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Multi-Scale Homogenization of Moving Interface Problems with Flux and Field Jumps.

By Sangmin Lee


The current choice of materials for extreme high temperature, oxidizing conditions in advanced flight vehicles is ceramic matrix composites (CMCs). Such composites are used in rocket nozzles, leading edges of the space shuttles, and thermal protection systems. CMCs used in these applications experience large thermal stresses and are subject to high temperature oxidation. These two effects progressively degrade the carbon fibers within the matrix and eventually lead to component failure. The overarching aim of this thesis is to develop a validated numerical model of carbon reinforced ceramic matrix composite oxidation. Such a model will lead to accurate prediction of CMC performance during operating conditions, development of improved safety factors for CMCs and design of CMCs with improved high temperature properties. CMC oxidation involves interplay of mechanisms at different length scales. At the macroscopic scale, the composite is subject to external thermo-chemo--mechanical boundary conditions in the form of ambient oxygen concentrations, heat flux and applied stresses. The intact matrix is porous, leading to entry of oxygen into the matrix due to concentration and pressure gradients. The tows in the CMC contain thousands of micro-scale carbon fibers that oxidize under these conditions. Fiber oxidation leads to deterioration in the mechanical stiffness, which in turn leads to increase in matrix damage in the presence of applied stresses. Increase in matrix damage leads to further ingress of oxygen and thus, increased oxidation. For modeling this strong stress--oxidation coupling, we need to model the interactions between two different length scales. At the micro--scale, we model the oxidation of individual carbon fibers using a level set technique. At the macro scale, oxidation of the interwoven tow structure is captured using homogenized mass transport and stress equilibrium equations. A computational homogenization approach has been developed to link these two simulations. Computational homogenization provides an attractive avenue for computing the macroscopic response in problems with discontinuities and non-linearities. In this thesis, we present series of developments that lead to a coupled micro--macro model of CMC oxidation

Topics: Multi--Scale Modeling, Interface Evolution, Oxidation of Carbon Composites
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