Continuum Dislocation Dynamics Based on the Second Order Alignment Tensor. Issue 1651 (14th January 2014)

• Record Type: Journal Article
• Authors: Hochrainer, Thomas
• Is Part Of: MRS proceedings. Issue 1651:(2014)
• Publication Date: 2014-01-14
• Subjects: dislocations, -- microstructure, -- metal; Electrical engineering -- Congresses; Physics -- Congresses; Materials -- Research -- Congresses; Materials science -- Congresses; 620.11
• DOI: 10.1557/opl.2014.53
• Languages: English
• ISSNs: 0272-9172

Abstract

ABSTRACT: In the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order alignment tensor is a symmetric second order tensor characterizing the orientation distribution of dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions but handle line length changes and segment reorientation consistently. We demonstrate that the presented equations allow predicting the evolution of a single dislocation loop in a non-trivial velocity field.