Phase-field simulation of thermal conductivity in porous polycrystalline microstructures

Mesoscale computer simulations are used to study the effective thermal conductivity of two-dimensional polycrystalline model microstructures containing finely dispersed stationary voids. The microstructural evolution is captured by phase-field modeling in which the competing mechanisms of curvature-driven grain-boundary (GB) migration and Zener pinning due to the void/grain-boundary interactions control the grain-growth kinetics. We investigate porosity fractions between 0% and 8% by systematically increasing the number of voids in the simulation cell. The temperature distribution throughout the microstructure at progressive instances in time is calculated by solving the solid-state heat-conduction equation. The thermal conductivity of each grid point is assigned a value according to the microstructural feature it represents (grain interiors, GBs, and voids) as determined by the phase-field order parameters. The effective conductivities of the microstructures are analyzed with respect to average grain size as well as porosity fraction, and good agreement with theoretical models is obtained.