Fracture dynamics of correlated percolation on ionomer networks

This article presents a random network model to the study fracture dynamics on a scaffold of charged and elastic ionomer bundles that constitute the stable skeleton of a polymer electrolyte membrane. The swelling pressure upon water uptake by this system creates the internal stress under which ionomer bundles undergo breakage. Depending on the local stress and the strength of bundle-to-bundle correlations, different fracture regimes can be observed. We use kinetic Monte Carlo simulations to study these dynamics. The breakage of individual bundles is described with an exponential breakdown rule and the stress transfer from failed to intact bundles is assumed to exhibit a power-law-type spatial decay. A central property considered in the analysis is the frequency distribution of percolation thresholds, which is employed to analyze fracture regimes as a function of the stress and the effective range of stress transfer. Based on this distribution, we introduce an order parameter for the transition from random breakage to crack growth regimes. Moreover, as a practically important outcome, the time to fracture is analyzed as a descriptor for the lifetime of polymer electrolyte membranes.