Abstract This study aims at introducing generalized fracture solutions for 3-D radial semi-elliptical surface cracks contained in rotating hollow disks to the literature. Normalized mode-I stress intensity factors (SIFs) are presented for a wide range of cases that involve different values of crack aspect ratio, depth, radial coordinate and geometric parameters of the disk. By leveraging the obtained numerical solutions, regression-based empirical equations are also generated as functions of the governing parameters of the problem. It is shown that for a specific crack shape and normalized depth, normalized SIFs decrease with increasing radial position and increase with increasing ratio of the inner and outer disk radii. A tangential stress-based procedure is also introduced and verified that can be used to determine the normalized SIFs for a crack of a radial position by employing the normalized SIFs of another crack of same features and located at a different radial coordinate. The usage and accuracy of the developed empirical equations are also verified on radial surface cracks in flat rotating disks and disks with practically used geometric details, such as outer rim and inner bore.

中文翻译：

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旋转空心盘中径向表面裂纹的应力强度因子解和方程

摘要 本研究旨在将旋转空心圆盘中包含的 3-D 径向半椭圆表面裂纹的广义断裂解决方案引入文献。针对涉及裂纹纵横比、深度、径向坐标和圆盘几何参数的不同值的各种情况，提出了归一化 I 型应力强度因子 (SIF)。通过利用获得的数值解，还可以生成基于回归的经验方程作为问题控制参数的函数。结果表明，对于特定的裂纹形状和归一化深度，归一化 SIF 随径向位置的增加而减小，并随盘内外圆盘半径比的增加而增加。还引入并验证了基于切向应力的程序，该程序可用于通过使用具有相同特征并位于不同径向坐标的另一个裂纹的归一化 SIF 来确定径向位置裂纹的归一化 SIF。所开发的经验方程的使用和准确性也在平面旋转盘和具有实际使用的几何细节的盘中的径向表面裂纹上得到验证，例如外轮辋和内孔。