Uniform distribution of dislocations in Peierls–Nabarro models for semi-coherent interfaces

Fanzon, Silvio; Ponsiglione, Marcello; Scala, Riccardo

Abstract

In this paper we introduce Peierls–Nabarro type models for edge dislocations at semi-coherent interfaces between two heterogeneous crystals, and prove the optimality of uniformly distributed edge dislocations. Specifically, we show that the elastic energy Γ -converges to a limit functional comprised of two contributions: one is given by a constant c∞> 0 gauging the minimal energy induced by dislocations at the interface, and corresponding to a uniform distribution of edge dislocations; the other one accounts for the far field elastic energy induced by the presence of further, possibly not uniformly distributed, dislocations. After assuming periodic boundary conditions and formally considering the limit from semi-coherent to coherent interfaces, we show that c∞ is reached when dislocations are evenly-spaced on the one dimensional circle.

Citation

Fanzon, S., Ponsiglione, M., & Scala, R. (2020). Uniform distribution of dislocations in Peierls–Nabarro models for semi-coherent interfaces. Calculus of Variations and Partial Differential Equations, 59(4), Article 141. https://doi.org/10.1007/s00526-020-01787-5

• Journal Article Type: Article
• Acceptance Date: May 31, 2020
• Online Publication Date: Aug 9, 2020
• Publication Date: Aug 1, 2020
• Deposit Date: May 9, 2023
• Publicly Available Date: May 15, 2023
• Journal: Calculus of Variations and Partial Differential Equations
• Print ISSN: 0944-2669
• Electronic ISSN: 1432-0835
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 59
• Issue: 4
• Article Number: 141
• DOI: https://doi.org/10.1007/s00526-020-01787-5
• Public URL: https://hull-repository.worktribe.com/output/4271010