Isotropic composite

Equiaxed particles, which ate well dispersed in the ceramic matrix, tend to produce isotropic composite behavior. The particles, either ceramic or metaUic, may be single crystal or polycrystalline in nature. 

The filler route has proved to be very efficient to obtain isotropic composites with relatively large improvements in matrix properties at small mass (volume) fractions of nanocarbon. For example, electrical percolation in epoxy has been obtained with only 0.0025 wt% of multi-wall nanotubes (MWNTs) [12]. Similarly, a 2.7-fold increase in matrix modulus has been observed on addition of 0.6 vol% MWNTs to polyvinyl alcohol (PVA) [13]. Although more modest compared to the previous two examples, a... 

To analyze the stress transfer in the fiber pull-out test of a multiple fiber composite, the specimen is treated as a three-cylinder composite (Zhou and Mai, 1992) where a fiber is located at the center of a coaxial shell of the matrix, which, in turn, is surrounded by a trans-isotropic composite medium with an outer radius fl. 

One of the most important properties which control the damage tolerance under impact loading and the CAI is the failure strain of the matrix resin (see Fig. 8.8). The matrix failure strain influences the critical transverse strain level at which transverse cracks initiate in shear mode under impact loading, and the resistance to further delamination in predominantly opening mode under subsequent compressive loading (Hirschbuehler, 1987 Evans and Masters, 1987 Masters, 1987a, b Recker et al., 1990). The CAI of near quasi-isotropic composite laminates which are reinforced with AS-4 carbon fibers of volume fractions in the range of 65-69% has... 

In an isotropic composite (chaotic distribution of fibre direction) E is given by = 0.2 Epar + 0.8 transv The first term follows from the answer to Question 19, the second one from 20, and the result is = 0.2 21 + 0.8 4.9 = 8.1 GPa. This value, therefore, approximates the highest attainable value with 25 vol% of glass... 

The value of / is 1 when the fibers are aligned and /j when the fibers are randomly oriented, i.e., isotropic composites. The value of /is decreased when the length of the fiber is less than the critical length (minimum chain length required for entanglement of the polymer chains). 

J.R. Vinson Plate and Panel Structures of Isotropic, Composite and Piezoelectric Materials,... 

These values hold for the case that the fibres are oriented in the stress direction. In reality the orientation of the fibres is at random in three dimensions we should, therefore, not only consider Ep but also the much smaller Et, which, even for very stiff fibres, is not higher than about Eo(l + 1,5-[Pg.179]

Equations rdating modulus to composition in isotropic composites are discussed in recent reviews by Manson and Sperling S and by Crowson and Arridge S ore than a dozen equations have been proposed. Tests on polymer composites ow that none of the available equations satisfactorily predicts tiie moduli of all types of composite at all concentrations of rigid particulate filler the best that can be dcme with any certainty is to define upper and lower bounds on the moduli. 

The current U.S. market for HDLDs is predominantly low-viscosity, clear, isotropic compositions. Besides the obvious differences in the physical appearance... 

The use of builders in liquid laundry formulations has effectively been restricted to citrates and fatty acid soaps (in isotropic compositions sold in the U.S. and Europe). Although liquid laundry products can contain tripolyphosphate, soda ash, NTA, and other common builders found in powder laundry, limitations on solubility (in a surfactant matrix) or regulatory concerns have restricted their utilization. There is a finite number of patents covering zeolite-built HDLDs, but problems... 

Isotropic composites, with uniform spatial distribution of filler particles... 

When the particles are chaotically scattered, the materials are called isotropic, i.e. their properties are identical in all directions. When the particles are distributed evenly within the matrix at a concentration gradient g (g -the vector indicating the direction of fastest change of particle concentration in the matrix), the composite is anisotropic and its properties depend upon the direction. The purpose of manufacturing isotropic composites is to place a respective component exactly in the site where properties of the composite article are to be realized most fully. 

The efficiency of reinforcement is related to the fiber direction in the composite and to the direction of the applied stress. The maximum strength and modulus are realized in a composite along the direction of the fiber. However, if the load is applied at 90° to the filament direction, tensile failure occurs at very low stresses, and this transverse strength is not much different than the matrix strength. To counteract this situation, one uses cross-pKed laminates having alternate layers of unidirectional libers rotated at 90°, as shown in Figure 3.47c. (A more isotropic composite results if 45° plies are also inserted.) The stress-strain behavior for several types of fiber reinforcement is compared in Figure 3.48. 

The stiffness of such a composite is close to the Hashin-Shtrikman lower bound for isotropic composites. Even if the spherical particles are perfectly rigid compared with the matrix, their stiffening effect at low concentrations is modest. Conversely, when the inclusions are more compliant than the matrix, spherical ones reduce the stiffness the least and platelet ones reduce it the most. Indeed, soft platelets are suggestive of crack-like defects. Soft platelets, therefore result not only in a compliant composite, but also a weak one. Soft spherical inclusions are used intentionally as crack stoppers to enhance the toughness of polymers such as polystyrene (high impact polystyrene), with a small sacrifice in stiffness. 

Moving to a larger scale, let us now look at the influence of microstructure on elastic behavior. As indicated in the previous section, the elastic constants are a fundamental property of single crystals through the geometry and stiffness of the atomic bonds. Thus, one may expect elastic behavior to be controlled simply by the choice of material. By using composite materials, however, one can control the final set of elastic properties with some precision, i.e., by mixing phases with different elastic constants. Clearly, it is useful to be able to predict the elastic constants of a composite from those of its constituents. This has been accomplished for many types of composite microstructures. For this section, however, the emphasis will be on (elastically) isotropic composites, i.e., composites contain-... 

Figure 3.9 Composite sphere assemblage used by Hashin (1983) for exact solutions to the elastic behavior of statistically isotropic composites.

The various approaches to the constitutive relationships for the elastic constants of statistically isotropic composites have also been used to describe other material properties, e.g., thermal and electrical conductivity. Of interest to this text is the thermal expansion behavior. The thermal expansion a of an isotropic composite is given by... 

For two-dimensional randomly oriented fibers in a composite, approximating theory of elasticity equations with experimental results yielded this equation for the planar isotropic composite stiffness and shear modulus in terms of the longitudinal and transverse moduli of an identical but aligned composite system with fibers of the same aspect ratio ... 

Even quasi-isotropic composition carbon FRPs, where the matrix performance has a more dominant role, can show a two—to four—fold improvement in fatigue resistance over steel and aluminium. It should be noted however that when stressed in the direction transverse to the fibres or in compression the fatigue life is substantially reduced. 

Fig. 15.5 Typical AFM images of uncross-linked (a and b) and cross-linked (c and d) isotropic composites with 10% w/w HPC of Avicel fibers a and c -bottom sinface band d-top surface [12]...

Small pieces were cut from each film, glued onto metal discs and attached to a magnetic sample holder located on top of the scanner tube. All the AFM images were taken at 25°C. Typical AFM images are presented in Fig. 15.5. Images of the surfaces of cross-linked and uncross-linked isotropic composite films with 10% (w/w HPC) of fibers are presented, as an example. 

Figure 15.7 displays the dependence between the Young s modulus of uncross-linked isotropic composites and their fiber content and shows that an in-plane distribution of the fibers in the composites is highly improbable. The same conclusion was drawn from the fit of the experimental data of the cross-linked composites. The predicted values of the Young s modulus for a 3D uniform distribution of the fibers are closer to that of the average values determined experimentally. Avicel fibers are not perfect rod objects (low aspect ratio Hd 5), being this the probable justification for a preferred 3D arrangement. 

Maimi P, Mayugo J A and Camanho P P (2008) A three-dimensional damage model for transversely isotropic composite laminates , / Comp Mater, 42(25), 2717-2745. 

The normal test for dynamic evaluation of materials or components is the Wohler fatigue test, to characterize fatigue behaviour. Hysteresis measurements are carried out on flax and glass mat-reinforced polypropylene, with a needle-punched flax mat using green and retted fibres to make plates with a quasi-isotropic composite structure, and with treatment by a coupling agent. 

Approximate formulae for four E, E, v i, G12) of the five elastic properties of a transversely isotropic composite can be developed using simple approaches based on the strength of materials concepts. These concepts do not necessarily satisfy in full all the elasticity requirements. The RVE considered consists of a uniform arrangement of straight, continnons fibres. 

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