Confirming the continuum theory of dynamic brittle fracture for fast cracks

Abstract

Crack propagation is the basic mechanism of materials failure. Experiments on dynamic fracture in brittle amorphous materials have produced results¹ that agree with theoretical predictions for single-crack motion at very low velocities. But numerous apparent discrepancies with theory have been observed^2,3,4 at higher velocities. In particular, the maximum crack velocities attained in amorphous materials are far slower than the predicted asymptotic value, v_R (ref. 3). Beyond a critical velocity, v_c ≈ 0.4v_R, an intrinsic instability has been observed⁵ in which a multiple-crack state is formed by repetitive, frustrated micro-branching events. These cause velocity oscillations and may explain the apparent anomaly. Here we report measurements of dynamic fracture in a brittle, amorphous material that are in quantitative agreement with the theoretical single-crack equation of motion, from the initial stages of propagation up to v_c. Beyond v_c, agreement breaks down owing to the appearance of the multiple-crack ensemble. But in this regime, the micro-branching process can momentarily produce a single-crack state which instantaneously attains its predicted single-crack velocity, for velocities up to 0.9v_R. Our results therefore confirm the validity of the single-crack continuum theory of elastic brittle fracture even in the dynamical regime where the crack morphology is complex.