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