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A Parabolic Notch Interacting With a Generalized Antiplane Singularity

Ma, Lifeng; Chen, Yifeng; Hills, David A.


Sir Joseph Pope Fellowship

Yifeng Chen

David A. Hills


In this study, the interaction of a parabolic notch with a generalized antiplane singularity is studied, and its analytical solution is derived. The singularity may be either an antiplane concentrated force or a screw dislocation, and separate solutions for each of these are found. The driving force present on the screw dislocation due to the notch free boundary is obtained. It is found that a dislocation-free zone may exist beneath the notch root surface when the screw dislocation is placed on the notch geometric symmetry axis, as the driving force will pull dislocations to the free boundary where they will be annihilated. The solutions developed in this study may be used as building blocks to model the damage of material near a parabolic notch under antiplane load conditions and therefore serve as a step in quantifying crack nucleation conditions, which is the novelty of the current study.


Ma, L., Chen, Y., & Hills, D. A. (2022). A Parabolic Notch Interacting With a Generalized Antiplane Singularity. Journal of Applied Mechanics, 89(9), Article 091001.

Journal Article Type Article
Acceptance Date Jun 18, 2022
Online Publication Date Jul 19, 2022
Publication Date Sep 1, 2022
Deposit Date Jul 29, 2022
Journal Journal of Applied Mechanics
Print ISSN 0021-8936
Electronic ISSN 1528-9036
Publisher ASME International
Peer Reviewed Peer Reviewed
Volume 89
Issue 9
Article Number 091001
Keywords Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics
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