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

40

5

( ) , s s N N l N l = = , *

( ) 0, 0 ; N l l = =

( ) * t

l 

C  = .

(8)

0

2 l K l K   = , 2 ( ) / ( ) /

Integration of the equation (7) with respect to the conditions (8) and the formulas

max

t

c

I

fC

2 th f K E   = , ( ) t l  0 / th

2 K l

0 ( ) / 

E

=

(Andreikiv et al. (2018a), Andreikiv et al. (2019), Andreikiv et al. (2016))

I

f

results in the following expression:

( ) K l K K R K K l K K    − − −   −    − −  ( ) 0 2 2 0 2 2 2 4 4 4 4 fC th 0 1 1 l f I fC l fC fC I E ( )

( ) K l K K l K − − ( ) 4 4 MI

l

4

n −

(9)

th

.

N

dl

dl

s

4

l l 

 

0

I

th

l

0

MI K and

I K are obtained by the existing formulas for the loadings M and

i M , that cause the

The values of

150 MPa

M   

105 MPa    and

correspondingly in the tube walls. Based on the S-N curve for steel 3

stresses

9 0 4.51 10 (cycle) (MPa) ,  − − −   1 2

0.1, R =

and the equation (7), the material characteristics are calculated:

0 f  = 5 2 10 MPa. E =  Substitution of these data into the formula (9) gives the residual lifetime of the boom under manoeuvre loading at the parameters mentioned earlier. On this basis, the relations of the residual boom lifetime s N versus the dimensionless initial crack length 0  are plotted in Fig. 4a under the stationary (curve 1 ) and manoeuvre (curves 2 - 4 ) loading at various shock number n due to uneven field surface. As can be seen from the comparison of these curves, the manoeuvre loading can reduce the residual lifetime of the boom more than by the factor of three. Further, by adding the obtained crack initiation period i N to the subcritical crack growth period, variation of the boom lifetime is obtained under the manoeuvre loading (variation of shock number at obstacles): 1767 1698 t    . It is known that the standard operating time of a field sprayer comprises seven years, and their annual workload is 550 hours. However, under the adopted maximum load range of the boom elements, the boom will operate approximately 3.2 seasons that does not correspond to the standard operating time of sprayers. Hence, it is necessary to reduce or eliminate the oscillations of the boom elements, as well as take into account the shocks due to field irregularities, as proposed earlier in this paper. 5. Lifetime of boom elements under manoeuvre loading and corrosive environment Important studies have also been conducted for (residual) lifetime determination of a long-range field sprayer boom, taking into account operating stress (manoeuvre loadings) and physical-chemical (corrosive medium of insecticide Nurelle D solution) factors. In this case, the problem statement differs from the last one only by consideration of the action of the corrosion medium. The problem is to determine the boom lifetime (the number of loading cycles * N N = ) that leads to its partial or full fracture. 440 MPa, 102 MPa m, fc K = 12.8 MPa m, th K =

b

а

Fig. 4. (a) Relation

s N  0  at stationary (curve 1 ) and manoeuvre (curves 2 , 3 , 4 ) loading: 1 – n = 0, 2 – 400, 3 – 600, 4 – 800; (b) relation s N  0 l : 1 – n = 0, 2 – 1000, 3 – 15000.

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