A Parabolic Notch Interacting With a Generalized Antiplane Singularity

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

Abstract

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.

Citation

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. https://doi.org/10.1115/1.4054865

• 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
• DOI: https://doi.org/10.1115/1.4054865
• Keywords: Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics
• Public URL: https://nottingham-repository.worktribe.com/output/9409340
• Publisher URL: https://asmedigitalcollection.asme.org/appliedmechanics/article-abstract/89/9/091001/1141846/A-Parabolic-Notch-Interacting-With-a-Generalized?redirectedFrom=fulltext