Phase-field Simulation Of Binary Alloy During Directional Solidification

The directional solidification technology offers an effective material preparation and forming method, and it is to be more extensive application in practical yield, so, the theory study of directional solidification is a central theme of solidification research. The solid/liquid interfacial morphology takes a crucial role on predicting the final solidification microstructures and inner defect. In this paper, the evolution of the interface formation of Ni-Cu binary during directional solidification is simulated using the phase-field method, the mode of crystal growth during directional solidification is showed at different simulation conditions, and the mechanism of crystal growth is discussed.In this paper, a two-dimensional phase-field model for directional solidification is developed by coupling the phase-field equation and the solute diffusion equation from consulted current phase-field theory. Based on the finite difference method with uniform grids, and the C code is taken to complete the phase-field simulation program of the crystal growth during directional solidification;the numerical methods to calculate the cell tip velocity, the solute distribution in solid, and the interface solute partition coefficient are put forward;the techniques of computer builder and dynamic display of cellular growth morphology from incorporating many points.In order to save computational time, the interface thickness is treated as an input parameter in present phase-field formulation. The effects of the interface thickness ξ, the anisotropy coefficient y and the magnitude of the noise α on the simulation are studied. The results indicate that, with the increment of ξ, the transition from cells to cellular dendrites then to dendrites occurs, and the cell tip velocities increase, the stability of the tip is descends;the anisotropy is smaller, smaller the tip velocity is, the side-branches are prone to grow, and form cellular dendrites;the amplitude of the fluctuation a has an important effect on interface morphology, when appropriate value is assigned to a, noise can enhance the emergence of side-branches, and form cellular dendrites, the tip velocity must be influenced at the same time;the effect of surface free energy σ on the microstructure is discussed during directional solidification, with the increment of σ, the diffusive layer of the solute becomes thinner and the structures are fine cells.The solute trapping in binary alloy during directional solidification is simulated, the results indicate that, the solute concentration gradient δ influences the solute diffusive layer thickness and the solute distribution profile within the diffusive layer inthe solid/liquid interface, it has an important effect on the partition coefficient k, with the increasing of S, the cell tip velocity Vtip and solute partition coefficient k increase correspondingly, the level of solute trapping is strong;the effect of solid diffusivity Ds on the interface formation and the solute distribution is discussed, with the increment of solid diffusivity Ds, the boundary diffusive layer becomes thicker, the front moving velocity decreases, then forms symmetrical cellular structures;the greater Ds is, the smaller partition coefficient k is, the solute trapping is eliminated. Then, when Z)y<10'7 cm2/s, the solid diffusivity has little influence on the interface front velocity and the solute distribution.