The Research Of The Key Technologies In Phase-Field Simulation With Alloy Dendrite Growth

Numerical simulation of microstructure plays an important role on the development and application of metallic materials, and it is also one of the main development directions which a computer used in the field of materials science. There are some microstructure numerical simulation methods: deterministic methods, stochastic methods and phase field method. Phase-field methods can be used to describe the complicated morphologies of dendritic growth without explicitly tracking the complex phase boundaries. It is expected as a powerful tool to describe complex phase transitions in non-equilibrium state. It is the frontier domain of the numerical simulation during solidification processes at present.Based on the Ginzburg - Landau theory of phase transitions, respectively, it established a principle of entropy of binary alloy phase field model and the principle of freedom to reduce the phase-field model of pure substances , and in the thin interface limit condition, it established a relationship between phase-field parameters and thermal physical parameters. Using uniform grid based on finite difference equations to discrete control equation, mesh generation used a dual grid. Numerical calculations, in order to avoid time step constraints, and improving computational efficiency, phase field and solute field equations used an explicit algorithm, that is forward Euler method; temperature control equation is adopted alternating direction implicit method (ADI method) .We analyzed the impact of anisotropy on the equilibrium shape and found a critical value. The critical value is 0.067,also we established a two-dimensional anisotropic phase field model, and two-dimensional anisotropic discrete items; respectively, two-dimensional interface energy anisotropy of the numerical simulation results obtained the result was consistent with the theoretical analysis; In greater than the critical value, the phase field model to simulate came out with the distortion.In the phase field model based on the noise derived mathematical model of phase field and temperature field disturbance disturbance mathematical equation; from the theoretical analysis of the phase field model, the introduction of noise, making noise, the introduction of three ways; noise generated on the lateral branches were simulated and found that thermal noise can lead to dendritic lateral instability is the main cause of the formation of lateral branches.Simulation under different undercooling solidification process of pure nickel dendrite growth, found that could explain the undercooling temperature on the secondary branch growth of the reasons; low undercooling dendrite radius increases with the undercooling decrease and the result is consistent with the edge of stability theory and the microscopic solvability of the theory.