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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

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The three-dimensional anisotropic moisture absorption behavior of quartz-fiber-reinforced bismaleimide (BMI) laminates is investigated by collecting 21 months of experimental gravimetric data. Laminates of six, twelve, and forty plies and various planar aspect ratios are used to determine the three-dimensional anisotropic diffusion behavior when exposed to full immersion in distilled water at 258C. The long-term moisture absorption behavior deviates from the widely used Fickian model, but can be accurately captured by the three-dimensional, anisotropic hindered diffusion model (3D HDM). Excellent agreement is achieved between experimental gravimetric data and the 3D HDM for all laminate thicknesses. Recovered model parameters are shown to slightly vary with laminate thickness due to the small changes in the cured-ply thickness. However, model parameters identified for a given laminate thickness are observed to accurately predict the absorption behavior of samples with different planar dimensions. Equilibrium moisture content of 1.72, 1.69, and 1.84% and corresponding diffusion hindrance coefficients of 0.807, 0.844, and 0.671 are recovered for six, twelve, and fortyply laminates, respectively, thus confirming strong non-Fickian behavior. Moisture absorption parameters may be determined successfully at 16.5 months of immersion, before reaching approximately 85% of the equilibrium moisture content at 21 months. Subsequent gravimetric measurements up to 21 months are consistent with the predicted long-term behavior. POLYM. ENG. FIG. 7. Effect of experimental time frame on recovery of three-dimensional HDM parameters, with emphasis on equilibrium moisture content recovery. Solid lines indicate 3D HDM predictions based on incomplete data.