Matrix-Erosion Tessellation: Comparing Particle Clustering Measures Extracted from Three-Dimensional vs Two-Dimensional Images

Abstract

Microvoids can nucleate from second-phase particles, grow, coalesce, and ultimately result in ductile failure. Since the rate of nucleation has been shown to be greatly increased by the clustering of second-phase particles, it is important to be able to characterize the particle distribution within an engineering alloy. Recent technological advances have made it possible to obtain three-dimensional (3-D) images of microstructural particle fields, but traditional two-dimensional (2-D) imaging of metallographic samples remains more convenient and cost-effective. Therefore, the extent to which the true nature of 3-D clustering can be quantified using only 2-D images is of genuine interest. In this study, matrix-erosion tessellation and dilational counting techniques are extended from 2-D to 3-D in order to measure the spatial distribution characteristics of various virtual 3-D particle fields. The effects of image resolution are first investigated and a minimum resolution parameter is proposed. Individual 2-D planes are then extracted from the 3-D virtual images for analysis and comparison with the 3-D results. The minimum number of features for the 2-D image to be representative of the 3-D system is then assessed. It was found that the use of 2-D images is appropriate for identifying the general distribution type (i.e., ordered, random, or clustered) and for comparing the relative amounts of clustering. The 2-D–based measures are also able to detect the presence of stringers in materials with a preferred cluster orientation (e.g., rolled sheet).