Title: Effects of morphology and geometry of inclusions on two-point correlation statistics in two phase composites

Authors: A. Tabei; S. Ahzi; D.S. Li; C.A. Lavender; H. Garmestani

Addresses: G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 801 Ferst Drive NW, Atlanta, GA 30332, USA ' ICUBE Laboratory, University of Strasbourg/CNRS, 2 Rue Boussingault, 67000 Strasbourg, France; School of Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, Atlanta, GA 30332, USA; Qatar Environment and Energy Research Institute, Qatar Foundation, P.O. Box 5825 Doha, Qatar ' Pacific Northwest National Laboratory, 902 Battelle Blvd, Richland, WA 99352,USA ' Pacific Northwest National Laboratory, 902 Battelle Blvd, Richland, WA 99352, USA ' School of Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, Atlanta, GA 30332, USA

Abstract: A spectral form of the two-point correlation functions for two-phase composites is presented and the effects of secondary phase morphology, geometry and volume fraction on the coefficients of the corresponding series are studied. Initially, a principal component analysis is performed on the coefficients of the series and then, the effects of different morphological and geometrical parameters of the second phase inclusions on two-point correlation functions are examined. A direct linkage between the principal components of the coefficients with the morphological features (inclusion shape, aspect ratio and size) is established and the influence of preferred orientation of the anisotropic inclusions is also investigated. Finally a composite hull is constructed using the principal components of the coefficients in a three-dimensional space, which helps in determining the interrelation of properties and microstructures of any composite containing these types of inclusions.

Keywords: composites; statistical properties; statistical methods; discontinuous reinforcement; particle reinforcement; two-point correlation functions; 2PCFs; secondary phase morphology; geometry; volume fraction; principal component analysis; PCA; composite materials; shape; aspect ratio; size; orientation; anisotropic inclusions; composite hull; microstructure.

DOI: 10.1504/IJTAMM.2014.069444

International Journal of Theoretical and Applied Multiscale Mechanics, 2014 Vol.3 No.1, pp.1 - 17

Received: 16 Jun 2014
Accepted: 07 Jan 2015
Published online: 16 May 2015 *

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