Numerical Simulation Of Dendritic Growth In The Solidification Of Al Alloys Using A Phase-field Method

Phase-field method can be used to describe the complicated morphologies ofdendritic growth without explicitly tracking the complex phase boundaries. It is expectedas a powerful tool to describe complex phase transitions in non-equilibrium state. It is thefrontier domain of the numerical simulation during solidification processes at present. The dendritic growth in the solidification of alloy is simulated by the phase-fieldmethod, a modified phase-field model is developed, some key problems in the numericalcomputation of the model are resolved, the mechanism of the dendritic growth duringsolidification of the alloy is discussed, and a favorable base for prediction of mechanicalproperty of casting is established. A modified phase-field model is developed on the basis of Ginzberg-Landau theory,which is consistent with WBM model and KKS model, but the extra potential in the WBMmodel and dilute solution limit in the KKS model disappear in this model. Therelationships between material properties and phase-field parameters can be determined ata thin-interface limit condition. The dependence of simulation results upon the mesh size,the interface anisotropy and noise is investigated, and how to choose the values of thesekey parameters is determined. The governing equations are discretized on uniform grids using the FiniteDifference method, and a double grid method is used for the mesh slice to save the time.The thermal governing equation is numerically solved using an alternating direct implicit(ADI) method, which is unconditionally stable, irrespective of the time step employed.The narrow solid/liquid interface method and the capturing solute diffusing boundarymethod are put forward to optimize the numerical computation of the phase-field model,which improve the calculating efficiency. For the simulation results being displayed realistically, the visualization in thesimulation of solidification is investigated, and the numerical methods of some keyparameters in the dendritic growth are put forward. A software system for the visualizationof microstructure simulation results is developed using the OpenGL technique for the firsttime, which realize the computer display of simulation results, and can integrate with thecomputational program of the phase-field model to realize dynamic display of the IIIsimulation results The free growth and directional growth of dendrite in the solidification of Al-Cubinary alloy under different undercoolings are simulated on the isothermal condition, Thecompetitive growth of the secondary arms, ripen and solute microsegregation in the freedendritic growth, and the plane-cell transition, the competitive growth of columnardendrite and merging process in the directional growth of dendrite are realized. The dendritic growth of alloy solidification is simulated using the non-isothermalmodel with temperature fixed on the boundary, and the effect of undercooling on thedendritic growth is studied. Increased melt temperature reduces sources of instability,which leads to less developed structure of the non-isothermal dendrite, to reduce thedendritic tip speed, and to increase the tip radius, but the Peclet number is more coincidentwith Ivanstov theory than the isothermal growth. The result shows that the non-isothermalsolidification simulation with considering the influence of the latent heat is morecoincident with the real solidification. But the temperature is prescribed on the boundaryof the computational domain, which does not accord with the real physical environment.Therefore, the non-isothermal simulation with Neumann boundary conditions is putforward; the simulation result is more coincident with the dendritic growth of the casting.Because the size of the computational domain is very small, the temperature of alloy meltwill heighten, therefore, this condition is suitable for the simulation with the highundercooling. The reca...