PSI - Issue 22

S.C. Wu et al. / Procedia Structural Integrity 22 (2019) 211–218 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

215

5

Fig. 2. A 5-stage block loads used into the fatigue life assessments of axle

In engineering, most of the stress level in load spectrum is far below the fatigue strength limit. However, it has been proved that those stress levels play a key role in fatigue damage. When k′ =2k-1, the Miner damage criteria need to be modified according to the FKM rules to get more conservative assessment results (Beretta and Regazzi, 2016). Thus, the damage can be expressed as:

1







k

k

+ 1

D

n S 

n S 







(6)

cri

i

i

i

i

k S N 

k S N

S S 

S S 

D D

D D

D

D

i

i

Under typical variable amplitude loading, the critical fatigue damage can be taken as D crit =0.3 in term of FKM Guidelines for steel components. 3.1. (X-x-x-x) type test program Until now, the alloy steel is the main material for hollow axle of high-speed railway in China and Europe, such as EA4T steel (Beretta and Regazzi, 2016) and LZ50 steel (Zhao et al., 2009), etc. Based on the ISIA, the test data of EA4T (as shown in Table 1) is studied in this part to show the applicability, accuracy and conservativeness of the proposed method for this kind of material. As shown in Table 1, the μ j and σ j is solved by the experimental results. Based on the values of two parameters, the value of CV is 0.077 under the 3th stress level. According to HB/Z 112-86, the minimum number corresponding to the CV is 9, so the value of σ 3 is accurate. If this stress level is taken as the based-line stress, there is no need to search for the suitable value for α , so the ISIA can reduce workload and be easy for the engineering application. In Table 1, the predicted results of TGM are reliable for enough experimental data and can be used as the basis for judging the rationality of other methods. Based on the BSIM and the ISIA, the parameters of fatigue life distribution under various stress levels for EA4T axle steel are determined as list in the table. Combing with the different methods to fit the P-S-N curve, the fitting results of the ISIA are compared with that of the TGM or the BSIM in Fig. 3 .

Table 1. Fatigue life data of EA4T steel

ISIA

BSIM

Number

S j (MPa)

m j

N ji

μ j

σ j

μ ISIA 4.36 5.02

σ ISIA 0.21 0.33

μ BSIM 4.36

σ BSIM 0.32

1 2

450 425

5

4.208, 4.463, 4.863, 4.907, 5.129 4.877, 4.938, 4.987, 5.055,5.105, 5.210, 5.280, 5.354, 5.649, 5.713 5.171, 5.376, 5.437, 5.469, 5.595, 5.717, 5.796, 5.871, 6.125,6.714 5.486, 5.723, 5.797, 5.937, 6.016, 6.209, 6.274

4.71 5.22

0.37 0.29

10

5.02

0.38

5.72

0.44

5.72

0.44

3

400

10

5.73

0.44

6.46

0.56

6.46

0.50

4

375

7

5.92

0.28