The purpose of this investigation is to characterize the delayed yielding and fracture phenomena in a viscoelastic ductile polymer where crack growth is associated with the formation and growth of a plastic zone at the tip of the crack. This investigation deals with the time before catastrophic failure occurs in front of the crack tip. The bulk material is considered viscoelastic as well as rate dependent and is modeled by a modified Bingham model used by Brinson. The yielded material in the crazed region is modeled by the viscoelastic-plastic model of Crochét. Our theoretical solution has been adapted to a plane stress polycarbonate Dugdale model to facilitate a simple experimental verification. Such results could be useful in predicting lifetime, reliability, and failure criteria in structural members made from viscoelastic-plastic materials.