PSI - Issue 75

Benjamin Causse et al. / Procedia Structural Integrity 75 (2025) 205–218 Author name / Structural Integrity Procedia (2025)

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Table 1. Data table results : loadings angle variation influence on service life according to Dang Van compared with Eurocodes

N DV *

N DV / N E **

N DV *

N DV / N E **

N DV *

N DV / N E **

 max [°]

 max [°]

 max [°]

1.00 0.99 0.94 0.88 0.80 0.71

0.62 0.53 0.45 0.38 0.32 0.27

0,23 0,20 0,18 0,17 0,16

0 5

1 023 999 1 008 992

30 35 40 45 50 55

631 945 542 256 459 914 387 131 324 943 273 510

60 65 70 75 80

234 732 207 057 187 337 173 554 164 456 159 281 / 157597

10 15 20 25

965 694 899 217 816 510 725 178

0,16 / 0,15

85 / 90

* Dang Van lifetime calculation with R 0 calibration and EN 1993-1-9:2005 ’s S -N curves, see Causse et al. 2024. ** with N E = 1 024 000 (considering  C = 160, and  = 2  R = 200 MPa, according to EN 1993-1-9:2005).

It can be seen that the variation in angle  of the main directions during the cycle has very little impact as long as  is less than 10°. The reduction in service life is then negligible, since the number of cycles calculated using the Dang Van criterion (N DV ) reaches 94% of the number of cycles (N E ) calculated according to the Eurocode (uniaxial). For a variation in angle  = 20°, then N DV = 80%×N E : service life falls by 20% in biaxial fatigue compared with uniaxial analysis. For  = 45°, then N DV = 38%×N E : the service life is then significantly reduced N DV = 38%×N E For  θ ≥ 37°, N DV ≤ 50×N E : Dang Van's lifespan has already been halved and is now falling rapidly in relation to the Eurocodes. For  θ ≥ 60°, N DV ≤ 20%×N E : Dang Van's service life falls below 20% of the Eurocodes service life, and tends towards 15% only for  θ = 90°. For  θ ≥ 90°, if the loading goes directly from 0° to  max , the lifetime is the same as for the case  =180°-  max but this is a theoretical case which is generally not applicable (For example N DV (100°) would be equal to N DV (80°)). If the loading continues to evolve until  max ≥ 90°, in a continuous manner (i.e. passing through the value  =180°-  =90° and then higher continuously), which is more realistic experimentally, then N DV ( ≥ 90°) = N DV (90°) : the number of cycles reaches the limit N DV = 15%×N E .