A Three Dimensional Cellular Automata Model for Dendrite Growth in Non-Equilibrium Solidification of Binary Alloy

Abstract

A three‐dimensional (3D) cellular automata (CA) model has been developed for simulation of dendrite growth during non‐equilibrium solidification. The heat and mass transports are calculated using 3D finite element (FE) method. The migration of solid/liquid (SL) interface is associated with effective free energy difference incorporating solute trapping and relaxation effects. The non‐equilibrium solute partition coefficient involving solute trapping and relaxation effects is used to calculate solute redistribution at SL interface. The interface curvature and anisotropy of surface energy are introduced to represent the characteristics of dendrite tip. The CA model has been applied to simulate the microstructure evolution of Fe‐1.5 wt.% C alloy. The grain morphology, solute and temperature distributions, and velocity of dendrite tip are characterized during both isothermal and non‐isothermal conditions. The velocity of dendrite tip and secondary dendrite arm spacing during directional solidification are validated and are in good agreements with previous experimental and mathematical results.

Rapid Multicomponent Alloy Solidification with Allowance for the Local Nonequilibrium and Cross-Diffusion Effects

“…Today, ultrashort energy sources allow rapid melting of layers as thin as several nanometers with re-solidification occurring on a time scale of picoseconds [ 39 ]. The corresponding solid–liquid interface velocity during re-solidification may exceed 1 m/s, which significantly suppresses the equilibrium partitioning of the species [ 19 , 25 , 26 , 27 , 30 ]. Figure 1 schematically shows the moving interface during re-solidification of a thin metal layer after ultrashort pulse laser melting.…”

“…This implies that the transition to diffusionless and partitionless solidification is a purely diffusive phenomenon—it occurs independently of the interface solidification kinetics as soon as the interface velocity reaches [ 25 , 26 , 27 ]. The LNDM has been also used to study various phenomena pertinent to rapid alloy solidification, for example, nonequilibrium kinetic phase diagrams [ 10 , 28 ], dendrite solidification [ 29 , 30 ], transient effects [ 19 , 31 ]. Moreover, the LNDM has been used in combination with other approaches such as cellular automata [ 30 ], discrete model [ 32 ], effective mobility approach [ 33 ], non-local approach [ 18 , 34 ], phase-field model [ 35 , 36 ], molecular dynamics, and Monte Carlo simulations [ 37 ].…”

Review on Modeling and Simulation of Continuous Casting

“…In recent years, a few models have started to simulate dendrite formation in steel, using cellular automata or phase‐field methods . Applications include the prediction of the columnar to equiaxed transition, secondary dendrite arm spacing, the delta to austenite massive‐like phase transformation, fracture strength during solidification, and how alloys affect hot tearing . Difficulties include finding material properties, such as interface energies, which depend on the models used to extract them, and the huge computational resources needed for fine‐grid 3D domains of sufficient size.…”

Solidification Simulation of Al-Si Alloys with Dendrite Tip Undercooling

“…This manuscript describes the impact of undercooling on flow behavior and temperature distribution and its effect on the primary dendrite arm spacing. Results of this macro-scale simulations model provides valid input such as boundary and initial conditions for thermal, solute and fluid flow regimes for the subsequent micro-scale models that further evaluate the morphology and details of microstructure developments during binary alloy solidification [34]. It is recommended in the future to investigate the impact of including the dendrite tip undercooling on the secondary dendrite arm spacings and the local solid fraction development in the mushy zone.…”