Non-singular screw dislocations as the Coulomb gas with smoothed out coupling and the renormalization of the shear modulus

TL;DR

This paper develops a field theory for non-singular screw dislocations in elastic cylinders, showing their equivalence to a Coulomb gas and analyzing how dislocation cores modify shear modulus renormalization.

Contribution

It introduces a gauge-translational model for non-singular screw dislocations and demonstrates their equivalence to a Coulomb gas with smoothed coupling, including effects on shear modulus.

Findings

Dislocations are equivalent to a 2D Coulomb gas with smoothed potential.

Finite dislocation cores modify the shear modulus renormalization law.

Two-point stress correlation functions are derived.

Abstract

A field theory is developed for a thermodynamical description of array of parallel non-singular screw dislocations in elastic cylinder. The partition function of the system is considered in the functional integral form. Self-energy of the dislocation cores is chosen in the form suggested by the gauge-translational model of non-singular screw dislocation. It is shown that the system of the dislocations is equivalent to the two-dimensional Coulomb gas. The coupling potential is prevented from a short-distance divergency since the core energies are taken into account. Two-point correlation functions of the stress components are obtained. Renormalization of the shear modulus caused by the presence of the dislocations is studied in the approximation of non-interacting dislocation dipoles. It is demonstrated that the finite size of the dislocation cores results in a modification of the renormalization law.