Modeling of Grain Growth in One and Two Phase Materials by 2D Cellular Automata

A cellular automaton (CA) is an algorithm that describes the discrete spatial or temporal evolution of a complex system by applying local deterministic or probabilistic transformation rules to the cells of a lattice. The lattice is typical regular and its dimensions can be arbitrary. In general CA modeling utilizes a regular lattice that is divided into cells of equal size. Each cell is characterized by different states. By taking into account the states of the cells of its neighbourhood, the state of the cell can be made to change by time stepping according to the transition rules. In this work, a deterministic as well as a probabilistic CA model is presented. In the deterministic approach, the net pressure on each grain boundary is calculated taking into account grain boundary curvature, precipitations and grain boundary mobility, whereas in the probabilistic approach advanced Moore's neighbourhood configuration is considered where both the nearest and next-nearest neighbours are used. The total transition probability is calculated by a developed probabilistic rule set, where the transition probability can be increased or decreased by energy gradients and precipitations, respectively. Both virtual or real microstructures can be generated or imported into the model initially. A comparison of calculated and measured grain growth is presented for a one phase material (austenitic stainless steel 304 L) and a two phase material (Ti-6Al-4V). The input of influencing factors such as precipitates on grain growth kinetics is presented in detail.