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  4. On notch and crack size effects in fatigue, Paris’ law and implications for Wöhler curves
 
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On notch and crack size effects in fatigue, Paris’ law and implications for Wöhler curves

Citation Link: https://doi.org/10.15480/882.2124
Publikationstyp
Journal Article
Date Issued
2018-04-01
Sprache
English
Author(s)
Ciavarella, Michele  
Papangelo, Antonio 
Institut
Strukturdynamik M-14  
TORE-DOI
10.15480/882.2124
TORE-URI
http://hdl.handle.net/11420/2207
Journal
Frattura ed integrità strutturale  
Volume
12
Issue
44
Start Page
49
End Page
63
Citation
Frattura ed Integrita Strutturale 44 (12): 49-63 (2018-04-01)
Publisher DOI
10.3221/IGF-ESIS.44.05
Scopus ID
2-s2.0-85045752468
As often done in design practice, the Wöhler curve of a specimen, in the absence of more direct information, can be crudely retrieved by interpolating with a power-law curve between static strength at a given conventional low number of cycles N0(of the order of 10-103), and the fatigue limit at a “infinite life”, also conventional, typically N∞=2·106or N∞=107cycles. These assumptions introduce some uncertainty, but otherwise both the static regime and the infinite life are relatively well known. Specifically, by elaborating on recent unified treatments of notch and crack effects on infinite life, and using similar concepts to the static failure cases, an interpolation procedure is suggested for the finite life region. Considering two ratios, i.e. toughness to fatigue threshold FK=KIc/∆Kth, and static strength to endurance limit, FR=σR/∆σ0, qualitative trends are obtained for the finite life region. Paris’ and Wöhler’s coefficients fundamentally depend on these two ratios, which can be also defined “sensitivities” of materials to fatigue when cracked and uncracked, respectively: higher sensitivity means stringent need for design for fatigue. A generalized Wöhler coefficient, k’, is found as a function of the intrinsic Wöhler coefficient k of the material and the size of the crack or notch. We find that for a notched structure, k<k’<m, as a function of size of the notch: in particular, k’=k holds for small notches, then k’ decreases up to a limiting value (which depends upon Ktfor mildly notched structures, or on FKand FRonly for severe notch or crack). A perhaps surprising return to the original slope k is found for very large blunt notches. Finally, Paris’ law should hold for a distinctly cracked structure, i.e. having a long-crack; indeed, Paris’ coefficient m is coincident with the limiting value of k’lim. The scope of this note is only qualitative and aims at a discussion over unified treatments in fatigue.
Subjects
Fatigue
Wöhler curve
Notch Sensitivity
Paris’ law
Ashby maps
DDC Class
600: Technik
Lizenz
https://creativecommons.org/licenses/by/4.0/
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