Fibers anisotropy

Zbou, L.M. and Mai. Y.W. (1993), On the single fiber pullout and pushout problem effect of fiber anisotropy. J. Appl. Math. Phys. (ZAMP) 44, 769-775. 

Kevlar fiber reinforced polyimide or epoxy CTE matched to ceramic, available from DuPont-Howe, dielectric constant = 3.6, moisture absorption reduced Relatively thick (over 4.5 mil), fiber anisotropy may produce non-uniform strains, microcracking problems... 

Optical Properties. When light falls on an object, it is either partially absorbed, reflected, or transmitted. The behavior of the object as it relates to each of these three possibiUties determines visual appearance. Optical properties of fibers give useful information about the fiber stmcture refractive indexes correlate well with fiber crystalline and molecular orientation and birefringence gives a measure of the degree of anisotropy of the fiber. 

The structure of CBCF is shown in the SEM micrograph in Fig. 4. The crenellated surface of the rayon derived carbon fibers is clearly visible, as is the phenolic derived carbon binder. The preferred orientation of the fibers (resulting from the slurry molding operation) is obvious in Fig. 4, and imparts considerable anisotropy to the material. The molding direction is perpendicular to the plane of the carbon fibers in Fig. 4. 

The strength of a bond increases with the wood density in the region of approx. 0.7 to 0.8 g/cm Above this density, a decrease of the bond strength occurs. Performance and properties of wood-based panels are strongly influenced by the properties of the used wood. The anisotropy as well as the heterogeneity, the variability of various properties and the hygroscopicity have to be taken into account. Also the orientation of the wood fibers bonding solid wood has to be considered. 

Composite materials have many distinctive characteristics reiative to isotropic materials that render application of linear elastic fracture mechanics difficult. The anisotropy and heterogeneity, both from the standpoint of the fibers versus the matrix, and from the standpoint of multiple laminae of different orientations, are the principal problems. The extension to homogeneous anisotropic materials should be straightfor-wrard because none of the basic principles used in fracture mechanics is then changed. Thus, the approximation of composite materials by homogeneous anisotropic materials is often made. Then, stress-intensity factors for anisotropic materials are calculated by use of complex variable mapping techniques. 

The quantitative assessment of the overall orientation of PET fibers is generally made on the basis of fiber optical anisotropy measurements, i.e., measurements of the optical birefringence of the fiber. The determination of the value of optical birefringence makes it possible to determine the value of Hermans function of orientation based on the equation ... 

Apart from the conditions of load transmission from fiber to matrix, the anisotropy of mechanical characteristics is also due to the considerable anisotropy of the fibers themselves in the longitudinal and transverse directions, especially in the case of fibrous reinforcements of polymeric nature [154]. 

Even though many potential factors can influence a design analysis, each application fortunately usually involves only a few factors. For example, TPs properties are dominated by the viscoelasticity relevant to the applied load. Anisotropy usually dominates the behavior of long-fiber RPs. 

RPs are either constructed from a single layer or built up from multiple layers. The properties of each layer are usually orthotropic, which is a special case of anisotropy. Fibers that remain straight in the single layer are desired. However, with many fabrics, they are woven into configurations that kink the fiber bundles severely. Such fabric constructions may be very practical since... 

Two approaches to the attainment of the oriented states of polymer solutions and melts can be distinguished. The first one consists in the orientational crystallization of flexible-chain polymers based on the fixation by subsequent crystallization of the chains obtained as a result of melt extension. This procedure ensures the formation of a highly oriented supramolecular structure in the crystallized material. The second approach is based on the use of solutions of rigid-chain polymers in which the transition to the liquid crystalline state occurs, due to a high anisometry of the macromolecules. This state is characterized by high one-dimensional chain orientation and, as a result, by the anisotropy of the main physical properties of the material. Only slight extensions are required to obtain highly oriented films and fibers from such solutions. 

Molecular orientation and the testing direction strongly influence the observed modulus of a polymer sample. Fibers are typically highly oriented and exhibit much higher modulus values than non-oriented samples prepared from the same polymer. In the case of films, we typically observe anisotropy a film exhibits a range of modulus values depending upon the testing direction. 

Anisotropy is frequently observed in soft materials, but the symmetry of anisotropy is varying. Fibers and films show, in general, less complex anisotropy than ordinary or photonic crystals. 

Some experiments are aiming at the study of structure evolution. In general, the studied material is isotropic or exhibits simple anisotropy (e.g., fiber symmetry). Most frequently the material is irradiated in normal-transmission geometry. A synchrotron beamline is necessary, because in situ recording during the materials processing is requested with a cycle time of seconds between successive snapshots (time-resolved measurements). 

To specify the components of the scattering vector by S 2 and s3 is only a suggestion. The specification meets the case that is of highest practical importance (anisotropy with fiber symmetry). 

Shape Change of Structural Entities. In many cases the growing anisotropy is not only a phenomenon of rotating structural entities, but also goes along with a deformation of the structural entities themselves. This case will be studied here. Only affine deformations shall be discussed. In practice, such processes are observed while thermoplastic elastomers are subjected to mechanical load, but also while fibers are spun. 

If the intended evaluation can be carried out on isotropic material, and thus the observed anisotropy is rather an obstacle than an advantage, the fiber pattern can be isotropized (cf. Sect. 8.4.2). This may, in particular, be helpful if lamellar structures are analyzed. If the focus of the study is on the anisotropic structure, the multidimensional CDF (cf. Sect. 8.5.5) may be a suitable tool for analysis. Several studies have demonstrated the power of the CDF method for the study of structure evolution during straining [174,177,181-183],... 

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