Force between two parallel screw dislocations and application to linear screw dislocation pileups - gauge theory results

Abstract

An analytic expression for the force between two parallel screw dislocations, derived earlier on the basis of the gauge theory of dislocations, has been used to investigate the static distribution of a given number N of parallel screw dislocations confined between two immobile dislocation obstacles. It is shown that in the limit of a continuous distribution of dislocations the equilibrium condition leads to a Fredholm 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 (η) of the obstacle separation to the core radius is an important parameter governing the nature of solution of the discrete equation. It is found that for a given N, there is a critical value ηc below which there does not exist any solution.