Aligned fiber approximation

A bed of aligned fibers is approximately transversely isotropic and flow parallel to the fibers is greatly favored over perpendicular flow. One could thus argue that Equation 11.7 should be generalized to incorporate a permeability tensor. Due to its lack of scientific... 

In a transverse direction, the thermal conductivity of a unidirectionally aligned fiber composite (i.e. transversely isotropic) can be approximated by the action-in-series model. This would give... 

For USAXS and SAXS data the tangent-plane approximation is valid and the relation between scattering angle and the units of reciprocal space are given by Eq. (2.7). If the scattering pattern is properly aligned with the vertical direction identical to a fiber axis or the polymer chain direction, then sy = 53. In similar manner the. vx-axis of the detector is related to the actual orientation of the sample with respect to the beam. 

It is assumed that the maximum stress in the next fiber located at a distance dj away is approximately equivalent to the composite tensile strength, cr. It follows then that the damage zone size, cq, for aligned short fiber composites is given by (Lauke et al., 1985)... 

Magnetism is yet another successful method for the alignment of individual peptide fibers. Magnetite (Fe304) particles approximately lOnm in size were noncovalently attached to diphenylanalanine nanotubes during fiber... 

One of the first examples of mesoscopic-macroscopic two-dimensional ordering within a structure involved a bacterial superstructure formed from the co-aligned multicellular filaments of Bacillus subtilis that was used to template macroporous fibers of either amorphous or ordered mesoporous silica [82], The interfilament space was mineralized with mesoporous silica and, following removal of the organic, a macroporous framework with 0.5 pm wide channels remained. Mesoporous silica channel walls in this hierarchical structure were curved and approximately 100 nm in thickness. Dense, amorphous walls were obtained by replacing the surfactant-silicate synthesis mixture with a silica sol solution. The difference in the mode of formation between porous and non-porous wall structures was explained in terms of assembly from close-packed mesoporous silica coated bacterial filaments in the former compared to consolidation of silica nanoparticles within interfilament voids in the latter. 

Secondary wall fibrils closer to the primary wall lie at an approximate 45° angle to the fiber axis (Figure 5.31), while this orientation becomes aligned more closely with the fibrillar axis as the fiber core, or lumen, is approached (Figure 5.32). 

An interesting aspect of the work on UHMW polyethylene was the possibility of studying the anisotropy of the conductivity since aligned samples of stretch-oriented fibers could be produced and the effect of fiber orientation investigated. These experiments showed charge transport to be favored by a factor of approximately 20 along the direction of the oriented fibers compared with perpendicular to the fibers. This represented the first measurement of anisotropic conduction using the PR-TRMC technique. 

Because the observed A/ for the 73M specimen in the parallel and perpendicular orientations was approximately 25 and 13 kHz respectively, it can be concluded that in this specimen the polymer chain axis is highly aligned with the fiber axis. Similar result was obtained for the 73R specimen. 

As we have seen, the presence of fibers in the matrix has the effect of stiffening and strengthening it. The tensile deformation behavior of fiber-reinforced composites depends largely on the direction of the applied stress in relation to the orientation of the fibers, as illustrated in Figure 3.48. The maximum strength and modulus are achieved with unidirectional fiber reinforcement when the stress is aligned with the fibers (0°), but there is no enhancement of matrix properties when the stress is applied perpendicular to the fibers. With random orientation of fibers the properties of the composite are approximately the same in all directions, but the strength and modulus are somewhat less than for the continuous-fiber reinforcement. 

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