Analysis of the Interaction Between Kinked Macro-crack and Kinked Micro-crack by the Dislocation Array Model

In this paper, the mutual influence of plastic behaviors between kinked macro-crack and kinked micro-crack is analyzed based on the distributed dislocation technique and the dislocation-free zone model. A novel theoretical model for the size of the plastic zone is proposed, where the length of the dislocation array calculated in a specific direction is utilized to characterize the size of the plastic zone at the crack tip. The results demonstrate that, compared with the length of the dislocation array distributed along the crack direction, the length of the dislocation array distributed at a certain specific angle can more accurately characterize the plastic zone at the crack tip. When compared with the results of finite element analysis, the relative error is within 0.2%. Within the theoretical framework of this paper, it is considered that when the dislocation array is set at the crack tip and forms an angle of approximately 25 degrees with respect to the horizontal direction, the calculated length of the dislocation array can effectively characterize the size of the plastic zone. The dislocation density increases with the decrease of the kinking angle of the crack. These results are conducive to predicting the plastic and fracture behaviors of materials containing kinked cracks.