Dislocation transport and line length increase in averaged descriptions of dislocations

TL;DR

This paper develops a continuum model for dislocation dynamics using a higher dimensional dislocation density tensor, bridging microscopic and mesoscopic scales in crystal plasticity.

Contribution

It introduces evolution equations for total dislocation density and average curvature, simplifying dislocation kinematics without extra dimensions.

Findings

Derived evolution equations accurately represent dislocation kinematics.

Bridged gap between microscopic simulations and continuum models.

Enhanced understanding of dislocation behavior in crystal plasticity.

Abstract

Crystal plasticity is the result of the motion and interaction of dislocations. There is, however, still a major gap between microscopic and mesoscopic simulations and continuum crystal plasticity models. Only recently a higher dimensional dislocation density tensor was defined which overcomes some drawbacks of earlier dislocation density measures. The evolution equation for this tensor can be considered as a continuum version of dislocation dynamics. We use this evolution equation to develop evolution equations for the total dislocation density and an average curvature which together govern a faithful representation of the dislocation kinematics without having to use extra dimensions.