Table of Contents
Textures and Microstructures
Volume 6 (1986), Issue 3, Pages 217-230
http://dx.doi.org/10.1155/TSM.6.217

Cubic Invariant Spherical Surface Harmonics in Conjunction With Diffraction Strain Pole-Figures

Laboratory for Metallurgy, Delft University of Technology, Rotterdamseweg 137, AL Delft 2628, The Netherlands

Received 15 January 1985

Copyright © 1986 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.

Abstract

Four kinds of cubic invariant spherical surface harmonics are introduced. It has been shown previously that these harmonics occur in the equations relating measured diffraction (line-shift) elastic strain and macro-stresses generating these strains for the case of textured cubic materials. As a consequence, these harmonics are important for the determination of unknown macro-stress tensor components if the o.d.f. expansion coefficients are known. On the other hand, they play a role in the determination of unknown o.d.f. expansion coefficients if the macro-stresses are known using for instance, a tensile test device on the diffractometer. Then, even the odd-order o.d.f. expansion coefficients can be obtained. In this paper, special attention is given to the mathematical construction of the cubic harmonics, the physical symmetry requirements they are subject to and some examples are given exhibiting both even and odd order harmonics.