Simulation by Cellular Automata of the Crystallization of a Matrix Containing a Mobile Second Phase
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mobile and can be pushed by the growing grains, as observed experimentally during recrystallization (e.g. Ref. [15]) or solidification (e.g. Refs. [16, 17]) of two-phase materials. The resulting inhomogenous particle distribution (enrichment at grain boundaries and depletion within grains) is usually undesirable. To the best of our knowledge, no computer simulation study has been presented for the case of a matrix crystallizing in the presence of mobile particles. In the present article, we use cellular automata simulations to investigate the above case. The effect of particle area fraction, particle settling rate and matrix grain nucleation rate upon the clustering of mobile particles is examined in two dimensions for the case of matrix grains nucleated under homogenous, continuous conditions. COMPUTATIONAL PROCEDURES We use the cellular automaton technique introduced by Hesselbarth and Gobel [6] for recrystallization of single-phase materials and extended by Pezzee and Dunand [13, 14] for twophase materials containing an immobile, inert second phase. We consider a two-dimensional field of 65,536 (2562) square cells oriented along orthogonal axes with periodic boundary conditions. Each cell is updated at discrete time-steps according to local, deterministic topological rules. cells, which can have two possible states (crystallized or uncrystallized), are subjected during each time-step to two sequential events: growth and nucleation. During the nucleation event, nuclei consisting of a single crystallized cell are distributed randomly on the field (but with no pair of nuclei as nearest neighbor) at a constant area fraction, corresponding to homogenous nucleation without particle-stimulated nucleation. During the growth event, those uncrystallized 457 Mat. Res. Soc. Symp. Proc. Vol. 398 01996 Materials Research Society
matrix cell with at least one of their nearest neighbors belonging to a crystallized grain become part of that grain. An alternating neighborhood of six cells is chosen for the growth event, resulting in equiaxed, octagonal grains before impingement, as described in more details in Refs. [6, 13, 14]. Particles are represented by single cells, which are assigned randomly on the whole field at time t=0. A particle moves only if at least one of its eight nearest neighboring cells belongs to a matrix grain, i.e., if it is in contact with a grain border. This is achieved by exchanging the position of the particle cell with that of any of its uncrystallized matrix neighbors. As particles accumulate at the moving grain border, they form clusters and restrict their respective motion. For a given time-step, the above particle pushing procedure is repeated until all particles in the clusters have had the opportunity to move once (and only once). Settling of particles, which occurs for instance during solidification when particles experience a buoyancy force significantly larger than the viscous drag force, is simulated by moving each particle randomly to any of the three uncrystallized neighboring matrix cell
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