Percolation Theory for Two-Phase Materials with Nonrandom Topologies
Percolation theory is commonly used to develop microstructure-property relationships for two-phase materials. Although many composite microstructures have engineered spatial correlations among the constituent phases, percolation-based models often assume random arrangement of the phases. Using 3-D microstructure simulations, we systematically study topologically-varied two-phase microstructures with different states of ordering or segregation. We find that the topological state of the microstructure strongly affects percolation behavior and that the percolation threshold changes by as much as ±0.20 when local correlations are introduced. In order to quantify these effects, we propose that all microstructures be mapped into a “correlation-space”, upon which percolation behavior is easily superimposed. In this way the correlation-dependence of properties such as the percolation threshold, connectivity length and mean cluster size of the microstructure can be easily predicted.
Megan Frary. "Percolation Theory for Two-Phase Materials with Nonrandom Topologies" TMS Annual Meeting. San Antonio, TX. Mar. 2006.
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