Sharp Phase Field Method.

Phase field modeling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretization scheme with a grid spacing small enough to preserve the continuous character of the theory. We present here a new formulation, which is intrinsically discrete, in which the interfaces are resolved with essentially one grid point with no pinning on the grid and an accurate rotational invariance, improving drastically the numerical capabilities of the method. We show that interfacial kinetic properties are reproduced with a high accuracy. Finally, we apply the model to a situation where conserved and nonconserved fields are coupled.

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.