S. Bhandarkar, M. Pecht and D. Barker
University of Maryland
College Park, MD 20742
In this paper, we discuss methods to obtain approximately, the transversely
isotropic effective properties of a composite consisting of non-dilute
concentrations of a reinforcement phase of cylindrical fibers, surrounded
by multiple layers of coatings or interphases and embedded in a matrix
material. All constituent phases are transversely isotropic with the plane
of isotropy being the fiber cross-section. All five independent effective
stiffness constants are obtained for this transversely isotropic multiphase
medium using a variant of the Mori-Tanaka  method. The transverse shear
stiffness, in particular, is obtained by implementing Christensen's 
(n+1)-phase cylindrical model within the context of the Mori-Tanaka method.
Results are found to agree with the work of other investigators such as
Benveniste , for their special cases such as n=3 and isotropic constituents.
In particular, for the uncoated case (n=2) and isotropic constituents,
results coincide with those from Hashin's composite cylinders assemblage
(CCA) model and with Christensen's 3-phase model results for the transverse
shear stiffness. For n=2 and transversely isotropic fibers, results coincide
with Hashin's  lower bounds. In more generalized examples, such as n=4,
results are shown to fall within the Hill  and Hashin  bounds for
a wide range of coating properties and volume fractions.
article is available to CALCE Consortium Members.