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.
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June 1988
Research Papers
Bounds on the Effective Transport and Elastic Properties of a Random Array of Cylindrical Fibers in a Matrix
S. Torquato,
S. Torquato
Department of Mechanical and Aerospace Engineering and Department of Chemical Engineering, Box 7910, North Carolina State University, Raleigh, NC 37695
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F. Lado
F. Lado
Department of Physics, Box 8202, North Carolina State University, Raleigh, NC 27695
Search for other works by this author on:
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. Jun 1988, 55(2): 347-354 (8 pages)
Published Online: June 1, 1988
Article history
Received:
September 21, 1987
Revised:
January 22, 1988
Online:
July 21, 2009
Citation
Torquato, S., and Lado, F. (June 1, 1988). "Bounds on the Effective Transport and Elastic Properties of a Random Array of Cylindrical Fibers in a Matrix." ASME. J. Appl. Mech. June 1988; 55(2): 347–354. https://doi.org/10.1115/1.3173681
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