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Modeling of Diffusion in the Presence of Bi-Axial Damage in Polymer Matrix Composite Laminates

Samit Roy, Weiqun Xu, Sneha Patel, and Scott Case

It is now well known that Fick’s Law is frequently inadequate for describing moisture diffusion in polymers and polymer composites. Non-Fickian or anomalous diffusion is likely to occur when a polymer composite laminate is subjected to external stresses that could give rise to internal damage in the form of matrix cracks. As a result, it is necessary to take into account the combined effects of temperature, stress (or strain), and damage in the construction of such a model. In this paper, a modeling methodology based on irreversible thermodynamics applied within the framework of composite macro-mechanics is extended to the case of a bi-axially damaged laminate. The model allows characterization of non-Fickian diffusion coefficients as well as moisture saturation level from moisture weight gain data for laminates with pre-existing damage. A symmetric damage tensor based on continuum damage mechanics is incorporated in this model by invoking the principle of invariance with respect to coordinate transformations. For tractability, the diffusion governing equations are simplified for the special case of a laminate with uniformly distributed matrix cracks that is subjected to a uniaxial tensile stress. The final equations obtained from this derivation indicate that both effective diffusivity and maximum saturation level for this particular case are quadratic functions of crack density. Comparisons with test data for a bi-axially damaged Graphite/Epoxy woven composite are provided for model verifications.