A finite element method for stress-assisted surface reaction and delayed fracture

When a stressed solid is in contact with an environment (a vapor or a liquid solution), the solid may gain mass from, or lose mass to, the environment. The surface reaction is driven by the interfacial and elastic energy and by the chemical potential difference between the solid and the environment. This paper presents a finite element method to simulate the stress-assisted surface reaction. The reduction of the total free energy associated with gaining unit volume of solid defines the driving force. A linear kinetic law is adopted, where the reaction rate is proportional to the driving force. The problem is described with a variational statement. The elastic field in the solid is solved repeatedly as the solid changes its shape. The solid shape is updated with a mesh adaptation procedure and according to the kinetic law. Numerical examples include shape changes of a wavy surface, and crack nucleation at a grain boundary.