Stress-promoted interface diffusion as a precursor of fracture

Stress-modulated surface mass transport offers a possible path to the ultimate fracture of brittle solids. A positive feedback between the local geometry, stress concentration, and chemical potential on a rough surface results in the formation of fracture precursor. Starting from general kinetic equations, we propose a reduced two-parameter description of a growing concavity. A suggested interpolation enables us to obtain an ordinary differential equation describing the precursor evolution; it starts from a smooth boundary and under certain conditions generates a cusp singularity. This sharp notch becomes a stress concentrator and facilitates direct brittle fracture. The diffusion-limited prefracture mechanism, though slow, circumvents a crack nucleation barrier and can be a determining factor for the durability of materials.