ABSTRACT
Quantitative characterization with image-analysis techniques is an important ingredient in predicting microstructure-property relations for heterogeneous materials. Innovative work in quantitative metallography has been done in [384, 449], where Dirichlet tessellations have been used to characterize particle geometries in steels and aluminum matrix composites by comparing actual with computer-generated microstructures. This work has characterized three-dimensional distributions, simulated from actual 2D micrographs, by pseudo-Saltykov transformation [348] and by the pair correlation functions [130]. Near-neighbor distances, cell volume fractions, and radial distribution functions have been determined for computer-generated patterns in [116] and have been compared with those for real materials. Pyrz et al. [329, 328, 327] have introduced novel geometric descriptors to stereologically quantify and distinguish between various nonrandom distributions in heterogeneous microstructures. The second-order autocorrelation function has been introduced in [450] to characterize the spatial distribution of constituent phases based on mosaic patterns. Lewandowski [236, 237] and Lloyd [256] have characterized clustering in metal matrix composites based on Dirichlet tessellation and have shown that damage preferentially initiates in clustered regions, and linkage occurs through the non-clustered regions. In a series of papers, Ghosh et al. [155, 156] have introduced the Voronoi cell based methods as a unifying tool for characterizing and modeling the response of non-uniform multiphase materials of arbitrary morphology. These studies have been effective in demonstrating the importance of characterizing detailed geometry of structure, essentially for 2D sections of microstructures. Section 4.1 of this chapter demonstrates the utilization of tessellation methods for microstructure characterization. Microstructures with different volume fractions, inclusion concentrations, and patterns are computer simulated and tessellated to yield a mesh of Voronoi cells. Various characterization functions based on geometric parameters are generated. Statistical measures for detecting geometric and behavioral anisotropy are compared for the different composite microstructures.
