Textures and Microstructures, 1991, Vols 14-18, pp. 169-174 Reprints available from the publisher Photocopying permitted by license only (C) 1991 Gordon and Breach Science Publishers SA Printed in the United Kingdom CONSTRUCTION OF A PSEUDO-MATERIAL REPRESENTATIVE OF A REAL TEXTURED MATERIAL FROM ODF OR DIRECT POLE, FIGURES. M. FRANCOIS *, J.M. SPRAUEL **, J.L. LEBRUN * Laboratoire de Micromzucture et Mcanique des Matriaux- LM3 URA CNRS 1219, ENSAM, 151 Bd de l’H6pita175013 PARIS *Now at LM3, ENSAM, 13617 AIX-EN-PROVENCE, FRANCE INTRODUCnON The averaging of an orientation dependant physical quantity over a textured material is a classical operation which is often made directly with the help of the harmonic expansion method coefficients (1). However, the us of a pseudo-material representing a real material is commonly found, for instance in the field of plastic deformation modelling (2) or elastic moduli calculation (3). In this representation, the material is considered as an aggregate of grains (or crystallites) characterized by their crystallographic orientation (among other characteristics which are beyond the purpose of the present paper).The property to be averaged is considered as constant throughout each grain; in such conditions, integral equations can be transformed into algebraic equations which make practical calculations much easier. The orientation of a grain is described by three independant parameters corresponding to the three rotational degrees of freedom of a solid. The most commonly used are the three Euler angles as defined by Bunge convention. A pseudo-material is thus a set of triplets of Euler angles. For practical calculations, the number of crystallites of a pseudo-material varies around a few hundreds or a few thousands. In the modelization of texture development induced by plastic deformation, it is common to start with an isotropic pseudo-material (2). In the case of the study of X-ray elastic properties of textured materials, a pseudo-material has been generated according to an ideal fiber texture (4). However, it could be interesting to be able to build a pseudo- material representative of any given experimental texture and to determine how accurate this representation is. The purpose of the present paper is to show how this can be done either from the ODF of the specimen calculated with classical methods or directly from experimental pole figures. CONSTRUCTION OF A PSEUDO-MATERIAL FROM THE ODF OF THE SPECIMEN. Following an example given by Humbert (5), the ODF obtained from pole figures is a computation of information concerning some 104 grains, however, commonly used pseudo-materials contain much less crystallites (102to 103) and must therefore be statistically representative of the ODF. The basic principle of such a fitting is to consider a pseudo-material as a particular sample taken randomly among an infinite 169