Calcul de la FDOC à différents ordres de développement. Choix de l'ordre en fonction de l'acuité de la texture dans le cas de tôles d'aluminium

Abstract

Quantitative analysis of textures of materials requires calculation of the crystallite orientation distribution function (CODF) by expanding pole figures as series of spherical harmonics; the accuracy of the function depends on the truncation order l of the developments. A criterion TRC has been used to obtain comparable truncation error estimations for different pole figures of a sample with a given order of development; in this way this criterion gives the value of the truncation order corresponding to a given accuracy. In the case of materials having cubic crystal symmetry, the expansion coefficients of the CODF have to satisfy relations of linear dependence: these relations have been determined for l up to 34, so that sharp textures may be considered. The calculation of the CODF at l = 34 is applied to textures having orthotropic symmetry in aluminium sheets. It is shown that an insufficient order of the series expansions may lead to important errors in the CODF values and in the nature of the preponderant preferred orientations.