Situating the Vector Density Approach Among Contemporary Continuum Theories of Dislocation Dynamics

Anderson, Joseph Pierre; Vivekanandan, Vignesh; Lin, Peng; Starkey, Kyle; Pachaury, Yash; El-Azab, Anter

doi:10.1115/1.4052066

Situating the Vector Density Approach Among Contemporary Continuum Theories of Dislocation Dynamics

Journal Article · Mon Aug 30 04:00:00 EDT 2021 · Journal of Engineering Materials and Technology

DOI:https://doi.org/10.1115/1.4052066· OSTI ID:1980668

Anderson, Joseph Pierre ^[1]; Vivekanandan, Vignesh; Lin, Peng; Starkey, Kyle; Pachaury, Yash; El-Azab, Anter

OSTI

Abstract

For the past century, dislocations have been understood to be the carriers of plastic deformation in crystalline solids. However, their collective behavior is still poorly understood. Progress in understanding the collective behavior of dislocations has primarily come in one of two modes: the simulation of systems of interacting discrete dislocations and the treatment of density measures of varying complexity that are considered as continuum fields. A summary of contemporary models of continuum dislocation dynamics is presented. These include, in order of complexity, the two-dimensional statistical theory of dislocations, the field dislocation mechanics treating the total Kröner–Nye tensor, vector density approaches that treat geometrically necessary dislocations on each slip system of a crystal, and high-order theories that examine the effect of dislocation curvature and distribution over orientation. Each of theories contain common themes, including statistical closure of the kinetic dislocation transport equations and treatment of dislocation reactions such as junction formation. An emphasis is placed on how these common themes rely on closure relations obtained by analysis of discrete dislocation dynamics experiments. The outlook of these various continuum theories of dislocation motion is then discussed.

Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0017718

OSTI ID:: 1980668

Journal Information:: Journal of Engineering Materials and Technology, Journal Name: Journal of Engineering Materials and Technology Journal Issue: 1 Vol. 144; ISSN 0094-4289

Publisher:: ASME

Country of Publication:: United States

Language:: English

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