Papers by Keyword: Phase Field Modellig

Abstract: Based on a thin interface limit 3D phase-field model by coupled the anisotropy of interfacial energy and self-designed AADCR to improve on the computational methods for solving phase-field, 3D dendritic growth in pure undercooled melt is implemented successfully. The simulation authentically recreated the 3D dendritic morphological fromation, and receives the dendritic growth rule being consistent with crystallization mechanism. An example indicates that AADCR can decreased 70% computational time compared with not using algorithms for a 3D domain of size 300×300×300 grids, at the same time, the accelerated algorithms’ computed precision is higher and the redundancy is small, therefore, the accelerated method is really an effective method.

Abstract: Thermodynamic stability of Grain boundary in materials under severe plastic deformation was simulated by the Monte Carlo and the phase field methods. Computer simulations were performed on 3-dimensional textured materials. The Monte Carlo simulation results were qualitatively in good agreement with those by the phase field model. The classification of the solution of differential equations based on the mean-field Hillert model describing temporal evolution of the scaled grain size distribution function was in good agreement with those given by the Computer simulations. The ARB experiments were performed for pure Al and Al alloys-sheets in order to validate the computer simulation results concerning the grain boundary stability of textured materials. With use of the Monte Carlo and the phase field methods. Effect of grain boundary mobilises and interface energy given by the computer simulations.

Abstract: Cahn-Hilliard type of phase field model coupled with elasticity is used to derive governing equations for the stress-mediated diffusion and phase transformation in thin films. To solve the resulting equations, a finite element (FE) model is presented. The partial differential equations governing diffusion and mechanical equilibrium are of different orders; Mixed-order finite elements, with C0 interpolation functions for displacement, and C1 interpolation functions for concentration are implemented. To validate this new numerical solver for such coupled problems, we test our implementation on thin film diffusion couples.

Abstract: Evolution of interdiffusion microstructures was examined in ternary Ni-Cr-Al solid-tosolid diffusion couples using two-dimensional (2D) phase field simulation. Utilizing Cahn-Hilliard and Allen-Cahn equations, multiphase diffusion couples containing of fcc-γ and B2-β solid solution phases were simulated with alloys of different compositions and phase contents. Chemical mobility as a function of composition with constant gradient energy coefficients was used in the simulation. Simulated microstructures in γ+β/γ and γ+β/γ+β diffusion couples were compared with the experimental microstructures reported in literature. As observed experimentally, the model predicted the recession of γ+β region in the γ+β/γ couple and a stationary interface in γ+β/γ+β couple. Concentration profiles developed across the diffusion couples demonstrated that the interdiffusion occurs in the γ phase as well as in the γ+β region. Formation of single-phase γ and β layers near the interface of γ+β/γ+β couples was also investigated using the volume fraction profile obtained from the simulated microstructure.

Abstract: This paper describes phase field simulations of the rafting behavior of γ’ phase with a simple interfacial dislocation network model. The interfacial dislocation network model accounts for the effect of the network on the lattice misfit between γ and γ’ phases and the subsequent rafting behavior. The model is implemented into the phase field simulation to see the dependence of the rafting behavior of γ’ phases on the interfacial dislocation network. Without the dislocation network model, the amount of the rafting was negligibly small. On the other hand, with the dislocation network model, the γ’ phases shows a large amount of rafting, which is in good agreement with the results of the experimental observations. Therefore, the combination of the phase field method and the simple interfacial dislocation network model developed in this work is appropriate for the simulation of the rafting of γ’ phases.

Abstract: The effects of second-phase particles on the recrystallization kinetics in two-dimensional polycrystalline structures were investigated. Numerical simulations of recrystallization were performed by coupling the unified subgrain growth theory with a phase-field methodology. Simple assumptions based on experimental observations were utilized for preparing initial microstructures. The following results were obtained: (1) The presence of second-phase particles retarded recrystallization speeds. (2) If the mean subgrain size was small enough recrystallized region covered whole system for various values of the particle fraction, f. (3) On the other hand, if the mean subgrain size was not small enough the progress of recrystallization was frozen at some point.

Abstract: 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.

Abstract: Abnormal grain growth (AGG) proceeds in case that normal grain growth is inhibited. It has long been known that the inhibition involves finely dispersed particles and/or the development of specific textures. There is another strong obstacle against the grain boundary (GB) motion; the solute atoms can reduce their energy by moving from the bulk into a GB. Resultant interaction between the solute atoms and a GB makes the GB motion more difficult. However the role of the GB segregation effect on AGG has not been clarified. In this study we simulate the 2D and 3D grain growth accompanying boundary segregation of solute atoms by using a phase-field model. It is shown that the segregation plays an important role on the occurrence of AGG. The boundary-segregation-induced AGG can take place when the average driving force of grain growth approaches a critical condition for pinning-depinning transition in solute-drag atmosphere.

Abstract: Abnormal grain growth (AGG) takes place in many metallic systems especially after recrystallization of deformed polycrystals. A famous example of AGG in metallic system is the Goss texture in Fe-3%Si steel. During high temperature annealing of Fe-3%Si sheet, a few near Goss {110} <001> grains grow exclusively fast and consume the matrix grains. Therefore, the grains which have near Goss orientation have special advantage over other grains. As a new approach to the growth advantage of AGG, we suggested the solid-state wetting mechanism, where a grain wets or penetrates the grain boundary or the triple junction of its neighboring grains. The solid-state wetting mechanism for the evolution of the Goss texture in Fe-3%Si steel was studied experimentally and by phase-field model (PFM) simulation.

Abstract: The micro structural evolution and the mechanism of recrystallization grain growth were studied during re-aging process in Cu-Ni-Si alloy containing finely pre-aging δ-Ni2Si precipitates using computer simulations based on a diffuse-interface phase-field kinetic model. In this model, the temporal evolution of the spatially dependent field variables is determined by numerically solving the time-dependent Ginzburg-Landau (TDGL) equations for the structural variables. The simulation results quantify the effects of the precipitation on recrystallization. It is shown that the finely dispersed pre-aging δ-Ni2Si precipitates exert a strong pinning effect on the recrystallization grain boundaries. The recrystallization grain growth for r = 3 fa = 0.015 can be described as R =1.04∗t 0.33 at the beginning, followed by a gradual transition to growth stagnation. The final grain size follows a Zener type relation lim 0.49 1.41 a R r f =     for 0.01 ≤ fa ≤ 0.21 and r = 2.5 or 3.