Phase field simulations of stress distributions in solidification structures

Phase field simulations of stress evolution during solidification processes are carried out, resulting in the generation of complicated stress distributions in solidification microstructures. The governing equations, which include the coupling relations among phase transformation, temperature and stress/strain, are numerically solved using the two-dimensional finite element method. To avoid complexity, mechanical properties of the liquid are applied under a simplified assumption that sufficiently small elastic constants can approximate the liquid behavior. A dendritic microstructure is considered in this study as a typical solidification microstructure. As a result, a complicated stress distribution in a dendrite is obtained. Especially, strong stresses are revealed to distribute at the bottom of sidebranches of a dendrite. Subsequently, a microstructure constructed with two dendrites is simulated, and it reveals that high stresses are generated in the regions where the liquid remains till the very last stage of the solidification. Finally, two types of dendritic patterns are investigated, and the stresses are revealed to strongly depend on the morphology of the microstructures.