Near edge tractions for a rounded quarter-plane pressed into an elastically similar half-plane

Eames, Beth; Hills, David; Moore, Madeleine

Abstract

Asymptotic forms are a useful way of representing the state of stress at a contact edge, allowing us to characterise the region in which cracks nucleate. The asymptotes must match the behaviour implied by the local geometry. In this paper, we study the behaviour of a flat contact with a circular arced edge (i.e. a flat and rounded contact); a geometry that has extensive applications. We show explicitly how the very convenient closed-form solution for this problem, derived from half-plane theory, may be collocated into the more realistic three-quarter plane far field solution, obtained from Williams’ solution. This provides a closed-form representation of the edge, correctly geared to the far-field solution, for the first time.

Citation

Eames, B., Hills, D., & Moore, M. (2023). Near edge tractions for a rounded quarter-plane pressed into an elastically similar half-plane. Tribology International, Article 108582. https://doi.org/10.1016/j.triboint.2023.108582

• Journal Article Type: Article
• Acceptance Date: May 5, 2023
• Online Publication Date: May 10, 2023
• Publication Date: Aug 1, 2023
• Deposit Date: May 16, 2023
• Publicly Available Date: May 18, 2023
• Journal: Tribology International
• Print ISSN: 0301-679X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Article Number: 108582
• DOI: https://doi.org/10.1016/j.triboint.2023.108582
• Keywords: Slightly rounded contacts; Asymptotes for contact edges; Conforming contacts with rounded edges; Fretting fatigue
• Public URL: https://hull-repository.worktribe.com/output/4291260