PSI - Issue 75

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

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1. Introduction 1.1. General issue

In the cableway installations sector, the Eurocodes, in particular EN 1993-1-9 (CEN/TC 250, 2005) are commonly used to assess the service life of safety components (see EN 13796-1 (CEN/TC 242, 2017), and EN 13107 (CEN/TC 242, 2015)). That is why the fatigue study for CE certification of cableway’s safety components is mainly carried out with a uniaxial fatigue approach. This methodology (see §1.2) is generally relevant for ski-lift carriers (in particular for structures resulting from beams assembly), however some rosettes may exhibit significant multiaxial stresses and/or high average compressive/tensile stress that may not be accurately considered in the Eurocode to predict life expectancy. That is why for such cases, multiaxial fatigue approach such as FKM Method (see §1.3) or Dang Van type criterion methods (see §1.4) should be performed to evaluate lifetime of cableways component. However, perform a multiaxial fatigue analysis such as Dang Van or FKM is way more technical than applying a basic uniaxial fatigue analysis according to EN 1993-1-9:2005. Before deciding to apply such complex analysis, is there a way to quickly determine whether and how taking into account multiaxiality will reduce (or enhance) life time compared to Eurocode? Before addressing this question, we briefly recall the principles of uniaxial and multiaxial fatigue lifetime evaluation with Eurocode (also noted EN 1993-1-9:2005), FKM and Dang Van criterion methods. Nomenclature N E fatigue life in number of cycles, assessed in uniaxial fatigue using Eurocode 3 (EN1993-1-9:2005). N DV fatigue life in number of cycles, assessed using multiaxial fatigue with the Dang Van criterion (*) . N DVcharts fatigue life in number of cycles, assessed using multiaxial fatigue with charts (abacuses) proposed in this paper with Dang Van criterion (*) . (*) see Causse et al. (2024) : Dang Van criterion calibrated in R =  min /  max = 0 with S-N curves from Eurocode 3 (EN1993-1-9:2005)  R stress amplitude during a harmonic loading cycle.  stress range during a harmonic loading cycle   =  R =  max -  min  m Average stress (also called mean stress) R Ratio : R = (  min )/(  max ) = (  m -  R ) / (  m +  R ),  C Detail category according to EN 1993-1-9:2005 (Eurocode 3): refers to the maximum stress range with a 75% confidence level and 95% probability of survival at 2×10 6 cycles taking into account the standard deviation, sample size and residual stress effects (see NOTE 1 under Figure 7.2 of EN 1993-1-9:2005). A Stress tensor matrix in the biaxial case, in the fixed reference frame of the rosette (Oxy)  I,   Principal stress I and II in a biaxial signal, with  I >   D Stress tensor matrix in the biaxial case, in the eigen reference frame (O ; σ I⃗⃗⃗ /||  I ||; σ II⃗⃗⃗⃗ /||  II ||) with a rotation of angle  with respect to (Oxy). P Transformation matrix from A to D (rotation matrix with an angle ) .

1.2. Eurocode uniaxial Fatigue lifetime evaluation Fatigue lifetime evaluation with Eurocode lies on the application of generalized Wöhler curves or S-N curves giving the maximum cyclic stress range against the number of cycles to failure for various constructional details (  C ) such as rolled, bolted or welded steel section connections (see tables 8.1 and 8.2 of EN 1993-1-9 (CEN/TC 250, 2005). Eurocode S-N curves are defined by equations (1a) and (1b), and service life (N E ) can be evaluated as shown below: