Abstract
Casting microstructure evolution is difficult to describe quantitatively by only a separate simulation of dendrite scale or grain scale, and the numerical simulation of these two scales is difficult to render compatible. A three-dimensional cellular automaton model couplling both dendritic scale and grain scale is developed to simulate the microstructure evolution of the nickel-based single crystal superalloy DD406. Besides, a macro–mesoscopic/microscopic coupling solution algorithm is proposed to improve computational efficiency. The simulation results of dendrite growth and grain growth of the alloy are obtained and compared with the results given in previous reports. The results show that the primary dendritic arm spacing and secondary dendritic arm spacing of the dendritic growth are consistent with the theoretical and experimental results. The mesoscopic grain simulation can be used to obtain results similar to those of microscopic dendrites simulation. It is indicated that the developed model is feasible and effective.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Li Y, Liu L, Huang T, et al. Simulation of stray grain formation in Ni-base single crystal turbine blades fabricated by HRS and LMC techniques. China Foundry, 2017, 14(2): 75–79.
Meng X, Li J, Zhu S, et al. Method of stray grain inhibition in the platforms with different dimensions during directional solidification of a ni-base superalloy. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 2014, 45(3): 1230–1237.
Cao L, Liao D, Lu Y, et al. Heat transfer model of directional solidification by lmc process for superalloy casting based on finite element method. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 2016, 47(9): 4640–4647.
Zhang H, Xu Q. Multi-scale simulation of directional dendrites growth in superalloys. Journal of Materials Processing Technology, 2016, 238: 132–141.
Szeliga D, Kubiak K, Motyka M, et al. Directional solidification of Ni-based superalloy castings: Thermal analysis. Vacuum, 2016, 131: 327–342.
Zhi X, Liu J, **ng J, et al. Effect of cerium modification on microstructure and properties of hypereutectic high chromium cast iron. Materials Science and Engineering: A, 2014, 603: 98–103.
Stefanescu D M. Science and Engineering of Casting Solidification. Switzerland: Springer, 2015.
Gandin C, Desbiolles J, Rappaz M, et al. A three-dimensional cellular automaton-finite element model for the prediction of solidification grain structures. Metallurgical and Materials Transactions A, 1999, 30(12): 3153–3165.
Gandin C, Rappaz M. A 3D Cellular Automaton algorithm for the prediction of dendritic grain growth. Acta Materialia, 1997, 45(5): 2187–2195.
Carozzani T, Digonnet H, Bellet M, et al. 3D CAFE simulation of a macrosegregation benchmark experiment. IOP Conference Series: Materials Science and Engineering, 2012, 33(1): 12087–12096.
Guillemot G, Gandin C, Combeau H, et al. A new cellular automaton—finite element coupling scheme for alloy solidification. Modelling and Simulation in Materials Science and Engineering, 2004, 12(3): 545–556.
Carter P, Cox D C, Gandin C A, et al. Process modelling of grain selection during the solidification of single crystal superalloy castings. Materials Science and Engineering A, 2000, 280(2): 233–246.
Meng X, Lu Q, Li J, et al. Modes of grain selection in spiral selector during directional solidification of nickel-base superalloys. Journal of Materials Science & Technology, 2012, 28(3): 214–220.
Xu Q, Zhang H, Qi X, et al. Multiscale Modeling and Simulation of Directional Solidification Process of Turbine Blade Casting with MCA Method. Metallurgical and Materials Transactions B, 2014, 45(2): 555–561.
Nastac L. Numerical modeling of solidification morphologies and segregation patterns in cast dendritic alloys. Acta Materialia, 1999, 47(17): 4253–4262.
Zhu M, Stefanescu D. Virtual front tracking model for the quantitative modeling of dendritic growth in solidification of alloys. Acta Materialia, 2007, 55(5): 1741–1755.
Pan S, Zhu M. A three-dimensional sharp interface model for the quantitative simulation of solutal dendritic growth. Acta Materialia, 2010, 58(1): 340–352.
Zhang X, Zhao J, Jiang H, et al. A three-dimensional cellular automaton model for dendritic growth in multi-component alloys. Acta Materialia, 2012, 60(5): 2249–2257.
Yuan L, Lee P D. A new mechanism for freckle initiation based on microstructural level simulation. Acta Materialia, 2012, 60(12): 4917–4926.
Rappaz M, Gandin CA. Probabilistic modelling of microstructure formation in solidification processes. Acta Metallurgica et Materialia, 1993, 41(2): 345–360.
Nastac L, Stefanescu D M. An analytical model for solute redistribution during solidification of planar, columnar, or equiaxed morphology. Metallurgical Transactions A, 1993, 24(9): 2107–2118.
Wang W, Lee P D, Mclean M. A model of solidification microstructures in nickel-based superalloys: predicting primary dendrite spacing selection. Acta Materialia, 2003, 51(10): 2971–2987.
Kurz W, Fisher D J. Dendrite growth at the limit of stability: tip radius and spacing. Acta Metallurgica, 1981, 29(1): 11–20.
Trivedi R. Interdendritic Spacing: Part II. A Comparison of Theory and Experiment. Metallurgical Transactions A, 1984, 15(6): 977–982.
Author information
Authors and Affiliations
Corresponding author
Additional information
*Jian-xin Zhou Male, born in 1975, Professor, Ph.D. His research interests mainly focus on computer applications in foundry industry, especially casting process simulation and smart manufacturing for foundry enterprises.
Rights and permissions
About this article
Cite this article
Guo, Z., Zhou, Jx., Yin, Yj. et al. Multi-scale coupling simulation in directional solidification of superalloy based on cellular automaton-finite difference method. China Foundry 14, 398–404 (2017). https://doi.org/10.1007/s41230-017-7146-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41230-017-7146-3
Key words
- multi-scale coupling
- dendritic growth
- grain growth
- directional solidification
- cellular automata
- numerical simulation