Dislocaton-Free Zone Model of Fracture Under Reverse Loading

The authors have shown previously that the presence of a dislocation-free zone (DFZ) between a crack tip and its plastic zone is closely related to the condition for dislocation emission from the crack tip. The local stress intensity at the crack tip is shielded by the dislocations in the plastic zone from the applied stress and, therefore, its magnitude is reduced. During unloading, the existing dislocations serve to increase the magnitude of the reversed local stress intensity as a result of antishielding from the applied stress intensity. We have examined the effect of reverse loading and antishielding on the local stress intensity, the size of the DFZ, and the associated distribution functions of dislocations. The numerical results show that, during reverse loading, two distinct equilibrium distributions of dislocations are possible solutions to the pileup integral equation, but these distributions result in different local stress-intensity factors. The true distribution can be selected from the two if the local stress-intensity factor is limited by the reversed critical stress-intensity factor for dislocation emission K_g. The negative dislocations generated during reverse loading or cyclic loading lead to crack growth.