Correlated Percolation in the Fracture Dynamics on a Network of Ionomer Bundles

Synopsis

Motivated by predicting the lifetime of polymer electrolyte membranes (PEMs), we map the fracture dynamics of a network of ionomer bundles onto a correlated percolation model. A kinetic Monte Carlo method is employed to study these dynamics. The swelling pressure upon water uptake causes the breakage events of ionomer bundles, and the strength of the bundle-to-bundle correlations is characterized by the stress field and the stress redistribution scheme. Local load sharing (LLS) and equal load sharing (ELS) are the two most frequently studied stress transfer schemes. We adopt a stress transfer scheme that follows a power-law-type spatial decay in this thesis as an intermediate scheme between the two limits of the ELS and the LLS. By tuning the magnitude of the stress field and the effective range of stress transfer, two fracture regimes, i.e., the random breakage (percolation-type) regime and the localization (correlated crack growth) regime, can be observed. A central property considered in this thesis is the frequency distribution of percolation thresholds. Based on this distribution, we introduce an order parameter to assess the crossover between these two fracture regimes. Moreover, the average percolation threshold is found to exhibit a peculiar variation, which has not been reported in previous correlated percolation studies.