Dislocation-free zone model of fracture comparison with experiments

Abstract

The dislocation-free zone (DFZ) model of fracture has been extended to study the relationship between the stress intensity factor, extent of plastic deformation, and crack tip geometry of an elastic-plastic crack as a function of applied stress. The results show that the stress intensity factor K decreases from the elastic value at first slowly, then goes rapidly to zero as the number of dislocations in the plastic zone increases. The crack with a zero stress intensity factor has its crack tip stress field completely relaxed by plastic deformation and hence is called a plastic crack. Between the elastic and plastic cracks, a wide range of elastic-plastic cracks having both a stress singularity and a plastic zone are possible. These elastic-plastic cracks with a DFZ are predicted if there is a critical stress intensity factor Kg required for the generation of dislocations at the crack tip. The expression for Kg is obtained from the crack tip dislocation nucleation model of Rice and Thomson. In most metals, the magnitude of Kg is less than the critical stress intensity factor for brittle fracture Kc. The values of K are determined from electron microscope fracture experiments for various metals and they are found to be in good agreement with the Kg predicted from the model. It is concluded that for most ductile and semibrittle metals, the mechanism of dislocation generation is more important than the fracture surface energy in determining the stress intensity factor at the crack tip.