Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock
A mathematical methodology for analysing pile-ups of large numbers of dislocations is described. As an example, the pile-up of n identical screw or edge dislocations in a single slip pane under the action of an external force in the direction of a locked dislocation in that plane is considered. As $...
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| Format: | Journal article |
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2007
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| _version_ | 1797073663871156224 |
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| author | Ockendon, J Voskoboinikov, R Chapman, S |
| author_facet | Ockendon, J Voskoboinikov, R Chapman, S |
| author_sort | Ockendon, J |
| collection | OXFORD |
| description | A mathematical methodology for analysing pile-ups of large numbers of dislocations is described. As an example, the pile-up of n identical screw or edge dislocations in a single slip pane under the action of an external force in the direction of a locked dislocation in that plane is considered. As $n \rightarrow \infty$ there is a well-known formula for the number density of the dislocations, but this density is singular at the lock and it cannot predict the stress field there or the force on the lock. This poses the interesting analytical and numerical problem of matching a local discrete model near the lock to the continuum model further away. |
| first_indexed | 2024-03-06T23:25:17Z |
| format | Journal article |
| id | oxford-uuid:6a2a24d6-8195-4321-ab39-cd4de63f3ec7 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:25:17Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:6a2a24d6-8195-4321-ab39-cd4de63f3ec72022-03-26T18:55:40ZContinuum and discrete models of dislocation pile-ups. I Pile-up at a lockJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6a2a24d6-8195-4321-ab39-cd4de63f3ec7Mathematical Institute - ePrints2007Ockendon, JVoskoboinikov, RChapman, SA mathematical methodology for analysing pile-ups of large numbers of dislocations is described. As an example, the pile-up of n identical screw or edge dislocations in a single slip pane under the action of an external force in the direction of a locked dislocation in that plane is considered. As $n \rightarrow \infty$ there is a well-known formula for the number density of the dislocations, but this density is singular at the lock and it cannot predict the stress field there or the force on the lock. This poses the interesting analytical and numerical problem of matching a local discrete model near the lock to the continuum model further away. |
| spellingShingle | Ockendon, J Voskoboinikov, R Chapman, S Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock |
| title | Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock |
| title_full | Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock |
| title_fullStr | Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock |
| title_full_unstemmed | Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock |
| title_short | Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock |
| title_sort | continuum and discrete models of dislocation pile ups i pile up at a lock |
| work_keys_str_mv | AT ockendonj continuumanddiscretemodelsofdislocationpileupsipileupatalock AT voskoboinikovr continuumanddiscretemodelsofdislocationpileupsipileupatalock AT chapmans continuumanddiscretemodelsofdislocationpileupsipileupatalock |