Modeling the oxidation of a polymer-derived ceramic with chemo-mechanical coupling and large deformations

To get a better insight into the coating behavior of a polymer-derived ceramic material, we model and simulate the diffusion, oxidation and reaction-induced volume expansion of a specimen without outer mechanical loads. In this macroscale approach, we use an oxidation state variable which determines the composition of the starting material and the oxide material. The model contains a reaction rate which is based on the change of the free energy due to a change of the concentrations of the starting material, the oxide material and a diffusing gaseous material. Using this, we model a growing oxide layer in a perhydropolysilazane (PHPS)-based polymer-derived ceramic (PDC), containing silicon filler particles. Within the mechanical part of the modeling, we use the Neo-Hookean material law which allows for the consideration of volume expansion and the diffusion kinematics in terms of finite deformations. We derive this continuum formulation in 3D and reduce it later to 1D, as we show that a 1D formulation is sufficient for thin oxide layers in our consideration. In such a case, the reaction-induced volume expansion is mostly limited to strains orthogonal to the oxide layer, as the bulk material hinders transversal deformation. Both formulations, i.e., 1D and 3D, are implemented in the finite element software FEAP. We perform a parameter study and fit the results with experimental data. We investigate the diffusion kinematics in the presence of volume expansion. Additionally, we discuss the influence of the elastic energy on the reaction rate.