Analytical modeling of orthotropic diffusivities in a fiber reinforced composite with discontinuities using homogenization

Thermo-oxidative aging in polymer matrix composites (PMC) is usually simulated using diffusion–reaction models in which temperature, oxygen concentration and weight loss effects are considered at the “smeared” macro-scale. Consequently, homogenization techniques are necessary to determine the effective diffusivity of the composite lamina based on diffusivities of the fiber and the polymer matrix phases. This paper describes a simple analytical methodology based on one-dimensional steady-state flow continuity consideration to determine the homogenized diffusivity in the direction transverse and longitudinal to the fibers, including physical discontinuities such as fiber/matrix debonding due to oxidative shrinkage. Computations of effective homogenized diffusivities as a function of fiber volume fraction are presented, and the effect of discontinuities on homogenized diffusivities is quantified. Comparisons with FEA results are also presented.