Papers by Keyword: Dendritic Growth

Abstract: The undercooled Fe₅₀Cu₅₀ alloy experiences a metastable liquid phase separation and separates into a Fe-rich zone and a Cu-rich zone within the gravity field. The growth characteristics of the Cu-rich zone were investigated by the glass fluxing method, and the achieved undercooling range was 20−261 K. The volume fraction of the Cu-rich zone decreases with the enhancement of the bulk undercooling. The microstructural morphologies of the Cu-rich zone are similar at all the undercooling conditions, that is, αFe dendrites and particles are distributed inside (Cu) phase matrix. The secondary dendritic arm spacing of αFe dendrites decreases with the increase in bulk undercooling. The growth mechanism of αFe dendrites was analyzed by using the LKT/BCT dendritic growth theory. The dendritic growth in the Cu-rich zone is mainly controlled by solute diffusion so that the dendritic growth velocity is only several millimeters per second. Besides, the calculated results indicate that there is only inconspicuous solute trapping during the solidification of Cu-rich zone.

Abstract: Through solving an extended Fick’s diffusion equation for the solidification front of a paraboloid of revolution, a generalized Ivantsov function is obtained. The relaxation effect of nonequilibrium liquid diffusion is taken into account. The solute profile in the interfacial region and in the bulk liquid during steady-state dendritic solidification is uniquely determined. It is concluded that the consideration of the relaxation effect and the diffuse interface of finite thickness which decreases with increasing of velocities are necessary for achieving the good model predictions.

Abstract: Phase field model coupled with flow field is solved by the adaptive finite element method. The simulation results show that the forced flow can induce side-branches though there is no thermal noise. When the flow velocity is low, the symmetry of dendrite morphology is slightly influenced by forced flow. With the increase of flow velocity, the symmetry of dendrite morphology is collapsed completely.

Abstract: A numerical model is developed to describe the dendritic growth of multicomponent aluminium alloys, based on a coupled deterministic continuum mechanics heat and species transfer model and a stochastic localized growth model that takes into account the undercooling temperature, curvature, kinetic, and thermodynamic anisotropy. The stochastic model receives temperature and concentration information from the deterministic model and the deterministic heat and species diffusion equations receive the solid fraction information from the stochastic model. The heat and species transfer models are solved on a regular grid by the standard explicit Finite Difference Method (FDM). The dendritic growth model of multicomponent alloy [1,2] is solved by a novel Point Automata (PA) approach [3,4] where the regular cells of the Cellular Automata (CA) method are replaced by the randomly distributed points and neighborhood configuration, similar as appears in meshless methods. The PA method was developed in order to circumvent the mesh anisotropy problem, associated with the classical CA method. The present paper extends our previous developments of Pa method to multicomponent alloys. A comparison of the results, obtained by the PA and CA method is shown for Al-5.3% Zn-2.35% Mg-1.35% Cu-0.5% alloy.

Abstract: An undercooled melt possesses an enhanced free enthalpy that enables to crystallize metastable solids in competition with their stable counterparts. Crystal nucleation selects the crystallographic phase whereas the growth dynamics controls microstructure evolution. We apply containerless processing such as electromagnetic and electrostatic levitation to containerlesss undercool and solidify metallic melts. Heterogeneous nucleation on container-walls is completely avoided leading to large undercooling with the extra benefit that the freely suspended drop is direct accessible for in situ observation of crystallization far away from equilibrium. Results of investigations of maximum undercoolability on pure zirconium are presented showing the limit of maximum undercoolability set by the onset of homogeneous nucleation. Rapid dendrite growth is measured as a function of undercooling by a high-speed camera and analysed within extended theories of non-equilibrium solidification. In such both supersaturated solid solutions and disordered superlattice structure of intermetallics are formed at high growth velocities. A sharp interface theory of dendrite growth is capable to describe the non-equilibrium solidification phenomena during rapid crystallization of deeply undercooled melts.

Abstract: Phase field method (PFM) offers the prospect of carrying out realistic numerical calculation on dendrite growth in metallic systems. The dendritic growth process of multiple dendrites and direcitonal solidification during isothermal solidifications in a Fe-0.5mole%C binary alloy were simulated using phase field model. Competitive growth of multiple equiaxed dendrites were simulated, and the effect of anisotropy on the solute segregation and microstructural dedritic growth pattern in directional solidification process was studied in the paper. The simulation results showed the impingement of arbitrarily oriented grains, and the grains began to impinge and coalesce the adjacent grains with time going on, which made the dendrite growth inhibited obviously. In the directional solidification, the maximum concentration gradient showed in the dendrite tip, and highest solute concentration existed at the bottom of the dendrites. With the increasing of the anisotropy, dendrite tip radius became smaller, and the crystal structure is more uniform and dense.

Abstract: Phase field equations for simulation of dendritic growth have a history of nearly twenty years. The existing phase field equations are directly derived through the Ginzburg-Landau equations. However, though widely used, the physical meaning of each variable in the equations is not clear. So the domestic and foreign researchers have made a lot of mistakes and interpretation. In this paper, with the solid fraction as a phase field variables in the field, based on thermodynamics and heat transfer theory, author gives a rigorous scientific phase variable diffusion model of the pure metal solidification and its derivation process.

Abstract: A phase field model has been developed to simulate the dendritic growth of Ti-Ni alloy subjected to a strong magnetic field. The influence of a strong magnetic field on the microstructure morphology and its evolution was successfully investigated by the model. The effect of the magnetic field intensity on the dendritic evolution has been further discussed. The simulating results revealed that with greater magnetic field intensity, the primary dendritic arms and the side branches were easier to coarsen. Besides, the dendritic tip growth rate increased with increasing magnetic field intensity, while the curvature radius had an opposite tendency. The microstructure evolution under a strong magnetic field was also studied combined with solidification thermodynamics theory. The results indicate that, the temperature of equilibrium solidification of Ti-Ni alloy changes with the presence of a strong magnetic field, and the morphology of dendritic grains will be affected eventually.

Abstract: A phase-field approach which incorporates mass and momentum and solute conservation equations for simulation of Al-Si binary alloy solidification is studied. The effect of force flow on the dendrite growth and solute profile during the solidification of binary alloy were investigated. The results indicate that dendritic grows unsymmetrically under a forced flow, the growth velocity of the upstream tip is faster than the downstream tip. With the force flow, the upstream tip grows faster due the thinner solute boundary layer. The solute gradient in the solid/liquid interface regions of the upstream tip is higher than that of the downstream tip. The faster the flow velocity, the greater the solute gradients in the solid/liquid interface regions of the upstream tip, the thinner the diffusion layer before the upstream tip. The downstream tip is opposed to the upstream tip. The simulations agree qualitatively with the solidification theoretical results.

Abstract: We study the effect of force convection and temperature on the double dendrite growth during the solidification of binary alloy using a phase-field model. The mass and momentum conservation equations are solved using the Simple algorithm, and the thermal governing equation is numerically solved using an alternating implicit finite difference method. The results indicate that dendritic grows unsymmetrically under a forced flow, the growth velocity of the upstream tip is faster than the downstream tip. The downstream tip of the first dendrite and the upstream tip of the second dendrite are influenced each other, the upstream tip of the second dendrite will Coarsen, and the concentration at the boundary between them is the highest. Moreover, the interaction between the two dendrites is more and more obvious with the increasing of the temperature.