Elastic properties composition dependence

Amorphous polymers well above Jg behave either as liquids or, if they are cross-linked, as rubbers the properties of rubbers are discussed in the next section. In the region close to Jg the viscoelastic properties dominate even at small strains and relatively short times and these are considered in the next chapter. This means that the static small-strain properties of amorphous polymers can be discussed meaningfully only when the polymers are well below Tg. Semicrystalline polymers are really composite materials. At temperatures well below the Tg of the amorphous regions the material has small-strain elastic properties that depend on the proper-... 

In a semicrystalline polymer, the crystals are embedded in a matrix of amorphous polymer whose properties depend on the ambient temperature relative to its glass transition temperature. Thus, the overall elastic properties of the semicrystalline polymer can be predicted by treating the polymer as a composite material... 

Three-dimensional distributions of the micro-residual stresses are very complicated, and are affected by the elastic properties, local geometry and distribution of the composite constituents within a ply. Many analytical (Daniel and Durelli, 1962 Schapery, 1968 Harris, 1978 Chapman et ah, 1990 Bowles and Griffin, 1991a, b Sideridis, 1994) and experimental (Marloff and Daniel, 1969 Koufopoulos and Theocaris, 1969 Barnes et ah, 1991 Barnes and Byerly, 1994) studies have been performed on residual thermal stresses, A two-dimensional photoelastic study identified that the sign and level of the residual stresses are not uniform within the composite, but are largely dependent on the location (Koufopoulos and Theocaris,... 

Acoustic microscopy has a special place in this powerful armoury. It depends on the elastic response of the material to acoustic waves, and therefore provides information on local changes in elastic properties thus, for example, it is particularly sensitive to fine cracks (which might not be observable by other techniques). It has already been applied to a wide range of materials, including biological specimens, minerals, semiconductor devices, composites, ceramics, etc. As is the case for all other techniques, it is essential to have a clear understanding of the contrast mechanisms, so that the observations can be interpreted with confidence. This book provides potential users, such as materials scientists and biologists, with a comprehensive account of the basic techniques, of the contrast mechanisms, and of the way the techniques can be applied to obtain information on microstructure in different types of specimen. 

The material described in this chapter can be used in the analysis of the dependence of the conductivity and elastic parameters of various polymeric materials. Providing both a critical evaluation of characterization methods and a quantitative description of composition-dependent properties the material given in this chapter should have broad appeal in both the academic and industrial sectors, being of particular interest to researchers in materials and polymer science. 

Such a composite will be further referred to as the Hashin-Strikman composite. The elastic properties of the Hashin-Strikman composite are described by the formulae that are obtained from the exactly solvable model of a single spherical inclusion of one phase in an infinite matrix of the second phase and depend only on the volume concentrations and elastic properties of the constituent phases. The properties of the Hashin-Strikman composite do not depend on the scale chosen. 

The results of calculations of the effective Poisson s ratio vp dependence on the bulk concentration of a rigid phase p at various values of a = log i/C/Au) are shown in Fig. 53. The calculations were made for Poisson s ratios of the phases ranging from 0.1 to 0.4. It can be seen that at percolation threshold Poisson s ratio of the isotropic fractal composite is vp = 0.2, when K jK > 0 it is also independent of the Poisson s ratios of the individual components of the composite. The Poisson s ratio obtained by us near the percolation threshold is in agreement with computer simulation results and the conjecture of Arbabi and Sahimi [161]. It has been shown that an approximate theoretical treatment of percolation on a cubic lattice exactly reproduces the Poisson s ratio obtained in computer simulation at the percolation threshold. This result may encourage one to use this approximation to describe various elastic properties of composites. It is worth noting that some critical indices have been calculated recently with a high degree of accuracy in the context of the present model. 

Grindability (in its many different definitions) is a composite material property, and depends on many primary material properties (e.g. particle hardness, bulk and shear moduli of elasticity) as well as its flow properties and other conditions like moisture content, humidity of the atmosphere or material composition (rank or ash content of coal, for example). It also depends on the type of mill used for its evaluation. There have been some attempts made by several authors to find correlations relating different measures of grindability the reader is referred to the literature for details of these54. 

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