Propagating cracks may deflect due to dynamic instability, running into pre-existing weak regions of heterogeneous media, or encountering variation in driving forces. The mechanical analysis of a kinked crack is of engineering significance for safety control and crack-network formation. Existing theories for kinked cracks relied on the perturbation method, as befit small kinks. The stress intensity factors (SIFs) are valid in the close proximity of the primary crack tip. As to the stress field of a kinked crack, it remains unsolved so far. In this work we develop an analytical solution to the stress fields of kinked cracks. By employing the conformal mapping and the Muskhelishvili approach, the close-form solution works for arbitrarily sized kinked cracks. The analytical theory is then validated using finite-element simulations. With this prior knowledge, we analyze the dependence of crack deflection on loading conditions, critical energy release rate, and the geometry of a kinked crack. We further demonstrate that such an analytical approach paves the way to obtain the solution of multiple-kinked cracks.

由于动态不稳定性、进入预先存在的非均质介质薄弱区域或遇到驱动力的变化，扩展裂缝可能会偏转。扭结裂纹的力学分析对于安全控制和裂纹网络的形成具有工程意义。现有的扭结裂纹理论依赖于微扰方法，适合小扭结。应力强度因子 (SIF) 在紧邻主要裂纹尖端处有效。至于扭结裂纹的应力场，至今仍未解决。在这项工作中，我们开发了扭结裂纹应力场的解析解。通过采用保角映射和 Muskhelishvili 方法，封闭形式的解决方案适用于任意大小的扭结裂缝。然后使用有限元模拟验证分析理论。有了这些先验知识，我们分析了裂纹偏转对加载条件、临界能量释放率和扭结裂纹几何形状的依赖性。我们进一步证明，这种分析方法为获得多扭结裂纹的解决方案铺平了道路。