PSI - Issue 75

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

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an average on amplitude stress ratio  m /  R =1.6 (see Figure 6 (b)). We were able to deduce from this by reading the charts N DV  /N E =0.73 (see Fig. 4) and N DV  /N E =0.64 (see Figure 5). Finally, we propose to evaluate N DVcharts by considering the combined influence of angle variation (  max ), form biaxiality (k=   /   ) and average stress on signal amplitude (  m /  R ) : N DVcharts /N E = N DV  /N E × N DV  /N E (see Table 2). Table 2. Number of Survival Cycles (N) on the hoop (J2, LC2,  C 160), according to Eurocode and Dang Van ((*) with R=0 calibration, according to Causse et al. 2024).

Method

Eurocode 3 (EN 1993-1-9:2005)   =  −  = 

Dang Van (*) Calculation

Dang Van (*) with Charts (**)

Stress tensor [MPa] N (for  ×  with  =1.35 ) N (for  ×  with  =0.8 ) N (for  ×  with  =1 ) N (for  ×  with  =1.35 ) N (for  ×  with  =1.5 ) N (for  ×  with  =2.44 ) (i.e.  =2  R =200 MPa)

see Fig. 6 (a) 3.82 × 10 6 43.65 × 10 6 14.3 × 10 6 3.82 × 10 6 2.78 × 10 6 0.647 × 10 6

see Fig. 6 (b) (**) 3.22 × 10 6 (**) 44.4 × 10 6 (**) 14.4 × 10 6 (**) 3.22 × 10 6 (**) 2.07 × 10 6 (**) 0.481 × 10 6

6.85 × 10 6 93.7 × 10 6 30.7 × 10 6 6.85 × 10 6 4.40 × 10 6 1.024 × 10 6

0.47 (for  =0.8 and 1) 0.56 (for  =1.35) 0.63 (for  =1.5 and 2.44)

N DV / N E

Not applicable (reference)

See Fig. 4 and 5 and 6 (b) = N DV  /N E × N DV  /N E = 0.73 × 0.64 = 0.47

(**) N DVcharts = N E × [(N DV  /N E ) × (N DV  /N E )] = N E × 0.73 × 0.64 (see Fig. 4, 5 and 6 (b)) i.e. N DVcharts = N E × 0.47 Note that this 0.47 value in our method is independent from  .

Table 2 shows that for  =1 and 0.8, the number of cycles in multiaxial fatigue calculated with our charts (abacus) or with a complete calculation according to Dang Van is about the same (N DVcalculated /N E = N DVcharts /N E ). For a partial fatigue safety coefficient  =1.35 to 2.44, we observe that the number of cycles in multiaxial fatigue evaluated with the abacuses is underestimated by 18% to 25% compared with a true Dang Van calculation, which is safe. Theoretically, we still need to better understand these variations, which will be the focus of our future research. However, in terms of order of magnitude , it can be seen that the Dang Van type multiaxial fatigue life assessment method using the charts (abacus) is very relevant , and is much easier and quicker to carry out than a full calculation using the Dang Van method. Finally, given the non-perfect shapes of the real signals and the error readings potentially generated by the graphical imprecision of the charts readings, we consider that we could have had an error of 20% in the other direction (unsafe). We therefore propose to keep a safety margin of 20% on the damage: E DVCharts = n wanted /N DV charts (with N DVCharts the maximal number of cycles to failure theoretically). If E DVcharts ≤ 0.8, multiaxial fatigue lifetime assessment with charts is sufficient. If E DVcharts > 0.8, then we suggest performing multiaxial fatigue with a full calculation such as Dang Van or FKM.