MULTISCALE MODELING OF SOLIDIFICATION OF MULTI-COMPONENT ALLOYS
Modeling solidification in the micro-scale is computationally intensive. To overcome this difficulty, a method combining features of front-tracking methods and fixed-domain methods is developed. To explicitly track the interface growth and shape of the solidifying crystals, a front-tracking approach based on the level set method is implemented. To easily model the heat and momentum transport, a fixed-domain method is implemented assuming a diffused freezing front where the liquid fraction is defined in terms of the level set function. The fixed-domain approach, by avoiding the explicit application of essential boundary conditions on the freezing front, leads to an energy conserving methodology that is not sensitive to the mesh size. Techniques including fast marching, narrow band computing and adaptive meshing are utilized to speed up computations. The model is used to investigate various phenomena in solidification including two- and three-dimensional dendrite growth of pure material and alloys, eutectic and peritectic solidification, convection effects on crystal and dendrite growth, planar/cellular/dendritic transition, interaction between multiple dendrites, columnar/equiaxed transition and etc. Interaction between thousands or even millions of crystals gives the overall behavior of the solidification process and defines the properties of the final product. A multiscale model based on a database approach is developed to investigate alloy solidification. Appropriate assumptions are introduced to describe the behavior of macroscopic temperature, macroscopic concentration, liquid volume fraction and microstructure features. These assumptions lead to a macroscale model with two unknown functions: liquid volume fraction and microstructure features. These functions are computed using information from microscale solutions of selected problems. A computationally efficient model, which is different from the microscale and macroscale models, is utilized to find relevant sample problems. The microscale solution of the relevant sample problems is then utilized to evaluate the two unknown functions (liquid volume fraction and microstructure features) in the macroscale model. The temperature solution of the macroscale model is further used to improve the estimation of the liquid volume fraction and microstructure features. Interpolation is utilized in the feature space to greatly reduce the number of required sample problems. The efficiency of the proposed multiscale framework is demonstrated with numerical examples that consider a large number of crystals. A computationally intensive fully-resolved microscale analysis is also performed to evaluate the accuracy of the multiscale framework.