Metallurgical and Materials Transactions A

, Volume 40, Issue 1, pp 36–45 | Cite as

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

  • W.B. Lievers
  • A.K. Pilkey


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).


Image Size Particle Volume Fraction Particle Cluster Particle Field Merging Event 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors acknowledge the financial support of the Centre for Automotive Materials and Manufacturing (CAMM), AUTO21, and the Natural Sciences and Engineering Research Council of Canada (NSERC).


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2008

Authors and Affiliations

  1. 1.Department of Mechanical and Materials EngineeringQueen’s UniversityKingstonCanada

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