Effective through-the-thickness diffusivity of plain-woven composite from analytical homogenization

Aging of composites is of great concern as it reduces durability. Diffusion plays an important role in aging, as it is responsible for transporting substance from the surface into the bulk. The microstructure of woven composites, which is complex and highly heterogeneous, makes diffusion analysis challenging. One way of simplifying the problem is by obtaining an effective diffusivity through homogenization and rules-of-mixtures. In this paper a homogenized through-the-thickness diffusivity of plain-woven composites is derived analytically with offset in the microstructure of the tows. A rule-of-mixtures based on Fickian diffusion and the volume fractions of constituents is proposed as an efficient way of obtaining the effective diffusion coefficient. The analytical expression is benchmarked against a three-dimensional orthotropic finite element analysis using material and geometrical parameters from the literature. Very good agreement between the two approaches is observed, which supports use of the homogenization. Notes on how this work could aid in understanding aging are included.