PSI - Issue 31

Sanjin Braut et al. / Procedia Structural Integrity 31 (2021) 33–37 Sanjin Braut et al. / Structural Integrity Procedia 00 (2019) 000–000

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2.2. Modified Locati method Locati (1955) introduced a method for accelerated fatigue testing. The method was originally conceived as a single sample test where the slope of the S-N curve must be known a priori. It is based on the Palmgren-Miner rule of linear damage accumulation assuming that a crack has initiated in the component:

n

m 

(1)

1

D

=

=

i

1 N =

i

i

where m is the number of stress steps, n i is the number of cycles tested within one step level and N i is the number of cycles obtained from the assumed S–N curve corresponding to the test stress level. The method assumes the gradual increment of loading starting from initial stress amplitude S 0 , which should be below the foreseen fatigue strength, Wang et al. (2019). After completing the first block of stress cycles (e.g. 10 6 ) the stress level is increasing for a fixed stress increment (e.g. 20 MPa) and the test continues completing the next block of cycles (same number of cycles), and so on, until the sample fails. It is appropriate for preliminary fatigue tests and production quality control. Due to the inherent scatter of fatigue test data, a single-sample test, no matter how well designed, is not statistically meaningful, Zhang et al. (2003). Therefore, in this study a group of five test samples were used. The blocks of each stress level had 2·10 7 cycles. The experiment showed that all blades survived the first loading block. Therefore, the stress was increased by 20 MPa, and the blades were cyclically loaded again for the next 2·10 7 cycles, and this was repeated until the blades fail. It was considered that a blade has failed when its natural frequency drops by more than 2%. Fatigue strength at 2·10 7 cycles was then determined by Palmgren-Miner's rule Eq. (1), with the assumed S–N curves. Two approximate representation of Basquin type S-N curves, namely one-slope and two-slope models, were used, Fig. 1.

a)

b)

Fig. 1. Basquin type S–N curves implemented in the Locati method (a) One-slope model; (b) Two-slope model

3. Results The blades, like the one presented in Fig. 2, are tested on the vibration shaker at the frequency of the first normal mode, which is equal to 382 Hz. Due to manufacturing inaccuracies, each blade has a slightly different value of natural frequency as shown in Table 2. The amplitude of cycling stresses was measured with a strain gauge that was bonded to the convex side of the blade near the root. Five blades were tested. Table 2 shows blade fatigue strength results obtained by 2 different S–N curve models, Stephens et al. (2000), Mlikota et al. (2018), Pastorcic et al. (2019), and Babić et al. (2020). Fig. 3, present cumulative distribution function (CDF) with confidence interval (CI) 95%. CDF shows probability of failure for every test data and it is obtained by using the software tool Reliability: A Python library for reliability