中文摘要：

采用滑动裂纹模型并结合现有张开斜裂纹的Ⅰ型分支裂纹扩展特性的研究成果，研究了闭合斜裂纹的Ⅰ型分支裂纹的渐近扩展特点，结果表明：1）闭合斜裂纹的Ⅰ型分支裂纹路径的渐近线为平行于最大主应力的一条直线，并得出了渐近线方程；和张开斜裂纹的翼型裂纹不同，闭合斜裂纹的翼型裂纹路径的渐近线不一定过初始裂纹中心点，该渐近线位置与初始裂纹面的摩擦系数、初始裂纹长度及初始裂纹角有关：2）闭合斜裂纹的Ⅰ型分支裂纹的扩展路径可以近似采用双曲线描述，并得出了描述Ⅰ型分支裂纹扩展路径的方程。采用ABAQUS二次开发对闭合斜裂纹的分支裂纹的扩展过程进行了数值模拟，并采用数值模拟和现有试验相结合的方法验证了以上结论的正确性。

英文摘要：

Based on the sliding-crack-model and the previous study on the wing crack of the open flaw under compression, the propagation characteristics of the wing crack from the closed initial flaw is studied. Then some conclusions are drawn as the following： 1） With the propagation of the closed flaw, the wing crack path is gradually close to the line, which is parallel to the direction of the most compressive stress, called by the asymptote of the wing crack path. Then the asymptote equation is determined in the paper. Compared with the open flaw, the asymptote of the wing crack from the closed flaw does not pass though the center point of the initial flaw, and its location is related to the initial flaw length, the initial flaw inclination angle and the friction coefficient of the flaw surfaces. 2） Owing to the asymptotic characteristics, the propagation path of the wing crack can be described by a hyperbolic equation approximately, and the hyperbolic equation is determined in the paper. Furthermore, the propagation characteristics of the wing crack are analyzed by the secondary development of ABAQUS. Then the comparative analysis on the propagation loading and path is made by the hyperbolic equation, by the numerical simulation and by the experiments, and the results show the propagation loading and path by the hyperbolic equation are in concordance with those by the numerical and experimental results, which shows the validity of the results in the paper.