Uniaxial definition

First, consider uniaxial tension loading in the 1-direction on a flat piece of unidirectionally reinforced lamina where only the gage section is shown in Figure 2-20. The specimen thickness is not just one lamina, but several laminae all of which are at the same orientation (a single lamina would be too fragile to handle). The strains and E2 are measured so, by definition,... 

In this review the definition of orientation and orientation functions or orientation averages will be considered in detail. This will be followed by a comprehensive account of the information which can be obtained by three spectroscopic techniques, infra-red and Raman spectroscopy and broad line nuclear magnetic resonance. The use of polarized fluorescence will not be discussed here, but is the subject of a contemporary review article by the author and J. H. Nobbs 1. The present review will be completed by consideration of the information which has been obtained on the development of molecular orientation in polyethylene terephthalate and poly(tetramethylene terephthalate) where there are also clearly defined changes in the conformation of the molecule. In this paper, particular attention will be given to the characterization of biaxially oriented films. Previous reviews of this subject have been given by the author and his colleagues, but have been concerned with discussion of results for uniaxially oriented systems only2,3). 

Definition. Fiber symmetry is uniaxial or cylindrical symmetry. Revolving the sample about the fiber axis does not change the scattering pattern, but tilting the sample with respect to the fiber axis does. 

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

Note 1 See 3.1.1 for the definition of a uniaxial nematic mesophase, 5.8.1 for the definition of uniaxial mesophase anisotropy, and Definitions 3.3 and 5.8.2 relating to biaxial mesophases. 

Note 2 From the definition of general homogeneous flow (Definition 1.5) G X = GX = constant) in the particular case of steady uniaxial elongation flow... 

Note 1 The stress tensor for a uniaxial deformation is given in Definition 3.1. 

Component stress tensor resulting from a compressive uniaxial deformation. Note See notes 1 and 2 of Definition 3.2. 

Note 3 From Definition 5.14, the absolute modulus in uniaxial deformation... 

Definition of molecular mass averages, 17 Deformation flexural, 825 plastic, 830 polarisation, 325 properties, 824 uniaxial, 825 De Gennes... 

Birefringent retarders are made of anisotropic uniaxial crystals such as calcite, a-quartz, sapphire, zinc sulphide, cadmium selenide and others. As Eq. (3.2-14) shows, the produced retardation is exact for a definite wavenumber or for its multiples. Between them all remaining possible polarization states are passed through. 

If we now generalize the definition of director to be the unit vector parallel to the major axis of the order parameter tensor, we find that at vanishingly low shear rates, where the order parameter tensor is nearly uniaxial, this definition reduces to the usual meaning of the term director. ... 

In uniaxial macroscopic deformation, the term draw ratio (DR) is customarily used to denote nominal draw (not molecular draw), or the change from the sample s initial dimension to its deformed state at each drawing step. Even though this is by no means a rigorous definition, it applies to deformations induced during simple sample extension or during stretching by differential roll speed. DR assumes full extension efficiency. 

Figure 18. Effect of interparticle distance, A, on plastic deformation of matrix strands between particles (a) definitions of the size parameters D = particle diameter, vP = particle volume content, aQ = applied stress, and aK = stress concentration (b) with a small interparticle distance, a uniaxial stress state is dominant between the particles and microvoids after cracking of the particles, and plastic yielding can be obtained and (c) with a large interparticle distance, thick matrix strands favor a triaxial stress state between the particles and microvoids, and plastic yielding is hindered.

Conversely, Ehlermann and Schubert (1987) sustained that compressibility results from materials of different composition cannot be compared and that flowability characterization through compressibility must be made specifically for each food variety. Moreover, confined uniaxial compression is a simple compression test that provides an approximate measure of the flowability of powders. Therefore, it is not suitable for silo design but may prove to be a convenient method for process control in any food laboratory (e.g., to evaluate particle cohesion). Table II offers a range value definition for flowability classification by comparing flow function (ratio between the maximum consolidation stress and unconfined yield stress) with compressibility. 

In the case of uniaxial tension, early authors introduced the nominal definition of strains (fuUy Lagrangian strains) for describing elastic deformation (27),... 

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