Dynamical Fracture Instabilities Due to Local Hyperelasticity at Crack Tips

Abstract

When materials break and cracks propagate, bonds between atoms are broken generating two new material surfaces. 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 deformation near a moving crack tip, a phenomenon referred to as hyperelasticity or nonlinear elasticity. Cracks moving at low speeds create atomically flat mirror-like surfaces, whereas cracks at higher speeds leave misty and hackly fracture surfaces. This change in fracture surface morphology is a universal phenomenon found in a wide range of different brittle materials, but the underlying physical reason has been debated over an extensive period. Using massively parallel large-scale atomistic simulations employing a new, simple atomistic material model allowing a systematic transition from linear elastic to strongly nonlinear material behaviors, we show that hyperelasticity can play a governing role in dynamical crack tip instabilities in fracture of brittle materials. We report a generalized model that treats the instability problem as a competition between different mechanisms controlled by local stress field and local energy flow near the crack tip. Our results indicate that the fracture instabilities do not only appear in defected materials, but instead are an intrinsic phenomenon of dynamical fracture. Our findings help to explain controversial experimental and computational results, including experimental observation of crack propagation at speeds beyond the shear wave speed in rubber-like materials.