Phase Field Model Simulation Research Articles

Abnormal Grain Growth Approached by Sub-Boundary Enhanced Solid-State Wetting

Abnormal grain growth (AGG), which is also called the secondary recrystallization, often takes place after primary recrystallization of deformed polycrystalline materials. A famous example is the evolution of the Goss texture after secondary recrystallization of Fe-3%Si steel. A selective AGG of Goss grains has remained a puzzle over 70 years in the metallurgy community since its first discovery by Goss in 1935. We suggested the sub-boundary enhanced solid-state wetting as a mechanism of selective AGG of Goss grains. According to this mechanism, if Goss grains have sub-boundaries of low energy, they have an exclusively high probability to grow by solid-state wetting along a triple junction compared with other grains without sub-boundaries. This aspect has been confirmed by Monte-Carlo and Phase Field Model simulations. The simulations showed that if the abnormally-growing grain has a high fraction of low energy boundaries with the matrix grains, it favors the sub-boundary enhanced solid-state wetting and produces many island and peninsular grains frequently observed near the growth front of abnormally-growing Goss grains. For example, the {111}<112> orientation has a S9 relationship with a Goss grain. Therefore, grains with the {111}<112> orientation provide a favorable condition for sub-boundary enhanced solid-state wetting. Three or four-sided grains with convex-inward boundaries, which are observed on a two-dimensional section of polycrystalline structures, are not shrinking but are growing, indicating that they are growing by wetting along a triple junction. These and other microstructural evidences of solid-state wetting could be observed relatively easily near the growth front of abnormally-growing Goss grains. The existence of sub-boundaries exclusively in abnormally-growing Goss grains has been experimentally confirmed. In order to understand why only Goss grains have sub-boundaries, the cold rolling process of the hot-rolled Fe-3%Si steel was analyzed by finite element method (FEM). The analysis showed that a small portion of Goss grains formed during hot rolling survives after cold rolling; the survived Goss grains have the lowest stored energy and are expected to undergo only recovery without recrystallization, producing sub-boundaries.

Dependence of Dendritic Growth on Convention with PFM Simulation

A binary alloy PFM (Phase-Field Model) which incorporates the flow field equations is constructed considering the dependence of microstructure on convention. Al-Cu binary alloy is investigated numerically based on the model, and the reasonable computational methods is studied for solving PFM, the effect of convention on dendritic growth and microsegregation patterns is implemented successfully. The computed results indicate that, the larger convention velocity U, the more developed the upstream dendritic branches is, and the more acutely the solute composition in the upstream dendritic solid fluctuates is. But the severity of microsegregation ahead of interface reduces. Nevertheless, the more undeveloped the downstream dendritic branches, the more acutely the solute composition in the the downstream dendritic solid fluctuates is, but the severity of microsegregation ahead of interface aggravates.

Phase field model simulations of hydrogel dynamics under chemical stimulation

Two decades ago, it has been observed experimentally that hydrogels immersed in a bath solution swells or shrinks under external stimulations (Ricka et al., Macromolecules 17:2916–2921, 1984). Recently, this fact has received renewed interest, since understanding the precise mechanisms underlying that kind of behavior has the potential to tailor most sensitive drug delivery systems based on hydrogels (Segalman and Witkowski, Mater Sci Eng C 2:243–249, 1995). Here we contribute to a precise understanding of the mechanisms responsible for the hydrogels’ swelling kinetics as well as dynamics by proposing for the first time a model approach that can resolve the inherent short-range correlation effects along the hydrogel–solution interface jointly with the long-range ionic transport fields. To that end, we investigate the swelling dynamics of hydrogels, which is a moving boundary problem, by a phase field model, which couples the Nernst–Planck equation for the concentration of mobile ions, Poisson equation for the electric potential, mechanical equation for the displacement, and an equation for the phase field variable. Simulation for two-dimensional case reveals that under the chemical stimulation, the hydrogel will swell or shrink if the concentration of mobile ions inside bath solution decreases or increases. This is in agreement with the experimental results qualitatively and validates our new model approach.

Phase-field model study of the crystal morphological evolution of hcp metals

An expression for anisotropic interfacial energy of hexagonal close-packed metals has been formulated which is able to reproduce published data obtained using the modified embedded-atom method, covering the variation in interface energy as a function of orientation for a number of metals. The coefficients associated with the expression can be determined fully by measured or calculated interfacial energies of just three independent crystal planes. Three-dimensional phase-field model simulations using this representation of interfacial energy have been found to yield convincing crystal morphologies. The apparent rate of crystal growth as a function of orientation in the phase-field simulation agrees with predictions made by surface energy theory.

Abnormal grain growth induced by sub-boundary-enhanced solid-state wetting: Analysis by phase-field model simulations

Abstract Abnormal grain growth (AGG) was approached by a new concept of sub-boundary-enhanced solid-state wetting using a phase-field model (PFM) simulation. If grains have sub-boundaries of very low-energy, they increase the probability of growing by solid-state wetting, compared with other grains of moderate anisotropy in grain boundary energy. As a result, the grains with sub-boundaries have an exclusive growth advantage and can grow abnormally. These aspects are shown in two- and three-dimensional PFM simulations.

Phase Field Model Simulation of Grain Growth in Three Dimensions under Isotropic and Anisotropic Grain Boundary Energy Conditions

Phase-field model (PFM) in multiple orientation fields was used to simulate the grain growth in three-dimensions (3-D) for isotropic and anisotropic grain boundary energy. In the simulation, the polycrystalline microstructure was described by a set of non-conserved order parameters and each order parameter describes each orientation of grains. For isotropic grain boundary energy, the simulation showed the microstructure evolution of normal grain growth. For anisotropic grain boundary energy, however, the simulation showed that certain grains which share a high fraction of low energy grain boundaries with other grains have a high probability to grow by wetting along triple junctions and can grow abnormally with a growth advantage of solid-state wetting. The PFM simulation shows the realistic microstructural evolution of island and peninsular grains during abnormal grain growth by solid-state wetting.

Phase Field Model Simulation of Abnormal Grain Growth by Solid-State Wetting

Abnormal grain growth (AGG) takes place in many metallic systems especially after recrystallization of deformed polycrystals. The growth advantage has been attributed to the high mobility of the grain boundaries of the abnormally-growing grains. As a new approach to the growth advantage of AGG, however, we suggested the solid-state wetting, where a grain wets or penetrates the grain boundary or the triple junction of neighboring grains just as the liquid phase wets along the grain boundary or the triple junction. If the energy sum of the two grain boundaries is lower than the energy of the other grain boundary in contact at the triple junction, the high energy grain boundary will be replaced by the two low energy grain boundaries through the wetting process. Once the solid-state wetting occurs, the triple junction, which tends to be a rate-determining step in grain growth, migrates much faster than the grain boundaries in contact and therefore, the triple junction constraint in grain growth disappears. Here, we studied the effect of solid-state wetting on AGG by phase field model (PFM) simulation and compared the microstructural feature of AGG with that observed experimentally in Fe-3%Si alloy. The misorientation angles between island and peninsular grains accompanied by AGG were measured using electron backscattered diffraction (EBSD). The PFM simulation shows the realistic microstructural evolution of island and peninsular grains during AGG by solid state wetting. Very high frequency of island and peninsular grains formed at or near the growth front of abnormally growing grains could be best explained by solid-state wetting.

Boundary Mobility and Energy Anisotropy Effects on Microstructural Evolution During Grain Growth

We have performed mesoscopic simulations of microstructural evolution during curvature driven grain growth in two-dimensions using anisotropic grain boundary properties obtained from atomistic simulations. Molecular dynamics simulations were employed to determine the energies and mobilities of grain boundaries as a function of boundary misorientation. The mesoscopic simulations were performed both with the Monte Carlo Potts model and the phase field model. The Monte Carlo Potts model and phase field model simulation predictions are in excellent agreement. While the atomistic simulations demonstrate strong anisotropies in both the boundary energy and mobility, both types of microstructural evolution simulations demonstrate that anisotropy in boundary mobility plays little role in the stochastic evolution of the microstructure (other than perhaps setting the overall rate of the evolution. On the other hand, anisotropy in the grain boundary energy strongly modifies both the topology of the polycrystalline microstructure the kinetic law that describes the temporal evolution of the mean grain size. The underlying reasons behind the strongly differing effects of the two types of anisotropy considered here can be understood based largely on geometric and topological arguments.

K-1803 結晶成長速度の実測値を利用した形態形成シミュレーション(G06-1 熱工学(1) : 吸着・凝固)(G06 熱工学部門一般講演)

Interfacial kinetics and anisotropy based on lattice structure have to be introduced into a simulation model to predict morphology of crystal growth quantitatively. We experimentally investigated the interfacial kinetics and tried to reproduce the growth process of real crystals by the phase field model (PFM). The crystal growth rate depends on the crystal direction, thus the interfacial growth rate was measured as a function of the supercooling and the direction with the static directional solidification stage. As a result, the anisotropic crystal growth rate was clarified for (010) plane of Salol and (0010) plane of ice. It was shown that two-dimensional PFM simulation involving the crystal growth rate data could reproduce very similar pattern to the real crystals.