Quantitative characterization of spatial clustering in three-dimensional microstructures using two-point correlation functions

Two-point, three-point, and higher order microstructural correlation functions are important class of statistical descriptors that are useful for characterization of spatial arrangement and heterogeneity of microstructural features. In this contribution, an unbiased, efficient, and robust practical technique is presented for estimation of direction dependent as well as orientation averaged two-point correlation functions in three-dimensional (3D) microstructures from the measurement performed on vertical metallographic planes. It is shown that if the direction dependence of the two-point correlations has an axis of symmetry then measurements on just one vertical plane containing the symmetry axis are sufficient for estimation of the direction dependent as well as mean two-point correlation functions, and measurements on at the most three vertical planes are sufficient if there is no symmetry axis. The new method is applied for characterization of spatial heterogeneity and clustering of SiC particles in a series of DRA composites having different degrees of microstructural heterogeneity and clustering. It is shown that numerous length scale parameters that characterize spatial heterogeneity and clustering can be extracted from the experimental data on two-point correlation functions.