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Elasto-plastic evolution of single crystals driven by dislocation flow
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Hudson, Thomas E. (Edward) and Rindler, Filip (2022) Elasto-plastic evolution of single crystals driven by dislocation flow. Mathematical Models and Methods in Applied Sciences, 32 (5). pp. 851-910. doi:10.1142/S0218202522500191 ISSN 0218-2025.
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WRAP-elasto-plastic-evolution-single-crystals-driven-dislocation-flow-2022.pdf - Accepted Version - Requires a PDF viewer. Download (1149Kb) | Preview |
Official URL: https://doi.org/10.1142/S0218202522500191
Abstract
This work introduces a model for large-strain, geometrically nonlinear elasto-plastic dynamics in single crystals. The key feature of our model is that the plastic dynamics are entirely driven by the movement of dislocations, that is, 1-dimensional topological defects in the crystal lattice. It is well known that glide motion of dislocations is the dominant microscopic mechanism for plastic deformation in many crystalline materials, most notably in metals. We propose a novel geometric language, built on the concepts of space-time “slip trajectories” and the “crystal scaffold” to describe the movement of (discrete) dislocations and to couple this movement to plastic flow. The energetics and dissipation relationships in our model are derived from first principles drawing on the theories of crystal modeling, elasticity, and thermodynamics. The resulting force balances involve a new configurational stress tensor describing the forces acting against slip. In order to place our model into context, we further show that it recovers several laws that were known in special cases before, most notably the equation for the Peach–Koehler force (linearized configurational force) and the fact that the combination of all dislocations yields the curl of the plastic distortion field. Finally, we also include a brief discussion on how a number of other effects, such as hardening, softening, dislocation climb, and coarse-graining, could be incorporated into our model.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QD Chemistry T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Elastoplasticity, Crystals -- Structure, Dislocations in crystals | ||||||||
| Journal or Publication Title: | Mathematical Models and Methods in Applied Sciences | ||||||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||||
| ISSN: | 0218-2025 | ||||||||
| Official Date: | May 2022 | ||||||||
| Dates: |
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| Volume: | 32 | ||||||||
| Number: | 5 | ||||||||
| Page Range: | pp. 851-910 | ||||||||
| DOI: | 10.1142/S0218202522500191 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | Electronic version of an article published as Mathematical Models and Methods in Applied Sciences,32(5) 2022, 851-910 https://doi.org/10.1142/S0218202522500191 © 2022 World Scientific Publishing Co Pte Ltd https://www.worldscientific.com/worldscinet/m3as | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 15 February 2022 | ||||||||
| Date of first compliant Open Access: | 12 April 2023 | ||||||||
| RIOXX Funder/Project Grant: |
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