Model investigation of the grain number to apply quantitative texture analysis averaging

One of the most important applications of an orientation distribution function (ODF) is the computation of physical property averages. A number of grains in a sample are investigated with regards to the averaging, and the use of an ODF is reasonable from the accuracy point of view. For this, a microstructure pattern has been generated and a random orientation with known distribution has been assigned to each grain. For such a model elastic moduli for discrete sets of grains with known volumes and orientations on the one hand and for known ODFs on the other hand have been computed. As can be predicted, both these approaches lead to the same values for the elastic moduli when the number of grains tends to infinity. The number of grains where the difference is significant is about 8000 for cubic symmetry and about 10000 for hexagonal symmetry for one of the texture models considered. In order to generate microstructure patterns, Voronoi cells have been applied and to generate orientations with known distribution Roberts's approach has been used.