Numerical Modeling Of Dendritic Growth Of Binary Alloys In Additive Manufacturing Using A Lattice Boltzmann-phase Field Method

Dendritic growth of alloys is a widespread microscopic phenomenon in additive manufacturing,involving a variety of complex non-equilibrium physical process.In particular,solute diffusion,melt convection,solid motion and their interaction play an important role in the formation of microstructure,which strongly affects and determines the macroscopic physical and mechanical properties of the final components.With the rapid development of computer hardware and computational technology,numerical simulation has become an indispensable part in the research on microstructure evolution of materials.In light of this,it is essential to reproduce the dendrite growth process during the solidification of molten pool in additive manufacturing by the mean of numerical simulation,leading to the deeper understanding of formation mechanism and evolution behaviour of dendritic morphologies,which paves the way for ensuring the service safety and mechanical integrity of final components.(1)Based on the basic principles of lattice Boltzmann(LB)method and phase field(PF)method,a LB-PF coupling model is constructed to describe the phenomena of solute diffusion,melt flow and solid motion during the dendrite growth of alloys.An anisotropic LB scheme is applied to solve the phase field equation describing the liquid-solid changes with interfacial anisotropic effect.Finite volume(FV)scheme is applied to solve the convective-diffusion equation of solute with anti-trapping current.The MRT-LB scheme based on Multiple-Relaxation-Time(MRT)collision operator is employed to compute the complex melt flow.Moreover,the MLS scheme is applied to realize the solid-liquid no-slip boundary conditions on complex dendrite surfaces in the framework of LBM,and the momentum exchange method which satisfies Galilean invariance is used to calculate the hydrodynamic force and torque acting on the dendrite.The location of dendrites after motion is updated based on the fifth-order WENO-Z scheme.(2)The simulations of static dendritic growth with single and multiple seeds at fixed locations in supersaturated melt of binary alloy are performed using the established LB-PF coupling model.The numerical accuracy and mesh independence of the model are quantitatively validated by simulating the static growth of single dendrite driven by solute diffusion.Al-Cu and Ti-Al binary alloys are chosen to simulate the free growth behavior of single dendrite under different initial supersaturations.By comparing the predicted results with the Lipton-Glicksman-Kurz(LGK)analytical model,the accuracy and reliability of the present model are further quantitatively validated.In addition,the effects of initial supersaturation and anisotropic strength on the free dendritic growth are analyzed.The simulation results show that tip velocity and solute P′eclet number at steady state both increase with the initial supersaturation.Moreover,the steady-state tip velocity increases linearly with the increase of anisotropic strength,while the steady-state tip radius decreases exponentially with the increase of anisotropic strength.Furthermore,multiple dendritic growth of Al-Cu binary alloy with various preferred crystallographic orientations for different initial concentration are simulated.(3)The simulations of moving dendritic growth with single and multiple seeds under gravity effect in supersaturated melt of binary alloy are performed using the established LB-PF coupling model.The solid motion model is quantitatively validated by simulating the sedimentation of circular particle in a cavity filled with incompressible viscous fluid under gravity effect.The simulations of growth and sedimentation of single dendrite of Ti-Al binary alloy in the supersaturated melt with different solid-liquid density ratios and different initial supersaturation are performed.The simulation results show that the solidification rate and settling velocity of dendrite both increase with the increase of solid-liquid density ratio,and the dendrite rotation is easier when the solid-liquid density is higher.The solidification rate increases with the increase of initial supersaturations,while the settling velocity decreases,and the fork phenomenon is more likely to occur when the initial supersaturation is big.The tilted dendrite swings back and forth during its sedimentation,and the curvilinear solute residue is formed at the rear of dendrite.Ti-Al binary alloy is selected to simulate the growth and sedimentation behaviour with multiple nucleation in supersaturated melt under gravity effect.A new LB-PF coupling model is established to simulate the growth and sedimentation behavior of dendrites in alloy melt.The related research results provide reference for further understanding the basic characteristics,evolution mechanism and control methods of dendrite growth in additive manufacturing,which paves the way for regulating the technological parameters of additive manufacturing,and improving the macroscopic mechanical properties of final components.