Numerical analyses of crack path instabilities in quenched plates

Crack path instabilities are observed in rapidly quenched rectangular glass plates whereby wavy crack patterns form as a result of the induced temperature gradients. The peculiar characteristic of these instabilities is that the speed of propagation is several order of magnitudes lower that the Rayleigh wave speed. Experimental studies have shown the dependence of the instabilities on certain geometrical, material, and experimental parameters (e.g. plate width, material toughness, speed of quenching). By perturbing these parameters cracks are observed to propagate along a straight line, oscillate with a periodic sinusoidal or semi-circle like morphology, or propagate in a supercritical manner. Here we formulate the problem of a propagating crack in a brittle thermoelastic material while considering the possibility of the crack undergoing bursts of supercritical crack propagation, by extending the model in Negri and Ortner (2008). We also describe a novel higher order computational framework for its numerical solution centered around Universal Meshes, Mapped Finite Element Methods, and Interaction Integral Functionals. We verify the convergence of the results and compare them against experiments. We reveal crack behaviors not previously observed. Particularly we discuss periods of sudden crack propagation, followed by temporary arrest and crack kinking. We identify various crack morphologies: sinusoidal, asymmetric, semi-circle, kinked and flattened oscillations. We investigate the frequency content of the oscillatory crack paths and study their relation to the dominating problem parameters. Additionally, we identify two new thresholds in phase space corresponding to the transition from oscillatory propagation to rapid propagation and arrest, as well as from permanent crack arrest to temporary crack arrest followed by kinking and branching.