Use of the dirichlet tessellation for characterizing and modeling nonregular dispersions of second-phase particles

Wray, P. J.; Richmond, O.; Morrison, H. L.

Affiliations

¹Basic Research Division, Research Laboratory, United States Steel Corporation, Monroeville, Pennsylvania 15146, USA

Abstract

For the purpose of modeling the behavior of materials containing nonregular dispersions of second-phase particles, it is necessary to identify the parameters that best characterize the spatial distributions within the dispersions. For nonrandom dispersions it is proposed that the division of array space into Dirichlet regions centered on each particle will not only uniquely define near neighbors, but will enable clustering and the anisotropy of spacing to be dealt with in a systematic fashion. Using the Dirichlet tessellation procedure, a random array of points is shown to remain random during deformation, and three different classes of nonrandom dispersions are examined quantitatively.

Links

DOI: 10.1016/0026-0800(83)90043-5

WoS: A1983QF66600003

Cited Works (1)

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Cited By (11)

Year	Entry
1998	Pilkey AK, Worswick MJ, Thomson CIE, Burger G, Lloyd DJ. Effect of second-phase particle clustering on formability of Al-Si sheet. In: Wilkinson DS, Poole W, Alpas A, eds. Advances in Industrial Materials. The Metallurgical Society of CIM; 1998:105-121.
1999	Li M, Ghosh S, Richmond O. An experimental–computational approach to the investigation of damage evolution in discontinuously reinforced aluminum matrix composite. Acta Mater. 1999;47(12):3515-3532.
2001	Yang N, Boselli J, Sinclair I. Simulation and quantitative assessment of homogeneous and inhomogeneous particle distributions in particulate metal matrix composites. J Microsc (Oxford). February 2001;201(pt 2):189-200.
1989	Lewandowski JJ, Liu C, Hunt WH Jr. Effects of matrix microstructure and particle distribution on fracture of an aluminum metal matrix composite. Mater Sci Eng. January 1989;A107:241-255.
1999	Li M, Ghosh S, Richmond O, Weiland H, Rouns TN. Three dimensional characterization and modeling of particle reinforced metal matrix composites, I: quantitative description of microstructural morphology. Mater Sci Eng. June 15, 1999;A265(1-2):153-173.
2000	Guillemer-Neel C, Feaugas X, Clavel M. Mechanical behavior and damage kinetics in nodular cast iron, I: damage mechanisms. Metall Mater Trans. December 2000;A31(12):3063-3074.
2009	Lievers WB, Pilkey AK. Matrix-erosion tessellation: comparing particle clustering measures extracted from three-dimensional vs two-dimensional images. Metall Mater Trans. 2009;A40(1):36-45.
1985	Spitzig WA, Kelly JF, Richmond O. Quantitative characterization of second-phase populations. Metallography. August 1985;18(3):235-261.
1997	Pilkey AK. Effect of Second-Phase Particle Clustering on Aluminum-Silicon Alloy Sheet Formability [PhD thesis]. Carleton University; July 15, 1997.
1992	Hunt WH Jr. Microstructural Damage Processes in an Aluminum Matrix-Silicon Particle Composite Model System Carnegie Mellon University; October 1992.
2006	Orlov OS. A Three-Dimensional Damage Percolation Model [PhD thesis]. University of Waterloo; 2006.