Oxidation and corrosion:

Composite materials are used in parts of, for instance, aerospace vehicles and jet engines and are exposed to very hot and hostile environments. In order to protect these materials from oxidation and corrosion, they are coated by several layers of materials. However, when material are subjected to high stresses, small cracks form and help oxygen and water vapor diffuse to the matrix and fibers and cause damage that shortens the lifetime of these parts. The lifetime of these materials depend on the size, the number, and the distribution of these cracks. In Most cases the presence of cracks accelerates the oxidation and corrosion of the material and change its mechanical properties, however, in some instances the volume expansion accompanying the oxidation might seal the cracks and slow down or stops further oxidation. In order to study the effects of oxidation we consider a material with a small crack and use bulk and Knudsen diffusion models for the gas in the crack. Oxygen and water get absorbed into the solid material, diffuse, and react causing the material to change density. The system is described by a two-dimensional two-phase model describing gas diffusion in the crack and diffusion, reaction, and convection in the solid material. The solid is described by a system of reaction-diffusion equations coupled to Navier-Stokes equations for viscous fluids using a volumetric law to account for volume conservation. This work is very interesting and challenging as it involves moving boundaries, moving sharp reaction fronts with complex geometries and contact problems for which Adaptive methods are most effective. The Model can be improved by replacing the viscous model with a visco-elastic one and including a contact model to describe the behavior of the material as the crack closes and discover its effects on further propagation of the crack. More work is needed to model full three dimensional systems with the presence of multiple cracks and fibers with different sizes and varying distributions.