Revisiting nucleation in the phase-field approach to brittle fracture
Revisiting nucleation in the phase-field approach to brittle fracture
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DOI：
10.1016/j.jmps.2020.104027
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发表时间：
2020-09
影响因子：
5.3
通讯作者：
Aditya Kumar;B. Bourdin;G. Francfort;O. Lopez-Pamies
中科院分区：
文献类型：
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作者：
Aditya Kumar;B. Bourdin;G. Francfort;O. Lopez-Pamies
自提出以来二十年了，现在很明显，Francfort 和 Marigo (1998) 被称为脆性断裂变分理论相场的正则化公式提供了一个强大的宏观理论来描述和预测任意准静态载荷条件下线弹性脆性材料中裂纹的扩展。在过去的十年中，人们对相场方法描述和预测裂纹成核的能力进行了深入的研究。本文的两个目标中的第一个是确定现有的整体断裂相场方法（无论其具体版本如何）无法模拟裂纹形核。之所以如此，是因为它缺乏一个基本要素：材料的强度。第二个目标是修改相场理论，使其能够模拟裂纹成核，无论是来自大的预先存在的裂纹、小的预先存在的裂纹、光滑和非光滑的边界点，还是在承受任意准静态载荷的大量结构内，同时保持标准相场公式模拟裂纹扩展的能力不受干扰。其中心思想是通过在控制相场演化的方程中添加外部驱动力，隐式地解释材料中固有微观缺陷的存在——其定义的宏观表现正是材料的强度。为了说明所提出的理论的描述性和预测能力，本文的最后部分提供了涵盖整个断裂成核设置的实验样本模拟。
Twenty years in since their introduction, it is now plain that the regularized formulations dubbed as phase-field of the variational theory of brittle fracture of Francfort and Marigo (1998) provide a powerful macroscopic theory to describe and predict the propagation of cracks in linear elastic brittle materials under arbitrary quasistatic loading conditions. Over the past ten years, the ability of the phase-field approach to also possibly describe and predict crack nucleation has been under intense investigation. The first of two objectives of this paper is to establish that the existing phase-field approach to fracture at large — irrespectively of its particular version — cannot possibly model crack nucleation. This is so because it lacks one essential ingredient: the strength of the material.The second objective is to amend the phase-field theory in a manner such that it can model crack nucleation, be it from large pre-existing cracks, small pre-existing cracks, smooth and non-smooth boundary points, or within the bulk of structures subjected to arbitrary quasistatic loadings, while keeping undisturbed the ability of the standard phase-field formulation to model crack propagation. The central idea is to implicitly account for the presence of the inherent microscopic defects in the material — whose defining macroscopic manifestation is precisely the strength of the material — through the addition of an external driving force in the equation governing the evolution of the phase field. To illustrate the descriptive and predictive capabilities of the proposed theory, the last part of this paper presents sample simulations of experiments spanning the full range of fracture nucleation settings.