Elastic properties orientation dependence

The present review shows how the microhardness technique can be used to elucidate the dependence of a variety of local deformational processes upon polymer texture and morphology. Microhardness is a rather elusive quantity, that is really a combination of other mechanical properties. It is most suitably defined in terms of the pyramid indentation test. Hardness is primarily taken as a measure of the irreversible deformation mechanisms which characterize a polymeric material, though it also involves elastic and time dependent effects which depend on microstructural details. In isotropic lamellar polymers a hardness depression from ideal values, due to the finite crystal thickness, occurs. The interlamellar non-crystalline layer introduces an additional weak component which contributes further to a lowering of the hardness value. Annealing effects and chemical etching are shown to produce, on the contrary, a significant hardening of the material. The prevalent mechanisms for plastic deformation are proposed. Anisotropy behaviour for several oriented materials is critically discussed. 

The viscous and elastic properties of orientable particles, especially of long, rod-like particles, are sensitive to particle orientation. Rods that are small enough to be Brownian are usually stiff molecules true particles or fibers are typically many microns long, and hence non-Brownian. The steady-state viscosity of a suspension of Brownian rods is very shear-rate- and concentration-dependent, much more so than non-Brownian fiber suspensions. The existence of significant normal stress differences in non-Brownian fiber suspensions is not yet well understood. 

These are covered with a sheath of para-crystaUine polyglucosan material surrounded by hemicellulose [29]. In most natural fibers, these micro-fibrils orient themselves at an angle to the fiber axis called the micro-fibril angle. The ultimate mechanical properties of natural fibers are found to be dependent on the microfibrillar angle. Gassan et al. have performed calculations on the elastic properties of natural fibers [30]. 

For cubic symmetry materials, three independent elastic properties that are orientation dependent are required to describe the mechanical behavior of the material. This anisotropy effect increases significantly the number of the nonzero elements in the FE stiffness matrix leading to alteration in the calculated stress components and the wave speed. In order to test these anisotropy effects, we plot the wave profiles of three different orientations and compare it with the isotropic behavior with a loading axis in the [001] directions as shown in Fig 8. We observed that under the same loading condition, the peak stress of [111] and [Oil] orientations are slightly higher than those of the [001] which is lower that that of isotropic material. Furthermore, wave speed varies moderately with orientation with the fastest moving wave in the [ 111 ] followed by [011 ], isotropic medium and [001 ] respectively. 

An epitaxial film is strained in the initial stages of film growth. The strain energy increases with film thickness and may eventually be relaxed by the introduction of misfit dislocations [14.32-14.35], see Fig. 14.7, or by formation of (110) twins in the YBCO [14.36]. The critical thickness at which the misfit dislocations form depends on the lattice mismatch and the elastic properties of the film. The misfit in epitaxial c-axis-oriented YBCO films is accommodated by the formation of twins and edge dislocations with Burgers vectors [100]ybco and [010]ybco [14.37],... 

Equations (A.7) also show that, in general, the prediction of a property that depends on a tensor of rank I will require knowledge of orientation averages of order /. The elastic constants of a material are fourth-rank tensor properties thus the prediction of their values for a drawn polymer involves the use of both second- and fourth-order averages, in the simplest case P ico O)) and P (x>s6)), and thus provides a more severe test of the models for the development of orientation. The elastic constants are considered in section 11.4. 

It has already been stated (p, 38) that sulphur forms chain molecules on quick coolii after beiii kept at 250 C. If plastic sulphur, obtained on pouring the melt into cold water, is stretched, crystals are formed, built up from oriented polymers, composed of Sg-units Very pronounced, highly elastic properties and a considerable tensile strength can be observed at this stage, depending upon the temperature of preparation and upon the time elapsing after the cooling process. 

As already mentioned, for the fixed direction of the nematic director n the shear modulus is absent because the shear distortion is not coupled to stress due to the material slippage upon a translation. The compressibility modulus B is the same as for the isotropic liquid. New feature in the elastic properties originates from the spatial dependence of the orientational part of the order parameter tensor, i.e. director n(r). It is assumed that the modulus S of the order parameter Qij r) is unchanged. In Fig. 8.4 we can see the difference between the translation and rotation distortion of a nematic. 

Mechanical properties of PMC are strongly influenced by the filler (by its size, type, concentration and dispersion) and by the properties of the matrix, as well as the extent of interfacial interactions and adhesion between them and their micro-structural configurations. The interrelation of these variables is rather complex. In FRC, the system is anisotropic where fibres are usually oriented uniaxially or randomly in a plane during the fabrication of the composite, and properties are dependent on the direction of measurement. Generally, the rule of mixture equations are used to predict the elastic modulus of a composite with uniaxially oriented (continuous) fibres under iso-strain conditions for the upper bound longitudinal modulus in the orientation direction (Equation 6.10). 

Because of the a(hcp) structure of titanium, elastic properties depend on the orientation of the titanium crysteds and the texture of polycrystalline titanium. Interstitial impiuities (e.g. oxygen... 

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