An analytical solution to the stress fields of kinked cracks

Abstract 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.