Three-Dimensional Multiscale Modeling of Dendritic Spacing Selection During Al-Si Directional Solidification

We present a three-dimensional extension of the multiscale dendritic needle network (DNN) model. This approach enables quantitative simulations of the unsteady dynamics of complex hierarchical networks in spatially extended dendritic arrays. We apply the model to directional solidification of Al-9.8 wt.%Si alloy and directly compare the model predictions with measurements from experiments with in situ x-ray imaging. We focus on the dynamical selection of primary spacings over a range of growth velocities, and the influence of sample geometry on the selection of spacings. Simulation results show good agreement with experiments. The computationally efficient DNN model opens new avenues for investigating the dynamics of large dendritic arrays at scales relevant to solidification experiments and processes.