Simulation of craze failure in a glassy polymer: rate dependent drawing and rate dependent failure models

The failure of a craze ahead of a crack growing under steady state conditions in a glassy polymer is investigated by modeling the craze microstructure using a highly anisotropic network of springs. A rate dependent drawing law is used to determine the shape of the craze-bulk interface. Approximate analytical results are developed to link the normal stress on the craze-bulk interface, the thickness of the craze and the far field stress intensity factor to the crack propagating velocity, through the craze failure criterion and the craze microstructural parameters. The accuracy of the analytical results is examined using a detailed numerical simulation. Our analysis shows that the rate independent craze failure criterion, which assumes the failure stress for fibrils ahead of the crack tip to be a material constant independent of the crack growth rate, leads to predictions of the dependence of the craze thickness and the fracture toughness on crack growth rate that are contrary to what is found experimentally. Rate dependent craze failure criteria are then proposed. Specifically, we study a case where the crack tip fibril breaks down by rate dependent chain scission and a case where the crack tip fibril fails by rate dependent chain disentanglement. For the rate dependent chain scission criterion, the results given by the rate independent constant failure stress criterion are retrieved in the limit of low crack propagation velocity. Also, there exists a critical stress intensity factor below which steady state crack propagation is impossible, i.e., crack growth becomes unstable.