Phase Field Simulation Of Grain Growth Research Articles

Mean-field modeling and Phase-field simulation of Grain Growth under Directional driving forces

Directional grain growth is a common phenomenon in the synthetic and natural evolution of various polycrystals. It occurs in the presence of an external driving force, such as a temperature gradient, along which grains show a preferred, yet competitive, growth. Novel additive manufacturing processes, with intense, localized energy deposition, are prominent examples of when directional grain growth can occur, beneath the melting pool. In this work, we derive a phenomenological mean-field model and perform 3D phase-field simulations to investigate the directional grain growth and its underlying physical mechanisms. The effect of the intensity of driving force is simulated and systematically analyzed at the evolving growth front as well as various cross-sections perpendicular to the direction of the driving force. We found that although the directional growth significantly deviates from normal grain growth, it is still governed by a power law relation 〈R〉∝tn, with an exponent n∼ 0.6–0.7. The exponent n exhibits a nontrivial dependence on the magnitude of the directional driving force, such that the lowest growth exponent is observed for intermediate driving forces. We elaborate that this can originate from the fact that the forces at grain boundary junctions evolve out of balance under the influence of the directional driving force. With increasing the driving forces, the growth exponent asymptotically approaches a value of n≈0.63, imposed by the largest possible grain aspect ratio for given grain boundary energies. The current combined mean-field and phase-field framework pave the way for future exploration in broader contexts such as the evolution of complex additively manufactured microstructures.

Insights into abnormal grain growth in copper thin films for reduced electrical resistivity: A quantitative multi-order-parameter phase-field study under finite element framework

Copper thin films are frequently utilized as microelectronic interconnects. Inducing abnormal grain growth (AGG) may result in reduced electrical resistivity of copper thin films. However, an in-depth understanding of AGG mechanism and quantitative simulation of microstructure evolution during AGG in copper thin films are still missing, prohibiting the regulation and even design of AGG process. In this paper, a multi-order-parameter phase-field (MOP-PF) model coupled with elastic mechanics under a finite element framework was first developed and applied to study the AGG mechanism in copper thin films. It was found that both elastic and grain boundary anisotropies can induce AGG, but elastic anisotropy dominates the evolution of individual grains. Subsequently, a quantitative simulation of microstructure evolution/kinetics during AGG in copper thin films was achieved by inputting the accurate materials parameters from theoretical/experimental data. A further combination with the Mayadas-Shatzkes model led to a quantitative prediction of the evolution of electrical resistivities, from which several feasible strategies were proposed for preparing high-performance copper thin films with reduced electrical resistivities. Furthermore, it is anticipated that the presently developed framework should be generally applicable for quantitative phase-field simulation of grain growth in bulk materials/films.

Evaluating microstructural parameters of three-dimensional grains generated by phase-field simulation or other voxel-based techniques

The MacPherson–Srolovitz relation expresses the rate of volume change of a grain in a three-dimensional polycrystalline system in terms of microstructural parameters—the mean grain width and the triple line length—as well as isotropic values for the grain boundary mobility and energy. We introduce methods to accurately determine these microstructural measures for grain structures described by a voxel-based microstructure representation, such as those generated by phase-field simulations, Monte Carlo Potts models, or three-dimensional reconstructions of experimentally measured polycrystalline microstructures. We evaluate the mean rate of volume change of grains during a phase-field simulation of grain growth and discuss the results in terms of the MacPherson–Srolovitz relation.

3-D phase-field simulation of grain growth: Topological analysis versus mean-field approximations

The characteristics of 3-D grain growth are investigated by a topological analysis of phase-field simulation results compared with theoretical mean-field theories. We found that the size distribution of the grains starting from an arbitrary narrow distribution crosses the self-similar Hillert distribution, and ends in a distribution with relatively longer tails of large grains in which the central peak shifted towards smaller grain size. The distribution of topological classes, as characterized by the number of facets per grain, is found to be time-invariant for the process as a whole. The obtained shape function is in good agreement with the analytical distribution function derived based on the average N-hedron model [Rios PR, Glicksman ME. Act Mater 2008;56:1165]. The volumetric growth rate per topological class also correlates well with the analytical approach obtained by Mullins [Mullins WW. Acta Mater 1956;3:900]. The relationship between grain size and its shape, however, deviates from theoretical predictions.

Phase-field Simulations of Grain Growth in Two-dimensional Systems Containing Finely Dispersed Coarsening Particles

In this study, we have performed phase-field simulations of grain growth in two-dimensional systems containing finely dispersed coarsening particles. In particular, the effects of the Ostwald ripening of particles on the grain growth kinetics and the morphology of the matrix grains have been investigated. After reaching a steady state, not only does the growth of the particles obey power-law kinetics, but also the growth of the matrix grains, with an exponent of 3. In the case of systems having a small fraction of immobile particles, the grain size distributions (GSDs) of the matrix grains become broader with a small fraction of particles. For systems containing particles that coarsen with simulation time, the GSDs become narrower with an increase in the area fraction of the particles, fp(0). We have applied both active parameter tracking (APT) algorithms and parallel coding techniques to the multi-phase-field (MPF) model to accelerate the computations and to embody large-scale calculations.

Dual-scale phase-field simulation of grain growth upon reheating of a microalloyed line pipe steel

Abstract The austenite grain growth of a microalloyed steel was investigated via annealing experiments and phase-field simulations using the phase-field code Micress. The technique described in a previous work was enhanced and applied to an Nb, Ti microalloyed linepipe steel for the case of isothermal heat treatment between 1 050 and 1 200 °C. The input parameters for the phase-field simulations were deduced from physical models based on the results of isothermal holding experiments. A further improvement was the use of the software package MatCalc to simulate at a lower scale the coarsening of the pinning particles. The results of these simulations showed good agreement with the experimental results.

113 二相混合組織における粒成長の三次元Phase-fieldシミュレーション(OS16.フェーズフィールド法とその応用(1),オーガナイズドセッション)

113 二相混合組織における粒成長の三次元Phase-fieldシミュレーション(OS16.フェーズフィールド法とその応用(1),オーガナイズドセッション)

Computer simulations of two-dimensional and three-dimensional ideal grain growth

We developed an efficient computation scheme for the phase-field simulation of grain growth, which allows unlimited number of the orientation variables and high computational efficiency independent of them. Large-scale phase-field simulations of the ideal grain growth in two-dimensions (2D) and three-dimensions (3D) were carried out with holding the coalescence-free condition, where a few tens of thousands grains evolved into a few thousand grains. By checking the validity of the von Neumann-Mullins law for individual grains, it could be shown that the present simulations were correctly carried out under the conditions of the ideal grain growth. The steady-state grain size distribution in 2D appeared as a symmetrical shape with a plateau slightly inclined to the small grain side, which was quite different from the Hillert 2D distribution. The existence of the plateau stems from the wide separation of the peaks in the size distributions of the grains with five, six, and seven sides. The steady-state grain size distribution in 3D simulation of the ideal grain growth appeared to be very close to the Hillert 3D distribution, independent of the initial average grain size and size distribution. The mean-field assumption, the Lifshitz-Slyozov stability condition, and all resulting predictions in the Hillert 3D theory were in excellent agreement with the present 3D simulation. Thus the Hillert theory can be regarded as an accurate description for the 3D ideal grain growth. The dependence of the growth rate in 3D simulations on the grain topology were discussed. The large-scale phase-field simulation confirms the 3D growth law obtained from the Surface Evolver simulations in smaller scales.

218 静的再結晶過程における結晶粒成長Phase-fieldシミュレーション(GS5 応力解析33)

218 静的再結晶過程における結晶粒成長Phase-fieldシミュレーション(GS5 応力解析33)

Quantitative characterization of the three-dimensional microstructure of polycrystalline Al-Sn using X-ray microtomography

Characterizing the three-dimensional topology of grain-boundary networks in polycrystalline materials is a crucial step in the modeling of properties that depend on the sample microstructure. Using absorption-contrast X-ray microtomography, we have carried out a large-scale microstructural characterization of polycrystalline Al doped with 2 at. pct Sn, which is immiscible in Al in the solid state. The segregation of Sn to the grain boundaries imparts a strong contrast in X-ray attenuation that can be reconstructed tomographically; however, the nonuniformity of the segregation process presents a formidable challenge to the automated segmentation of the reconstructions. By employing an iterative grain-finding algorithm followed by a novel grain-boundary-network optimization routine (based on a phase-field simulation of grain growth), we were able to extract reliable values for the size and topology of nearly 5000 individual grains in polycrystalline Al-Sn. The distributions and averages of these data deviate significantly from the corresponding microstructural parameters of the three-dimensional (3-D) Poisson-Voronoi tessellation often used to model polycrystalline samples. Much better agreement was observed with microstructures generated by the computer simulation of three-dimensional grain growth.