The results of discrete dislocation simulations were presented which revealed the development of the plastic zone ahead of a mode-III crack under constant load. It was found that the equilibrated zone was circular, in agreement with continuum mechanics predictions of the elastic-perfectly plastic mode-III crack. The size of the equilibrated zone scaled as the square of the applied load (KIII); again in agreement with continuum results. The zone approached saturation exponentially, with a time that scaled as KIII2/σp3; where σp was the Peierls stress. These results delineated conditions under which the classical continuum predictions of elastic–plastic fracture mechanics were applicable.

Discrete Dislocation Simulations of the Development of a Continuum Plastic Zone ahead of a Stationary Mode-III Crack. N.Zacharopoulos, D.J.Srolovitz, R.LeSar: Journal of the Mechanics and Physics of Solids, 2003, 51[4], 695-713