The phase field method has gathered significant attention in the past decade due to its versatile applications in engineering contexts, including fatigue crack propagation modeling. Particularly, the phase field cohesive zone method (PF-CZM) has emerged as a promising approach for modeling fracture behavior in quasi-brittle materials, such as concrete. The present contribution expands the applicability of the PF-CZM to include the modeling of fatigue-induced crack propagation. This study critically examines the validity of the extended PF-CZM approach by evaluating its performance across various fatigue behaviours, encompassing hysteretic behavior, S-N curves, fatigue creep curves, and the Paris law. The experimental investigations and validation span a diverse spectrum of loading scenarios, encompassing pre- and post-peak cyclic loading, as well as low- and high-cyclic fatigue loading. The validation process incorporates 2D and 3D boundary value problems, considering mode I and mixed-modes fatigue crack propagation. The results obtained from this study show a wide range of validity, underscoring the remarkable potential of the proposed PF-CZM approach to accurately capture the propagation of fatigue cracks in concrete-like materials. Furthermore, the paper outlines recommendations to improve the predictive capabilities of the model concerning key fatigue characteristics.

翻译：相场方法因其在工程领域（包括疲劳裂纹扩展建模）中的广泛适用性，在过去十年中引起了广泛关注。尤其值得关注的是，相场内聚力方法（PF-CZM）已成为模拟混凝土等准脆性材料断裂行为的一种有前景的方法。本文扩展了PF-CZM的适用性，将其应用于疲劳诱发裂纹扩展的建模。本研究通过评估该扩展PF-CZM方法在不同疲劳行为中的表现（包括滞回特性、S-N曲线、疲劳蠕变曲线以及Paris定律），严格检验了其有效性。实验研究与验证涵盖多种加载场景，包括峰前和峰后循环加载，以及低周和高周疲劳加载。验证过程涉及二维和三维边值问题，考虑了I型及混合模式疲劳裂纹扩展。研究结果表明，所提出的PF-CZM方法在广泛范围内均具有有效性，展现出准确捕捉混凝土类材料疲劳裂纹扩展的巨大潜力。此外，本文还提出了改善模型在关键疲劳特性方面预测能力的建议。