PSI - Issue 19

H. Heydarinouri et al. / Procedia Structural Integrity 19 (2019) 482–493 H. Heydarinouri et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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6

riveted elements in different studies including the number of rivets in a line. Based on Table 1, the minimum value of  is equal to 144, which can be used for the fatigue design of riveted members as a lower bound of CAFL. Using this value for  results in the lowest line for the CAFL. Therefore, the simple equation proposed for the design is:

72 ( 1 ) 1 0.5 R R  

   

(18)

D

Table 1. The value of  in different experimental studies Study d (mm)

f k

ut (MPa) S

w (mm) Number of rivets in a line

(MPa) 

21 19 20 21 19 22 22 19 20 23

125

24 12 22

388 344

2.38 2.39 2.37 2.25 2.47 2.43 2.39 2.29 2.38 2.3

163 144

Bruhwiler et al. (1990)

70

Akesson (2010) and Al-Emrani (2002)

115

391.8

165.3 173.3 169.6 155.8 158.4 187.4 249.8 236.1

82.5

4

390 390 385 385 448 572 562

Baker and Kulak (1985)

89

12

177.5

>> 4 >> 4 >> 4

Fisher et al. (1987)

152

Reemsnyder (1975)

110.4

Graf (1935)

79

4

Ghafoori et al. (2015b)

115

One free hole

3. Comparison of the proposed criterion with the existing experimental data Available experimental results from the sources of Table 1 are plotted in Fig. 2 altogether. The results have been collected from the experimental studies in which the fatigue cracks have initiated from the rivet holes, and not from the rivets themselves. In this figure, the criterion proposed by DIN and ÖNORM, Eurocode (2005) and the one pro posed in this study are plotted using Eq. (3), Eq. (5-b) and Eq. (18), respectively. In different studies, different number of cycles has been assumed for being run-out. The minimum number of cy cles considered was 7 million (Brühwiler et al., 1990), While in some others the fatigue tests were stopped after 20 million cycles (Akesson, 2010, Brühwiler et al., 1990). It is worth mentioning that for each test series, the CAFL line can be plotted using Eq. (10). The proposed criterion in Fig. 2 is the lowest line obtained by Eq. (18).

280

Proposed criterion Eurocode (2005) DIN and ÖNORM (Taras and Greiner, 2010) Brühwiler et al. (1990) Baker and Kulak (1985) Reemsnyder (1975) Fisher et al. (1987) Al-Emrani (2002) Akesson (2010) Ghafoori et al. (2015b) Graf (1935)

Red markers: Cracked Green markers: Run-out

240

200

160

120

Stress Range (MPa)

80

40

0

-1 -0.8 -0.6 -0.4 -0.2 0

0.2 0.4 0.6 0.8

1

R

Fig. 2. Stress range versus stress ratio for different experimental studies Fig. 2 shows that the proposed criterion can predict the limit between fatigue failure and run-outs fairly well. On the other hand, the criterion proposed by DIN and ÖNORM as well as Eurocode (2005) are conservative in the stress ratios smaller than around 0.4. However, in the majority of the previous studies, the stress ratio was between 0.1 and 0.3. To the best of authors’