An intrinsic nonlinear scale governs oscillations in rapid fracture

Abstract: When branching is suppressed, rapid cracks undergo a dynamic instability from a straight to an oscillatory path at a critical velocity $v_c$. In a systematic experimental study using a wide range of different brittle materials, we first show how the opening profiles of straight cracks scale with the size $\ell_{nl}$ of the nonlinear zone surrounding a crack's tip. We then show, for all materials tested, that $v_c$ is both a fixed fraction of the shear speed and, moreover, that the instability wavelength is proportional to $\ell_{nl}$. These findings directly verify recent theoretical predictions and suggest that the nonlinear zone is not passive, but rather is closely linked to rapid crack instabilities.