Texture, Stress, and Microstructure

Texture, Stress, and Microstructure / 1993 / Article

Open Access

Volume 21 |Article ID 789189 | https://doi.org/10.1155/TSM.21.233

David D. Sam, E. Turan Onat, Pavel I. Etingof, Brent L. Adams, "Coordinate Free Tensorial Representation of the Orientation Distribution Function With Harmonic Polynomials", Texture, Stress, and Microstructure, vol. 21, Article ID 789189, 18 pages, 1993. https://doi.org/10.1155/TSM.21.233

Coordinate Free Tensorial Representation of the Orientation Distribution Function With Harmonic Polynomials

Accepted20 Apr 1993

Abstract

The crystallite orientation distribution function (CODF) is reviewed in terms of classical spherical function representation and more recent coordinate free tensorial representation (CFTR). A CFTR is a Fourier expansion wherein the coefficients are tensors in the three-dimensional space. The equivalence between homogeneous harmonic polynomials of degree k and symmetric and traceless tensors of rank k allows a realization of these tensors by the method of harmonic polynomials. Such a method provides for the rapid assembly of a tensorial representation from microstructural orientation measurement data. The coefficients are determined to twenty-first order and expanded in the form of a crystallite orientation distribution function, and compared with previous calculations.

Copyright © 1993 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.


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