Large deformation continuum dislocation theory: kinks, jogs and dislocation--vacancy interaction

It is well-known that plastically deformed crystals contain very high vacancy concentrations. However, crystal plasticity is usually modelled purely conservative. We show that a large deformation theory based on dislocation flux equations naturally leads to jogged dislocation densities which are not tied to a single slip plane. Further dislocation motion will therefore in general not be conservative, such that a co-evolving vacancy concentration field needs to be considered. We therefore conclude that the assumption of conservative crystal plasticity is not tenable in large deformations. Small example calculations are used to illustrate the evolution of kinks, jogs, and vacancy concentrations in continuum simulations of dislocation intersections. Continuum thermodynamics is employed to derive a coupled constitutive theory for dislocation vacancy evolution in large deformations. The resulting theory is discussed in light of recent experimental finding on ductile fracture.