On stress-affected propagation and stability of chemical reaction fronts in solids

Abstract

This paper is concerned with the influence of mechanical stresses on the equilibrium, propagation, and stability of chemical reaction fronts in solids. A localized chemical reaction between diffusing and solid constituents is considered. A concept of the chemical affinity tensor is used to quantify how mechanical stresses and strains arising in a solid due to the reaction and external loading affect the chemical reaction rate and the reaction front velocity. A kinetic equation in the form of the dependence of the front velocity on the normal component of the affinity tensor is formulated and used in the coupled problem “diffusion–chemistry–mechanics”. A notion of stress-affected and stress-induced chemical reactions is introduced. An analytical procedure of the linear stability analysis developed earlier for stress-induced phase transformations is extended to the case of chemical reactions in elastic solids. A stability analysis is performed for an axially symmetric chemical reaction front. Considering a cylinder undergoing a chemical reaction, we study stable and unstable configurations in the cases of stress-affected and stress-induced reactions. A competition between the global kinetics of the reaction front and the local kinetics of perturbations is demonstrated. A destabilizing effect of an inner hole is discussed. A numerical procedure is proposed for studying the stability and evolution of the reaction front, where the reaction front propagation is realized via iterative remeshing of the domain. The numerical procedure is validated by the results obtained analytically. Propagation of stable and unstable reaction fronts is simulated.