Connectivity and percolation in simulated grain-boundary networks

Random percolation theory is a common basis for modelling intergranular phenomena such as cracking, corrosion or diffusion. However, crystallographic constraints in real microstructures dictate that grain boundaries are not assembled at random. In this work a Monte Carlo method is used to construct physically realistic networks composed of high-angle grain boundaries that are susceptible to intergranular attack, as well as twin-variant boundaries that are damage resistant. When crystallographic constraints are enforced, the simulated networks exhibit triple-junction distributions that agree with experiment and reveal the non-random nature of grain-boundary connectivity. The percolation threshold has been determined for several constrained boundary networks and is substantially different from the classical result of percolation theory; compared with a randomly assembled network, about 50-75% more resistant boundaries are required to break up the network of susceptible boundaries. Triple-junction distributions are also shown to capture many details of the correlated percolation problem and to provide a simple means of ranking microstructures.