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 elastic 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.

Figure 1

$h{K}_{\mathrm{II}}^{(1)}/ϵK_{\mathrm{I}}^{(0)}$ as a function of $\eta h$ for two different velocities. The squares correspond to $v=0.8c_R$ and the circles correspond to $v=0.85c_R$. The onset of instability occurs at $v_c$, $0.8c_R<v_c<0.85c_R$, where $K_{\mathrm{II}}^{(1)}$ first changes sign from positive to negative. The wave number at the onset of instability is approximately given by ${\eta }_{c}h\approx 1.4$.