Interaction and passing stress of two threading dislocations of opposite sign in a confined channel

The binding and unbinding of two threading dislocations in a channel of width d is considered in the context of the persistent slip band (PSB) problem. It is shown that previous analytical estimates of the overall passing stress between two screw-like threading arms have only qualitative validity. In particular, earlier treatments do not recognize the importance of bowing corrections in all limits, and neglect the effects of the opposing dislocation's misfit arms on the passing stress. As an alternative, accurate numerical escape functions are presented for the case of d?=?1?µm, in a form suitable for approximate scaling to other values of d. Although the numerical prediction for the overall passing stress is in good agreement with experimental values of the flow stress observed in the presence of PSBs, we argue that this in fact represents a disagreement, since it is well known that the flow stress in the soft-channel parts of the inhomogeneous PSB structure is reduced by long-range internal back stresses to values significantly below the average macroscopic flow stress of the PSB structure. We suggest that a statistical treatment including the effects of annihilation and of dislocations interacting over a range of separations can account for the discrepancy.