Model for interaction of dislocation arrays with a crack

We examine the case of two arrays of discrete edge dislocations in the presence of a semi-infinite crack. The arrays are symmetrically located about the plane of the crack and pass through the tip. From the elasto-static formulation for isotropic materials utilizing complex variable functions, we have developed the required equilibrium forces. The analysis gives the number of dislocations in equilibrium with the crack at a given load, and the size of the dislocation free zone. The resulting analysis also yields the size of the plastic zone and an estimate of the critical threshold for further dislocation emission. These results will be compared with dislocation analysis results reported by other workers, especially Lin and Thomson [Lin IH, Thomson R. Cleavage, dislocation emission, and shielding for cracks under general loading. Acta Met 1986;(34):187–206]. The applicability of these results for a quantitative description of the phenomenon fatigue thresholds will also be briefly considered.