Near threshold fatigue curve based on the dislocation free zone model of fracture

Abstract

Dislocation pileup along an inclined direction from a crack tip has been observed in metals during tensile deformation in an electron microscope. Dislocations are emitted from the crack tip, move through a dislocation free zone, and pile up in the plastic zone. The problem of inclined pileup of screw dislocations at a crack tip with a dislocation free zone has been solved by applying the Wiener–Hopf method. The result can be used to calculate the crack tip blunting and the local stress intensity K for the applied stress intensity K 3. According to the fatigue theory of Laird or Neumann, the crack propagation per cycle has the order of magnitude of the blunting. The blunting versus K 3 is then plotted. It has the shape of the near threshold fatigue curve. To plot this curve, the local stress intensity K has been assumed to be the critical value K g for the dislocation emission at the crack tip.