Determining Grain-scale Vorticity Axes from Crystallographic Orientation Data

Abstract:

Aggregates deformed by crystal plastic mechanisms often contain grains that exhibit crystallographic distortion (e.g., kinking, undulose extinction, subgrain development). In such grains, crystallographic orientations are typically dispersed along small circles on lower hemisphere equal-area plots. Thus, we consider that an intragranular dispersion axis represents a grain-scale axis of material rotation, and its position coincides with that of a highly localized vorticity axis.

We present a new method for determining the position of a grain-scale vorticity axis from intragranular crystallographic orientation data. This method leverages a method of rotational statistics known as principal geodesic analysis to identify a single best-fit rotational axis that matches the rotational dispersion of crystallographic orientations in a deformed grain. We further demonstrate that populations of such grain-scale vorticity axes can be used to infer a preferred vorticity axis for volumes of deformed aggregates. As an example of this type of application, we calculate intragranular vorticity axes from a sample-scale selection of grains (i.e., all the grains mapped in an EBSD orientation map) and use kernel density estimation to identify a preferred, sample-scale vorticity axis. The results of our bulk analysis match the vorticity axis inferred in previous studies of rocks deformed in the same shear zones.