The role of neighborhood density in the random cellular automata model of grain growth

Michał Czarnecki, Mateusz Sitko, Łukasz Madej

AGH University of Science and Technology, Faculty of Metals Engineering and Industrial Computer Science, al. Mickiewicza 30, 30-059 Krakow, Poland.

DOI:

https://doi.org/10.7494/cmms.2021.3.0760

Abstract:

The paper focuses on adapting the random cellular automata (RCA) method concept for the unconstrained grain growth simulation providing digital microstructure morphologies for subsequent multi-scale simulations. First, algorithms for the generation of initial RCA cells alignment are developed, and then the influence of cells density in the computational domain on grain growth is discussed. Three different approaches are proposed based on the regular, hexagonal, and random cells’ alignment in the former case. The importance of cellular automata (CA) cell neighborhood definition on grain growth model predictions is also highlighted. As a research outcome, random cellular automata model parameters that can replicate grain growth without artifacts are presented. It is identified that the acceptable microstructure morphology of the solid material is obtained when a mean number of RCA cells in the investigated neighborhood is higher than ten.

Cite as:

Czarnecki, M., Sitko, M., & Madej, L. (2021). The role of neighborhood density in the random cellular automata model of grain growth. Computer Methods in Materials Science, 21(3), 129–137. https://doi.org/10.7494/cmms.2021.3.0760

Article (PDF):

Keywords:

Random cellular automata, Grain growth, Digital material representation

References:

Boguń, K., Sitko, M., Mojżeszko, M., & Madej, Ł. (2021). Cellular Automata-based computational library for development of digital material representation models of heterogenous microstructures. Archives of Civil and Mechanical Engineering, 21(2), 61. https://doi.org/10.1007/s43452-021-00211-9.

Falco, S., Jiang, J., De Cola, F., & Petrinic, N. (2017). Generation of 3D polycrystalline microstructures with a conditioned Laguerre-Voronoi tessellation technique. Computational Materials Science, 136, 20–28. https://doi.org/10.1016/j.commatsci.2017.04.018.

Groß, J., Köster, M., & Krüger, A. (2019). Fast and Efficient Nearest Neighbor Search for Particle Simulations. In: Computer Graphics and Visual Computing (CGVC) 2019, 12th–13th September 2019, Bangor University, United Kingdom, 55–63. https://doi.org/10.2312/cgvc.20191258.

Hajder, L., & Madej, Ł. (2020). Sphere Packing Algorithm for the Generation of Digital Models of Polycrystalline Microstructures with Heterogeneous Grain Sizes. Computer Methods in Materials Science, 20(1), 22–30.

Li, H., Sun, X., & Yang, H. (2016). A three-dimensional cellular automata-crystal plasticity finite element model for predicting the multiscale interaction among heterogeneous deformation, DRX microstructural evolution and mechanical responses in titanium alloys. International Journal of Plasticity, 87, 154–180. https://doi.org/10.1016/j.ijplas.2016.09.008.

Liu, J., Dai, Q., Chen, J., Chen, S., Ji, H., Dua, W., Deng, X., Wang, Z., Guo, G., & Luo, H. (2017). The two dimensional microstructure characterization of cemented carbides with an automatic image analysis process. Ceramics International, 43(17), 14865–14872. https://doi.org/10.1016/j.ceramint.2017.08.002.

Maazi, N., & Lezzar, B. (2020). An efficient Monte Carlo Potts method for the grain growth simulation of single-phase systems. Computer Methods in Material Science, 20(3), 85–94. https://doi.org/10.7494/cmms.2020.3.0722.

Madej, L. (2017). Digital/virtual microstructures in application to metals engineering – A review. Archives of Civil and Mechanical Engineering, 17(4), 839–854. https://doi.org/10.1016/j.acme.2017.03.002.

Madej, L., Legwand, A., Mojzeszko, M., Chraponski, J., Roskosz, S., & Cwajna, J. (2018a). Experimental and numerical two- and three- dimensional investigation of porosity morphology of the sintered metallic material. Archives of Civil and Mechanical Engineering, 18(4), 1520–1534. https://doi.org/10.1016/j.acme.2018.06.007.

Madej, L., Sitko, M., Legwand, A., Perzynski, K., & Michalik, K. (2018b). Development and evaluation of data transfer protocols in the fully coupled random cellular automata finite element model of dynamic recrystallization. Journal of Computational Science, 26, 66–77. https://doi.org/10.1016/j.jocs.2018.03.007.

Owusu, P.A., Leonenko, V.N., Mamchik, N.A., & Skorb, E.V. (2019). Modeling the growth of dendritic electroless silver colonies using hexagonal cellular automata. Procedia Computer Science, 156, 43–48. https://doi.org/10.1016/j.procs.2019.08.128.

Pietrzyk, M., & Madej, L. (2017). Perceptive Review of Ferrous Micro/Macro Material Models for Thermo‐Mechanical Processing Applications. Steel Research International, 88(10).

Pietrzyk, M., Kusiak, J., Kuziak, R., Madej, L., Szeliga, D., & Gołąb, R. (2014). Conventional and Multiscale Modeling of Microstructure Evolution During Laminar Cooling of DP Steel Strips. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 45(13), 5835–5851. https://doi.org/10.1007/s11661-014-2393-z.

Pietrzyk, M., Madej, L., Rauch, L., & Szeliga, D. (2015). Computational Materials Engineering Achieving high accuracy and efficiency in metals. Elsevier Science.

Pokharel, R., Lind, J., Li, S.F., Kenesei, P., Lebensohn, R.A., Suter, R.M., & Rollett, A.D. (2015). In-situ observation of bulk 3D grain evolution during plastic deformation in polycrystalline Cu. International Journal of Plasticity, 67, 217–234. https://doi.org/10.1016/j.ijplas.2014.10.013.

Roters, F., Diehl, M., Shanthraj, P., Eisenlohr, P., Reuber, C., Wong, S.L., Maiti, T., Ebrahimi, A., Hochrainer, T., Fabritius, H.O., Nikolov, S., Friák, M., Fujita, N., Grilli, N., Janssens, K.G.F., Jia, N., Kok, P.J.J., Ma, D., Meier, F., Werner, E., Stricker, M., Weygand, D., & Raabe, D. (2019). DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Computational Materials Science, 158, 420–478. https://doi.org/10.1016/j.commatsci.2018.04.030.

Shterenlikht A., Margetts L., & Cebamanos L. 2018. Modelling fracture in heterogeneous materials on HPC systems using a hybrid MPI/Fortran coarray multi-scale CAFE framework, Advances in Engineering Software, 125, 155–166. https://doi.org/10.1016/j.advengsoft.2018.05.008.

Svyetlichnyy, D.S. (2013). Modeling of grain refinement by cellular automata. Computational Materials Science, 77, 408–416. https://doi.org/10.1016/j.commatsci.2013.04.065.

Szyndler, J., & Madej, Ł. (2015). Numerical analysis of the influence of number of grains, FE mesh density and friction coefficient on representativeness aspects of the polycrystalline digital material representation – Plane strain deformation case study. Computational Materials Science, 96(pt. A), 200–213. https://doi.org/10.1016/j.commatsci.2014.08.037.

Tegeler, M., Shchyglo, O., Kamachali, R.D., Monas, A., Steinbach, I., & Sutmann, G. (2017). Parallel multiphase field simulations with OpenPhase. Computer Physics Communications, 215, 173–187. https://doi.org/10.1016/j.cpc.2017.01.023.

Walizer, L.E., & Peters, J.F. (2011). A bounding box search algorithm for DEM simulation. Computer Physics Communications, 182(2), 281–288. https://doi.org/10.1016/j.cpc.2010.09.008.