Parallel fibers uniform

The torsion-tube test described by Whitney, Pagano, and Pipes [2-14] involves a thin circular tube subjected to a torque, T, at the ends as in Figure 2-29. The tube is made of multiple laminae with their fiber directions aligned either all parallel to the tube axis or all circumferentially. Reasonable assurance of a constant stress state through the tube thickness exists if the tube is only a few laminae thick. However, then serious end-grip difficulties can arise because of the flimsy nature of the tube. Usually, the thickness of the tube ends must be built up by bonding on additional layers to introduce the load so that failure occurs in the central uniformly stressed portion of the tube (recall the test specimen criteria). Torsion tubes are expensive to fabricate and require relatively sophisticated instrumentation. If the shearing strain y 2 is measured under shear stress t.,2, then... 

Real situations demand more uniformity in composite properties than can be provided by unidirectional composites. Therefore lamina stacking sequences are made where the fiber orientation is altered to provide good properties in all directions. Lamina composed of fiber and matrix in which the fibers are all parallel to each other are stacked on top of each other with a systematic variation in fiber direction. These lamina are then bonded together and the resulting material has more uniformity in properties. Likewise in short fiber or discontinuous fiber composites fiber orientation is random. Therefore properties in directions other than parallel to the fiber (i.e. off-axis) are important70>. 

Assume that the fibers in a filter are cylindrical they are parallel to each other and are uniformly assembled. Consider cake filtration in which particles are collected with the deposited particles forming a layer of porous structure as shown in Fig. 7.13(a). Thus, to account for the total pressure drop, three basic flow modes are pertinent (1) flow is parallel to the axis of fibers (2) flow is perpendicular to the axis of the cylinder and (3) flow passes through a layer of a homogeneous porous medium. In the analysis of the first two modes given later, Happel s model [Happel, 1959] is used, while for the third mode, Ergun s approach [Ergun, 1952] is used. 

Consider a unidirectional composite with fibers so long that end effects can be ignored, as shown in Figure 15.7. Assume further an ideal composite in which matrix and fibers are linearly elastic, the two are perfectly adhered, and the fibers are uniformly distributed. When a load is applied parallel to the fibers (axis 1), the strain in the fibers and in the matrix are the same (2,6,7,11) ... 

It is assumed that the tube is made of a composite material which is composed of stiff duetile fibers arranged in a parallel uniform array in a ductile matrix. The eomposites of metal-metal type are eonsidered, first of all. However, the combination of a ductile matrix with brittle fibers can be easily accounted for, as well. As an example of the latter ease serves the aluminium alloy reinforced with boron fibers. 

Back-reflection pinhole camera. If the incident beam is normal to the sheet specimen and therefore parallel to the fiber axis, and a projection like that shown in Fig. 9-10(b) is made (projection plane parallel to sheet), then both the incident beam and the fiber axis coincide with the center of the projection. If the texture is ideally sharp, the (hkl) pole figure will consist of one or more concentric circles centered on the center of the projection, and the chance that one of these pole circles will coincide with the concentric reflection circle is essentially zero no reflection will occur. But if the texture has enough scatter, one of the pole circles will broaden into a band wide enough to touch the reflection circle at all points a Debye ring of uniform intensity will be formed. See Prob. 9-7. Thus a uniform Debye ring is not always evidence for randomly oriented grains. 

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