PSI - Issue 22

Carlos D.S. Souto et al. / Procedia Structural Integrity 22 (2019) 376–385 Author name / Structural Integrity Procedia 00 (2018) 000–000

378

3

1 / 3 ∆ σ

∆ σ D = (2 / 5)

C = 0 . 737 ∆ σ C

(2)

And for variable amplitude loading: For m = 3 and N ≤ 5 × 10 6 → ∆ σ m

m C · 2 × 10 6 R · N R = ∆ σ

R · N R = ∆ σ

(3)

For m = 5 and 5 × 10 6 ≤ N ≤ 1 × 10 8 → ∆ σ m

m D · 5 × 10 6

(4)

1 / 5 ∆ σ

∆ σ L = (5 / 100) (5) Where m is the inverse slope of the S-N curve, N R is the number of cycles to failure, ∆ σ C is the reference value of the fatigue strength at N C equal to 2 million cycles, ∆ σ D is the fatigue limit for constant amplitude stress ranges at N D equal to 5 million cycles, and ∆ σ L is the cut-o ff limit for stress ranges at N L equal to 100 million cycles. D = 0 . 549 ∆ σ D

Fig. 1: Design S-N curves according to the EN1993-1-9 standard.

2.2. Palmgren-Miner rule

The fatigue life of a structure may be estimated based on the design S-N curves selected from the EN1993-1-9 standard and using the Palmgren-Miner rule, or simply Miner’s rule (Miner, 1945). Under variable amplitude loading, the fatigue life is estimated by the calculation of the total accumulated damage, D , done by each cycle in the stress spectrum. In practice, the spectrum is simplified into a manageable number of stress bands. The Palmgren-Miner rule states that where there are k di ff erent stress bands in a spectrum, the damage done by each band, D i , is defined as D i = n i / N i , where n i is the number of cycles in the band during the design’s life and N i is the endurance under that stress range. In this way, to avoid failure during the design’s lifetime, the following inequation must be satisfied:

k i = 1

k i = 1

n i N i ≤

D i =

1

(6)

D =

m 1 D  

m 2 D  

D =    k i = 1

+    k i = 1

n i · ∆ σ m 1 i 2 × 10 6 · ∆ σ

n i · ∆ σ m 2 i 5 × 10 6 · ∆ σ

(7)

 ∆ σ i > ∆ σ D

 ∆ σ D > ∆ σ i > ∆ σ L