Numerical investigations of helical dislocations based on coupled glide-climb model

Helical dislocations are widely observed in metallic, ionic and covalent crystals and have significant impacts on the material properties. In this paper, a coupled glide-climb model is proposed based on three-dimensional discrete dislocation dynamics (3D-DDD) to reveal the intrinsic formation mechanism of helical dislocations. First, a dislocation climb model controlled by the diffusion of the supersaturated vacancies is developed and validated. Then, a sequentially coupled scheme is adopted to bridge the time scale separation between dislocation climb and glide. By incorporating the dislocation climb model into the 3D-DDD framework, a coupled glide-climb model is established to investigate the formation of helical dislocations. From the aspect of kinematics, dislocation climb gives rise to winding up, and the prismatic glide ensures the spaces between spirals. While from the aspect of kinetics, it is the applied stress, the osmotic force and line tension that act together to drive the dislocation line into a helix. The simulations further quantitatively reveal that: (1) It is the evolution velocity that breaks the stable equilibrium state and drives the helix into a configuration with multiple turns; (2) Both the external stress and the initial dislocation configurations influence the final helical configuration and the number of spirals increases linearly with the external stress, which are very similar to the buckling configuration of a column under axial loading which is sensitive to the critical loading and initial geometry imperfection; (3) The formation time of helical dislocation decreases exponentially with the vacancy concentration.