Driving Forces and Boundary Conditions in Continuum Dislocation Mechanics

TL;DR

This paper develops a continuum dislocation mechanics framework by deriving driving forces, boundary conditions, and analyzing dislocation behaviors like bowing and cross-slip, providing exact solutions and insights into microstructure evolution.

Contribution

It introduces a comprehensive field theory for dislocation mechanics, including new boundary conditions and exact solutions for dislocation evolution.

Findings

Derived driving forces for dislocation velocity and nucleation.

Established boundary conditions for dislocation density.

Provided exact solutions for polygonal loop expansion.

Abstract

As a guide to constitutive specification, driving forces for dislocation velocity and nucleation rates are derived for a field theory of dislocation mechanics. A condition of closure for the theory in the form of a boundary condition for dislocation density is also derived. Kinematical features of dislocation evolution like initiation of bowing of a pinned screw segment, and initiation of cross-slip of a screw segment are discussed. An exact solution for the expansion of a polygonal loop as well as representation within the theory of dislocation level Schmid and non-Schmid behavior, and unloaded stress-free and steady microstructures are also discussed.