| The dendrite growth in the undercooled melt of pure substance and binary single phase alloy is simulated by the phase-field method,some key problems in modeling and numerical computation of this kind of advanced microstructure simulation method are resolved,the dendrite growth behaviors under the different conditions are finely described,and the mechanism of the dendrite growth in the undercooled melt is discussed. The main research work and conclusions are as follows:(1) The phase-field models of pure substance and binary single phase alloy are derived in consideration of the interface anisotropy and noise,and the relations of the phase-field model parameters and the materials parameters are set up.(2) Based on the Finite Difference method with uniform grids,the phase-field simulation program of the dendrite growth into the undercooled melt are completed;the numerical methods to calculate the dendrite tip velocity,tip radius,secondary arm spacing,solid fraction,and solute partition coefficient are put forward,and the influence of the number of the fitting points on the simulation result is considered for the first time in the direct calculation of dendrite tip radius;the techniques of computer picture builder and dynamic display of dendrite morphology,solute and temperature distribution are developed.(3) The dependence of simulation results on the space step Ax,the initial nucleus radius r0,the interface width parameter ?is studied,and how to choose the values ofthese parameters is settled. The result indicated that for the space step, should be fulfilled;however,the value of initial nucleus radius may be chosen in a large range according to the capillary length d0 with the precondition that initial nucleus can't be melted;the value of E is determined synthetically by the dimensionless undercooling A,anisotropy parametery,interface kinetic coefficient,thermal diffusivity DT,and the larger A or y,the less is ?that ensure the credible results,but for (1 or DT,it is just on the contrary to A or y.(4) Aiming at the status quo that the size of the phase-field simulation is relatively small,the influence of the constant temperature boundary condition and Zero-Neumann temperature boundary condition on the simulation results is discussed,and the idea that the correct temperature boundary condition should be adopted according to the different computation regions is presented. When the computationregion is limited to an unchanged size,the Zero-Neumann temperature boundary condition leads to a decaying dendrite growth velocity,whereas the constant temperature boundary condition leads to an increasing dendrite growth. The former is consistent with the real equiaxed dendrite growth in castings,but the latter is in contradiction with it. In this case,the Zero-Neumann condition is preferable to the constant temperature condition. When the computation region is enlarged continually with the computational time according to the increasing thermal diffusion scale,the Zero-Neumann and the constant temperature boundary conditions give the consistent results on tip velocities and tip radii. In this case,two types of temperature boundary conditions both are appropriate.(5) After the value of the capillary length do and thermal diffusivity DT is determined on the condition of decreasing computation quantity,the equiaxial crystal growth into the undercooled melt of pure substance is simulated,and the dependence of dendrite growth upon the noise,undercooling,interface characteristic and other thermal-physical parameters is investigated. The results indicated that the noise triggers the growth of side-branches,but doesn't influence the steady state of the dendrite tip. In the low undercooled melt,the thick thermal diffusion layer surrounding the equiaxial crystal suppresses the growth of its side-branches,so the equiaxial crystal presents the morphology of no side-branches,whereas in the high undercooled melt,the thin thermal diffusion layer is advantageous to the growth of the side-branch,so the equiaxial cr...
|
PDF Full Text Request