Crossover between different growth regimes in crack formation

Abstract

The formation of cracks in brittle materials is investigated for arbitrary dependence of the crack growth on the stresses at its boundary. It is shown that, despite the possible complexity of the growth law, the shape of the crack for large sizes and long times is determined by the high-stress limit of the growth law, provided only that the probability of cracking increases with stress. This result may help to explain the appearance of long and straight cracks in many fracture processes. Other pattern-formation models are expected to show the same features.