Simulation Of The Dendritic Sidebranching Growth In The Undercooling Melt Of The Pure Metal Using Phase-field Method

Dendritic are intricate patterns that make up the microstructure of many important commercial alloys. Understanding the dynamical process is very necessary. Studing dendritic growth has many years history, the emission of sidebranching is a hotspot to metallurgists. The phase-field method is very powerful in simulation of dendritic growth, the widely appeal of this approach is free of tracking the interface of solid-liqiud.The object of this dissertation is to present a quantitative study of free dendritic sidebranching growth of pure metal with noise using the phase-field method. The section I gives the formulation of the phase-field model that incorporates both noise and melt convection, which based on the methodology developed by Karma. The section II not only describes the initial conditions and boundary conditions, but solves the phase-field and temperature-field equations using the finite difference formulas on uniform mesh. The section III focus on programming and calculating the tip velocity and radius by virtue of MATLAB software. The section IV investigates the evofution of dendritic growth without noise, and studies the influence of anisotropic coefficient y, the coupling coefficient X and undercooling A on the grain morphologies. The section V simulates the evolution of sidebranching growth with noise, studies the connection between the parameters that discussed in the section IV and the dendritic growth.The noise free calculated results indicate that, the grid spacing has effect on efficiency and precision, anisotropic coefficient y and the coupling coefficient X exceed critical value, the interface shape is discontinuity with corner, when the undercooling is great, the thermal diffusion is thin, which is advantageous to the growth of the sidebranching.Simulation to incorporate noise show that both the parameters mentioned in the section IV and the noise amplitude affect the sidebranching growth. The nonconserved noise, not influencing sidebranching growth, is neglected for saving computational time. With the increment of undercooling A, the thermal diffusion layer collected around the equiaxed dendritic is more thin, which is advantageous to the growth of the sidebranching and the dendritic presents the morphology of developed sidebranching. The noise amplitude can enhance the emergence of sidebranching with no influence...