Table of Contents
Textures and Microstructures
Volume 22, Issue 3, Pages 139-167

Review of Deterministic Methods of Calculation of Polycrystal Elastic Constants

Instytut Podstaw Metalurgii PAN, ul. W.S. Reymonta 25, Kraków 31-149, Poland

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper is a critical review of non-stochastic (referred here as deterministic) methods of calculation of effective elastic constants of single phase statistically homogeneous polycrystals. The methods are briefly described. They are compared and grouped according to their basic assumptions. Their degree of generality is discussed. The analysis of their compliance with formal requirements is provided. Moreover, the possible but unknown completions and generalizations of some methods are considered. For most methods, example calculations are carried out for a special case of quasi-isotropic aggregate with cubic crystal symmetry. To make the paper self-contained, well-known essentials of the problem of effective constants are included.