Anisotropicity transverse

Boyd (39) has reviewed the published data and theories of anisotropic transverse shrinkage. He has concluded, in agreement with Bosshard s (40) contention, that the dominant factor is the greater degree of lignification in the radial walls. This characteristic reduces sorption of water (Figure 11). Boyd also attributes a significant effect to the preponderance of radially flattened thick-walled cells in the latewood of some woods, particularly conifers. 

Figure 9.25 The ratio R- Rg (sttetched)// (unstretched) as a function of sample elongation (100) , longitudinal V, longitudinal O, transverse, anisotropic , transverse, end-on A, transverse, anisotropic A, transverse, end-on. ...

The thermal expansion behaviour of ultra high modulus polyethylene is very anisotropic. Transverse to the draw direction the thermal expansion coefficient is positive and comparable to that for isotropic polymer. In the draw direction the coefficient is negative and very small ( v 10" / ). For low molecular weight polymers the value... 

The transverse modulus is lower partly because the cell wall is less stiff in this direction, but partly because the foam structure is intrinsically anisotropic because of the cell shape. When wood is loaded across the grain, the cell walls bend (Fig. 26.5b,c). It behaves like a foam (Chapter 25) for which... 

Consider the situation of a thin unidirectional lamina under a state of plane stress as shown in Fig. 3.9. The properties of the lamina are anisotropic so it will have modulus values of E and Ei in the fibre and transverse directions, respectively. The values of these parameters may be determined as illustrated above. 

Note that no assumptions involve fiber-reinforced composite materials explicitly. Instead, only the restriction to orthotropic materials at various orientations is significant because we treat the macroscopic behavior of an individual orthotropic (easily extended to anisotropic) lamina. Therefore, what follows is essentially a classical plate theory for laminated materials. Actually, interlaminar stresses cannot be entirely disregarded in laminated plates, but this refinement will not be treated in this book other than what was studied in Section 4.6. Transverse shear effects away from the edges will be addressed briefly in Section 6.6. 

E. Reissner, A Consistent Treatment of Transverse Shear Deformations in Laminated Anisotropic Piates, AIAA Journal, May 1972, pp. 716-718. 

Anisotropic material In an anisotropic material the properties vary, depending on the direction in which they are measured. There are various degrees of anisotropy, using different terms such as orthotropic or unidirectional, bidirectional, heterogeneous, and so on (Fig. 3-19). For example, cast plastics or metals tend to be reasonably isotropic. However, plastics that are extruded, injection molded, and rolled plastics and metals tend to develop an orientation in the processing flow direction (machined direction). Thus, they have different properties in the machine and transverse directions, particularly in the case of extruded or rolled materials (plastics, steels, etc.). 

In an anisotropic material, the properties depend on the direction in which they are tested. For example, rolled metals, which are anisotropic, tend to develop a crystal orientation in the rolling direction. Thus rolled and sheet-metal products have different mechanical properties in the two major directions. Also, extruded plastic film can have different properties in the machine and transverse directions. These materials are oriented biaxi-ally and are anisotropic. (As reviewed above under EXTRUSION, Orientation). 

For a calculation of d. see R- H. Fowler. Statistical Thermodynamics. Second Edition, Cambridge University Press. 1956. p. 127. In Section 1.5a of Chapter 1 we defined the compressibility and cautioned that this compressibility can be applied rigorously only for gases, liquids, and isotropic solids. For anisotropic solids where the effect of pressure on the volume would not be the same in the three perpendicular directions, more sophisticated relationships are required. Poisson s ratio is the ratio of the strain of the transverse contraction to the strain of the parallel elongation when a rod is stretched by forces applied at the end of the rod in parallel with its axis. 

If these concepts of curve analysis shall be applied to the anisotropic scattering of polymer fibers, one should choose to study either the longitudinal or the transversal density fluctuations. According to the decision made, the fiber scattering must be projected either on the fiber axis or on the cross-sectional plane. This results in scattering curves with a one- or a two-dimensional Porod s law. Because modern radiation sources always feature a point-focus, the required plots for the separation of fluctuation and transition zone are readily established (cf. Table 8.3). 

The parts are often anisotropic. Properties are different in the machine and the transverse directions. 

J. P. da Silva, H. E. Hemandez-Figueroa, and A. M. F. Frasson, Improved vectorial finite-element BPM analysis for transverse anisotropic media, Journal of Lightwave Technology 21, 567-576 (2003). 

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