A finite element simulation on fully coupled diffusion, stress and chemical reaction

Abstract

The oxidation of metallic materials at high temperatures is accompanied by atomic/ionic diffusion and stress. There exist stress effects on atomic/ionic diffusion and oxidation rate as well as diffusion-induced stress. In this work, we extend the models of diffusion-induced stress and reaction-induced stress to develop a coupled diffusion, reaction and mechanics model in the framework of linear elasticity by introducing a kinetic relationship between reaction rate and hydrostatic stress. This model demonstrates the effects of hydrostatic stress on chemical equilibrium constant and reaction rate, which are associated with reaction-induced stress. Using the diffusion-reaction-mechanics model, numerical analyses of three different cases are performed: a plate-like structure with fixed boundaries and constant concentration of solute atoms on surfaces, the growth of an oxide layer of a Cr–Fe alloy and the carburization of semi-infinite stainless steel. The numerical results reveal the presence of large compressive stresses and stress gradient in the oxide scale. Comparing the numerical results to experimental data available in literature, we illustrate the need of incorporating the interaction between stress and diffusion and the stress dependence of reaction rate in the growth analysis of the oxide layer and the carburized layer. It is expected that this model is applicable to other systems, such as lithium-ion and sodium-ion batteries.