A lattice Boltzmann–cellular automaton study on dendrite growth with melt convection in solidification of ternary alloys

A lattice Boltzmann （LB）-cellular automaton （CA） model is employed to study the dendrite growth of A1-4.0 wt%Cu- 1.0 wt%Mg alloy. The effects of melt convection, solute diffusion, interface curvature, and preferred growth orientation are incorporated into the coupled model by coupling the LB-CA model and the CALPHAD-based phase equilibrium solver, PanEngine. The dendrite growth with single and multiple initial seeds was numerically studied under the conditions of pure diffusion and melt convection. Effects of initial seed number and melt convection strength were characterized by new- defined solidification and concentration entropies, The numerical result shows that the growth behavior of dendJ-ites, the final microstructure, and the micro-segregation are significantly influenced by melt convection during solidification of the ternary alloys. The proposed solidification and concentration entropies are useful characteristics bridging the solidification behavior and the microstructure evolution of alloys.

Simulation of Dendritic Growth with Melt Convection in Solidification of Ternary Alloys

A cellular automaton-lattice Boltzmann coupled model is extended to study the dendritic growth with melt convection in the solidification of ternary alloys. With a CALPHAD-based phase equilibrium engine, the effects of melt convection, solutal diffusion, interface curvature and preferred growth orientation are incorporated into the coupled model. After model validation, the multi dendritic growth of the Al-4.0 wt%Cu-1.0 wt%Mg alloy is simulated under the conditions of pure diffusion and melt convection. The result shows that the dendritic growth behavior, the final microstructure and microsegregation are significantly influenced by melt convection in the solidification.

Anisotropic lattice Boltzmann-phase-field modeling of crystal growth with melt convection induced by solid-liquid density change

Density change is ubiquitous in phase transformation, and it can induce melt convection which strongly influences the crystal growth. Here, an anisotropic lattice Boltzmann-phase-field method was extended to predict the dendritic growth under the shrinkage or expansion melt convection by density change induced. A novel LB equation with an anisotropic coefficient was constructed to model the advancement of ordering parameter, coupling with the passive scalar LB equation for convective and diffusive heat transfer during phase transition. We studied dendritic growth and shape selection with melt convection induced by density change in crystal growth. Results show that the melt convection induced by density change affects strongly the dendritic growth. The shrinkage flow results in a higher tip velocity while the expansion flow leads to a slower one. Predicted Péclet number with respect to the relative density change was compared with an analytical solution. Moreover, the modified selection parameter has been verified by numerical simulations.

Numerical simulation on dendritic growth of Al-Cu alloy under convection based on the cellular automaton lattice Boltzmann method

A numerical model is developed by coupling the cellular automaton(CA)method and the lattice Boltzmann method(LBM)to simulate the dendritic growth of Al-Cu alloy in both two and three dimensions.An improved decentered square algorithm is proposed to overcome the artificial anisotropy induced by the CA cells and to realize simulation of dendritic growth with arbitrary orientations.Based on the established CA-LBM model,effects of forced convection and gravity-driven natural convection on dendritic growth are studied.The simulation results show that the blocking effect of dendrites on melt flow is advanced with a larger number of seeds.The competitive growth of the converging columnar dendrites is determined by the interaction between heat flow and forced convection.Gravity-driven natural convection leads to highly asymmetric growth of equiaxed dendrites.With sinking downwards of the heavy solute,chimney-like or mushroom-like solute plumes are formed in the melt in front of the columnar dendrites when they grow along the gravitational direction.More details on dendritic growth of Al-Cu alloy under convection are revealed by 3D simulations.

Thermodynamics of Molten Pool Predicted by Computational Fluid Dynamics in Selective Laser Melting of Ti6Al4V:Surface Morphology Evolution and Densification Behavior

The three-dimensional physical model of the randomly packed powder material irradiated by the laser beam was established,taking into account the transformation of the material phase,the melt spreading and the interaction of the free surface of the molten pool and the recoiling pressure caused by the material evaporation during the selective laser melting.Influence of the processing parameters on the thermal behavior,the material evaporation,the surface morphology and the densification behavior in the connection region of the molten pool and the substrate was studied.It was shown that the powder material underwent the transformation from the partial melting state to the complete melting state and finally to the overheating state with the applied laser energy density increasing from 167 J/mm^(3) to 417 J/mm^(3).Therefore,the solidified track ranged from the discontinuous tracks with the rough surface to the continuous tracks with residual porosities,then to the continuous and dense tracks and terminally to the fluctuated tracks with the increase in the laser energy density.Meanwhile,the laser energy effect depth was maintained the positive relationship with the laser energy density.The vortex velocity obtained in the free surface of the molten pool towards to the rear region in the opposite laser scan direction promoted the melt convection to the edge region of the molten pool as the laser energy density was higher than 277 J/mm^(3),demonstrating the efficient energy dissipation from the center of the irradiation region to the whole part of the molten pool and the attendant production of the sufficient melt volume.Therefore,the efficient spreading of the molten pool and the metallurgical bonding ability of the melt with the substrate was obtained at the optimized laser energy density of 277 J/mm^(3).However,the severe material evaporation would take place as the melt was overheated,resulting in the formation of the residual pores and poor surface quality.

Simulation of the Influence of Pulsed Magnetic Field on the Superalloy Melt with the Solid-Liquid Interface in Directional Solidification

The effect of the pulsed magnetic field on the grain refinement of superalloy K4169 has been studied in directional solidification.In the presence of the solid-liquid interface condition,the distributions of the electromagnetic force,flow field,temperature field,and Joule heat in front of the solid-liquid interface in directional solidification with the pulsed magnetic field are simulated.The calculation results show that the largest electromagnetic force in the melt appears near the solid-liquid interface,and the electromagnetic force is distributed in a gradient.There are intensive electromagnetic vibrations in front of the solid-liquid interface.The forced melt convection is mainly concentrated in front of the solid-liquid interface,accompanied by a larger flow velocity.The simulation results indicate that the grain refinement is attributed to that the electromagnetic vibration and forced convection increase the nucleation rate and the probability of dendrite fragments survival,for making dendrite easily fragmented,homogenizing the melt temperature,and increasing the undercooling in front of the solid-liquid interface.

Phase and Microstructure Selection During Directional Solidification of Peritectic Alloy Under Convection Condition

A phase and microstructure selection map used for peritectic alloy directionally solidified under convection condition was presented,which is based on the nucleation,constitutional undercooling criterion（NCU criterion）,and the highest interface temperature criterion.This selection map shows the relationships between the phase/microstructure,the G/V ratio（G is the temperature gradient,V is the growth velocity）,and the alloy composition under different convection intensities and nucleation undercoolings.Comparing with the results from directional solidification experiments of Sn–Cd peritectic alloys,this selection map was generally in agreement with the experimental results.

In situ radiographic study of the grain refining behavior of Al_(3)Sc during the solidification of Al-10Cu alloy

Grain refinement of Al alloys inoculated by rare earth elements,such as Sc,has been extensively acknowledged,while the practical behavior of how inoculant Al_(3)Sc particles affect the refinement in solidification has not been clarified due to the non-transparency of the solidification process.Here,the microstructural evolution of primary Al_(3)Sc particles andα-Al grains in Al-10 wt.%Cu alloy solidifications with 0.2 wt.%,0.6 wt.%,and 1.0 wt.%Sc additions was investigated by in situ synchrotron X-ray radiography.The detailed mechanisms of curve motion of grains(CMG)and melt convection were revealed.The efficient grains nucleation,uniformly scattered small initial grains,and long duration of melt convection contributed to the best refinement in the 0.6 wt.%Sc addition sample.This work provides a deep insight into grain refinement in solidification with Sc addition,which will enlighten the composition design and casting process of Al alloys inoculated by rare earth elements.