Packing fraction reinforcement

The factor (j) in eq. (4) depends, as it is shown in Table 1, on the volume fraction of the reinforcing material v, the ratio of moduli rg, Poisson s ratio v, the shape factor of the reinforcing material expressed by the length-to-diameter ratio 1/d, the maximum possible packing fraction for a hard filler v, the voids fraction in the... 

The micromechanical models used for the comparison was Halpin-Tsai (H-T) [89] and Tandon-Weng (T-W) [90] model and the comparison was performed for 5 wt% CNT/PP. It was noted that the H-T model results to lower modulus compared to FEA because H-T equation does not account for maximum packing fraction and the arrangement of the reinforcement in the composite. A modified H-T model that account for this has been proposed in the literature [91], The effect of maximum packing fraction and the arrangement of the reinforcement within the composite become less significant at higher aspect ratios [92],... 

Z, Z and Z represent the Young s modulus or tensile strengths of the composite, matrix and fiber, respectively, A is twice the fiber aspect ratio (I and d are the fiber length and diameter, respectively), r/j accounts for the relative moduli of the fiber and matrix, Vf is the fiber volume fraction, fy depends upon the particle packing fraction, and is the maximum packing fraction of the reinforcement. 

In these expressions, Ef, and Er are the moduli of the composite, fiber, and resin, is the volume fraction of fiber, A is the average aspect ratio of the fiber, and W is the maximum packing fraction. Application of the equation is limited to small strains. (Natural fibers, plastics and composites. Wallenberger FT, Weston NE (eds). Springer, New York, 2003 Murphy J (1998) Reinforced plastics handbook. Elsevier Science and Technology Books, New York Engineering plastics and composites. Pittance JC (ed), SAM International, Mate-rials Park, OH, 1990) L... 

The fibre volume fraction depends heavily on the method of manufacture. A uni directional composite may have a fibre volume fraction as high as 75%. However, this can only be achieved if all the fibres are highly aligned and closely packed. A more typical fibre volume fraction for uni directional composites is 65%. If the fibre configuration is changed to put fibres in other directions, then the maximum fibre packing is reduced further. A typical fibre volume fraction for bi-directional reinforcement (woven fibre) is 40% and a typical volume fraction for random in-plane reinforcement (chopped strand mat) is 20%. 

The relationships between Pr and cj) have been derived for suspensions of monodispersed hard spheres in Newtonian liquids. However, most real systems are polydispersed in size and do not necessarily consist of spherical particles. It has been found that here also Simha s Eq. 7.24, Mooney s Eq. 7.28, or Krieger-Dougherty s Eq. 7.8 are useful, provided that the intrinsic viscosity and the maximum packing volume fraction are defined as functions of particle shape and size polydispersity. For example, by allowing with composition, it was possible to describe the Pr versus cj) variation for bimodal suspensions (Chang and Powell 1994). Similarly, after values of [q] and (j)i were experimentally determined, Eq. 7.24 provided good description for the versus cj) dependence of several multiphase systems, e.g., PVC emulsions and plastisols, mica-reinforced polyolefins, and sealant formulations (Utracki 1988, 1989). 

For most applications, resistance to sfiesses in more than one direction is essential, and in these cases, a unidirectional composite is not acceptable. Strength and stiffness in both dimensions of a plane, as in a car body panel, or isotropically in all three dimensions is normally required. Consequently, the orientation or the fibres must be modified to provide resultants in the required directions. This may be achieved in two directions by the use of woven or knitted cloths or with non-woven, random felts or mats. In three dimensions, random orientation of the reinforcement is usually the only possibility. However, the maximum strength attainable drops sharply in multidirectional composites, not only because of the smaller fraction of fibres contributing to resisting the stress but also becanse the maximum packing density of the reinforcing fabric decreases and hence the overall volume fraction of reinforcement decreases. Despite this fall-off, the strength of the fibres is snch that a very substantial reinforcement may still result. 

There are several models used to predict permeation of gases through filled polymer membranes [37,38]. Many of these simply take into account the permeabihties and fractional volumes of the constituent polymers, while others also include factors for dealing with the shape of the reinforcing elements as well as their packing in the composite. 

The possibility of rheological effects (shear, relaxation), molecular orientation, and molecular fractionation taking place are further reinforced by industrial observation of the melt flow between the pack and the spinneret capillaries. Here, it has been found that the space between the pack and the spinneret capillaries is a critical factor in determining fiber properties. The sensitivity of these properties to this distance strongly indicates the possible effects of relaxation, changes in molecular orientation, or fractionation, all of which could influence fiber properties. 

These qualitative effects can be described quantitatively within the framework of percolation model of reinforcement and multifractal model of gas transport processes for nanocomposites polymer/organoclay [3, 4]. It has been supposed that two structural components are created for a barrier effect to fire spreading actually organoclay and densely packed regions on its surface with relative volume fractions (p and (p respectively. In other words, it has been supposed, that the value should be a diminishing function of the sum ((p -l-(pp. For this supposition verification let us estimate the values (p and (p The value (p is determined according to the well-known equation [5] ... 

Hence, the stated above results have demonstrated, that intercomponent adhesion level in natural nanocomposites (polymers) has structural origin and is defined by nanoclusters relative fraction. In two temperature ranges two different reinforcement mechanisms are realized, which are due to large friction between nanoclusters and loosely packed matrix and also perfect (by Kemer) adhesion between them. These mechanisms can be described successfully within the frameworks of fractal analysis. 

Fiber reinforcements are compacted in a consolidation procedure in which external loads are applied to compress fibers, to squeeze air and resin out, to suppress voids, and to increase the fiber volume fraction. Before compaction, the fiber reinforcement networks are unable to carry traction stresses at/or below a certain initial critical fiber volume fraction,. As the fiber volume fraction, pj, increases under compression, the network can carry a rapidly increasing load. Eventually, the fiber volume fraction of the network approaches a theoretical maximum based on the relevant close-packed geometry, and cannot increase without an enormous increase in load. The compressibility of the fiber reinforcement network is dependent not only on the elastic properties of fibers, but also on the configuration of the fiber reinforcement network as well, that is... 

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