Dislocations are line defects and known as the main carriers of the permanent deformation of crystals. The presence of dislocations strongly influences many properties of materials. In this thesis, we focus on dislocation dynamics, and model the dislocation motion from atomistic schemes to continuum description.
Firstly, we develop a mesoscopic dislocation dynamics model for vacancy-assisted dislocation climb by upscalings from a stochastic model on the atomistic scale. Our models incorporate microscopic mechanisms of (i) bulk diffusion of vacancies, (ii) vacancy exchange dynamics between bulk and dislocation core, (iii) vacancy pipe diffusion along the dislocation core, and (iv) vacancy attachment- detachment kinetics at jogs leading to the motion of jogs. Our mesoscopic model consists of the vacancy bulk diffusion equation and a dislocation climb velocity formula. The effects of these microscopic mechanisms are incorporated by a Robin boundary condition near the dislocations for the bulk diffusion equation and a new contribution in the dislocation climb velocity due to vacancy pipe diffusion driven by the stress variation along the dislocation. Our climb formulation is able to quantitatively describe the translation of prismatic loops at low temperatures when the bulk diffusion is negligible. Using this new formulation, we derive analytical formulas for the climb velocity of a straight edge dislocation and a prismatic circular loop. Our dislocation climb formulation can be implemented in dislocation dynamics simulations to incorporate all the above four microscopic mechanisms of dislocation climb.
Secondly, we show that the self-climb formulation derived in the previous chapter is able to quantitatively describe the properties of self-climb of prismatic loops that were observed in experiments and atomistic simulations. We also present DDD implementation method of this self-climb formulation. Simulations performed show evolution, translation, coalescence of prismatic loops and the interaction between a prismatic loop and an infinite edge dislocation are in excellent agreement with available experimental and atomistic results.
Thirdly, we consider a system of parallel straight dislocation walls and develop a continuum description of the short-range interaction of dislocations by using asymptotic analysis. The dynamics of the system is then described by evolution equations for a pair of dislocation density potential functions. This derived continuum model is able to describe the anisotropic dislocation interaction and motion. It is shown that the continuum model is wellposed after being incorporated with the short-range interaction terms. The derived continuum model is validated through comparison with the discrete dislocation dynamical simulation results.