Crack nucleation from a single notch caused by stress-dependent surface reactions

The surface of a solid under stress is unstable if there is mass exchange and transportation along the surface. A notch on the surface can be a preferred site for crack nucleation. This paper studies the evolution of a surface notch under stress dependant reaction. The surface is represented by a family of curves with many degrees of freedom, and the elastic field is solved using complex conformal mapping method. In the numerical simulations, the notch either deepens immediately and forms singular tip; or becomes perfectly flat after long time; or becomes blunter first, evolving slowly for a long time, then nucleates new surface instability and finally forms sharp tip; or becomes near flat first, then forms a bump on the surface. When the activation strain is small or the reaction is near equilibrium, the notch stability is mainly determined by the competition of strain energy and surface energy, and the sign of stress has little effect. When the surface reaction is away from equilibrium and activation strain is not small, stresses with different signs give totally different surface stability behaviors, depending on whether the solid is losing mass to or gaining mass from the environment.