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.

在快速淬火的矩形玻璃板中观察到裂纹路径的不稳定性，由于诱导的温度梯度，形成了波浪形的裂纹图案。这些不稳定性的独特特征是传播速度比瑞利波速度低几个数量级。实验研究表明，不稳定性取决于某些几何形状，材料和实验参数（例如板宽，材料韧性，淬火速度）。通过扰动这些参数，可以观察到裂纹沿直线传播，以周期性的正弦或半圆状形态振荡或以超临界方式传播。在这里，我们通过扩展Negri和Ortner（2008）中的模型，在考虑脆性可能经历超临界裂纹扩展爆发的同时，制定了脆性热弹性材料中扩展性裂纹的问题。我们还针对通用网格，映射有限元方法和交互积分函数为其数值解决方案描述了一种新颖的高阶计算框架。我们验证结果的收敛性，并将其与实验进行比较。我们揭示了以前未观察到的裂纹行为。特别是，我们讨论了裂纹突然扩展，暂时停止和裂纹扭结的时期。我们确定了各种裂纹形态：正弦波，不对称，半圆形，扭结和扁平振荡。我们研究了振动裂纹路径的频率含量，并研究了它们与主要问题参数的关系。此外，我们在相空间中确定了两个新的阈值，分别对应于从振荡传播到快速传播和停止，以及从永久性裂纹停止到暂时性裂纹停止再到弯折和分支的过渡。