Fibers isotropy

Ceramic matrix composites are candidate materials for high temperature stmctural appHcations. Ceramic matrices with properties of high strength, hardness, and thermal and chemical stabiUty coupled with low density are reinforced with ceramic second phases that impart the high toughness and damage tolerance which is required of such stmctural materials. The varieties of reinforcements include particles, platelets, whiskers and continuous fibers. Placement of reinforcements within the matrix determines the isotropy of the composite properties. 

For rayon fiber based eomposites (Seetions 3 and 4) the fiber and powdered resins were mixed in a water slurry in approximately equal parts by mass. The isotropie piteh earbon fiber eomposites (Seetion 5) were manufaetured with less binder, typically a 4 1 mass ratio of fiber to binder being utilized. The slurry was transferred to a molding tank and the water drawn through a porous sereen under vacuum. In previous studies [2] it was established that a head of water must be maintained over the mold screen in order to prevent the formation of large voids, and thus to assure uniform properties. The fabrieation proeess allows the manufaeture of slab or tubular forms. In the latter case, the cylinders were molded over a perforated tubular mandrel covered with a fine mesh or screen. Moreover, it is possible to mold eontoured plates, and tubes, to near net shape via this synthesis route. 

Figure 9.4. The orientation of structural entities (rods) in space with respect to the (vertical) principal axis and the values of for, the uniaxial orientation parameter (Hermans orientation function) for (a) fiber orientation, (b) isotropy, (c) film orientation...

One of these methods is called kinetic calibration, in which analyte absorption from the sample to the liquid coating (PDMS) on the fiber is related to analyte desorption from the coating to the sample. The isotropy of absorption and desorption in the kinetic calibration has been described by Chen et al.31 In kinetic calibration, also called in-fiber standardization, desorption of a radio-labeled standard (preloaded on the fiber coating) into the sample is used to calibrate the extraction (absorption/adsorption in the case of a liquid/solid coating) of analyte from the sample into the fiber. This calibration approach considerably facilitates the use of SPME for the on-site field sampling of water, where the control of flow velocity or addition of a standard to the matrix is very difficult. 

Determining mechanical characteristics of fibrous materials is far from simple, mainly because of their small diameter. In particular, in the case of anisotropic fibers such as carbon or aramid, we need to determine five elastic constants, assuming isotropy in the cross-sectional plane. Figure 9.3 shows three of the five elastic constants the longitudinal Young s modulus of fiber, E or E, the transverse Young s modulus E22 or Ej, and the principal shear modulus, or Not shown are the two Poisson ratios the longitudinal Poisson s ratio of... 

These examples show that pSAXS experiments are an easy way to analyze the isotropy of the porosity in activated carbon fibers and to observe the development of porosity with the activation process. 

The examples presented in this work illustrate the suitability of pSAXS technique to characterize activated carbon fibers. It has been shown the isotropy features in activated carbon fibers prepared from different precursors and using different activating agents. In addition, this technique is able to obtain scattering measurements across the fiber diameter, which has allows us to obtain maps of pores distribution. The present results show that... 

If this process is repeated, one finds only three values of Poisson s ratio are needed, not six. For fiber-reinforced materials, the number of elastic constants may be further reduced if other symmetries appear. For example, in some materials short fibers are randomly oriented in a plane and this gives transverse isotropy. That is, there is an elastically isotropic plane but the stiffness and compliance constants will be different normal to this plane (five elastic constants are needed). 

An orthotropic material is called transversely isotropic when one of its principal planes is a plane of isotropy, i.e. at every point there is a plane on which the mechanical properties are the same in all directions [2]. Unidirectional carbon fibers packed in a hexagonal array with a relatively high volume fraction can be considered transversely isotropic, with the 2-3 plane normal to the fibers as the plane of isotropy (Figure 22.2). For a transversely isotropic material, it should be noted that the subscripts 2 and 3 (for a 2-3 plane of symmetry) in the material constants are interchangeable. Hence... 

It is also found that the orientation coefficient of these macroscopic fibers along the melt flow direction increases with the addition of LCPs. This can be attributed to the decrease of the melt viscosity. Favored orientation of reinforcing fibers leads to high anisotropy of final materials, which can be taken as a disadvantage if isotropy of the materials is needed. By working with in situ composites, novel technologies have been developed to decrease the anisotropy of final composites [151-156]. These approaches can also be utilized in the case of the in situ hybrid composite, due to their similarity to the in situ composite. 

With respect to continuous lamellar composites containing ribbons or tapes, isotropy in the plane is essentially provided at large ribbon aspect ratios (width to thickness) without any angle dependency [12]. The corresponding Eq. (2.12) is similar to Eq. (2.7) for fibers. To summarize the information in Table 2.2 ... 

Fibers that are randomly oriented in the plane or in space may provide isotropy but at the expense of the overall composite modulus... 

Isotropy in a plane may be achieved with aligned ribbons the modulus value in this case is approximately equal to that of an oriented continuous fiber composite tested in the longitudinal direction. 

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