In this paper, we extend the micromechanics-based phase-field model to simulate fatigue failure. The coupling of a micromechanics-based framework with the phase-field approach helps to differentiate between failure modes, by distinguishing between open and closed microcracks. This integrated framework links continuum field variables, such as plastic strain and damage variable, to micromechanical mechanisms like frictional sliding and microcrack opening. We first improve the algorithm’s stability during loading–unloading in the tensile regime through a modification of the plasticity evolution equations. Next, we incorporate fatigue damage accumulation and deterioration due to cyclic loading into the micromechanics-based phase-field model. A fatigue degradation function, driven by free energy accumulation, is introduced to degrade the fracture energy upon reaching a specified threshold during cyclic loading. Various cyclic loads are applied to benchmark tests, both with and without imperfections (e.g. holes, inclusions, voids), under plane strain conditions to capture diverse failure modes. The results demonstrate the model’s capability to accurately describe tensile, shear, and mixed-mode fracture under cyclic loading. Furthermore, the model effectively simulates key features of fatigue behavior, including crack nucleation, growth, and coalescence.

中文翻译：

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基于微观力学的疲劳断裂变分相场建模


在本文中，我们扩展了基于微观力学的相场模型来模拟疲劳失效。基于微力学的框架与相场方法的耦合有助于通过区分开放和闭合的微裂纹来区分失效模式。这个集成框架将连续场变量（如塑性应变和损伤变量）与微机械机制（如摩擦滑动和微裂纹张开）联系起来。我们首先通过修改塑性进化方程来提高算法在拉伸状态下加载-卸载过程中的稳定性。接下来，我们将循环载荷引起的疲劳损伤积累和劣化合并到基于微观力学的相场模型中。引入了由自由能积累驱动的疲劳退化函数，以在循环载荷期间达到指定阈值时降低断裂能量。在平面应变条件下，将各种循环载荷应用于基准测试，包括有缺陷和无缺陷（例如孔、夹杂物、空隙），以捕获不同的失效模式。结果表明，该模型能够准确描述循环载荷下的拉伸、剪切和混合模式断裂。此外，该模型还有效地模拟了疲劳行为的关键特征，包括裂纹成核、增长和聚结。