Effective dislocation lines in continuously dislocated crystals. III. Kinematics

TL;DR

This paper investigates the kinematics of continuously dislocated crystals using dislocation density tensors, establishing consistency with plasticity theories and providing a mathematical framework for effective dislocation lines.

Contribution

It introduces a class of dislocation line congruences and links their kinematics to physical plasticity relations, advancing the theoretical understanding of dislocated crystal behavior.

Findings

Dislocation line congruences are characterized in terms of density tensors.

The kinematics aligns with Orowan-type relations in plasticity.

Mean curvature of glide surfaces relates to dislocation motion.

Abstract

A class of congruences of principal Volterra-type effective dislocation lines associated with a dislocation density tensor is distinguished in order to investigate the kinematics of continuized defective crystals in terms of their dislocation densities (tensorial as well as scalar). Moreover, it shown, basing oneself on a formula defining the mean curvature of glide surfaces for principal edge effective dislocation lines, that the considered kinematics of continuized defective crystals is consistent with some relations appearing in the physical theory of plasticity (e.g. with the Orowan-type kinematic relations and with the treatment of shear stresses as driving stresses of moving dislocations).