Simulation by Cellular Automata of the (RE)Crystallization of a Matrix Containing an Inert Second Phase
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containing equiaxed particles much smaller than the final grain size. They concluded that, at high stored energies, the recrystallization growth is not affected by the particles. Grain coarsening during and after recrystallization was however found to be strongly inhibited by particles. Nes et al. (9) investigated the recrystallization behavior of a matrix containing stringers of densely spaced particles, and found that the growth rate was direction-dependent, leading to elongated grains in the direction of the stringers. In the present study, we focus solely on the impingement exerted by particles on growing grains, in order to study this geometric effect independently of other effects found in experimental studies of crystallization and recrystallization in two-phase materials, e.g. particle-stimulated nucleation, grain-boundary pinning by particles or particle dragging or pushing by moving boundaries. Impingement by a second phase may become important when the specific area of matrix-particle interface is high, i.e., for high volume fractions, high aspect ratios and small sizes of particles, in such materials as those formed by phase separation through solidification or solid state precipitation, in metal- or ceramic matrix composites and in foamed materials. COMPUTATIONAL PROCEDURES Hesselbarth and Gobel (15) first used cellular automata to simulate recrystallization in a material consisting of a field of cells with two possible states - recrystallized and unrecrystallized - evolving with time according to local topological rules. Time is discretized in time-steps, which are divided in growth and nucleation events. During the nucleation event, single-cell nuclei are randomly dis295 Mat. Res. Soc. Symp. Proc. Vol. 321. 'ý,1994 Materials Research Society
tributed in the field; only those that are nucleated on an unrecrystallized cell are considered. During the growth event, the entire field is updated according to the following rules: - a recrystallized cell remains recrystallized, - an unrecrystallized cell becomes recrystallized if at least one of its neighbors is recrystallized. It becomes part of the same grain as the recrystallized neighbor. We add to the original model by Hesselbarth and Gobel (15) two rules to take into account the presence of inert particles (17): - at time t=O, second-phase particles are placed randomly on the field with a minimum spacing of two cells between particles; these particles do not grow. - matrix grains neither nucleate nor grow within particles. The following parameters were used in the present study: (i) a two-dimensional field of 262,144 (5122) square cells oriented along orthogonal axes with periodic boundary conditions; (ii) homogenous nucleation conditions, with a matrix nucleation rate of 4.104 for each nucleation step; (iii) a neighborhood of six altemrning neighbors for the growth phase (15); (iv) an unrecrystallized cell with recrystallized neighbors belonging to more than one grain becomes part of any of the competing grains with the same probability. Two paramete
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