FORCE BETWEEN 2 PARALLEL SCREW DISLOCATIONS AND APPLICATION TO LINEARSCREW DISLOCATION PILEUPS - GAUGE-THEORY RESULTS

An analytic expression for the force between two parallel screw disloc ations, derived earlier on the basis of the gauge theory of dislocatio ns, has been used to investigate the static distribution of a given nu mber N of parallel screw dislocations confined between two immobile di slocation obstacles. It is shown that in the limit of a continuous dis tribution of dislocations the equilibrium condition leads to a Fredhol m integral equation of first type which does not admit any nontrivial solution. Implication of this result is discussed. For a finite number of dislocations, the ratio (eta) of the obstacle separation to the co re radius is an important parameter governing the nature of solution o f the discrete equation. It is found that for a given N, there is a cr itical value eta(c) below which there does not exist any solution.