Effect of a micro-crack on the kinked macro-crack

The solution of an infinite plane containing an arbitrarily located micro-crack and a kinked macro-crack is presented based on the distributed dislocation technique (DDT). The stress field, the plastic zone of the macro-crack tip (PZ) and the stress intensity factors at the macro-crack tip (SIFs) are obtained. The influence of the micro-crack on the kinked macro-crack is investigated. The results show the effect of the micro-crack on SIFs increases with the micro-crack length increasing, the distance d decreasing and the micro-crack angle decreasing. The micro-crack has an amplifying effect on mode I SIF at about -80°<θ<60°, while it has a shielding effect at about -90°<θ<-80° and 60°<θ<90°. The micro-crack has an amplifying effect on mode II SIF at about -90°<θ<20°, while it has a shielding effect at about 20°<θ<90°. The micro-crack ahead of PZ has a little amplifying effect on PZ. As the micro-crack is close to the macro-crack tip, plastic zones of the micro-crack tip and macro-crack tip will join together. PZ is split into two pieces by the micro-crack located in PZ. The micro-crack behind PZ has no effect on PZ. These results are helpful to analyze the fracture or fatigue behaviors of materials.