Selecting a set of discrete orientations for accurate texture reconstruction

Abstract

This paper is concerned with the reconstruction of textures by a limited number, N∗, of equally weighted orientations. Such reconstruction is frequently required in the simulation of physical phenomena which depend on texture, e.g. recrystallization using cellular automata or texture evolution during plastic deformation. The orientation distribution function (ODF) to be reconstructed is given as discrete probabilities on a grid in Euler space. The N∗ orientations used in the reconstruction are sampled from those N grid orientations for which the respective Euler space boxes overlap with the fundamental zone of the original ODF. We compare a probabilistic and a deterministic reconstruction scheme using strong and intermediate experimental textures as well as random artificial textures as test-case. The quality of ODF reconstruction is quantified by comparing the N crystallite volume fractions resulting from original and reconstruction in terms of (i) the root mean squared deviation and (ii) the correlation factor of a linear regression. The quality of both reconstruction schemes exhibits a scaling with N∗/N. In terms of both quality measures, the deterministic sampling scores higher than probabilistic sampling for given N∗/N. However, if N∗≪N deterministic sampling progressively sharpens the reconstructed texture with decreasing N∗/N due to systematic over-weighting of orientations with originally high probability at the expense of low-probability ones. Therefore, a combined method is proposed, which for N∗<N draws a random subset of N∗ orientations from a population containing N orientations, where this population is itself generated by prior deterministic sampling from the discrete ODF. The reconstruction quality achieved by this hybrid method is naturally identical to deterministic sampling for N∗⩾N and asymptotically declines with decreasing N∗ to settle at the levels of probabilistic sampling for N∗<N/10—without systematic sharpening of the reconstructed texture.