Modeling of dendrite growth with cellular automaton method in the solidification of alloys

Dendrite growth is the primary form of crystal growth observed in laser deposition process of most commercial metallic alloys. The properties of metallic alloys strongly depend on their microstructure; that is the shape, size, orientation and composition of the dendrite matrix formed during solidification. Understanding and controlling the dendrite growth is vital in order to predict and achieve the desired microstructure and hence properties of the laser deposition metals. A two dimensional (2D) model combining the finite element method (FE) and the cellular automaton technique (CA) was developed to simulate the dendrite growth both for cubic and for hexagonal close-packed (HCP) crystal structure material. The application of this model to dendrite growth occurring in the molten pool during the Laser Engineered Net Shaping (LENS®) process was discussed. Based on the simulation results and the previously published experimental data, the expressions describing the relationship between the cooling rate and the dendrite arm spacing (DAS), were proposed. In addition, the influence of LENS process parameters, such as the moving speed of the laser beam and the layer thickness, on the DAS was also discussed. Different dendrite morphologies calculated at different locations were explained based on local solidification conditions. And the influence of convection on dendrite growth was discussed. The simulation results showed a good agreement with previously published experiments. This work contributes to the understanding of microstructure formation and resulting mechanical properties of LENS-built parts as well as provides a fundamental basis for optimization of the LENS process

Modeling Dendritic Solidification of Al-3%Cu Using Cellular Automaton and Phase-Field Methods

We compared a cellular automaton (CA)-finite element (FE) model and a phase-field (PF)-FE model to simulate equiaxed dendritic growth during the solidification of cubic crystals. The equations of mass and heat transports were solved in the CA-FE model to calculate the temperature field, solute concentration, and the dendritic growth morphology. In the PF-FE model, a PF variable was used to identify solid and liquid phases and another PF variable was considered to determine the evolution of solute concentration. Application to Al-3.0. wt.% Cu alloy illustrates the capability of both CA-FE and PF-FE models in modeling multiple arbitrarily-oriented dendrites in growth of cubic crystals. Simulation results from both models showed quantitatively good agreement with the analytical model developed by Lipton-Glicksman-Kurz (LGK) in the tip growth velocity and the tip equilibrium liquid concentration at a given melt undercooling. The dendrite morphology and computational time obtained from the CA-FE model are compared to those of the PF-FE model and the distinct advantages of both methods are discussed

Comparison of Cellular Automaton and Phase-Field Models to Simulate Dendritic Solidification

In this work, a cellular automaton (CA)-finite element (FE) model and a phase-field (PF)-FE model were developed to simulate dendritic solidification of both cubic and hexagonal crystal materials. Validation of the both models was performed by comparing the simulation results to the analytical model developed by Lipton-Glicksman-Kurz (LGK), showing qualitatively good agreement in the tip growth velocity at a given melt undercooling. Dendritic solidification in cubic materials is illustrated by simulating the solidification in aluminum alloy Al-3wt%Cu. Results show that both models successfully simulate multiple arbitrarily-oriented dendrites for cubic materials. Application to magnesium alloy AZ91 (approximated with the binary Mg-8.9wt%Al), illustrates the difficulty of modeling dendrite growth in hexagonal systems using CA-FE regarding mesh-induced anisotropy and a better performance of PF-FE in modeling multiple arbitrarily-oriented dendrites

Comparison of Cellular Automaton and Phase Field Models to Simulate Dendrite Growth in Hexagonal Crystals

A cellular automaton (CA)-finite element (FE) model and a phase field (PF)-FE model were used to simulate equiaxed dendritic growth during the solidification of hexagonal metals. In the CA-FE model, the conservation equations of mass and energy were solved in order to calculate the temperature field, solute concentration, and the dendritic growth morphology CA-FE simulation results showed reasonable agreement with the previously reported experimental data on secondary dendrite arm spacing (SDAS) vs cooling rate. In the PF model, a PF variable was used to distinguish solid and liquid phases similar to the conventional PF models for solidification of pure materials. Another PF variable was considered to determine the evolution of solute concentration. Validation of both models was performed by comparing the simulation results with the analytical model developed by Lipton-Glicksman-Kurz (LGK), showing quantitatively good agreement in the tip growth velocity at a given melt undercooling. Application to magnesium alloy AZ91 (approximated with the binary Mg-8.9 wt% Al) illustrates the difficulty of modeling dendrite growth in hexagonal systems using CA-FE regarding mesh-induced anisotropy and a better performance of PF-FE in modeling multiple arbitrarily-oriented dendrites growth

Large-scale parallel lattice Boltzmann-Cellular automaton model of two-dimensional dendritic growth Large-scale parallel lattice Boltzmann -cellular automaton model of two-dimensional dendritic growth Manuscript Title: Large-scale parallel lattice Boltzma

Abstract An extremely scalable lattice Boltzmann (LB) -cellular automaton (CA) model for simulations of two-dimensional (2D) dendritic solidification under forced convection is presented. The model incorporates effects of phase change, solute diffusion, melt convection, and heat transport. The LB model represents the diffusion, convection, and heat transfer phenomena. The dendrite growth is driven by a difference between actual and equilibrium liquid composition at the solid-liquid interface. The CA technique is deployed to track the new interface cells. The computer program was parallelized using Message Passing Interface (MPI) technique. Parallel scaling of the algorithm was studied and major scalability bottlenecks were identified. Efficiency loss attributable to the high memory bandwidth requirement of the algorithm was observed when using multiple cores per processor. Parallel writing of the output variables of interest was implemented in the binary Hierarchical Data Format 5 (HDF5) to improve the output performance, and to simplify visualization. Calculations were carried out in single precision arithmetic without significant loss in accuracy, resulting in 50% reduction of memory and computational time requirements. The presented solidification model shows a very good scalability up to centimeter size domains, including more than ten million of dendrites