Bounds on the Effective Transport and Elastic Properties of a Random Array of Cylindrical Fibers in a Matrix

[+] Author and Article Information
S. Torquato

Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, Box 7910, North Carolina State University, Raleigh, NC 37695

F. Lado

Department of Physics, Box 8202, North Carolina State University, Raleigh, NC 27695

J. Appl. Mech 55(2), 347-354 (Jun 01, 1988) (8 pages) doi:10.1115/1.3173681 History: Received September 21, 1987; Revised January 22, 1988; Online July 21, 2009


This paper studies the determination of rigorous upper and lower bounds on the effective transport and elastic moduli of a transversely isotropic fiber-reinforced composite derived by Silnutzer and by Milton. The third-order Silnutzer bounds on the transverse conductivity σe , the transverse bulk modulus ke , and the axial shear modulus μe , depend upon the microstructure through a three-point correlation function of the medium. The fourth-order Milton bounds on σe and μe depend not only upon three-point information but upon the next level of information, i.e., a four-point correlation function. The aforementioned microstructure-sensitive bounds are computed, using methods and results of statistical mechanics, for the model of aligned, infinitely long, equisized, circular cylinders which are randomly distributed throughout a matrix, for fiber volume fractions up to 65 percent. For a wide range of volume fractions and phase property values, the Silnutzer bounds significantly improve upon corresponding second-order bounds due to Hill and to Hashin; the Milton bounds, moreover, are narrower than the third-order Silnutzer bounds. When the cylinders are perfectly conducting or perfectly rigid, it is shown that Milton’s lower bound on σe or μe provides an excellent estimate of these effective parameters for the wide range of volume fractions studied here. This conclusion is supported by computer-simulation results for σe and by experimental data for a graphite-plastic composite.

Copyright © 1988 by ASME
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