Dependence of equilibrium Griffith surface energy on crack speed in phase-field models for fracture coupled to elastodynamics
Dependence of equilibrium Griffith surface energy on crack speed in phase-field models for fracture coupled to elastodynamics
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DOI：
10.1007/s10704-017-0234-y
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发表时间：
2017-10-01
影响因子：
2.5
通讯作者：
Dayal, Kaushik
中科院分区：
文献类型：
--
作者：
Agrawal, Vaibhav;Dayal, Kaushik
用于裂纹扩展的相场模型能够模拟复杂的裂纹模式，而不需要复杂且昂贵的跟踪和随着裂纹扩展而重新划分网格。在没有惯性的情况下，裂纹的演化是从一个变分的能量起点得到的，并得到了一个耦合到弹性静力学的序参数方程。仔细的数学分析表明，这与格里菲斯的断裂模型是一致的。最近在这个公式中加入惯性的努力已经用弹性动力学取代了弹性静力学。在这篇简短的笔记中，我们研究了弹性动力增强，发现它有效地使Griffith表面能量依赖于裂纹的速度。也就是说，考虑到两个相同的试件，每个试件都被两个试件中以不同速度扩展的单个裂纹断裂，预计最终的平衡构形在名义上是相同的；然而，相场断裂模型通过弹性动力学增强实现了最终的构形--特别是Griffiths表面能量贡献--这取决于裂纹速度。物理原因是在弹性动态环境中应力的有限松弛时间使得裂纹区变宽，超出在准静态环境中观察到的值。一旦裂纹扩大，即使在试件达到平衡后，“无法愈合”的状态也会阻止它松弛。在相场模型中，参考构型中的裂纹宽度与裂纹的物理张开无关，而是Griffiths表面能的量度。这一观察结果表明，在裂纹速度较大的环境中不应使用弹性动力学相场断裂模型。
Phase-field models for crack propagation enable the simulation of complex crack patterns without complex and expensive tracking and remeshing as cracks grow. In the setting without inertia, the crack evolution is obtained from a variational energetic starting point, and leads to an equation for the order parameter coupled to elastostatics. Careful mathematical analysis has shown that this is consistent with the Griffith model for fracture. Recent efforts to include inertia in this formulation have replaced elastostatics by elastodynamics. In this brief note, we examine the elastodynamic augmentation, and find that it effectively causes the Griffith surface energy to depend on the velocity of the crack. That is, considering two identical specimens that are each fractured by a single crack that grows at different velocities in the two specimens, it is expected that the final equilibrium configurations are nominally identical; however, the phase-field fracture models augmented with elastodynamics achieve final configurations-in particular, the Griffiths surface energy contributions-that depend on the crack velocity. The physical reason is that the finite relaxation time for the stresses in the elastodynamic setting enables the cracked region to widen, beyond the value observed in the quasistatic setting. Once the crack widens, the "no-healing" condition prevents it from relaxing even after the specimen reaches equilibrium. In phase-field models, crack width in the reference configuration is unrelated to the physical opening of the crack but is instead a measure of Griffiths surface energy. This observation suggests that elastodynamic phase-field fracture models should not be used in settings where the crack velocity is large.