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 are formed. The behaviour is observed in many different brittle materials, but the underlying physical principles, though extensively debated, remain unresolved. Most existing theories of fracture 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. 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 and local energy flow 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 and computational results.