Low-speed fracture instabilities in a brittle crystal

Abstract

Multiscale models predict detailed features of surfaces left by crack propagation and rationalize the occurrence of fracture instabilities in a technologically important material, silicon. As a crack propagates along the most stable cleavage plane in silicon at relatively low speeds (800 metres per second), an instability suddenly appears. The authors find that beyond the very tip of the crack, when fracture speed is slow enough, bonds are broken one atomic layer below the fracture plane leading to a systematic downward deflection of the crack. Conversely, deflecting of fracture on another cleavage plane of silicon occur when the fracture speed is very high. Preliminary simulations reveal that similar instabilities could occur in diamond and silicon carbide. When a brittle material is loaded to the limit of its strength, it fails by the nucleation and propagation of a crack1. The conditions for crack propagation are created by stress concentration in the region of the crack tip and depend on macroscopic parameters such as the geometry and dimensions of the specimen2. The way the crack propagates, however, is entirely determined by atomic-scale phenomena, because brittle crack tips are atomically sharp and propagate by breaking the variously oriented interatomic bonds, one at a time, at each point of the moving crack front1,3. The physical interplay of multiple length scales makes brittle fracture a complex ‘multi-scale’ phenomenon. Several intermediate scales may arise in more complex situations, for example in the presence of microdefects or grain boundaries. The occurrence of various instabilities in crack propagation at very high speeds is well known1, and significant advances have been made recently in understanding their origin4,5. Here we investigate low-speed propagation instabilities in silicon using quantum-mechanical hybrid, multi-scale modelling and single-crystal fracture experiments. Our simulations predict a crack-tip reconstruction that makes low-speed crack propagation unstable on the (111) cleavage plane, which is conventionally thought of as the most stable cleavage plane. We perform experiments in which this instability is observed at a range of low speeds, using an experimental technique designed for the investigation of fracture under low tensile loads. Further simulations explain why, conversely, at moderately high speeds crack propagation on the (110) cleavage plane becomes unstable and deflects onto (111) planes, as previously observed experimentally6,7.