Papers by Keyword: Phase-Field Method

Abstract: Phase field method (PFM) was employed to investigate the crystal growth of Mg-Al alloy, on the basis of binary alloy model, the fluid field equation was coupled into the phase-field models, and the marker and cell (MAC) method was used in the numerical calculation of micro structural pattern. In the cast process, quantitative comparison of different anisotropy values that predicted the dendrite evolution were discussed in detail, and when the fluid flow rate reaches a high value, we can see the remelting of dendrite arms.

Abstract: Liquid phase sintering (LPS) is widely used as a materials processing technique for hightemperature applications. In LPS, particle-particle contact size and distribution, 3-D coordination number, connectivity, and contiguity are important microstructure parameters which, to a large extent, determine the mechanical properties of the sintered materials. These features all depend on the grain size, solid volume fraction and dihedral angle during sintering. The dihedral angle is an important parameter in LPS. It is the angle formed between the 2 solid-liquid interfaces at the intersection of a grain boundary with the liquid. A higher solid volume fraction, on the other hand, favors a larger 3-D coordination number, connectivity, and contiguity. In practice, studying the correlation between these parameters and direct measurement of them is not a trivial task. Among them, 3-D measurement of dihedral angle is believed to be the most challenging one. In the current study, phase-field modeling is employed to simulate LPS in two phase systems (solid and liquid). Simulations are performed for the different ratios of grain boundary to solid-liquid energies and the different solid volume fractions. To create initial structures with high solid volume fraction, an advanced particle packing algorithm is employed. An extended sparse bounding-box algorithm is used to speed-up the computations and makes it computationally efficient for 3-D simulations. Contiguity, connectivity, and three dimensional coordination number were measured in the self similar regime. The results were compared with empirical rules and experimental data and are used to estimate the mean 3-D dihedral angle.

Abstract: A phase field model of three-phase composite ceramic tool materials with two kinds of nanoparticles is set up in this research. The three-dimensional simulation algorithm is modified and a new efficient algorithm is established. The microstructure evolution of three-phase nanoceramic tool materials is more efficiently and successfully simulated in 200x200x200 unit size. Microstructure evolution of single-phase and three-phase ceramic tool materials is simulated respectively. It can be found that the peak value of grain size distribution for three-phase nanoceramic tool material is smaller than average diameter. It indicates that the nanoparticles not only restrain grain boundary migration, but also prevent the elimination of small grains and refine matrix grains.

Abstract: The Phase Field model of solidification processes was carried out coupled with temperature field model. The influence of interface atomic time on dendrite growth morphology in undercooled melt was simulated with pure nickel. The experimental results show that when the interface atomic motion time parameter is minor, the liquid-solid interfaces were unstable, disturbance can be amplified easily so the complicated side branches will grow, and the disturbance speed up the dendrite growth. With the increase of , the liquid-solid interfaces become more stable and finally the smooth dendrite morphology can be obtained.

Abstract: Micro to nano scale study of dendrite structure is important in order to have better properties control of casting product. The present study concerns on the morphological study of dendrite structure by phase-field simulation, in order to obtain the morphological growth of this structure that close its real morphology. Focus was given on the morphological growth of dendrite structure of Al-Si cast alloys, therefore thermodynamic data were taken for this type of materials. Anisotropy noise, strength of anisotropy and different undercooled conditions were applied as the variable parameters in the present works. It was observed that by introducing higher anisotropy noise, higher degree fragmentation of dendrite structure was obtained. Similar condition was obtained by introducing higher strength of anisotropy value, that higher degree of fragmentation was obtained. Both of these phenomena was also supported by the heat flux rate features of these variations that higher heat flux rate to almost all direction was obtained with the higher value of anisotropy noise and strength of anisotropy. In addition it was also observed that higher degree fragmentation of dendrite only possible to occur if sufficient undercooled condition established.

Abstract: A twin boundary model was established to describe the multi-variant interface in the martensitic materials. The modified semi-implicit Fourier-spectral method was proposed to solve the 3-D phase-field equation. Self-accommodation plays an important role in the micro-structural evolution during the loading and unloading. The external compressive stress can cause the rearrangement of martensites from three variants to one variant. After releasing the loading, another variant can nucleate and grow in one variant at the twin boundary. Cyclic stress may lead to the redistribution of martensite variants besides the rearrangement.

Abstract: The phase field method is effective in simulating the formation of solidification microstructure. Based on the phase field models of coupling flow field and noise field proposed by Tong and Beckermann, using finite difference method to solve control equation, apartly simulating the dendritic morphology under the condition of convection or none convection, and drawing the following conclusions after comparing the results: in the side, the dendrite will no longer be symmetrical under the condition of countercurrent and downstream, the dendrite tip grows faster with countercurrent than that of the latter, while the dendrite grows almost naturally in the vertical direction of convection.

Abstract: Using fractal theory simulation of dendrite crystal DLA growth model of pure substance, the undercooling during solidification process of crystal nucleation is simulated; and then in the crystal nuclei are formed on the basis of a pure substance, the phase field model and combined with the finite difference method further differentiation simulation of dendrite crystal growth. According to MATLAB programming, the simulation results obtained by field and temperature field can be seen in the DLA growth, growth model with random premise, for the same kind of material simulated dendrite crystal have both similarities and differences exist. Then, we can get the conclusion, through fractal growth of DLA model with phase field model of dendrite nucleation, growth process is carried out the simulation results, a simple by phase field model is more accord with the dendrite crystal in the experiment.

Abstract: The densification and grain growth during sintering of alumina-zirconia (Al₂O₃ZrO₂) ceramics were simulated using a modified phase field method, which considered simultaneously a density field, a composition filed and orientation fields. The results indicate that the model can capture the main microstructure features in the different stages of sintering. A higher relative green density leads to a higher final density and a larger final grain size in the sintered ceramics. A higher volume fraction of the ZrO₂ phase results in a lower relative density and a smaller final grain size.

Abstract: In this paper, a phase field model based on Ginzburg-Landau theory is used to analyze the topological phenomena during grain growth. The simulation results show that two topological transformations exist during the grain growth—Neighbor Switching and Grain Annihilation; and we have found different kinds of topological events during the disappearance of a grain: direct vanishing of trilateral grain and pentagonal grain, as well as neighbor switching，which are right with classical topological theory and Euler formula. The simulation results are similar with experiments.