F. Berto, Frattura ed Integrità Strutturale, 34 (2015) 169-179; DOI: 10.3221/IGF-ESIS.34.18 177 creating an additional stress concentration effect linked to the nominal stress component parallel to the notch inclination angle . Finally it is worth mentioning that another consistent approach for mixed-mode loading is based on the strain energy density (SED) averaged on a defined control volume [35]. This approach has been successfully used to assess the static behaviour of notched plates made of brittle material as well as the high-cycle fatigue strength of welded joints. In the presence of pointed notches subjected to mixed mode 1–2 loading conditions, the control volume (a semicircular sector under plane strain or plane stress conditions) is introduced as constant, at first for mode 1 loading conditions. In the case of blunt U- or V-notches, the crescent shape control volume is rigidly rotated with respect to the notch bisector line and centred in the point of maximum tangential stress (or maximum strain energy density) on the notch edge resulting in an ‘equivalent’ mode 1 loading condition. One of the main advantages of the average SED approach is that it can be applied using coarse meshes. 2α (°) β (°) M 0 (°) s ρ* (mm) ρ f (mm) t K Eq.(28) K t (ρ f ) FEM Δ (%) 45 15 0.272 0.169 –13.50 2.56 0.05 0.128 16.90 16.93 0.17 0.1 0.256 12.06 12.57 4.07 0.2 0.511 8.61 9.24 6.86 0.3 0.767 7.07 7.81 9.47 30 0.592 0.340 –25.73 3.16 0.05 0.158 14.62 14.73 0.75 0.1 0.316 10.58 10.92 3.11 0.2 0.631 7.67 8.18 6.28 0.3 0.947 6.36 6.97 8.79 45 1.053 0.516 –36.52 4.24 0.05 0.212 11.08 11.19 0.99 0.1 0.424 8.18 8.56 4.48 0.2 0.848 6.05 6.65 9.03 Table 2 : FNR results for mixed mode loading conditions; normal stress failure criterion combined with the MTS criterion for 0 ; different values of the microstructural support length * and the mode ratio M. C ONCLUSIONS ased on FNR concept used in combination with the normal stress criterion for the averaged notch stress and the maximum tangential stress criterion for the crack propagation angle, the support factor has been analytically and numerically determined for V-notches with root hole subjected to in-plane mixed mode loading. A suitable definition and quantification of the mode ratio for pointed V-notches has been found. Taking advantage of a recently conceived analytical frame for V-notches with root hole, the original Neuber procedure for determining the fictitious notch radius and the support factor has been applied to out-of-bisector crack propagation, the propagation direction being determined by the maximum tangential stress criterion as a function of the mode ratio and the notch opening angle. Different values of this length, of the notch depth and of the notch opening angle have been considered as well as different mode ratios. The obtained values of the support factor are well suited for engineering usage in structural strength assessments. The relative deviations have been found variable from case to case. A large set of cases have been found to be characterized by relative deviations less than 10%, directly using the original Neuber’s procedure. R EFERENCES [1] Neuber, H., Kerbspannungslehre, 2nd edn, Springer-Verlag, Berlin, (1958). [2] Neuber, H., Űber die Berücksichtigung der Spannungskonzentration bei Festigkeitsberechnungen. Konstruktion, 20 (1968) 245-251. B

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