Abstract The bi-material interface arc crack has been the focus of interest in the composite community, where it is usually referred to as the fiber-matrix interface crack. In this work, we investigate the convergence properties of the Virtual Crack Closure Technique (VCCT) when applied to the evaluation of the Mode I, Mode II and total Energy Release Rate of the fiber-matrix interface crack in the context of the Finite Element Method (FEM). We first propose a synthetic vectorial formulation of the VCCT. Thanks to this formulation, we study the convergence properties of the method, both analytically and numerically. It is found that Mode I and Mode II Energy Release Rate (ERR) possess a logarithmic dependency with respect to the size of the elements in the crack tip neighborhood, while the total ERR is independent of element size.

中文翻译：

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纤维/基体界面裂纹问题的有限元解：虚拟裂纹闭合技术的收敛特性和模式混合

摘要 双材料界面弧裂纹一直是复合材料界关注的焦点，通常将其称为纤维-基体界面裂纹。在这项工作中，我们研究了虚拟裂纹闭合技术 (VCCT) 在有限元方法背景下应用于评估纤维-基体界面裂纹的模式 I、模式 II 和总能量释放率时的收敛特性(有限元)。我们首先提出了 VCCT 的合成矢量公式。由于这个公式，我们从分析和数值上研究了该方法的收敛特性。发现模式 I 和模式 II 能量释放率 (ERR) 与裂纹尖端邻域中的元素大小具有对数相关性，而总 ERR 与元素大小无关。