Theory and computation of fracture formation in polymer electrolyte membranes

We present a physical-statistical model of fracture formation in polymer electrolyte membranes. The membrane is considered as a cross-linked network of ionomer bundles. Water that fills the pore spaces between bundles causes stress on them, incurring bundle breakage. The problem of fracture formation and propagation is mapped onto a bond percolation problem. It was solved previously for the random percolation case of the weak-stress regime (Melchy and Eikerling, J. Phys. Condens. Matter 27, 325103, 2015). This work focuses on the high-stress regime where breakage events become correlated because of the stress redistribution upon bundle breakage. We have implemented a rejection-free kinetic Monte Carlo method to simulate correlated bundle breakage events on regular lattices. Fracture rates of bundles are expressed through an exponential breakdown rule. So far, we have evaluated a global power-law stress redistribution scheme. Using this approach, we study the effect of the initial stress, correlation length and lattice anisotropy on fracture propagation. Different regimes or fracture propagation corresponding to random and correlated percolation are identified and the impact of relevant parameters transitions between these regimes as well as on the time to fracture is analyzed.