Abstract

Fracture is one of the most challenging ‘multi-scale’ problems to model: since crack propagation is driven by the concentration of a long-range stress field at an atomically sharp crack tip, an accurate description of the chemical processes occurring in the small crack tip region is therefore essential, as is the inclusion of a much larger region in the model systems. Both these requirements can be met by combining a quantum mechanical description of the crack tip with a classical atomistic model that captures the long-range elastic behaviour of the surrounding crystal matrix. Examples of the application of these techniques to fracture problems include low-speed dynamical fracture instabilities in silicon, interactions between moving cracks and material defects such as dislocations or impurities, very slow crack propagation via kink formation and migration, and chemically activated fracture, where cracks advance under the concerted action of stress and corrosion by chemical species such as oxygen or water.