We perform material microstructure prediction simulations using the phase-field method and large-scale simulations using GPUs and supercomputers. In large-scale phase-field simulations, we have performed the world’s largest simulations of dendrite solidification and grain growth, and continue to produce results that can only be achieved by large-scale simulations.

We have been conducting competitive growth simulations of columnar dendrites, where the dendrite spacing and alignment in single crystals, the mechanism of unusual selection in bi-crystals, and the formation mechanism of columnar structures in polycrystals have been investigated. This research has been made possible only through large-scale three-dimensional simulations using a supercomputer.

By coupling the phase-field and lattice Boltzmann method, we enabled simulations of dendrite growth with liquid flow. It is very important to consider liquid flow in solidification simulations of alloys because the solidification morphology varies significantly depending on natural and forced convection. However, owing to the high computational cost of liquid flow simulation, it is necessary to develop a more efficient numerical scheme to enable simulations on a realistic scale.

The solidification structure can be roughly classified into columnar and equiaxed structures. Because equiaxed grains are isolated in the liquid phase, they move in the liquid phase owing to the solid-liquid density difference under gravity. Because this motion causes serious solidification defects such as segregation and cracking, it is necessary to represent the motion of the solid for reproducing the formation process of the equiaxed structure. In this study, the phase-field method was used for the first time to stably represent equiaxed dendrite growth with motion, and the method has been extended to polycrystalline solidification problems.

During solidification, alloys are subjected to external forces, such as solidification shrinkage, centrifugal force (centrifugal casting), press-in (die casting), gravity, and rolling (continuous casting). When equiaxed grains in a solid-liquid coexistence state are subjected to external forces, they behave differently from pure liquid and solid because of the interaction between solids depending on the solid fraction and grain shape. Among them, dilatancy is well known, which increases the apparent volume and causes segregation bands and cracks. Because the semi-solid deformation behaves in a peculiar way, our study is focused on modeling this phenomenon and clarifying it numerically.

During the casting process of an alloy, the liquid flows with solidification. Solidification proceeds by dendrite growth, and thus the liquid flows between the dendrite network. Permeability is a measure of the flowability of a liquid through a dendrite network and is an important parameter in macroscale casting simulations. In this study, the permeability for the flow of an interdendritic liquid is estimated numerically. The computational procedure of permeability is as follows: the dendrite microstructure is obtained by the phase-field simulation (Step 1); the interdendritic liquid flow is computed using the lattice Boltzmann method (Step 2); and the permeability is computed based on Darcy’s law using the results of Step 2 (Step 3).

The phase-field method has the disadvantage of high computational cost because it requires fine meshes to express a smooth profile of the phase-field variable in the thin interface region. To reduce the computational cost and accelerate the simulation, we develop an adaptive mesh refinement (AMR) method for phase-field simulations, in which fine meshes are placed only near the interface and coarse meshes are used in other regions. In addition, we have applied the AMR phase-field method to multi-GPU parallel computation to achieve large-scale and high-speed computations.

Solid metallic materials generally have polycrystalline structures. When they are heat-treated at high temperatures, grain growth occurs, in which the crystal grains become coarse. Heat treatment of plastically deformed metallic materials causes static recrystallization, whereas the hot working of metallic materials causes dynamic recrystallization. Grain growth also occurs during the recrystallization process. Thus, grain growth is an important phenomenon that determines the material microstructure of the final product. In this study, we simulate the grain growth and recrystallization of polycrystalline materials using the multi-phase-field method, which uses multiple phase-field variables.

As the performance of computers has improved, it is becoming possible to simultaneously perform two numerical and/or experimental methods, which were originally conducted at different scales. By integrating these two methods through data assimilation, we are working on new applications of numerical simulations. The following figures show our research on obtaining interfacial and grain boundary properties by integrating molecular dynamics (MD) and phase-field (PF) methods through data assimilation.

We develop a multi-phase-field model that enables the simulation of multi-phase flow with an arbitrary number of phases. The multi-phase-field model for multi-phase flow is expected to have various applications, such as drug discovery in drug delivery systems, evaluation of solid-gas-liquid three-phase flow in alloy solidification, and evaluation of multi-phase flow behavior with large deformation in vivo.

Galvanizing is applied to metal surfaces for corrosion protection and aesthetic appearance. In the hot-dip galvanizing process, dendrites with unusual shapes (several tens of microns in thickness and several millimeters in diameter) grow in the thin coating film and form beautiful patterns called spangles. The phase-field method is used to elucidate the formation mechanism of the spangles.

The most important aspects of structural design are strength and light weight. To increase strength, we can make the members thicker, but this makes the structure heavier. To improve the fuel efficiency of airplanes and automobiles, it is important to reduce the weight. In this case, it is necessary to aim for light materials as well as to design the shape and topology of the structure or to arrange multiple materials appropriately. We study the application of the phase-field method to a topology-optimization design for a structure with multiple materials.