A cellular automata model for simulating grain structures with straight and hyperbolic interfaces

• Published in: International journal of minerals, metallurgy and materials Vol. 19; no. 8; pp. 699 - 710
• Main Author: A. Ramirez-Lopez M, Palomar-Pardave D. Muhoz-Negron C. Duran- Valencia S. Lopez-Ramirez G. Soto-Cortes
• Format: Journal Article
• Language: English
• Published: Springer Berlin Heidelberg University of Science and Technology Beijing 01.08.2012; Springer Nature B.V; Department of Molecular Engineering, Mexican Institute of Petroleum, Mexico%Materials and Energy Department, Metropolitan Autonomous University, Mexico%Department of Industrial Engineering, Technological Autonomous Institute of Merdco, Mexico%Department of Molecular Engineering, Mexican Institute of Petroleum, Mexico; Materials and Energy Department, Metropolitan Autonomous University, Mexico; Department of Industrial Engineering, Technological Autonomous Institute of Merdco, Mexico
• Subjects: Algorithms; Automata theory; Boundary conditions; Cellular automata; Cellular structure; Ceramics; Chaos theory; Characterization and Evaluation of Materials; Chemistry and Materials Science; Columns (structural); Composites; Computer simulation; Corrosion and Coatings; Glass; Grain growth; Grain size distribution; Grain structure; Grains; Materials Science; Mathematical models; Metallic Materials; Natural Materials; Nodes; Nucleation; Random numbers; Routines; Sequences; Simulation; Solidification; Surfaces and Interfaces; Thin Films; Transition zone; Tribology; 元胞自动机; 功能节点; 双曲线; 成核时间; 接口; 晶粒结构; 模型模拟; 直线; computational methods; grain growth; algorithms; interfaces; grain size and shape; computer simulation; cellular automata
• ISSN: 1674-4799; 1869-103X
• DOI: 10.1007/s12613-012-0616-0

A description of a mathematical algorithm for simulating grain structures with straight and hyperbolic interfaces is shown. The presence of straight and hyperbolic interfaces in many grain structures of metallic materials is due to different solidification conditions, in- eluding different solidification speeds, growth directions, and delaying on the nucleation times of each nucleated node. Grain growth is a complex problem to be simulated; therefore, computational methods based on the chaos theory have been developed for this purpose. Straight and hyperbolic interfaces are between columnar and equiaxed grain structures or in transition zones. The algorithm developed in this work involves random distributions of temperature to assign preferential probabilities to each node of the simulated sample for nucleation according to previously defined boundary conditions. Moreover, more than one single nucleation process can be established in order to gen- erate hyperbolic interfaces between the grains. The appearance of new nucleated nodes is declared in sequences with a particular number of nucleated nodes and a number of steps for execution. This input information influences directly on the final grain structure （grain size and dislribution）. Preferential growth directions are also established to obtain equiaxed and columnar grains. The simulation is done using rou- tines for nucleation and growth nested inside the main function. Here, random numbers are generated to place the coordinates of each new nucleated node at each nucleation sequence according to a solidification probability. Nucleation and growth routines are executed as a func- tion of nodal availability in order to know if a node will be part of a grain. Finally, this information is saved in a two-dimensional computa- tional array and displayed on the computer screen placing color pixels on the corresponding position forming an image as is done in cellular automaton.