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 Ficks 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.