Prof Alain Karma - Northeastern University, USA
Multiscale modeling of dendritic microstructures: bridging the dendrite tip and grain scales
A. Karma, Y. Song and D. Tourret
Physics Department, Northeastern University, Boston, USA
The last two decades has witnessed major progress in quantitative modeling of dendritic microstructures using the phase field method. However, with perhaps the exception of very dilute alloys, this method still falls short of modeling dendritic evolution on a grain scale that is typically several orders of magnitude larger than the dendrite tip scale. To bridge this length scale gap, we have developed a multiscale “dendritic needle network” (DNN) model  that rigorously tracks the growth dynamics of the primary, secondary and higher order branches of the dendritic network. Each branch is treated as a thin needle whose instantaneous velocity V and tip radius R are determined by combining a standard solvability condition, which fixes the product R2V, with a solutal flux condition that determines separately the product RV2 and hence R and V independently. This talk will discuss the theoretical underpinnings of the DNN model and present examples of application to equiaxed and columnar growth in two and three dimensions. The results shed new light on the emergence of scaling laws that describe the evolution of the dendritic grain envelope.
- D. Tourret and A. Karma, Acta Materiala 61, 6474-6491 (2013).