We present a mixture theory based approach for process modeling in ceramic matrix composites. The model is derived from a consistent thermodynamic framework for diffusive-reactive flow of an anisotropic, non-linear viscoelastic fluid through a poroelastic body. A salient feature of the method is that the constraints due to stoichiometry are taken into account in a physically and mathematically consistent manner. Maximization of the rate of entropy production due to dissipation, heat conduction, and chemical reactions results in a set of equations for the evolution of the natural configuration, the heat flux vector, and evolution of the concentration of the chemical constituents. Both diffusion-dominated and reaction-dominated processes are considered. A multiscale finite element method is proposed for the mixture model that yields numerical schemes with enhanced stability properties. The multiscale method comes equipped with a built-in error estimation module that helps distinguish modeling errors from numerical errors. Efficient solution of coupled mechanical and thermal fields is facilitated via a staggered solution procedure that retains program modularity and therefore can be coupled with commercial codes using user defined interfaces. An interactive processing and modeling program is developed in conjunction with Rolls-Royce as our industrial partners for validation of the modeling approach.
Benefit: This effort will result in a cost effective ICMSE based modeling and analysis tools for optimizing the processing technologies in CMC manufacturing. The new methods developed under this project will be implemented in modular form so that they can be easily integrated into the research and commercial finite element analysis packages via User Defined Modular Interconnects typically provided by such programs. High end graphics tools will be integrated into the overall computational framework for easy comprehension of the intricate stress and interface fields that develop during the processing of CMCs. It will thus help material designers speed up the process design cycle for efficient manufacturing of CMCs with very well calibrated properties.
