Mode I fatigue limit of notched structures: A deeper insight into Finite Fracture Mechanics
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ORIGINAL PAPER
Mode I fatigue limit of notched structures: A deeper insight into Finite Fracture Mechanics Alberto Sapora · Pietro Cornetti · Alberto Campagnolo · Giovanni Meneghetti
Received: 17 May 2020 / Accepted: 24 September 2020 © The Author(s) 2020
Abstract In the present contribution, the coupled stress-energy criterion of Finite Fracture Mechanics (FFM) is applied to assess the fatigue limit of structures weakened by sharp V- and U-notches and subjected to mode I loading conditions. The FFM is a critical-distance-based approach whose implementation requires the knowledge of two material properties, namely the plain material fatigue limit and the threshold value of the stress intensity factor (SIF) range for the fatigue crack growth of long cracks. However, the FFM critical distance is a structural parameter, being a function not only of the material but also of the geometry of the notched component. Experimental notch fatigue results taken from the literature and referred to a variety of materials and geometrical configurations are compared with FFM theoretical estimations, obtained through simple semi-analytical relationships. The case of semi-circular edge notches is also dealt with. Keywords Finite Fracture Mechanics · Fatigue limit · Mode I · U-notch · V-notch · Edge crack
A. Sapora (B)· P. Cornetti Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy e-mail: [email protected] A. Campagnolo · G. Meneghetti Department of Industrial Engineering, University of Padova, Via Venezia, 1, 35131 Padova, Italy
Nomenclature a a0 a¯ a0V c K tg K th V K I,th
KI K IV K IU lc l¯c lth n R Y
notch depth El Haddad-Smith-Topper length parameter of the material dimensionless notch/crack depth, a¯ = a/lth parameter accounting for sensitivity to “small” V-notches length of a crack stemming from the notch tip elastic stress concentration factor referred to the gross section of the specimen threshold value of the mode I SIF range for long cracks threshold value of the mode I NSIF range for deep notches mode I stress intensity factor of a crack mode I notch stress intensity factor of a sharp V-notch mode I notch stress intensity factor of a Unotch finite crack advance according to FFM dimensionless crack advance threshold crack length fitting parameter in the SIF expressions related to U- and semicircular notches notch tip radius shape functions related to the SIFs for Uand semicircular notches
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Symbols β ζ λ μ ξ σ0 σ f ψ ω
concepts have been adopted in the technical literature to assess their fatigue strength behaviour: shape factor to determine the notch stress intensity factor of sharp V-notched components notch acuity, ζ = a/R first eigenvalue in Williams’ equations referred to pure mode I loading coefficient linking the SIF of a crack and the NSIF of the sharp V-notch from whose tip the crack is stemming notch amplitude depending parameter linking K IV to the material properties plain material fat
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