Multiscale modeling of alloy solidification using a database approach

A two-scale model based on a database approach is presented 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. This work addresses the selection of sample problems relevant to the interested problem and the utilization of data from the microscale solution of the selected sample problems. A computationally efficient model, which is different from the microscale and macroscale models, is utilized to find relevant sample problems. In this work, the computationally efficient model is a sharp interface solidification model of a pure material. Similarities between the sample problems and the problem of interest are explored by assuming that the liquid volume fraction and microstructure features are functions of solution features extracted from the solution of the computationally efficient model. The solution features of the computationally efficient model are selected as the interface velocity and thermal gradient in the liquid at the time the sharp solid-liquid interface passes through. An analytical solution of the computationally efficient model is utilized to select sample problems relevant to solution features obtained at any location of the domain of the problem of interest. The microscale solution of selected 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.