A methodology for determining average lattice orientation and its application to the characterization of grain substructure

Abstract

Lattice orientation data often are available at a collection of locations within a grain, and an average of these lattice orientations is useful in data analysis. We define an average orientation based on misorientation angles, which leads to a nonlinear least-squares problem that may be solved numerically. This average orientation then serves as the basis for several related quantities that characterize the misorientation structure within a grain. The spread of a grain in (mis)orientation space is determined, as is a spatial correlation of the misorientation parameters. The method is applied to experimental data from electron backscattered diffraction (EBSD) scans and to simulation data from finite-element analyses of the deformation of a polycrystal. The quantities characterizing the grain substructure are found to evolve with strain and to illuminate trends in the microstructural evolution.