Material volume fraction

Material Volume fraction (V/) Density (kg/m ) Tensile strength (GN/m ) Tensile modulus (GN/m )... 

Fig. 47. Craze structural parameter versus craze material volume fraction v, from Eq. 20. The numerical values of = 0.048 0.007 leads to = 0.3 0.08, and indicates that the craze material volume fraction is not effected by the toluene vapors. From Ref. by permission of the publishers, Butterworth and Co. Ltd.

The power of the theory developed by Shih et al. (1) lies in the fact that it is possible to experimentally determine if a system is in the strong- or weak-link. The strain at the limit of linearity increases as a function of the volume fraction of network material for the weak-link regime while it decreases for the strong-link regime. Below we derive expressions for the relationship between the strain at the limit of linearity and network material volume fraction. 

Young s modulus of a randomly oriented material. Volume fraction of a component. 

Fig. 15. (a) TEM image of wax-polymer correlated plates resembling a top view of a shish-kebab morphology (b) Cartoon of the polymer-wax aggregate consisting of monolayer of stretched wax molecules embedded into thicker homogeneous polymer layer the thickness and material volume fraction characterizing each layer are indicated (Radulescu et al., 2008). 

The effective solid phase conductivity, is related to the respective active material volume fractions, eg, in the anode and cathode electrodes, which is expressed in terms of Bruggeman correction for tortuosity and often with a value... 

By variation of ceramic volume fraction and selection of the best fitting PZT material we can as well adjust the dielectric constant of the piezocomposite within a wide range. Therefore, we can choose the best piezocomposite material for each probe type to get optimum pulse form and amplitude. 

Foams have a wide variety of appHcations that exploit their different physical properties. The low density, or high volume fraction of gas, enable foams to float on top of other fluids and to fiU large volumes with relatively Httle fluid material. These features are of particular importance in their use for fire fighting. The very high internal surface area of foams makes them useful in many separation processes. The unique rheology of foams also results in a wide variety of uses, as a foam can behave as a soHd, while stiH being able to flow once its yield stress is exceeded. 

In an amorphous material, the aUoy, when heated to a constant isothermal temperature and maintained there, shows a dsc trace as in Figure 10 (74). This trace is not a characteristic of microcrystalline growth, but rather can be well described by an isothermal nucleation and growth process based on the Johnson-Mehl-Avrami (JMA) transformation theory (75). The transformed volume fraction at time /can be written as... 

Two approaches have been taken to produce metal-matrix composites (qv) incorporation of fibers into a matrix by mechanical means and in situ preparation of a two-phase fibrous or lamellar material by controlled solidification or heat treatment. The principles of strengthening for alloys prepared by the former technique are well estabUshed (24), primarily because yielding and even fracture of these materials occurs while the reinforcing phase is elastically deformed. Under these conditions both strength and modulus increase linearly with volume fraction of reinforcement. However, the deformation of in situ, ie, eutectic, eutectoid, peritectic, or peritectoid, composites usually involves some plastic deformation of the reinforcing phase, and this presents many complexities in analysis and prediction of properties. 

The exact properties depend upon the materials used, grain size, binder content, volume fraction of each constituent, and processing method. 

The abrasion resistance of cobalt-base alloys generally depends on the hardness of the carbide phases and/or the metal matrix. For the complex mechanisms of soHd-particle and slurry erosion, however, generalizations cannot be made, although for the soHd-particle erosion, ductihty may be a factor. For hquid-droplet or cavitation erosion the performance of a material is largely dependent on abiUty to absorb the shock (stress) waves without microscopic fracture occurring. In cobalt-base wear alloys, it has been found that carbide volume fraction, hence, bulk hardness, has Httie effect on resistance to Hquid-droplet and cavitation erosion (32). Much more important are the properties of the matrix. 

Sohd rocket propellants represent a very special case of a particulate composite ia which inorganic propellant particles, about 75% by volume, are bound ia an organic matrix such as polyurethane. An essential requirement is that the composite be uniform to promote a steady burning reaction (1). Further examples of particulate composites are those with metal matrices and iaclude cermets, which consist of ceramic particles ia a metal matrix, and dispersion hardened alloys, ia which the particles may be metal oxides or intermetallic compounds with smaller diameters and lower volume fractions than those ia cermets (1). The general nature of particulate reinforcement is such that the resulting composite material is macroscopicaHy isotropic. 

Eiber volume fraction is a quantitative measure of degree of reinforcement of the matrix material in a fiber-reinforced composite. If the volume of a composite material is D and the volume of the fibers is and that of the matrix is then... 

Aesthetic dental ceramics are essentially glass-matrix materials with varying volume fractions of crystalline fillers. Crystalline fillers are used in the glass matrix both for dispersion strengthening, usually at volume fractions of 40—70%, and for altering optical properties, usually at low volume fractions. Dental ceramics are generally manufactured from two distinct classes of materials, ie, beneficiated feldspathic minerals and glass—ceramics. 

A composite material consists of flat, thin metal plates of uniform thickness glued one to another with a thin, epoxy-resin layer (also of uniform thickness) to form a multi-decker-sandwich structure. Young s modulus of the metal is Ej, that of the epoxy resin is E2 (where E2 < Ej) and the volume fraction of metal is Vj. Find the ratio of the maximum composite modulus to the minimum composite modulus in terms of Ej, E2 and V. Which value of gives the largest ratio ... 

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