Coupling quantum and continuum scales to predict crack tip dislocation nucleation

A quantum-continuum multiscale coupling of Kohn–Sham density functional theory to continuum material is presented that can handle mechanics problems in metals when long-range stress fields are present, such as occurs for dislocations and cracks. The method has quantifiable and controllable coupling errors that can be minimized at computationally tractable system sizes. Using both generalized gradient and local density approximation exchange–correlation functionals, the nucleation of a dislocation from a crack tip in aluminum is then predicted. Both functionals yield similar results, and predictions using Rice’s continuum Peierls model are within 20% of the quantum values. This multiscale method is easily extendable to crack-tip problems involving alloys and chemical embrittlements.