Such interactions were studied both analytically and numerically. It was found that, when these dislocations were placed on a cylinder around the crack tip (with their slip planes all passing through the tip), the slip force which was exerted upon a dislocation by another dislocation (and its images) was zero; regardless of their locations on the cylinder. Other zero slip-force positions also existed inside, as well as outside of, this cylinder. The results showed that a plastic zone around a crack tip was stable.

C.F.Qian, K.Li, H.Chen, J.C.M.Li: Mechanics of Materials, 1996, 24[3], 221-7