Initiation and Propagation of Localized Deformation Zones in Polymer Glasses

We propose a theory for the initiation and propagation of localized deformation zones, such as crazes, in polymer glasses. Local density perturbations in the material are potential sites for the initiation of the deformation zones and are assumed to exist as clusters within the material, with the density decreasing from ρm at the edge of each cluster to ρ0 at its center. Nonlinear stress-strain response of the polymer as a function of density is incorporated in the model. Application of a far-field tensile stress in a previously unstrained solid causes localization of the strain field which initiates from the center of the defect region when the maximum local principal stress is greater than the local craze initiation stress. Propagation occurs in a plane normal to the maximum principal stress direction. Since the strength of the craze zone depends on the local density, and is sensitive to hydrostatic pressure, an equation of state, which relates pressure to local density of the craze zone is incorporated into the model. Several numerical analyses were conducted for uniaxial and biaxial loading using nonlinear finite-element analysis run on a Cray C-90 supercomputer. The results show close prediction of the propagation of highly localized sheets characteristic of crazes observed experimentally. An orthogonal network of crazes is predicted under biaxial loading; such behavior has also been observed experimentally. The present model predicts both craze initiation and propagation as a function of fundamental mechanical properties, and these predictions are close to behavior observed experimentally in structural polymers.