Uniaxial characterising

Note 5 From a crystallographic point of view, the uniaxial nematic structure is characterised by the symbol Dooh in the Schoenflies notation (Wmm in the International System). 

A simple bubble machine is devised and successfully applied in characterising lightly crosslinked PE resins for foam expansion. The biaxial stress-strain relationship is deduced from the air injection rate and pressure. The effects of strain rate, temperatnre and crosslinker level on the stress-strain behavionr are investigated. Uniaxial extension experiments are also performed and compared with biaxial extension data. 5 refs. 

Rheological properties of filled polymers can be characterised by the same parameters as any fluid medium, including shear viscosity and its interdependence with applied shear stress and shear rate elongational viscosity under conditions of uniaxial extension and real and imaginary components of a complex dynamic modulus which depend on applied frequency [1]. The presence of fillers in viscoelastic polymers is generally considered to reduce melt elasticity and hence influence dependent phenomena such as die swell [2]. 

Nematic phases are characterised by a uniaxial symmetry of the molecular orientation distribution function f(6), describing the probability density of finding a rod with its orientation between 6 and 6 + d0 around a preferred direction, called the director n (see Fig. 15.49). An important characteristic of the nematic phase is the order parameter (P2), also called the Hermans orientation function (see also the discussion of oriented fibres in Sect. 13.6) ... 

Desiccation effects on the mechanical behaviour of the rock are characterised by the changes in the Young s modulus, uniaxial strength and associated strains. 

The discussion of the most general form of biaxial orientation involves fairly complicated mathematics. Further discussion in this section and in the sections on the characterisation of orientation is therefore largely restricted to a special simple type of distribution of orientations of the structural units. This distribution is the simplest type of uniaxial orientation, for which the following conditions apply. 

For the simplest type of uniaxial orientation the distribution function reduces to N(6), where N(6)do) is the fraction of units for which OX3 lies within any small solid angle dco at angle 6 to 0X3. By characterising the distribution is meant finding out as much as possible about N 6) for the various types of structural unit that may be present in the polymer. 

For uniaxially stretched networks, the molecular deformations are characterised by the radii of gyration R u an respectively parallel and perpendicular to the stretching direction. From the small-angle scattering function, the molecular deformation of a stretched elastic phantom chain has been calculated for three cases 1) Free-fluctuation phantom network... 

The second type of explanation for finding values of R less than 3 involves the assumption that the emission and absorption axes of the fluorescent molecule are not coincident. Kimura et al. have considered a model in which the absorption and emission axes each have, independently, a cylindrically symmetric distribution of orientations around a third unique axis in the molecule, and Nobbs et al. have considered a model which includes both this and the possibility that there is a fixed angle between the emission and absorption axes which are otherwise uniformly distributed around a third unique axis. In the more general model at least three parameters are required to specify the relationships between the directions of the emission and absorption axes and that of the unique axis of a fluorescent molecule and these are not generally known. For orthotropic symmetry, five v, are required to characterise the distribution of orientations of the unique axes and if the constant NqIo is included, there is a total of at least nine unknown quantities. No attempt has so far been made to evaluate these from intensity measurements on an orthotropic sample. For a uniaxial sample only two parameters, cos O and cos O, are required for characterising the distribution of orientations and by making various approximations the total number of unknown quantities can be reduced to six. Their evaluation then becomes a practical possibility. 

The choice of fluorescent probe depends on a variety of factors. It has already been pointed out that what is determined directly is information which characterises the distribution of orientations of the fluorescent molecules. The ideal experiment would be one in which the polymer molecules themselves contained fluorescent groups. Stein has considered the theory of the fluorescence method specifically for a uniaxially oriented fluorescent rubber but no experiments to study orientation have been reported for such a system. Nishijima et al have, however, made some qualitative observations on the polarisation of the fluorescent light from polyvinylchloride films which had been first stretched and then irradiated with light of wavelength 185 nm to produce fluorescent polyene segments. 

The current application of NMR methods to the study of polymeric materials falls essentially into two categories. Of initial interest is its potential for characterising molecular orientation rather more precisely than has hitherto been possible in the past, using other methods. At present, experimental inaccuracies and mathematical complexities pose a limitation to its application to those polymer systems involving low symmetries. Set against this, is its well established success in characterising orientation in uniaxially drawn semi-crystalline polymers and perhaps even more impressively its application to non-crystalline polymers. Secondly, we have seen that the anisotropy of the second moment can also be quantitatively analysed in the case of various forms of molecular motion. Providing the firequency of molecular motion is comparable to the NMR line width it will have a predictable effect on the second moment anisotropy and this has already been studied in a number of oriented polymer systems. The implications for a molecular interpretation of mechanical relaxations are clear. 

Exponential correlations were established for the prediction of uniaxial compressive strength ratio/ratio of static and dynamic elastic modulus of rock mass from the intact rock uniaxial compressive strength/elastic modulus and joint factor (Ramamurthy, 1993), which includes joint frequency, joint inclination andjoint strength. These relations are useful in characterisation of jointed rock mass by knowing the intact rock properties and the joint factor. 

One approach to characterising the molecular orientation in both uniaxially and biaxially oriented samples of PET makes use of the ratio of the absorption bands near 1250 and 1725 cm, the first of which shows parallel dichroism and the second perpendicular dichroism. An equation is developed that relates this ratio to the molecular orientation with respect to the direction of measurement. Thus, it is possible to determine individually the orientation functions with respect to the machine and transverse directions (131). 

Atlanta, Ga., 26th-30th April 1998, p.2223-7. 012 NEW APPROACH TO THE CHARACTERISATION OF MOLECULAR ORIENTATION IN UNIAXIALLY AND BIAXIALLY STRETCHED SAMPLES OF PETP Cole K C Daly H B Sanschagrin B Nguyen K T ... 

Particle failure induces microcracks in the material. They deform to form ellipsoidal cavities. In between the particles, the matrix is only single-phase and thus has an increased ductility. The cavities thus grow by slipping of the matrix (see sections 6.2.3 and 6.2.5) on planes of maximum shear stress (e.g., in a uniaxial stress state at 45° to the loading direction). The matrix between the cavities is drawn to thin tips or ridges. The finally formed fracture surface is characterised by a large number of dimples formed in this way. The size of the dimples is in the range of a few micrometres. Sometimes, this kind of fracture is called fibrous fracture. 

Maltby, L.P. Enstad, G.G. (1993) Uniaxial tester for quality control and flow property characterisation of powders. Bulk Solids Handling, 13, 135. 

Stanley-Wood, N.G. Abdelkarim, A.M. (1983b) Proc ofRILEM/CNR Int. Symp on Principles Applications of Pore Structural Characterisation, Milan (eds J.M. Haynes P. Rossi-Doria). Arrowsmith, Bristol. Stanley-Wood, N.G., AbdelKarim, A., Johansson, M.E., Sadeghnejad, G. Osborne, N. (1990) The variation in, and correlation of, the energetic potential and surface areas of powders with degree of uniaxial compaction. Powder Technol. 60, 15-26. 

All low molecular weight thermotropic nematic liquid crystals so far characterised are uniaxial, so they have just two principal refractive indices, ne and tio, and the difference between these is the birefringence An = (n - no). The optic axis is coincident with the director, and the principal refractive indices are often denoted as fi s tu (parallel to the director), and fii = iio (perpendicular to the director). 

Unified equations that couple rate-independent plasticity and creep [114] are not readily available for SOFC materials. The data in the hterature allows a simple description that arbitrarily separates the two contributions. In the case of isotropic hardening FEM tools for structural analysis conveniently accept data in the form of tabular data that describes the plastic strain-stress relation for uniaxial loading. This approach suffers limitations, in terms of maximum allowed strain, typically 10 %, predictions in the behaviour during cycling and validity for stress states characterised by large rotations of the principal axes. 

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