Fracture Related to a Dislocation Distribution

The plastic flow at the crack tip is characterized by a model compatible with slip line theory. From this model it is shown that a continuous distribution of dislocations may be derived. Then assuming that these dislocations are emitted from the crack tip and move along slip lines to their final position, the Peach-Koehler force is used to calculate the plastic work involved. Since the plastic zone size is dependent on crack length, two plastic effects are present upon propagation. Primarily the distribution of dislocations present moves along with the crack tip, secondarily new dislocations are emitted to fill the larger plastic zone. These effects yield plastic work which is dependent on both σ² and σ⁴, with σ being the applied stress. This dependancy yields a critical stress relationship different from that proposed by either Irwin or Orowan. It also leads to the determination of a subcritical flaw size, i.e., one which will never become unstable.