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

Abstract

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

Moisture uptake and resulting mechanical response of bio‐based composites. II. composites

“…It has been shown that most often polymer composites follow a Fickian diffusion process . However, for explaining mechanisms behind non‐Fickian behavior other models can be used . Different methods of measuring water uptake are investigated on laminates and in order to define the diffusion coefficient moisture uptake studies in glass fiber/epoxy composites have been carried out.…”

The effects of temperatures and volumetric expansion on the diffusion of fluids through solid polymers

“…; Helbling and Karbhari; LaPlante et al ; Grace and Altan). In the Langmuir model, the macroscopic sorption is modeled by two stages, consisting of a Fickian diffusion‐dominated stage and a relaxation‐dominated stage, where fluid molecules interact with the macromolecular structure of the polymer.…”

“…This interaction of processes is categorized as "anomalous diffusion behavior." Many of the above studies consider empirical and ad-hoc models to describe the non-Fickian diffusion process in polymers, for example the so-called Langmuir model (Carter and Kibler 6 ; Lee and Peppas 10 ; Perreux and Suri 11 ; Popineau et al 12 ; Helbling and Karbhari 13 ; LaPlante et al 14 ; La Saponara 15 ; Grace and Altan 16 ). In the Langmuir model, the macroscopic sorption is modeled by two stages, consisting of a Fickian diffusion-dominated stage and a relaxation-dominated stage, where fluid molecules interact with the macromolecular structure of the polymer.…”

Experimental and theoretical investigation of non-Fickian moisture absorption of quartz/BMI laminates fabricated by preconditioned prepregs

“…The methods to recover the absorption parameters as well as the utility and accuracy of the HDM has been investigated in recent publications [15,16]. The governing equations for the three-dimensional, anisotropic hindered diffusion model can be expressed as,…”