Elastic Properties Of Polycrystals Research Articles

Calculation of averaged elastic properties of materials having noncircular character of pole figures

An important application of quantitative description of textures of materials is calculation of the averaged physical properties of polycrystals. In this study, such properties are elastic parameters of materials. In recent years, the effect of crystallographic texture on the average values of elastic properties of polycrystals has been analyzed in many studies. Researchers often restrict themselves to the consideration of average values of Young’s or shear moduli, which are related to the components of the elastic compliance tensor. The simplest scheme of averaging of all components of the elastic compliance tensor is considered. Complicated (not angular) normal distributions of general character are used as the weight function. A practical example of application of these techniques to calculation of elastic compliance moduli of magnesium and titanium polycrystals is proposed.

Direction-dependent elastic grain-interaction models – a comparative study

Mechanical and diffraction (X-ray) elastic constants (diffraction (X-ray) stress factors for macroscopically elastically anisotropic specimens) can be calculated for polycrystalline specimens from single-crystal elastic data by employing elastic grain-interaction models. Traditionally, only so-called isotropic grain-interaction models are considered: all directions in the polycrystal are taken equivalent with respect to the grain interaction. Only recently, so-called direction-dependent, i.e. anisotropic grain-interaction models, have been proposed. These models can express the effects of the reduced dimensionality of thin films, of the surface anisotropy of bulk polycrystals and of a grain-shape (morphological) texture on the elastic properties of polycrystals. In this work, the available, recently proposed direction-dependent grain-interaction models will be compared, in particular on the basis of numerical calculations of diffraction and mechanical elastic constants, of variances of certain orientation-dependent stress and strain tensor components and of the distributions of strains in the Euler (orientation) space. It will be demonstrated that the so-called Vook–Witt and inverse Vook–Witt models become (but only approximate) equivalent to the Eshelby–Kröner model for certain grain-shape textures.

Use of Irreducible Spherical Tensors in the Calculation of the Mean Elastic Properties of Polycrystals

Use of Irreducible Spherical Tensors in the Calculation of the Mean Elastic Properties of Polycrystals

Description of the elastic properties of polycrystals by means of irreducible spherical tensors

Abstract We have expressed the elastic tensors in an irreducible spherical basis from a Cartesian basis in order to deal more easily with rotation operations. This allows us to calculate, in a very effective way, the elastic mean values of polycrystals and to determine the number of independent tensor components.

Elastic properties of polycrystals in the Voigt-Reuss-Hill approximation

The problem of calculating polycrystalline elasticity from texture has been treated in the most general way in the framework of the Voigt–Reuss–Hill (VRH) approximation. The analytical solution involves only the even texture coefficients up to fourth order, which can be derived with a limited number of experimental pole figures (e.g. one pole figure for hexagonal polycrystals). The present analysis has been applied to the prediction of the fourth-rank elastic tensors and Young's modulus for a rolled zinc sheet.

Elastic properties of polycrystals with trigonal crystal and orthorhombic specimen symmetry

Equations for evaluating the effective elastic response of a polycrystalline aggregate exhibiting trigonal crystal symmetry (point groups 3̄m or 32) and orthorhombic sample symmetry (mmm) are presented. The analysis uses the spherical harmonic representation of the orientation distribution function (ODF) to describe the texture. The aggregate elastic constants are determined through the Voigt and Reuss procedures in which the crystallites’ stiffnesses and compliances, respectively, are averaged over all orientations, weighted by the ODF. Results are given in analytic form and require only five coefficients of the ODF for the exact representation of the aggregate characteristics. An example of the application of the results is given for two different textures predicted by the fully constrained Taylor theory for a calcite polycrystal.

Effect of stress-induced anisotropy and porosity on elastic properties of polycrystals

Recent ultrasonic measurements performed on hot-pressed polycrystalline materials as a function of pressure and temperature simultaneously indicate that the interiors of the specimens may not be strain free. Residual strain arising from the fabrication process produces an anisotropic effect separate from any anisotropy that may arise simply from relative grain orientations that may or may not be randomized. Internal strain has a significant effect on measurements of the bulk modulus and particularly of its pressure derivative. The effect of residual porosity and permeability on the pressure derivative of the bulk modulus is also examined.