Modeling of diffusion in the presence of damage in polymer matrix composites

It is now well known that FickÕs Law is frequently inadequate for describing moisture di€usion in polymers and polymer composites. Non-Fickian or anomalous di€usion 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 e€ects of temperature, stress, and damage in the construction of such a model. In this article, a modeling methodology based on irreversible thermodynamics applied within the framework of composite macro-mechanics is presented, that would allow characterization of non-Fickian di€usion coecients from moisture-weight-gain data for laminated composites. 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 di€usion-governing equations are simpli®ed for the special case of a laminate, with uniformly distributed matrix cracks, that is subjected to a uniaxial tensile stress. The ®nal form for e€ective di€usivity obtained from this derivation indicates that the e€ective di€usivity for this case is a quadratic function of crack density. A ®nite element procedure that extends this methodology to more complex shapes and boundary conditions is also presented. Comparisons with test data for a 5-harness satin textile composite are provided for model veri®cations