Isotropic properties

Particle or discontinuously reinforced MMCs have become important because they are inexpensive compared to continuous fiber-reinforced composites and they have relatively isotropic properties compared to the fiber-reinforced composites. Figures la and b show typical microstmctures of continuous alumina fiber/Mg and siUcon carbide particle/Al composites, respectively. 

Composites fabricated with the smaller floating catalyst fiber are most likely to be used for applications where near-isotropic orientation is favored. Such isotropic properties would be acceptable in carbon/carbon composites for pistons, brake pads, and heat sink applications, and the low cost of fiber synthesis could permit these price-sensitive apphcations to be developed economically. A random orientation of fibers will give a balance of thermal properties in all axes, which can be important in brake and electronic heat sink applications. 

Two simple invariants, U, and U5, were shown in the previous subsubsection to be the basic indicators of average laminate stiffnesses. For isotropic materials, these invariants reduce to U. =Qi. and U5 = Qqq, the extensional stiffness and shear stiffness. Accordingly, Tsai and Pagano suggested the orthotopic invariants U., and U5 be called the isotropic stiffness and isotropic shear rigidity, respectively [7-16 and 7-17]. They observed that these isotropic properties are a realistic measure of the minimum stiffness capability of composite laminates. These isotropic properties can be compared directly to properties of isotropic materials as well as to properties of other orthotropic laminates. Obviously, the comparison criterion is more complex than for isotropic materials because now we have two measures, and U5, instead of the usual isotropic stiffness or E. Comparison of values of U., alone is not fair because of the degrading influence of the usually low values of U5 for composite materials. 

Isotropic carbon is obtained by the pyrolysis of a hydrocarbon, usually methane, at high temperature (1200-1500°C) in a fluidized bed on a graphite substrate.Under these conditions, a turbostratic structure is obtained which is characterized by very little ordering and an essentially random orientation of small crystallites. In contrast to graphite which is highly anisotropic, such a structure has isotropic properties (see Ch. 7). Isotropic carbon is completely inert biologically. Its properties are compared to alumina, another common implant material, in Table 17.8. Notable is its high strain to failure. 

Isotropic properties, silicon, 22 482, 483t Isotropic soap phase, 22 726 Isovaleraldehyde. See also 3-Methyl butanal... 

A droplet of liquid, which has a random structure and thus isotropic properties, takes a true spherical form at equilibrium. This is because a sphere is the form with minimum surface energy in the case of an isotropic material. Gibbs considered that a crystal, which has a regular structure for which anisotropy is the... 

Compression molding at elevated temperature and pressure was used to achieve bulk specimens with three dimensionally isotropic properties. Successful... 

Thiele(I4>, who predicted how in-pore diffusion would influence chemical reaction rates, employed a geometric model with isotropic properties. Both the effective diffusivity and the effective thermal conductivity are independent of position for such a model. Although idealised geometric shapes are used to depict the situation within a particle such models, as we shall see later, are quite good approximations to practical catalyst pellets. 

HIPing is considerably more complex and expensive than hot-pressing but for monolithic silicon nitride it normally produces a superior product with near-isotropic properties at low additive contents. However, with silicon nitride whisker composites, whisker bridging and the formation of whisker nests can be more of a problem.5... 

Prepreg. Fabric is impregnated with 25 percent of liquid resin and laid in the mold. To insure isotropic properties, or to maximize properties in a specific direction, successive layers of impregnated fabric are carefully oriented in different directions. The mold is closed, pressed, and heated till cured. Products made from such impregnated fabrics have much higher strength than simple random fiber reinforcements. 

Biaxial orientation leads to isotropic properties in blown film, that is, properties that are eqnal in the two primary directions the film was stretched (i.e., parallel to the flat bit ). Orientation in the machine direction of the film is controlled primarily by take-up ratio, defined above. To control orientation in the transverse direction, we measure something called the blow-up ratio, while the forming ratio provides an indication of the degree of isotropy. 

The structure of syntactic foams is composed of closed-cell microspheres and matrix resins, and the resultant foam has the advantages of (a) isotropic properties not available in other types of foams (b) very low water absorption due to highly closed-cell structures and (c) very high compressive strengthAveight ratio. Table 40 shows properties of syntactic foams composed of epoxy resin and glass microspheres. 

For a single-channel problem, only one term in the sum in Eq. (56) is to be considered. On the other hand, it is not unusual for multichannel chemical reactions to have a multiexponential form of reaction probability. Reduction to a single exponential form can depend on individual cases under study. For our cluster system, in which various isotropic properties dominate due to the identical particle composition (see Ref. 39), it is quite likely that there are very many critical points that are topologically equivalent or energetically similar to each other. In these cases, averaging should work. In the two familiar means over variables (X i = 1,2,..., M ... 

In Equation (6.1), the terms are subscripted x because certain solids (e.g., wood, single crystals, and some highly oriented materials like pyrolitic graphite) have different thermal condnctivities in different directions, and the subscript indicates the direction of heat flow. Most engineering materials, however, may be treated as isotropic (properties independent of direction) and the snbscript dropped. The minus (-) sign in Equation (6.1) arises from the fact that heat flows from a high temperature to a lower one, and therefore (dT / dx) is inherently negative hence, the thermal conductivity and the heat flux are positive. 

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