Chemical reaction planar fronts with a viscoelastic reaction product

TL;DR

This paper models the propagation of chemical reaction fronts in elastic solids transforming into viscoelastic materials, analyzing how stresses and material parameters influence front velocity and stress relaxation using analytical solutions.

Contribution

It introduces a new model incorporating a chemical affinity tensor and viscoelastic transformation to study reaction front kinetics and stress effects in elastic solids.

Findings

Reaction front velocity depends on external strains and material parameters.

Stress relaxation behind the front can be explicitly modeled using a linear solid model.

Analytical solutions reveal conditions for front retardation or acceleration.

Abstract

A stress-affected chemical reaction front propagation is considered utilizing the concept of a chemical affinity tensor. A reaction between an elastic solid and diffusing constituents, localized at the reaction front, is considered. As a result of the reaction, the elastic constituent transforms into viscoelastic one. The reaction is accompanied by volume expansion that in turn may result in stresses at the reaction front which affect the front velocity through the normal component of the chemical affinity tensor. Considering a plane strain problem with a planar chemical reaction front propagation under uniaxial deformation, we focus on the studies of the reaction front kinetics in dependence on external strains and material parameters with the use of the notion of the equilibrium concentration. Then stress relaxation behind the propagating reaction front is modelled. A standard linear solid model is used for the reaction product, and its particular cases are also considered. Analytical solutions are obtained which allow to study in explicit form the influence of strains and material parameters on the front retardation or acceleration and stress relaxation.