Fatigue crack growth modelling by successive blocking of dislocations

Abstract

Work hardening and the study of instability is incorporated into the description of the growth of a crack in terms of the successive blocking of the plastic zone by slip barriers, such as grain boundaries, and the subsequent initiation of the slip in neighbouring grains. A simple equation is derived to determine the critical position of the crack tip in relation to the grain boundary where the plastic zone is blocked at the moment of slip transmission. The intermittent pattern of decelerating and accelerating behaviour of short cracks and the existence of non-propagating cracks is explained. Instability in crack growth is seen to occur when the rate of hardening is insufficient to compensate for the increase in crack driving force in relation to the increase in crack length. This is associated with fracture toughness. The transition point between the short and long crack régimes is seen to occur when the size of the plastic zone is of the order of the microstructural parameter.