Crack propagation threshold in single-crystal silicon: a cleavage plane-crackons model
Experiments revealed the discontinuities in the dependence of the crack speeds on the crack driving force. Despite great efforts, until now, previous theoretical methods, such as linear elastic fracture mechanics and molecular dynamics calculations, failed to elucidate the issue of speed gap. Herein, the cleavage plane-crackons model for crack propagation has been proposed. The normalized crack propagation speed of silicon is proportional to the one-fourth power of the quantum numbers. This motion equation is consistent with experimental results of silicon. It clarifies the underlying mechanism of the long-standing issue of the speed gap. The relationship between quantum numbers and the roughness of the surface of the cracks has been established. The critical quantum number for the onset of unstable crack propagation in single-crystal silicon has been determined. The correspondence between the critical quantum number and fracture toughness has been discovered. This methodology lead to insights into the underlying mechanism of the fracture processes. It is not limited to silicon and can be extended to other crystalline material to understand and predict the fracture behaviors.