Instabilities of quasi-static crack patterns in quenched glass plates

Abstract

We have produced controlled quasi-static crack propagation in thin glass plates to study crack instabilities. Quasi-static fractures can exhibit drastic changes in morphology when the control parameter is varied. The thermal stress and the velocity of the crack tip depend on the temperature difference between two heat reservoirs (Δ T) and the speed of descent of the sample ( V). For large V and Δ T, cracks went from straight to oscillating and then to branched in a phase diagram for these three patterns. The transition from straight to oscillating is a super-critical Hopf bifurcation. Approaching the transition line from below in the phase diagram, the relaxation time of the damped oscillating crack scaled with Δ T and V. Above the transition line, amplitude of oscillations scaled with Δ T and V. The wavelength λ of the crack oscillation was measured at the onset of oscillation. Introducing two non-dimensional parameters R and μ, we successfully compared the conditions for the onset of straight crack propagation and oscillation with theory and numerical simulation. Further above the onset of oscillation we observed period doubling.