TY - JOUR
T1 - Bounds on the effective transport and elastic properties of a random array of cylindrical fibers in a matrix
AU - Torquato, S.
AU - Lado, F.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1988
Y1 - 1988
N2 - 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 ne, 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 fourpoint 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.
AB - 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 ne, 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 fourpoint 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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U2 - 10.1115/1.3173681
DO - 10.1115/1.3173681
M3 - Article
AN - SCOPUS:0024034210
VL - 55
SP - 347
EP - 354
JO - Journal of Applied Mechanics, Transactions ASME
JF - Journal of Applied Mechanics, Transactions ASME
SN - 0021-8936
IS - 2
ER -