Non-Fickian Three-Dimensional Moisture Absorption in Polymeric Composites: Development and Validation of Hindered Diffusion Model

Abstract

The importance of environmental damage consideration in the design of polymeric composite structures is discussed, with emphasis on the relationship between absorbed moisture content and material property degradation. A brief overview of existing predictive models of moisture diffusion and their limitations is presented. The three-dimensional anisotropic Fickian diffusion model is expanded to include the effects of the interaction of diffusing molecules with the chemical and physical structure of polymeric composites. The numerical solution of this novel hindered diffusion model is obtained for a three-dimensional, anisotropic domain by using a forward-time centered-space finite difference technique. The numerical solution method is verified by comparing the results to known analytical solutions of a one-dimensional, gLangmuir-typeh diffusion model and for the limiting case of the three-dimensional Fickian model. The proposed three-dimensional anisotropic hindered diffusion model (3D HDM) and its one-dimensional isotropic version are successfully applied to three experimental moisture absorption data sets reconstructed from existing literature.

An analytical solution based on a judicious approximation to the 3D HDM is developed in an effort to increase the utility of the model in the recovery of polymeric composite diffusion properties from experimental data. The effectiveness of the recovery of absorption properties is assessed using artificially generated gsynthetich experimental data. The anisotropic diffusivities, equilibrium moisture content (M), and molecular binding (fÁ) and unbinding (fÀ) probabilities that govern three-dimensional hindered diffusion are recovered using least-squares regression. Using both Fickian and non-Fickian synthetic moisture absorption data, diffusivities and equilibrium moisture content are recovered with less than 1% error. Values of fÁ and fÀ are recovered with less than 3% error in the non-Fickian diffusion case. It is shown that equilibrium moisture content can be successfully determined much earlier using only partial gravimetric data obtained from the initial phases of moisture absorption, even in the presence of considerable measurement error.

The three-dimensional anisotropic moisture absorption behavior of a quartz-fiber-reinforced bismaleimide (BMI) laminate 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 25<C. The long-term moisture absorption behavior deviates from the widely-used Fickian model, but excellent agreement is achieved between experimental gravimetric data and the 3D HDM. Diffusion through the laminate edges occurs 15 times faster on average than diffusion through the thickness, further highlighting the importance of anisotropic diffusion consideration.