Table of Contents
Textures and Microstructures
Volume 21, Issue 1, Pages 55-62
http://dx.doi.org/10.1155/TSM.21.55

Numerical Determination of the Variation Width of Feasible ODFs

Laboratory of Metallurgy of Polycrystalline Materials (LM2P), University of Metz, Ile du Saulcy, Metz 57045, France

Accepted 17 June 1992

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.

Abstract

Within all known methods of calculating a model orientation density (odf) from a given set of pole densities (pdfs) the set of all feasible odfs and in particular its associated variation width remained unaccessible up to now.

Here, the variation width is mathematically well defined for the continuous and the discrete setting of the fundamental projection equation of texture goniometry. For the discrete case it is shown that it can be numerically determined by a sequence of optimization problems with extremely simple objective functions.

The general solution is exemplified for the SANTA FE model data.