Detailed simulation of craze fibril failure at a crack tip in a glassy polymer

A discrete network of springs is used to model the failure of a craze in front of a crack under small-scale yielding conditions. The material outside the craze is assumed to be linearly isotropic elastic. Craze failure occurs when the first fibril ahead of the crack tip reaches the breaking force. The location of the craze-bulk interface is determined by a drawing law, which states that the craze fibrils are drawn from the bulk into the craze when the stress at the craze-bulk boundary reaches the drawing stress σd. Solving this fully coupled problem, we determine the fracture toughness Gc in terms of the fibril breaking force, the drawing stress and the craze microstructural parameters. The simulation results show that the force on the fibril directly ahead of the crack tip is underestimated by the uniform strip model proposed by Brown (Macromolecules, 1991, 24, 2752) by about 20%, even for thick crazes. A simple closed-form expression is obtained which relates the fracture toughness to the drawing stress and the craze microstructural parameters.