Oscillatory Instability in Two-Dimensional Dynamic Fracture

The stability of a rapid dynamic crack in a two dimensional infinite strip is studied in the framework of Linear Elasticity Fracture Mechanics supplemented with a modified principle of local symmetry. It is predicted that a single crack becomes unstable by a finite wavelength oscillatory mode at a velocity $v_c$, $0.8c_R<v_c<0.85c_R$, where $c_R$ is the Rayleigh wave speed. The relevance of this theoretical calculation to the oscillatory instability reported in the companion experimental Letter is discussed.