Dendritic Needle Network Modeling of the Columnar-to-Equiaxed Transition. Part II: Three Dimensional Formulation, Implementation and Comparison with Experiments

Abstract

The dendritic needle network (DNN) model tracks the diffusion-controlled growth of branches in the hierarchically structured dendritic network, thereby bridging the well-separated scales traditionally simulated by phase-field and coarse-grained models. In particular, the DNN model relaxes the assumptions on the dendrite growth kinetics and grain structures commonly used in the coarse-grained models. In part I of this paper, we proposed a two-dimensional (2D) version of the DNN model and applied it to investigate the Columnar-to-Equiaxed Transition (CET) to clarify the influence of these assumptions on the prediction of the CET. In order to overcome the limitations inherent in a 2D model, part II presents here a fully three-dimensional (3D) version of the DNN model and its application to the CET. After validation of the 3D model, we perform simulations to study the solidification of Al-7wt.%Si alloy and compare the results to the experimental measurements conducted on board of the International Space Station (ISS)in the framework of the CET in SOLidification processing project. The comparison shows that the present 3D DNNmodel is able to provide quantitative prediction of the position and the type of CET at experimental time and length-scales, without any adjustable parameters.

Keywords: solidification, columnar-to-equiaxed transition, multi-scale modeling, dendritic needle network model