CONTINUUM AND DISCRETE MODELING OF CRAZE FAILURE AT A CRACK-TIP IN A GLASSY POLYMER

The problem of craze failure near the tip of a crack embedded inside a craze is investigated by modeling the crazed material as a highly ani sotropic network of springs. This model is based on the presence of cr oss-tie fibrils in the craze microstructure. These cross-tie fibrils g ive the craze some small lateral load-bearing capacity so that they ca n transfer stress between the main fibrils. This load transfer mechani sm allows the force on the fibril directly ahead of the crack tip in t he center of the craze to reach the breaking force of the chain even t hough the force on a main fibril as it is being drawn at the craze/bul k interface is much lower. When the craze is sufficiently wide, the di screte network model can be approximated as an anisotropic continuum. Explicit expressions are derived which relate the shear and tensile mo dulus of the crazed material to the underlying microstructural variabl es such as fibril spacing, fibril diameter and volume fraction. The pr edictions of the continuum model are compared with those of the discre te model. We focus on the case of a thin craze where the continuum app roximation is shown to be inadequate. The results of our model are use d to predict the molecular weight dependence of the fracture toughness of polymer glasses, fracture toughness of diluted entanglement networ ks, and the kinetics of polymer welding.