In this work, a recently proposed high-cycle fatigue cohesive zone model, which covers crack initiation and propagation with limited input parameters, is embedded in a robust and efficient numerical framework for simulating progressive failure in composite laminates under fatigue loading. The fatigue cohesive zone model is enhanced with an implicit time integration scheme of the fatigue damage variable which allows for larger cycle increments and more efficient analyses. The method is combined with an adaptive strategy for determining the cycle increment based on global convergence rates. Moreover, a consistent material tangent stiffness matrix has been derived by fully linearizing the underlying mixed-mode quasi-static model and the fatigue damage update. The enhanced fatigue cohesive zone model is used to describe matrix cracking and delamination in laminates. In order to allow for matrix cracks to initiate at arbitrary locations and to avoid complex and costly mesh generation, the phantom node version of the eXtended finite element method (XFEM) is employed. For the insertion of new crack segments, an XFEM fatigue crack insertion criterion is presented, which is consistent with the fatigue cohesive zone formulation. It is shown with numerical examples that the improved fatigue damage update enhances the accuracy, efficiency and robustness of the numerical simulations significantly. The numerical framework is applied to the simulation of progressive fatigue failure in an open-hole [$\pm$45]-laminate. It is demonstrated that the numerical model is capable of accurately and efficiently simulating the complete failure process from distributed damage to localized failure.

翻译：本文提出一种基于新型高周疲劳内聚力区模型（该模型仅需有限输入参数即可描述裂纹萌生与扩展）的鲁棒高效数值框架，用于模拟复合材料层合板在疲劳载荷下的渐进失效过程。通过引入疲劳损伤变量的隐式时间积分方案，增强了该疲劳内聚力区模型，允许采用更大的循环增量步并实现更高效的分析。该方法结合了基于全局收敛率的自适应循环增量确定策略。此外，通过完全线性化底层混合模式准静态模型及疲劳损伤更新，推导出一致的材料切线刚度矩阵。增强型疲劳内聚力区模型用于描述层合板中的基体开裂和分层。为允许基体裂纹在任意位置萌生并避免复杂昂贵的网格生成，采用了扩展有限元法（XFEM）的幻影节点版本。针对新裂纹段的插入，提出了与疲劳内聚力区公式一致的XFEM疲劳裂纹插入准则。数值算例表明，改进的疲劳损伤更新显著提升了数值模拟的精度、效率和鲁棒性。将该数值框架应用于含孔[±45]层合板的渐进疲劳失效模拟，验证了该模型能够准确高效地模拟从分布式损伤到局部失效的完整失效过程。