Discrete dislocation simulations of the development of a continuum plastic zone ahead of a stationary Mode III crack

We present results from discrete dislocation simulations showing the development of the plastic zone in front of a Mode III crack under constant load. We find that the equilibrated zone is circular, in agreement with continuum mechanics predictions of the elastic-perfectly plastic Mode III crack. The size of the equilibrated zone scales as the square of the applied load (K_III), also in agreement with the continuum results. The zone approaches saturation exponentially, with a time that scales as K_III²/σ_p³, where σ_p is the Peierls stress. These results delineate conditions under which the classical, continuum predictions of elastic-plastic fracture mechanics are applicable.