Delayed fracture of ceramics caused by stress-dependent surface reactions

Consider a ceramic in an environment, corroding gradually by a surface reaction. When in addition subject to a mechanical load, the ceramic loses mass preferentially at grain-boundary grooves where stress concentrates, so that atomistically sharp cracks may nucleate. Before becoming a crack, a groove maintains local equilibrium at its root; after, it loses local equilibrium. The crack further propagates by breaking atomic bonds, often assisted by environmental molecules. This paper models the groove-to-crack evolution. The groove changes shape to reduce the free energy due to the combined effects of surface tension, grain-boundary tension, elasticity, and chemical potential difference between the solid and the environment. At any point on the surface, the reaction rate is taken to be proportional to the free energy reduction per unit volume of mass loss. The ceramic body is modeled by a half plane bounded by a curve, whose shape is described by a conformal mapping of many terms, allowing the elastic field in the body to be solved analytically. A variational method leads to a set of ordinary differential equations to evolve the shape. The model predicts threshold loads, and the times required, for crack nucleation.