Correlations between the crystallographic texture and grain boundary character in polycrystalline materials

A method is presented to determine the misorientation probability distribution function in polycrystalline materials based on a known, analytical or numerical, representation of the associated orientation probability distribution function, i.e., texture. The proposed formulation incorporates the local grain-to-grain orientation correlations by combining local or macroscopic statistical information, and finds a natural interpretation through the well-known stereographic projection (pole-figure) representation. The proposed formulation distinguishes between antiparallel crystallographic orientations, as well as cone-angle and polar angle misorientations. For fiber-textured samples, it is quantitatively shown that highly oriented samples are equivalent to polycrystals with a high density of low-angle misorientations, while completely random (untextured) materials are equivalent to microstructures with a high probability of large-angle misorientations.