Oscillatory instability of ultra-high-speed brittle cracks

Abstract

Experiments in thin brittle gels have shown that cracks can attain extreme speeds approaching the shear wave speed when micro branching, which limits propagation to smaller speeds in thick samples, is suppressed. Furthermore, these studies revealed the existence of an oscillatory instability with an intrinsic system-size-independent wavelength above a threshold speed [1]. We investigate this oscillatory instability using a phase-field model of two-dimensional dynamic brittle fracture that includes elastic nonlinearity and has unique capability to describe experimentally observed ultra-high-speed cracks that accelerate above 90% of their sonic velocity. Our simulation results demonstrate that cracks undergo a dynamic oscillatory instability controlled by small-scale elastic nonlinearity near the crack tip. This instability occurs above an ultra-high critical velocity and features an intrinsic wavelength that increases proportionally to the ratio of the fracture energy to an elastic modulus, in quantitative agreement with experiments. This ratio emerges as a fundamental scaling length for nonlinear effects assumed to play no role in the classical theory of cracks, but shown by our computations to strongly influence crack dynamics.