Anisotropy of elastic properties

Bel] Belyatskaya, I.S., Serebryakov, V.G., Anisotropy of Elastic Properties in Iron-Chromium-Cobalt Alloys , Phys. Met. Metallogr., 49(5), 189—190 (1980), translated from Fiz. Met. Metallovd., 49(5), 1113-1114 (1980) (Experimental, Phys. Prop., 5)... 

The chapter begins with an overview of elastic anisotropy in crystalline materials. Anisotropy of elastic properties in materials with cubic symmetry, as well as other classes of material symmetry, are described first. Also included here are tabulated values of typical elastic properties for a variety of useful crystals. Examples of stress measurements in anisotropic thin films of different crystallographic orientation and texture by recourse to x-ray diffraction measurements are then considered. Next, the evolution of internal stress as a consequence of epitaxial mismatch in thin films and periodic multilayers is discussed. Attention is then directed to deformation of anisotropic film-substrate systems where connections among film stress, mismatch strain and substrate curvature are presented. A Stoney-type formula is derived for an anisotropic thin film on an isotropic substrate. Anisotropic curvature due to mismatch strain induced by a piezoelectric film on a substrate is also analyzed. 

In this chapter, elastic constants of single crystals are first summarized, and the anisotropy of elastic properties of single crystals is discussed using Young s modulus, Poisson s ratio, etc. Then, the elastic properties of dislocations are discussed using elastic constants of single crystals, followed by a summary of the elastic moduli of polycrystalline intermetallics. 

The SiC-Si matrix composite contains besides SiC fibrous particles some residual non-reacted carbon fibre material. Due to the highly anisotropic microstructure and anisotropy of elastic properties of the carbon fibres their presence gives rise to a high anisotropy of the Young s moduli. At a 22.3% content of carbon fibres the ratio is as high as 45.8% while at... 

The introduction of large gas phase volumes into the polymer alters the physical characteristics of the material volume weight, permeability to fluids and gases, and physico-mechanical properties. Moreover, the properties of the polymer matrix itself are changed (owing to orientation effects, supermolecular structure of the polymer in the walls, ribs and tension bars of cells), which drives up the value of specific strength on impact, and results in anisotropy of elasticity. 

Convergence of estimates of the melting curve of iron places a tighter constraint on the temperature at the ICB. Experimental measurements and theoretical calculations of elastic properties and plastic deformation of iron offer new interpretations for the inner core anisotropy. Prehminary results have been obtained on the properties of liquid iron, which allow a more direct comparison between laboratory measurements and seismic observations. 

Chapter 6 heralds the second part of the book and introduces the reader to anisotropy of the magnetic and electric properties of mesophases. Following in Chapter 7 there is a focus on the anisotropy of transport properties, especially of electrical cOTiductivity. Without these two chapters (Chapters 6 and 7), it would be impossible to discuss electro-optical properties in the third section of the book. Further, Chapters 7 and 8 deal with the anisotropy of the properties of elasticity and viscosity. Chapter 8 is more difficult than the others, and in order to present the theoretical results as clearly as possible, the focus is on the experimental methods for the determinatimi of Leslie viscosity coefficients from the viscous stress tensor of the nematic phase. Chapter 9 terminates the discussion of the anisotropy of... 

One can see firom Table n that the conditions of polymers preparation essentially influence their thermal and mechanical properties. The data of Table II show an evident anisotropy of the properties of polymer aligned in the magnetic field. First of all, noteworthy is the high value of elasticity modulus for the aligned polymer in the direction perpendicular to the direction of the magnetic field. It is about four times... 

The symmetry of a crystal type is relevant because frequently it is reflected in its material properties. A cubic crystal, for instance, has the corresponding symmetries in its mechanical properties. The lower the symmetry of a crystal, the more complicated is the anisotropy of its properties. This will be discussed in chapter 2, using the elastic properties as an example. 

The contribution of translational order parameters to the anisotropy of physical properties of liquid crystals has not been studied in detail. Evidence suggests that there is a very small influence of translational ordering on the optical properties, but effects of translational order can be detected in the measurement of dielectric properties. There are strong effects in both elastic properties and viscosity, but the statistical theories of these properties have not been extended to include explicitly the effects of translational order. 

Elasticity is a macroscopic property of matter defined as the ratio of an applied static stress (force per unit area) to the strain or deformation produced in the material the dynamic response of a material to stress is determined by its viscosity. In this section we give a simplified formulation of the theory of torsional elasticity and how it applies to liquid crystals. The elastic properties of liquid crystals are perhaps their most characteristic feature, since the response to torsional stress is directly related to the orientational anisotropy of the material. An important aspect of elastic properties is that they depend on intermolecular interactions, and for liquid crystals the elastic constants depend on the two fundamental structural features of these mesophases anisotropy and orientational order. The dependence of torsional elastic constants on intermolecular interactions is explained, and some models which enable elastic constants to be related to molecular properties are described. The important area of field-induced elastic deformations is introduced, since these are the basis for most electro-optic liquid crystal display devices. 

Anisotropy of the elastic constants results in a change of elastic properties of dislocations in intermetallics. We have textbooks for calculation of the elastic properties of dislocations using anisotropic elasticity theory (Hirth and Lothe, 1968 Steeds, 1973). The results calculated from the elastic constants of single crystals are summarized. 

Other physical properties. Anisotropy of thermal and electrical conductivity, coefficient of thermal expansion, elasticity, and dielectric constant may also provide information on internal structure. These properties, however, have so far been little used in structure determination, because they are less easily measured than those already considered consequently not very much experimental evidence is available for the purpose of generalizing on the relations between such properties and structural features. For further information on these subjects, see Wooster (1938), Nye (1957). 

The essential difference between treatments of chemical processes in the solid state and those in the fluid state is (aside from periodicity and anisotropy) the influence of the unique mechanical properties of a solid (such as elasticity, plasticity, creep, and fracture) on the process kinetics. The key to the understanding of most of these properties is the concept of the dislocation which is defined and extensively discussed in Chapter 3. In addition, other important structural defects such as grain boundaries, which are of still higher dimension, exist and are unknown in the fluid state. 

Theoretical analysis indicates that occurrence of such convective instabilities depends on anisotropy of electrical conductivity and dielectric properties in the initial aligned nematic material. That is, conductivity parallel to the direction of alignment must differ from conductivity perpendicular to this direction. Calculation of the stability condition requires knowledge not only of these anisotropic electrical properties but also of anisotropic elastic and viscous properties which oppose disruption of the alignment and flow. 

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