PSI - Issue 42

Snezana Kirin et al. / Procedia Structural Integrity 42 (2022) 351–355

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Author name / Structural Integrity Procedia 00 (2019) 000–000

lengths. Amplitude loading is defined as R=0.79 (in ABAQUS input data file) for 21 MPa (maximum stress 100 MPa, minimum stress 79 MPa, [21]). Calculation is based on the Raju-Newman solution for a surface crack in a thin-walled cylindrical shell, [22]: � � � � �� � � � � � 2 � � 2 � � � � � 3 � � � � � � 4 � � � � � � where Q is the shape factor [25], and other quantities are defined in Fig. 3. The corresponding coefficients 0 -G 3 are determined by matching of the results with finite element analysis results, as presented in [25]. In the case presented here, G 0 =1.317, G 1 =0.751 for the angle=90 0 , whereas G 2 and G 3 are calculated as presented in Table 2, since they depend of crack geometry.

Figure 5. Pipe with external surface crack, Do - outer diameter, t - wall thickness, a – crack depth, c – crack half-length

Results obtained for the design pressure are presented in Table 2 and Fig. 6, predicting cca. 30 Years of life for new pipe with a corrosion defect 1.75 x 26 mm.

Table 2. Crack depth vs. Number of cycles, N, for the design pressure

a

c/a

a/t

a/c

Q

G2(ø=90) G3(ø=90) F total

N ( θ = π /2)

1.75 7.429 0.251 2.44 5.328 0.350 3.13 4.153 0.448 3.82 3.403 0.547 4.51 2.882 0.646 5.2 2.500 0.745 5.89 2.207 0.844 6.58 1.976 0.943 6.9 1.884 0.989

0.135 0.188 0.241 0.294 0.347 0.400 0.453 0.506 0.531

1.054 1.093 1.140 1.194 1.255 1.323 1.396 1.476 1.515

0.556 0.556 0.557 0.558 0.558 0.559 0.560 0.561 0.561

0.457 0.458 0.459 0.460 0.461 0.462 0.464 0.465 0.466

1.874 1.883 1.892

0

60040106 93325879

1.902 114350930 1.911 128754708 1.921 139185707 1.931 147050879 1.941 153166064 1.946 155543824

sum of years

0 1 2 3 4 5 6 7 8

Crack depth (a)

0

10

20

30

40

Number of years

Fig. 6. Crack depth vs. number of years (1 year corresponds to 5,046,000 cycles)

4. Discussion and conclusions Comparison with other crack-like defects (3.5 and 5.25 mm) is shown in Table 3. As one can see, remaining life is drastically reduced with increased crack depth, almost 10 times for ½ depth (3.5 mm) and close to 50 times for ¾ depth (5.25 mm), compared with ¼ depth (1.75 mm).

Table 3. Number of cycles for crack to grow through the thickness Crack depth, mm Number of cycles Years 1.75 155,543,824 30.8 3.5 16,030,191 [26] 3.2 5.25 3,325,312 [21] 0.66