Abstract
The application of cellular automata in materials science requires the conversion of the automata's rules and abstract general properties to rules and properties associated with the material and phenomena under study. In this paper we propose a model which uses cellular automata to simulate recrystallization and grain growth during isothermal and non-isothermal treatments of cold worked polycrystalline materials. The algorithm's spatial and temporal scaling is based on known experimental results for recrystallization and grain growth in highly cold-worked commercially pure titanium grade 2. In the recrystallization, the best agreement between experimental and computational results in terms of the process kinetics and the average diameter of recrystallized grains is obtained from a nucleation model that considers the temperature-dependent nuclei formation rate. In the simulation of grain growth after primary recrystallization, the results indicate the normal growth of an equiaxed grain structure whose kinetics and dimensions are comparable to those observed experimentally.
Highlights
Processes and natural phenomena are usually modeled by partial differential equations that govern the continuous spatial and temporal evolution of the relevant quantities that describe the system under study
To computationally implement the recrystallization and grain growth model with the cellular automata algorithm, we used a two-dimensional matrix with 300x300 cells
An important aspect of the application of cellular automata is the scaling of time and space
Summary
Processes and natural phenomena are usually modeled by partial differential equations that govern the continuous spatial and temporal evolution of the relevant quantities that describe the system under study. Possible solutions to such equations are only obtained numerically, with the differential formulation transformed, for example, into a finite difference scheme to be implemented computationally using an appropriate algorithm. It is possible to describe the spatiotemporal evolution of complex systems by models that are implemented using algorithms involving cellular automata[1,2]. Each cell is characterized by a finite number of attributes or properties. The cellular automaton evolves in almost imperceptible steps over time, so that at each level of time, the properties associated with each cell are updated according to well-defined transformation rules. Among the several possibilities for defining the neighborhood of a given cell, the ones most commonly used are those proposed by von Neumann and Moore, which consider, respectively, the 4 and 8 nearest neighbors for a
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