Recrystallization Simulation by Use of Cellular Automata

Abstract

This report is about cellular automaton models in materials science.It gives an introduction to the fundamentals of cellular automataand reviews applications particularly for predicting recrystallizationphenomena. Cellular automata for recrystallization are typicallydiscrete in time, physical space, and orientation space and oftenuse quantities such as dislocation density and crystal orientationas state variables. They can be defined on a regular or non-regular2D or 3D lattice considering the first, second, and third neighborshell for the calculation of the local driving forces. The kinetictransformation rules are usually formulated to map a linearizedsymmetric rate equation for sharp grain boundary segment motion.While deterministic cellular automata directly perform cell switchesby sweeping the corresponding set of neighbor cells in accord withthe underlying rate equation, probabilistic cellular automata calculatethe switching probability of each lattice point and make the actualdecision about a switching event by evaluating the local switchingprobability using a Monte Carlo step. Switches are in a cellularautomaton algorithm generally performed as a function of the previousstate of a lattice point and the state of the neighboring latticepoints. The transformation rules can be scaled in terms of timeand space using for instance the ratio of the local and the maximumpossible grain boundary mobility, the local crystallographic texture,the ratio of the local and the maximum occurring driving forces,or appropriate scaling measures derived from a real initial specimen.The cell state update in a cellular automaton is made in synchronyfor all cells. The present report will particularly deal with theprediction of the kinetics, microstructure, and texture of recrystallization.Couplings between cellular automata and crystal plasticity finiteelement models will be also discussed.