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

41

6

The boom lifetime can be determined by the relation (4). The initiation period

i N of a crack of depth cycles. Further, the crack

6 3 10

i N  

is determined by the approach presented above and equals

0.001m

0 l =

1 l l = to its complex configuration followed by crack propagation to its 2 l l = , causing full fracture of the boom element, see the formula (4). The subcritical growth period of s s N N N = + is determined similarly to the previous based on the first law of thermodynamics, (1) (2) s

propagates in two stages: crack growth

critical size

the fatigue crack

some principles of physical chemistry and is reduced to the mathematical model:

2 ) (1 ) ( R  −

 

(

max    + + 2 ) t scc

max    − 0 t scc

dl dN





,

(10)



n



( ) l

) −  i 

2 −  scc  

2

2

0  0, 25 (1 ) R − 

(

l l

 





max − − t

c

Mt

1

i

=

( ) ( ) j s j N N l N l = = ; ( 1, 2) j = , ( ) * t l  ( ) , j s

( ) 0

0, N l =

j l −

=

C  = .

;

(11)

1

After integration of the equation (10) with respect to the conditions (11) and taking n to be large, the formula is derived for the determination of the subcritical crack growth period: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 0 I 2 2 2 2 2 2 0.001 0 2 0 2 2 4 4 0 MI 2 2 2 2 2 2 0 0.001 I 0 2 0 [ ] [ ( ) ][ 1 [ ] ] 0, 25 1 [ ] . ( )[ 1 [ ] ] l f fC s I scc I scc f l scc scc I scc f E K K l N dl K l K R K l K E R K l K n dl l l K l K R K l K E          −  − − − + + − − − − − − + +   (12) caused by the loading in the wall of a rectangular pipe of size 60 60 3 mm.   Using these functions, the experimentally obtained characteristics of steel 3 in corrosive environment (Babii et al. (2020), Leshchak et al. (2020)), the residual lifetime of the boom is obtained by the formula (12) under manoeuvre loading and corrosive medium. On this basis, Fig. 4b presents the plotted relations of the residual lifetime s N versus the initial crack length 0 l under stationary (curve 1 ) and manoeuvre (curves 2, 3, 4 ) loading at various shock number n of the field sprayer due to an uneven field. The comparison of these curves shows that the manoeuvre operating mode can decrease the residual boom lifetime more than by the factor of four. At 0 n = , the parts of the subcritical growth period of the corrosive-fatigue crack are calculated: (1) 4.6 s N = cycles, (2) 9986 s N = cycles. After substitution of the obtained values , i N (1) , s N (2) s N into the formula (4), the total boom lifetime is determined: 4 301 10 N    cycles or * 836 h. N  Thus, under the maximum oscillation amplitudes of the boom elements and the action of corrosive environment, the boom will operate about 1.5 seasons that does not correspond to the standard operation time of field sprayers. Compared to the results obtained earlier without the effect of corrosion medium, the corrosion environment reduces the lifetime almost by half. Therefore, the vibration reduction and corrosion protection of the boom elements are of considerable importance. 6. Conclusions Based on the fundamental principles of modern fatigue theory and the energy approach in fracture mechanics, the computation model is built for residual lifetime determination of a field sprayer boom under manoeuvre loading (its oscillations). It has been shown that the manoeuvre loading can reduce the residual lifetime of the long-range field sprayer boom from steel 3 almost by a factor of three and the standard service life of the sprayer more than by two. Furthermore, the computational model is developed for (residual) lifetime determination of a field sprayer boom under manoeuvre loading and corrosive environment. Using the formulated model, the boom lifetime is determined under the given operating conditions and corrosive environment, the solution of insecticide Nurelle D, which The functions of the stress intensity factors , MI K I K are taken from the handbook (Murakami (1987), Savruk (1988)) for the stresses 90 MPa,    130 MPa M   