Evaluating the effectiveness of Flinn's k-value versus Lode's ratio

Abstract

Lode's ratio (ν) and Flinn's k-value are the most commonly used parameters for characterizing the shape of ellipsoids. Both parameters characterize this shape by utilizing ratios of the lengths of the principal axes. For oblate, plane strain, and prolate ellipsoids, k and ν have an exact relationship, but such is not true for any other ellipsoids. In fact, as k approaches zero and infinity, the possible range in ν is 1.0, i.e., 50% of its total range. Correspondingly, as ν approaches zero from either the right or the left, the possible range in k is 50% of its total range.Given the inherent differences between k and ν, we use synthetic datasets as a means of comparing the relative effectiveness of these two shape parameters in different strain regimes. Lode's ratio demonstrated a largely strain-shape-independent set of standard deviations whereas the k-value datasets were significantly dependent on both strain shape and magnitude. Furthermore, the geometry of the confidence regions within the Flinn diagram are very much strain regime dependent, so datasets with a range of k-values are difficult to compare. In view of these results, we encourage investigators to carefully evaluate their choice of ellipsoid shape parameter and the related graphical representation.