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Characterizing Heterogeneity in the Distribution of Particles in Multiphase Materials

Published online by Cambridge University Press:  01 February 2011

Jeremy W. Leggoe
Jeremy W. Leggoe*
Affiliation:
Chemical Engineering Department, Texas Tech UniversityBox 43121, Lubbock, Texas, 79409
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Abstract

Advances in the development of multiscale failure models are dependent on the development of techniques for accurately characterizing the nature of spatial heterogeneity. Nth-nearest neighbor statistics offer a means of quantitatively and qualitatively characterizing deviation from complete spatial randomness (CSR). This investigation has determined the mean distances to the Nthnearest neighbor for CSR dispersions of monodisperse spheres in 2D and 3D for N up to 200. To evaluate data obtained from micrographs, mean Nth-nearest neighbor distances have also been collected for planar slices through 3D arrays of monodisperse spheres. Results are presented for a volume fraction of 0.20 in the form of an “Inhibition Ratio”, which compares the results collected for finite disks and spheres with the values expected for 2D and 3D point processes.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 882: Symposium EE – Linking Length Scales in the Mechanical Behavior of Materials , 2005 , EE5.5
Copyright
Copyright © Materials Research Society 2005

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References

1 Cressie, N.A.C., Statistics for Spatial Data, Wiley Interscience, New York (1993)Google Scholar
2 Murphy, A.M. Howard, S.J. and Clyne, T.W. Mater. Sci. Technol. 14, 959 (1988)Google Scholar
3 Leggoe, J.W. Hu, X.Z. and Bush, M.B. Eng. Fracture Mech. 53, 873 (1996)Google Scholar
4 Shen, H. and Lissenden, C.J. Mater. Sci. Eng. A338, 2355 (2002)Google Scholar
5 Gonzalez, C. Segurado, J. and Llorca, J. J. Mech. Phys. Solids 52, 1573 (2004)Google Scholar
6 Leggoe, J.W. Mammoli, A.A. Bush, M.B. and Hu, X.Z. Acta Mater. 46, 6075 (1998)Google Scholar
7 Khvastunkov, M.S. and Leggoe, J.W. Scripta Mater. 51, 309 (2004)Google Scholar
8 Rintoul, M.D. and Torquato, S. J. Colloid Interface Sci. 186, 467 (1997)Google Scholar
9 Sheehan, N. and Torquato, S. J. Appl. Phys. 89, 53 (2001)Google Scholar
10 Leggoe, J.W. J. Mater. Sci. Lett., submitted (2005)Google Scholar
11 Thompson, H.R. Ecology 37, 391 (1956).Google Scholar
12 Torquato, S. Random heterogeneous Materials - Microstructure and Macroscopic Properties, Springer-Verlag, New York (2002)Google Scholar
13 Tewari, A. and Gokhale, A.M. Comp. Mater. Sci 31, 13 (2004)Google Scholar
14 Tewari, A. and Gokhale, A.M. Mater. Sci. Eng. A385, 332 (2004)Google Scholar
15 Lu, B. and Torquato, S. Phys. Rev. A 45, 5530 (1992)Google Scholar