This paper applies a phase field model for polycrystalline solidification in binary alloys to simulate the formation and growth of the columnar dendritic array under the isothermal and constant cooling conditions. The solidification process and microsegregation in the mushy zone are analysed in detail. It is shown that under the isothermal condition solidification will stop after the formation of the mushy zone, but dendritic coarsening will progress continuously, which results in the decrease of the total interface area. Under the constant cooling condition the mushy zone will solidify and coarsen simultaneously. For the constant cooling solidification, microsegregation predicted by a modified Brody- Flemings model is compared with the simulation results. It is found that the Fourier number which characterizes microsegregation is different for regions with different microstructures. Dendritic coarsening and the larger area of interface should account for the enhanced Fourier number in the region with well developed second dendritic arms.
This paper employs the phase-field method to study the splitting behaviour of a single coherent particle under an applied uniaxiai stress. It finds that the splitting behaviour is greatly influenced by the initial shape of precipitates, the bulk free energy condition, the degree of supersaturation and the ratio of the interfacial energy to the elastic strain energy, etc. The simulated results demonstrate that the aspect ratio of the particle determines whether the splitting can occur and how many split plates can be obtained. The splitting of particle is sensitive to the interracial energy, i.e. the splitting becomes more and more difficult with increasing the ratio of the interracial energy to the elastic strain energy. And increasing the magnitude of the applied stress is favourable to the splitting. The splitting process is also explained from the point of view of the corresponding diffusion potential.
A phase-field method was employed to study the influence of elastic field on the nucleation and microstructure evolution. Two kinds of nucleation process were considered： one using fixed nucleation probability and the other calculated from the classical nucleation theory. In the latter case, the simulated results show that the anisotropic elastic strain field yields significant effects on the behavior of nucleation. With a large lattice misfit between the matrixes and the precipitates, the nucleation process does not appear fully random but displays some spatial correlation and has a preference for the elastic soft direction. However, with a small lattice misfit, this bias does not look quite clear. On the contrary, in the case of fixed nucleation probability, the elastic field has no influence on the nucleation process. The lattice mismatch also exerts influences on the microstructure morphology： with lattice mismatch becoming larger, the microstructure proves to align along the elastic soft direction.
ZHANG Yu-xiang WANG Jin-cheng YANG Yu-juan YANG Gen-cang ZHOU Yao-he
Phase field investigation reveals that the stability of the planar interface is related to the anisotropic intensity of surface tension and the misorientation of preferred crystallographic orientation with respect to the heat flow direction. The large anisotropic intensity may compete to determine the stability of the planar interface. The destabilizing effect or the stabilizing effect depends on the misorientation. Moreover, the interface morphology of initial instability is also affected by the surface tension anisotropy.
The effect of interaction among γ′ ordered domains on the interdiffusion process in γ＋γ′ and γ＋γ′/γ＋γ′ diffusion couples is investigated by using the phase-field method, in which bulk free energy and mobility are linked with thermodynamic and kinetic databases. Simulated results show that the interaction among γ′ ordered domains has great influence on the microstructure, the interdiffnsion velocity and the volume fraction ofγ′ phase on both sides of the diffusion couples.
