By employing a variational phase field model, we investigated the dynamic brittle fracture of poly (methyl methacrylate) (PMMA) through computer simulation. Without the explicit fracture criterion, current simulations not only successfully reproduced the crucial experimental observations on crack propagation, such as crack patterns, velocity evolutions and limit crack velocity but also discovered some new features not reported in the experimental study yet. Through quantifying the energy flux into the crack tip and fracture energy, we observed that the crack bifurcation of PMMA always occurs with the energy flux into the crack tip exceeding a critical value and proposed that crack bifurcation obeys an energy criterion. Based on this criterion, the long-standing challenge of limit crack velocity in experiments is successfully predicted by continuum theory, which unveils that crack bifurcation sets the upper limit for crack velocity. Combining the crack bifurcation criterion and continuum theory provides a rational explanation for complex path selection of cracks.

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动态脆性断裂分岔判据及极限裂纹速度的来源

通过采用变相场模型，我们通过计算机模拟研究了聚甲基丙烯酸甲酯 (PMMA) 的动态脆性断裂。在没有明确的断裂准则的情况下，当前的模拟不仅成功地再现了裂纹扩展的关键实验观察结果，例如裂纹模式、速度演变和极限裂纹速度，而且还发现了一些尚未在实验研究中报告的新特征。通过量化进入裂纹尖端的能量通量和断裂能，我们观察到 PMMA 的裂纹分叉总是随着进入裂纹尖端的能量通量超过临界值而发生，并提出裂纹分叉服从能量准则。基于这个标准，连续介质理论成功预测了实验中长期存在的极限裂纹速度挑战，该理论揭示了裂纹分岔设定了裂纹速度的上限。裂纹分岔准则与连续介质理论相结合，为裂纹的复杂路径选择提供了合理的解释。