Abstract:

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 [1] method. The transverse shear stiffness, in particular, is obtained by implementing Christensen's [2] (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 [3], 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 [4] lower bounds. In more generalized examples, such as n=4, results are shown to fall within the Hill [5] and Hashin [6] bounds for a wide range of coating properties and volume fractions.
 

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