Unidirectional geometry. .

The use of porous membranes as templates for electrode structures was pioneered by Martin and coworkers nearly 20 years ago, and this approach has since been extended to include numerous electrode compositions and geometries " and applications beyond energy storage, including sensing and separations. In this approach, chemical and electrochemical routes are used to fill in the cylindrical, uniform, unidirectional pores of a free-standing membrane with electrochemically active materials and... 

The [10°] off axis tension specimen shown in Fig 3.23 is another simple specimen similar in geometry to that of the [ 45 ]s tensile test. This test uses a unidirectional laminate with fibers oriented at 10° to the loading direction and the biaxial stress state (i.e. longitudinal, transverse and in-plane shear stresses on the 10° plane) occurs when it is subjected to a uniaxial tension. When this specimen fails under tension, the in-plane shear stress, which is almost uniform through the thickness, is near its critical value and gives the shear strength of the unidirectional fiber composites based on a procedure (Chamis and Sinclair, 1977) similar to the [ 45°]s tensile test. 

As noted earlier, CVl is nsed primarily to form ceramic-fiber-reinforced ceramic matrix composites. The most common of these combinations is SiC fiber/SiC matrix composites. One commercially available product has a two-dimensional 0/90 layup of plain weave fabric and fiber volume fraction of about 40%. This same composite can be fabricated with unidirectional fibers and with 45° architectures. The most commonly used SiC fiber for the preforms is Nicalon , the mechanical properties for which were provided earlier in Section 5.4.2.7. A number of other carbide and nitride fibers are also available, including Si3N4, BN, and TiC. Preform geometries can be tailored to the application in order to maximize strength and toughness in the direction of maximnm stresses. The reactions used to form the matrix are similar to those used in CVD processes (cf. Section 7.2.4) and those described previously in Eq. (3.105). 

In-Plane Shear Properties. The basic lamina in-plane shear stiffness and strength is characterized using a unidirectional hoop-wound (90°) 0.1 -m nominal internal diameter tube that is loaded in torsion. The test method has been standardized under the ASTM D5448 test method for in-plane shear properties of unidirectional fiber-resin composite cylinders. D5448 provides the specimen and hardware geometry necessary to conduct the test. The lamina in-plane shear curve is typically very nonlinear [51]. The test yields the lamina s in-plane shear strength, t12, in-plane shear strain at failure, y12, and in-plane chord shear modulus, G12. 

A first step in the validation of this approach is to test simple specimens under controlled conditions and to compare predictions with measured failure load values. First lap shear geometries were examined, then an L-geometry was studied in more detail. The bond-line in these small specimens was very similar to that in the quasi-unidirectional fracture specimens as the small dimensions allow panels to be pressed uniformly after assembly (which is not the case for industrial top-hat stiffeners). 

Standard Mode I Double Cantilever Beam specimens for delamination testing of a unidirectional (UD) IM7/977-2 composite were Z-pinned with two separate blocks of Z-Fiber reinforcement. The reinforced beam configuration was such as to provoke an unstable delamination, propagating between the two Z-pin blocks. Crack resistance curves for these specific geometry specimens of IM7/977-2 indicate that the unstable delamination cracks are arrested by the second Z-pin block, with the crack propagation resistance being dictated primarily by the Z-pinning density within a block. Acoustic emission analysis is used to interpret visual observations and other test data. 

Firstly, the geometry of the support must be considered. The radial flow through a cylindrical support is quite different from the unidirectional flow encountered in flat supports. Fortunately, in most cases the compact layer thickness is small compared to the curvature radius of the support surface. The filtration process can then approximately be described as one-dimensional filtration [54]. 

Secondly, the unidirectional compact growth geometry must be considered as shown in Fig. 6.31. The velocity v of the compact/suspension boundary must be defined as... 

We shall see later that it is often advantageous to consider the temporal or spatial development of a velocity field in terms of diffusion and convection processes. In this framework, the basic concept of diffusion over a distance -Jvi in a time increment t plays a critical role in helping to determine the extent of boundary influence on the flow. It should be recognized however, that the class of unidirectional flows is a special case in that the direction of diffusion is always at right angles to the direction of motion. In most flows this will not be true, and the influence of the boundary geometry will be propagated by means of momentum transport by both diffusion and convection. 

In this analysis, we neglect entry and exit effects and concentrate on the fully developed flow regime where the motion (u, v, w) is independent of 9. In a straight circular tube, we have already seen that the velocity field takes the form [(0, 0, w(r)]. However, in the case of a coiled tube, the tube geometry is no longer unidirectional, and there is no reason to suppose that the velocity field will be so simple. The equations of motion and continuity, specified in dimensional form, for a fully developed, 3D flow are... 

Although the flow geometry is relatively simple, the boundaries no longer correspond to coordinate surfaces. On the other hand when the parameter e is small, they deviate only slightly from the coordinate surfaces v = d/2 of the Cartesian coordinate system. We denote the velocity component in the z direction as w. The exact flow problem is to solve the unidirectional flow equation,... 

Because the boundary geometry depends on x, the unidirectional velocity component is now a function of both x and y. 

Figure 17.3 General geometries of PCET reactions defined by the spatial configuration of the four transfer elements, De, Dp, Ae, and Ap. In the Type A reaction, ET and PT coordinates are unidirectional with little or no site-differentiation. The latter case is formally an HAT reaction. Type B also represents unidirectional PCET, but with significant differen-...

Huang H, Talreja R. Effect of void geometry on elastic properties of unidirectional fibre reinforced composites. Compos Sci Technol 2005 65 1964-81. 

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