A comprehensive three-dimensional (3D) stochastic model for simulating the evolution ofdendritic crystals during the solidification of binary alloys was developed. Themulti-scale model takes into account all the length scales (e.g., macro, micro- andmeso-scales) required to accurately predict the evolution of dendritic morphologies duringsolidification of alloys. The model includes time-dependent computations for temperaturedistribution, solute redistribution in the liquid and solid phases, curvature, and growthanisotropy. Stochastic models previously developed for simulating dendritic grains in 2Dwere modified to control the nucleation and growth of dendrites in 3D. 3D mesoscopiccomputations at the dendrite tip length scale were performed to simulate the evolution ofcolumnar and equiaxed dendritic morphologies including segregation patterns and comparedthen with predictions based on 2D mesoscopic computations.
