Papers by Keyword: Phase-Field Method

Abstract: The conformation of volume free energy is very important for microstructure simulation with phase-field method. However, the conformation of volume free energy is still correspondingly simple and ideal at present. In this paper, a new conformation method of free energy is mentioned. Free energy of each phase at appointed states is calculated by Thermo-Calc software. Free energy of each phase is fitted by multiple-point function according to sub- regular solution model. It is obtained that the free energy data and phase graph data of α phase, θ phase and L phase in the extension, temperature (791-841) K and component (0-35)Cu(at.%) with Al-Cu eutectic alloy.

Abstract: The typical Landau free energy functional with the fourth power of a solute composition field is not suitable for representing spinodal decomposition of a dilute Ag solute field in Al-Ag alloy. Facing this challenge, a new free energy density function is proposed for spinodal decomposition of a dilute Ag solute field of Al-Ag alloy. The evolution of the solute field in Al-4.2% Ag alloy is studied by phase-field method using this new function. The simulated results reveal that the precipitate free zone (PFZ) around the precipitated phase is an ellipse and its width is about two times that of phase, while in the region far from PFZ, a GPZ pattern of Ag solute field appears due to spinodal decomposition.

Abstract: The dendrite growth process was simulated with the Phase Field Model coupled with the fluctuation. The effect of fluctuation intensity on the dendrite morphology and the thermal fluctuation together with the phase field fluctuation on the forming of side branches were investigated. Result shows that with the decrease of thermal fluctuation amplitude, the furcation of dendrites tip also decreased, transverse dendrites become stronger and lengthways dendrites becomes degenerate, Doublon structure disappeared, finally a quite symmetrical dendrites structure formed. Thermal fluctuation can result in the unsteadiness of dendrites side branches, it is also the main reason of forming side branches, yet phase field fluctuation has little contribution to the side branches, it is usually ignored in the calculation; when the value of F_u is appropriate, the thermal noise can lead the side branches, but cannot change the steady behavior of the dendrites’ tip.

Abstract: In order to obtain the directional microstructure of different supersaturation and growing velocity, three simulations is calculated with different initial temperature. When the initial temperature is 1576K, and the supersaturation and growing velocity are smaller. The average space length of columnar crystals is bigger, and the directional microstructure grows by the wide columnar crystals. Microsegregation is smaller; when the initial temperature is 1574K, the supersaturation and growing velocity increase. when the initial temperature falls to 1566K, the planar interface comes back, and microsegregation decreases rapidly. The directional microstructure grows by the thinnest columnar crystals. At the same time, the transverse solute profiles and solute boundary layer are also talked in this paper.

Abstract: The effect of initia gamma prime particle size on coarsening kinetics of gamma prime precipitates in Nickel-based superalloys has been studied by means of phase field method which takes into account the lattice misfit. The simulation shows that the gamma prime precipitate morphology at the late stage of coarsening is independent of initial particle size, and the rectangle-like precipitates dominate the matrix which is in good agreement with experimental studies. The coarsening exponent increases with initial size, while the coarsening rate constant exhibits no apparent regularity. Although the coarsening trend is independent of initial particle size, the precipitate size increases with initial size at a given aging time. Through precipitate size distribution calculation, it is found that the size distribution is fairly stable, which is not sensitive to the initial particle size.

Abstract: A new phase field model coupled with external field was used to simulate 2D and 3D grain growth processing. The simulation results showed that 2D grain size distribution under external field was inhomogeneous. The evolutions of 2D grain under different external field strength were roughly the same, but the grain number was obviously different with the changes of external fields. Under the external field, the relationship between 2D grain area and time was linear. 3D grain distribution was inhomogeneous in the direction of the external field gradient. The nucleation gradually decreased in the direction of change.

Abstract: Phase-field method can be used to describe the complicated morphologies of crystal growth without explicitly tracking the complex phase boundaries. The conformation of volume free energy is very important for microstructure simulation with phase-field method. However, the conformation of volume free energy is still correspondingly simple and ideal at present. In this paper, a new conformation method of free energy is mentioned. Free energy of each phase at appointed states is calculated by Thermo-Calc software. In order to avoided calculation, free energy of each phase is fitted by multiple-point function according to sub- regular solution model. It is obtained that the free energy data and phase graph data of α phase, θ phase and L phase in the extension, temperature (791-841) K and component (0-35)Cu(at.%) with Al-Cu eutectic alloy. The new phase model is also founded, and used to calculate microstructure evolution of Al-Cu eutectic alloy.

Abstract: The phase field method has been applied to simulate the microstructural evolution of a commercial single crystal Ni-based superalloy during both, HIP and annealing treatments. The effects of applying high isostatic pressure on the microstructural evolution, which mainly retards the diffusion of the alloying elements causing the loss of the orientational coherency between the phases is demonstrated by the simulation and experimental results

Abstract: Segregation of solute atoms and vacancies to migrating D03–type antiphase boundaries (APBs) in Fe3Al of the stoichirometric and an Al-rich compositions has been investigated in detail by a phase-field method developed in the previous study [Koizumi et al. Acta Mater 2009;57:3039] focusing on the quantitative relationship among the segregation, APB energy, driving-force, drag-force and APB mobility. It has been revealed that the drag-force by solute segregation depends considerably on the alloy composition and is responsible for the significant composition dependence of the migration kinetics of D03-APB whereas the composition dependences of driving-force and mobility are negligibly small.

Abstract: 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.