  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 pipe diffusion and the jog
structure on dislocations 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.
