Instabilities in dynamic fracture
Cracks, the major vehicle for material failure, undergo various dynamic instabilities in brittle materials. Despite their fundamental importance and apparent similarities to other instabilities in condensed-matter and materials physics, these instabilities remain poorly understood. In particular, they are not explained by the classical theory of cracks, which is based on the linearized field theory of elasticity. We develop a 2D theory capable of predicting arbitrary paths of dynamic cracks, incorporating small-scale, near crack-tip elastic nonlinearity. We show that cracks undergo a high-speed oscillatory instability controlled an intrinsic nonlinear elastic length, in quantitative agreement with experiments. The instability is shown to exist, with the same salient properties, in materials exhibiting widely different near crack-tip elastic nonlinearity, highlighting its universal character. We further show that upon increasing the driving force for fracture, a tip-splitting instability emerges, which is experimentally demonstrated. The theory culminates in a comprehensive stability phase diagram of 2D brittle fracture.