A new framework for rotationally invariant two-point spatial correlations in microstructure datasets

Abstract

Quantification of the material internal structure (i.e., microstructure) is central to establishing the highly sought-after process-structure-property (PSP) relationships central to any materials design effort. In recent years, two-point spatial correlations (a subset of the n-point spatial correlations) have garnered significant attention because of their tremendous potential in arriving at practically useful PSP linkages. The central advantage of the two-point spatial correlations is that they capture an exceedingly large number of directionally resolved microstructure statistics. However, they are sensitive to the selection of the observer reference frame. In a number of practical applications, there is a critical need to establish the directionally resolved microstructure statistics, while attaining invariance to the observer reference frame (i.e., the statistics extracted are independent of the selection of the observer frame). A framework for defining and computing such observer-frame invariant two-point spatial correlations does not exist at the present time. This paper addresses this gap by introducing a new form of two-point spatial correlations, hereafter called rotationally invariant two-point spatial correlations. The theoretical framework for these new rotationally invariant two-point spatial correlations is introduced in this paper, and demonstrated through a comprehensive case study.