PSI - Issue 40

Aleksey Antimonov et al. / Procedia Structural Integrity 40 (2022) 17–26 Aleksey Antimonov, Nadezhda Pushkareva / Structural Integrity Procedia 00 (2019) 000 – 000

22 6

To assess the possibility of using the expression (7), we have used the data of Poljanskij et al. (1984), in which the value of the relative deformation was determined by the coordinate grids method. The mesh grid was applied to the outer surface of pipe samples, which were then bent. According to the experimental data, the dependence of the deformation on the ratio of the deflection h to console length l and pipe diameter D     0,773 0,546 3, 271 / / 2 h l D   . (8) The difference between the calculated and experimental data does not exceed 18%. This makes it possible to use the formula (7) for determining the deformation range. The calculated value  in this formula should be considered as the deformation cycle amplitude. For example, in case of symmetric loading cycle for deformation range we will have

Dh l

.

(9)

2 2 2

       

max

min

Then, at the asymmetric loading cycle we obtain   1 2 2 2 D h h D h l l      ,

(10)

where deflections h 1 and h 2 depend on the stress cycle type. Finally, the formula for calculating the number of cycles before failure will be

1

 



2

l

0,26

ln 1

N

.

(11)



D h     

1 16

The calculation results according to the formulas (7) and (8) for pipes of various sizes are presented in Fig. 7. The results of calculating according to this formula for pipes of various sizes, depending on l at  h = 42 mm , are presented in Fig. 8.

Figure 7. Comparison of calculation results according to the formulas (7) and (8) for different pipes sizes: 1,3,5 – calculations by the formula (7); 2,4,6 – calculations by the formula (8) Pipes sizes, mm: 1 and 2 - 17x3,7; 3 and 4 – 13x3,35; 5 and 6 – 9,6x2,95.

Figure 8. The results of calculating the number of cycles before failure according to the formula (11). Pipes sizes, mm: 1 – 9,6x2,95; 2 – 13x3,35; 3 – 17x3,7.