An analytical expression for the force between 2 parallel screw dislocations, which had been derived on the basis of the gauge theory of dislocations, was used here to investigate the static distribution of a given number of parallel screw dislocations which were confined between 2 immobile dislocation obstacles. It was shown that, in the limit of a continuous distribution of dislocations, the equilibrium condition led to a Fredholm integral equation of the first type which did not have any non-trivial solution. For a finite number of dislocations, the ratio of the obstacle separation to the core radius was an important parameter, and governed the nature of the solution to the discrete equation. It was found that, for a given number of dislocations as above, there was a critical value below which no solution existed.

Force Between Two Parallel Screw Dislocations and Application to Linear Screw-Dislocation Pile-Ups – Gauge-Theory Results. M.C.Valsakumar, D.Sahoo, S.Kanmani: Bulletin of Materials Science, 1997, 20[4], 601-5