The case of 2 arrays of discrete edge dislocations in the presence of a semi-infinite crack was examined. The arrays were symmetrically located about the plane of the crack, and passed through the tip. From the elasto-static formulation for isotropic materials, utilizing

complex variable functions, the required equilibrium forces were developed. The analysis gave the number of dislocations in equilibrium with the crack at a given load; and the size of the dislocation-free zone. The resultant analysis also yielded the size of the plastic zone and an estimate of the critical threshold for further dislocation emission. These results were compared with the dislocation-analysis results of other workers. The applicability of these results to a quantitative description of fatigue thresholds was also briefly considered.

Model for Interaction of Dislocation Arrays with a Crack. R.A.Masumura, C.S.Pande, Y.T.Chou: International Journal of Fatigue, 2005, 27[10-12], 1170-4