Multiscale Theory of Dislocation Climb

Dislocation climb is a ubiquitous mechanism playing a major role in the plastic deformation of crystals at high temperature. We propose a multiscale approach to model quantitatively this mechanism at mesoscopic length and time scales. First, we analyze climb at a nanoscopic scale and derive an analytical expression of the climb rate of a jogged dislocation. Next, we deduce from this expression the activation energy of the process, bringing valuable insights to experimental studies. Finally, we show how to rigorously upscale the climb rate to a mesoscopic phase-field model of dislocation climb. This upscaling procedure opens the way to large scale simulations where climb processes are quantitatively reproduced even though the mesoscopic length scale of the simulation is orders of magnitude larger than the atomic one.