Non-fickian three-dimensional hindered moisture absorption in polymeric composites: Model development and validation

A new, three-dimensional, anisotropic non-Fickian diffusion model is developed to characterize moisture absorption in polymeric composites. The new hindered diffusion model extends the classical Fickian theory to include the effects of the interaction of diffusing molecules with the chemical and physical structure of polymeric composites. The numerical solution of the hindered diffusion model is obtained for a three-dimensional, anisotropic domain by using a forward-time, centered-space finite difference technique. The moisture weight gain over time predicted by the model is shown to mimic a wide variety of anomalous absorption behavior, often exhibited by anisotropic composite laminates. The accuracy of the numerical solutions is verified by comparing the results to known analytical solutions of a one-dimensional, “Langmuir-type” diffusion model and for the limiting case of the three-dimensional Fickian model. The utility of the proposed hindered diffusion model is demonstrated by accurately recovering the absorption behavior of three different material systems reported in literature. First, it is shown that the hindered diffusion model can accurately predict the moisture absorption data for unidirectional glass-reinforced epoxy plates of varying dimensions exposed to a relative humidity of 80%. Second, the one-dimensional version of the model is applied to experimental moisture absorption data for isotropic epoxy resin samples of different thicknesses. Anomalous effects due to sample thickness reported in the original article are accurately captured. Third, the proposed model is shown to be more accurate than a two-stage diffusion model applied to moisture absorption data obtained from a woven 3-ply carbon fiber reinforced bismaleimide composite. POLYM. COMPOS., 34:1144–1157, 2013. © 2013 Society of Plastics Engineers