Crack nucleation in variational phase-field models of brittle fracture
Crack nucleation in variational phase-field models of brittle fracture
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DOI：
10.1016/j.jmps.2017.09.006
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发表时间：
2018
影响因子：
5.3
通讯作者：
Erwan Tanné;Tianyi Li;B. Bourdin;J. Marigo;C. Maurini
中科院分区：
文献类型：
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作者：
Erwan Tanné;Tianyi Li;B. Bourdin;J. Marigo;C. Maurini
相场模型有时称为梯度损伤或弥散裂纹模型，是脆性材料中裂纹扩展数值模拟的广泛使用的方法。理论结果和数值证据表明，他们可以根据格里菲斯准则预测预先存在的裂纹的扩展。对于一维问题，研究表明，只要用材料的内部或特征长度来确定正则化参数，它们就可以预测临界应力下的成核。在本文中，我们利用数值模拟来研究常见几何形状中的裂纹成核，而对于这些几何形状，封闭式解决方案不可用。我们使用 U 形和 V 形切口来表明，当应力集中或奇点的强度发生变化时，成核载荷从强度准则预测的载荷平滑地变化为韧性准则预测的载荷。我们对两种类型的几何形状进行了验证和验证数值模拟。我们考虑无限或细长域中的椭圆腔问题，以表明变分相场模型正确地考虑了结构和材料尺寸效应。我们的主要主张是，通过在广泛的材料和几何形状中进行验证和验证，可以通过最小化变分相场模型中的非线性能量来准确预测裂纹成核，并且不需要引入临时准则。
Phase-field models, sometimes referred to as gradient damage or smeared crack models, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’ criterion. For a one-dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter be identified with the material’s internal or characteristic length. In this article, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from that predicted by a strength criterion to that of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.Our main claim, supported by validation and verification in a broad range of materials and geometries, is that crack nucleation can be accurately predicted by minimization of a nonlinear energy in variational phase field models, and does not require the introduction of ad-hoc criteria.