Micromechanics of moisture diffusion in composites with impermeable fibers

The objective of this paper is to determine the effect of fiber volume fraction on effective diffusivity of composites with impermeable Fibers using finite elements. Both hexagonal and square fiber arrangements were studied. It is found that for low to moderate fiber fractions (V-f < 40%) the effective diffusivity was essentially the same for both fiber arrangements and the calculated values agreed very well with Hashin's formula. For high fiber fractions (V-f > 40%) there were significant differences, but the behavior was still quite simple. A very simple closed-form formula, which consists of Hashin's formula for part of the range and a straight line for the rest, is proposed for calculating the effective diffusivity as a function of fiber volume fraction. The simple formula predictions matched the finite element predictions extremely well.