Asymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundary

Handle URI:
http://hdl.handle.net/10754/597622
Title:
Asymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundary
Authors:
Hall, Cameron L.
Abstract:
In 1965, Armstrong and Head explored the problem of a pile-up of screw dislocations against a grain boundary. They used numerical methods to determine the positions of the dislocations in the pile-up and they were able to fit approximate formulae for the locations of the first and last dislocations. These formulae were used to gain insights into the Hall-Petch relationship. More recently, Voskoboinikov et al. used asymptotic techniques to study the equivalent problem of a pile-up of a large number of screw dislocations against a bimetallic interface. In this paper, we extend the work of Voskoboinikov et al. to construct systematic asymptotic expressions for the formulae proposed by Armstrong and Head. The further extension of these techniques to more general pile-ups is also outlined. As a result of this work, we show that a pile-up against a grain boundary can become equivalent to a pile-up against a locked dislocation in the case where the mismatch across the boundary is small. © 2010 Taylor & Francis.
Citation:
Hall CL (2010) Asymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundary. Philosophical Magazine 90: 3879–3890. Available: http://dx.doi.org/10.1080/14786435.2010.499859.
Publisher:
Informa UK Limited
Journal:
Philosophical Magazine
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
14-Oct-2010
DOI:
10.1080/14786435.2010.499859
Type:
Article
ISSN:
1478-6435; 1478-6443
Sponsors:
This publication is based on work supported by Award No. KUK-C1-013-04, made by the King Abdullah University of Science and Technology (KAUST). I would like to acknowledge the contributions of John R. Ockendon (Oxford), S. Jonathan Chapman (Oxford), Roman E. Voskoboynikov (Kurchatov) and Graeme C. Wake (Massey), with whom I discussed various aspects of this work.
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Full metadata record

DC FieldValue Language
dc.contributor.authorHall, Cameron L.en
dc.date.accessioned2016-02-25T12:43:13Zen
dc.date.available2016-02-25T12:43:13Zen
dc.date.issued2010-10-14en
dc.identifier.citationHall CL (2010) Asymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundary. Philosophical Magazine 90: 3879–3890. Available: http://dx.doi.org/10.1080/14786435.2010.499859.en
dc.identifier.issn1478-6435en
dc.identifier.issn1478-6443en
dc.identifier.doi10.1080/14786435.2010.499859en
dc.identifier.urihttp://hdl.handle.net/10754/597622en
dc.description.abstractIn 1965, Armstrong and Head explored the problem of a pile-up of screw dislocations against a grain boundary. They used numerical methods to determine the positions of the dislocations in the pile-up and they were able to fit approximate formulae for the locations of the first and last dislocations. These formulae were used to gain insights into the Hall-Petch relationship. More recently, Voskoboinikov et al. used asymptotic techniques to study the equivalent problem of a pile-up of a large number of screw dislocations against a bimetallic interface. In this paper, we extend the work of Voskoboinikov et al. to construct systematic asymptotic expressions for the formulae proposed by Armstrong and Head. The further extension of these techniques to more general pile-ups is also outlined. As a result of this work, we show that a pile-up against a grain boundary can become equivalent to a pile-up against a locked dislocation in the case where the mismatch across the boundary is small. © 2010 Taylor & Francis.en
dc.description.sponsorshipThis publication is based on work supported by Award No. KUK-C1-013-04, made by the King Abdullah University of Science and Technology (KAUST). I would like to acknowledge the contributions of John R. Ockendon (Oxford), S. Jonathan Chapman (Oxford), Roman E. Voskoboynikov (Kurchatov) and Graeme C. Wake (Massey), with whom I discussed various aspects of this work.en
dc.publisherInforma UK Limiteden
dc.subjectasymptotic analysisen
dc.subjectdislocation interactionsen
dc.subjectdislocation theoryen
dc.subjectgrain boundariesen
dc.titleAsymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundaryen
dc.typeArticleen
dc.identifier.journalPhilosophical Magazineen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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