/M steels are discussed.

Microstructure and mechanical behavior of porous sintered steels

Deformation behavior of (Cu, Ag)–Sn intermetallics by nanoindentation

Physical property-porosity models based on minimum solid areas of idealized stackings of either: (1) spherical particles partially bonded (e.g. sintered), or (2) spherical pores in a solid matrix are shown to agree with appropriate physical property data for bodies whose porosity is reasonably represented by such stackings. Appropriate physical properties are those determined mainly by local stress or flux, e.g. elastic properties, strengths, and electrical and thermal conductivity. The minimum solid areas are, respectively, the: (1) bond (e.g. neck) area between particles defining pores smaller than the particles, or (2) minimum web thickness between adjacent pores being more than or equal to the surrounding particles (e.g. bubbles in a foam). Combinations of the models for mixtures of basic porosity types and changes in basic model parameters (e.g. stacking) over the significant porosity range covered, are shown to agree with the literature (mainly mechanical) property data for bodies of appropriate porosity combinations. Areas of further development and testing are noted.

Evaluation and extension of physical property-porosity models based on minimum solid area

This paper compares the applicability of a few theoretical models for determining effective elastic moduli, using published experimental data on ceramic materials in a porosity range of 0–40% and on a cellular material with a porosity of about 90%. As the experimental data for the effective Poisson's ratio involve a large scatter, a set of numerical experiments using the finite element method was carried out to obtain the variation of the effective Poisson's ratio with porosity. These variations show that the effective Poisson's ratio approaches 0.25 with increasing porosity, irrespective of the material Poisson's ratio. The effect of pore shapes on the effective elastic moduli and the Poisson's ratio has also been analyzed using FEM.

N. Ramakrishnan

Papers

Effective Elastic Moduli of Porous Ceramic Materials