Dynamical fracture instabilities due to local hyperelasticity at crack tips

As the speed of a crack propagating through a brittle material increases, a dynamical instability leads to an increased roughening of the fracture surface. Cracks moving at low speeds create atomically flat mirror-like surfaces; at higher speeds, rougher, less reflective ('mist') and finally very rough, irregularly faceted ('hackle') surfaces(1-5) are formed. The behaviour is observed in many different brittle materials, but the underlying physical principles, though extensively debated, remain unresolved(1-4). Most existing theories of fracture(6-12) assume a linear elastic stress-strain law. However, the relation between stress and strain in real solids is strongly nonlinear due to large deformations near a moving crack tip, a phenomenon referred to as hyperelasticity(13-17). Here we use massively parallel large-scale atomistic simulations-employing a simple atomistic material model that allows a systematic transition from linear elastic to strongly nonlinear behaviour-to show that hyperelasticity plays a governing role in the onset of the instability. We report a generalized model that describes the onset of instability as a competition between different mechanisms controlled by the local stress field(6-8) and local energy flow(13,14) near the crack tip. Our results indicate that such instabilities are intrinsic to dynamical fracture and they help to explain a range of controversial experimental(1-5,18) and computational(19-26) results.