Isotropic factor

This relation is only valid for a crystal with isotropic /-factor. The effect of crystal anisotropy will be treated in Sect. 4.6.2. The function h(6) describes the probability of finding an angle 6 between the direction of the z-axis and the y-ray propagation. In a powder sample, there is a random distribution of the principal axes system of the EFG, and with h 6) = 1, we expect the intensity ratio to be I2J li = I, that is, an asymmetric Mossbauer spectrum. In this case, it is not possible to determine the sign of the quadmpole coupling constant eQV. For a single crystal, where h ) = — 6o) 5 delta-function), the intensity ratio takes the form... 

Table Bl.12.3 Spin-dependent factor f(T) for the isotropic second-order quadnipole shift.

Advantages. Compared to DOR, a small rotor can be used allowing relatively fast spiiming speeds high RF powers can be attained and if the coil is moved with the rotor a good filling factor can be obtained. In the isotropic dimension high-resolution spectra are produced and the second dimension retains the anisotropic information. 

Also in this case, Tp corresponds to a relaxation time which determines the coupling of the modulated variable to the external bath. The pressure scaling can be applied isotropically, whidi means that the factor is the same in all three spatial directions. More realistic is an anisotropic pressure scaling, because the box dimensions also change independently during the course of the simulation. 

F = direct view factor Ey, fraction of isotropic radiation from Aj intercepted directly by Aj. 

Figure 4.11. Diagrammatic sketches of atomic lattice rearrangements as a result of dynamic compression, which give rise to (a) elastic shock, (b) deformational shock, and (c) shock-induced phase change. In the case of an elastic shock in an isotropic medium, the lateral stress is a factor v/(l — v) less than the stress in the shock propagation direction. Here v is Poisson s ratio. In cases (b) and (c) stresses are assumed equal in all directions if the shock stress amplitude is much greater than the material strength.

We saw in Chapter 2 that, when boundary energies were the dominant factor, we couid easiiy predict the shapes of the grains or phases in a materiai. Isotropic energies gave tetrakaidecahedrai grains and sphericai (or iens-shaped) second-phase particies. 

Nazem [31] has reported that mesophase pitch exhibits shear-thinning behavior at low shear rates and, essentially, Newtonian behavior at higher shear rates. Since isotropic pitch is Newtonian over a wide range of shear rates, one might postulate that the observed pseudoplasticity of mesophase is due to the alignment of liquid crystalline domains with increasing shear rate. Also, it has been reported that mesophase pitch can exhibit thixotropic behavior [32,33]. It is not clear, however, if this could be attributed to chemical changes within the pitch or, perhaps, to experimental factors. 

For example, a 1 MeV point isotropic source of gamma-radiation has a buildup factor ol 2.1 when penetrating a mean-free thickness of water. If the build-up factor is ignored, equation 8.3-11 is exp(-l) = 0.36. Hence, 36% of the radiation passes through the shield. But when the buildup factor is included, 2.1 0.36 = 76% of the radiation penetrates the shield. 

For a specially orthotropic square boron-epoxy plate with stiffness ratios 0 /022= 10 and (Di2-t-2D66) = 1, the four lowest frequencies are displayed in Table 5-3 along with the four lowest frequencies of an isotropic plate. There, the factor k is defined as... 

Fracture is caused by higher stresses around flaws or cracks than in the surrounding material. However, fracture mechanics is much more than the study of stress concentration factors. Such factors are useful in determining the influence of relatively large holes in bodies (see Section 6.3, Holes in Laminates), but are not particularly helpful when the body has sharp notches or crack-like flaws. For composite materials, fracture has a new dimension as opposed to homogeneous isotropic materials because of the presence of two or more constituents. Fracture can be a fracture of the individual constituents or a separation of the interface between the constituents. 

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. 

Such oriented composites should also have electrical anisotropy. Indeed, for the composite material with

sample amounts to 5 x 10 5 Ohm-1 cm-1 which is also below... 

For those not familiar with this type information recognize that the viscoelastic behavior of plastics shows that their deformations are dependent on such factors as the time under load and temperature conditions. Therefore, when structural (load bearing) plastic products are to be designed, it must be remembered that the standard equations that have been historically available for designing steel springs, beams, plates, cylinders, etc. have all been derived under the assumptions that (1) the strains are small, (2) the modulus is constant, (3) the strains are independent of the loading rate or history and are immediately reversible, (4) the material is isotropic, and (5) the material behaves in the same way in tension and compression. 

Stiffness For an isotropic material with a modulus of elasticity E, the bending stiffness factor (El) of a rectangular beam b wide and h deep stiffness is ... 

In many isotropic materials the shear modulus G is high compared to the elastic modulus E, and the shear distortion of a transversely loaded beam is so small that it can be neglected in calculating deflection. In a structural sandwich the core shear modulus G, is usually so much smaller than Ef of the facings that the shear distortion of the core may be large and therefore contribute significantly to the deflection of a transversely loaded beam. The total deflection of a beam is thus composed of two factors the deflection caused by the bending moment alone, and the deflection caused by shear, that is, S = m + Ss, where S = total deflection, Sm = moment deflection, and Ss = shear deflection. 

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