Unidirectional properties

Other semi-2-IPNs [52] processed by the freeze-drying method included IPN from 4,4 -bismaleimido diphenylmethane (BMI) and linear BTDA/3,4 -ODA polyamic acid that were dissolved in 1,3,5-trioxane (Fig. 16). The resulting semi-2-IPNs exhibited higher Tgs and reduced phase separation, and contained no plasticizing solvent. A comparison of unidirectional properties of composites prepared by the freeze-dry process to those by traditional solvent evaporation process is presented in Table 13. The freeze-drying method for the preparation of IPNs appears to be superior to previous technology. 

Compared with other polymeric materials. LCPs have very high unidirectional properties. Iei/nt7 1 (Celanese Corp.t resins are primarily aromatic polyesters based on p-hydroxybenzoic acid and hydroxynaphthoic acid monomers. Xytlar " (Celanese Carp.) injection molding resins are polyesters based on terephthalic acid. />. p -dihydruxybiphenyl and p-hydroxybenzoic acid Differences in monomers are primarily responsible for the differences in specific properties and end uses. The fibrous nature of the polymers imparls good impact strengths. 

A combination of the chaotic mixing mechanism and the selection of an optimum mixing regime enables structures to be obtained at selected parts of the striation-to-droplet structures achieved by Scott and Makosco described in Section 14.5. The chaotic mixing mechanism supports the development of a unidirectional striated ( tape ) structure which provides the multiple layers required for the unidirectional properties required in films for oxygen barrier and impact properties and in some circumstances for electrical properties. The incorporated material can be a masterbatched additive or a second polymer. 

There are three basic types of engineered composites (1) laminates, (2) particle-reinforced composites, and (3) fiber-reinforced composites. In particle-reinforced composites, one can make the distinction between small (submicron) particle composites, where the particles are incorporated in the microstructure, vs. large particle composites, where the particles themselves actually do the work or carry the load. The reinforcing fibers can be discontinuous or continuous. The fibers in discontinuous fiber-reinforced composites can be randomly oriented to provide isotropic properties or aligned to enhance a specific property in a specific direction. Continuous fiber composites are generally designed for their unidirectional properties but can be crisscrossed to obtain multidirectional property enhancement such as in a filament-woimd pressure container. All possible permutations of metal, ceramic, and pol)uner are foimd in the laminated as well as in the reinforced composites. 

Chemical properties of deposited monolayers have been studied in various ways. The degree of ionization of a substituted coumarin film deposited on quartz was determined as a function of the pH of a solution in contact with the film, from which comparison with Gouy-Chapman theory (see Section V-2) could be made [151]. Several studies have been made of the UV-induced polymerization of monolayers (as well as of multilayers) of diacetylene amphiphiles (see Refs. 168, 169). Excitation energy transfer has been observed in a mixed monolayer of donor and acceptor molecules in stearic acid [170]. Electrical properties have been of interest, particularly the possibility that a suitably asymmetric film might be a unidirectional conductor, that is, a rectifier (see Refs. 171, 172). Optical properties of interest include the ability to make planar optical waveguides of thick LB films [173, 174]. 

The difference between the bounds defined by the simple models can be large, so that more advanced theories are needed to predict the transverse modulus of unidirectional composites from the constituent properties and fiber volume fractions (1). The Halpia-Tsai equations (50) provide one example of these advanced theories ia which the rule of mixtures expressions for the extensional modulus and Poisson s ratio are complemented by the equation... 

The tensile strength of a unidirectional lamina loaded ia the fiber direction can be estimated from the properties of the fiber and matrix for a special set of circumstances. If all of the fibers have the same tensile strength and the composite is linear elastic until failure of the fibers, then the strength of the composite is given by... 

This is an important relationship. It states that the modulus of a unidirectional fibre composite is proportional to the volume fractions of the materials in the composite. This is known as the Rule of Mixtures. It may also be used to determine the density of a composite as well as other properties such as the Poisson s Ratio, strength, thermal conductivity and electrical conductivity in the fibre direction. 

Example 3.2 PEEK is to be reinforced with 30% by volume of unidirectional carbon fibres and the properties of the individual materials are given below. Calculate the density, modulus and strength of the composite in the fibre direction. 

The properties of a unidirectional fibre will not be nearly so good in the transverse direction compared with the longitudinal direction. As a material in service is likely to be subjected to stresses and strains in all directions it is important to be aware of the properties in all directions. The transverse direction will, of course, be the weakest direction and so it is necessary to pay particular attention to this. 

Some typical elastic properties for unidirectional fibre composites are given in Table 3.4. 

Typical elastic properties of unidirectional fibre reinforced plastics... 

The previous section illustrated how to obtain the elastic properties of a unidirectional lamina. In practice considerably more information may be required about the behavioural characteristics of a single lamina. To obtain details of the stresses and strains at various orientations in a single ply the following type of analysis is required. 

Consider the situation of a thin unidirectional lamina under a state of plane stress as shown in Fig. 3.9. The properties of the lamina are anisotropic so it will have modulus values of E and Ei in the fibre and transverse directions, respectively. The values of these parameters may be determined as illustrated above. 

Example 3.6 A unidirectional composite consisting of carbon fibres in a PEEK matrix has the fibres aligned at 25° to the loading axis. If the fibres and matrix have the properties indicated below, calculate Ex, Ey, Gxy, Vxy, and Vyx. 

Example 3.7 A thin unidirectional Kevlar fibre/epoxy composite has the properties listed below. If the fibres are aligned at 6 to the x-axis, show how... 

Fig. 3.11 Variation of properties in unidirectional composite as a function of fibre angle...

The previous analysis has shown that the properties of unidirectional fibre composites are highly anisotropic. To alleviate this problem, it is common to build up laminates consisting of stacks of unidirectional lamina arranged at different orientations. Clearly many permutations are possible in terms of the numbers of layers (or plies) and the relative orientation of the fibres in each... 

The Plate Constitutive equations can be used for curved plates provided the radius of curvature is large relative to the thickness (typically r/h > 50). They can also be used to analyse laminates made up of materials other than unidirectional fibres, eg layers which are isotropic or made from woven fabrics can be analysed by inserting the relevant properties for the local 1-2 directions. Sandwich panels can also be analysed by using a thickness and appropriate properties for the core material. These types of situation are considered in the following Examples. 

Example 3.16 A unidirectional carbon hbre/PEEK laminate has the stacking sequence [O/SSa/—352]t- If it has an in-plane stress of = 100 MN/m applied, calculate the strains and curvatures in the global directions. The properties of the individual plies are... 

As an illustration of the results of the measurements just described, the mechanical properties for four unidirectionally reinforced composite materials, glass-epoxy, boron-epoxy, graphite-epoxy, and Kevlar 49 -... 

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