PSI - Issue 36

Oleksandr Andreykiv et al. / Procedia Structural Integrity 36 (2022) 36–42 Oleksandr Andreykiv, Andri і Babii, Iryna Dolinska et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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3

а

b

c

Fig. 2. (a) Loading scheme of a boom element; (b) boom element with a rectilinear surface crack; (c) boom element with a complex crack.

3. Determination of the fatigue crack initiation period Calculation of the crack initiation period for these structural elements is performed with respect to the relations   N ln in the finite life region at the S - N curve. Based on the results of (Romaniv et al. 1990), it can be concluded that this relation is almost linear in semilogarithmic scale and can be analytically presented as follows:

1

1 ) N N −

0 lg(

0  −

=

.

(2)

0  , 0 N are the fatigue fracture characteristics in the finite life region ( 4 10

7 10 N   ) that are determined

Here,

based on experimental studies. Hence, the period of fatigue crack initiation

i N for the structural element, where the external loading causes the

time-variable stresses of amplitude  , can be determined by:

1

0  − −

0 10 (3) Further, let us calculate the crack initiation period in a rectangular steel 3 tube with the cross-section of 40 25 3 mm.   According to experimental studies, the stress range   in tube walls can vary within 140 180 MPa     under the constant tube cross-section sizes , h , H t . The application of the formula (3) requires the determination of the material characteristics 0  and 0 N . For this purpose, the S - N curve is built for steel 3 (Fig. 3) based on the study of Babii et al. (2020). Using the least squares method (Lawson et al. (1995)), the equation (3) and the S-N curve, the constants are calculated: 8 0 6.3 10 N   cycles, 0 88.23 MPa.   Then the fatigue crack initiation period i N is approximately determined to be 6 6.3 10 i N =  , or 1750 h. i t = i N N = .

b

a

Fig. 3. (a) S-N curve for steel 3; (b) fatigue crack growth curve.