## Effect of crack on elbow strength of main steam pipeline

Crack is a common defect on the **main steam pipeline**. Because it causes local discontinuity of the pipeline, the crack position often produces relatively large stress concentration [1]. The crack itself has the characteristics of propagation, so its influence on the safe operation of the main steam pipeline has certain uncertainty. Whether the crack propagates or not is related to the load, temperature and medium characteristics of the main steam pipe. Some shape and size cracks are safe under certain conditions, but their safety will change with time [2-5]. As for the main steam pipeline and its accessories, in addition to bearing high temperature, high pressure, vibration and other loads, the possible crack defects will seriously affect its safe operation, so it is necessary to analyze the main steam pipeline with cracks, determine the impact of different size cracks on the strength of the main steam pipeline, so as to evaluate the reasonable use of the main steam pipeline with cracks and modify the pipeline Provide basis. In this study, the elbow is taken as the analysis object, and the elbow with cracks is analyzed to determine the effect of cracks on the main steam pipeline [6-10].

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Structural dimension and bearing load of main steam pipe elbow

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Structure and size of main steam pipe elbow

Taking 90 ° push elbow as the analysis object, the elbow is made of P92 by hot extrusion of forged steel pipe. Because the elbow structure is simple, its model is not simplified in the analysis process. The elbow structure and its dimensions are shown in Figure 1.

Fig.1 Elbow structure and dimension diagram

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Load on pipe elbow of main steam pipe

In order to make the analysis results reflect the stress-strain state of the elbow under the actual operation, the pressure and temperature on the main steam pipe during the actual operation of the utility boiler are taken. The internal pressure of the elbow is 27.6mpa, and the working temperature is 610 ℃. In addition, a dynamic impact load is applied, which is 1.5 times of the internal pressure.

Besides the above loads, the elbow also bears the impact force of the fluid in the pipeline. This is because the flow direction of the medium in the pipeline changes at the elbow position, and the fluid will produce a certain impact force on the elbow. It can be seen from the analysis that the impact force generated by the fluid with a flow speed of 40 m / s only increases the load borne by the elbow by 0.15 MPa, which has little impact on the strength of the elbow [11-13], so it can be ignored.

Figure.2 Schematic diagram of regularization treatment process of surface cracks

Fig.3 Regularization process of near surface crack

The regularization process of near surface cracks is shown in Figure 3. In Figure 3, the ratio of crack length to depth L / h ≥ 0.5, and the ratio of crack depth to wall thickness h / b < 0.7. The buried depth of the crack e ≤ 0.4h, and e < C, and the nearest distance from the crack to the surface C ≥ 0.4h. The crack regularization shown in Fig. 3 (a) is treated as a rectangular crack shown in Fig. 3 (b). The depth of the rectangular crack is the sum of the crack depth and the nearest distance from the crack to the surface (H + e). The crack can be regularized as a surface crack. This method is only suitable for near surface cracks. If this method is used to deal with deep buried cracks, a large error will be generated [14-16].

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Distribution of crack on elbow

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Single crack elbow

The standardized treatment of cracks on single crack elbow can be divided into the following two cases: ① cracks with depth of 4 mm, 6 mm, 10 mm, 20 mm, 30 mm, 40 mm and length of 50 mm; ② cracks with depth of 10 mm and length of 5 mm, 10 mm, 25 mm, 50 mm, 75 mm, 100 mm, 150 mm, 200 mm.

For single crack elbow, the influence of different size cracks at 45 ° position on elbow strength is analyzed. The location of single crack on the elbow is shown in Figure 4.

Fig.4 Single crack location

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Double crack elbow

Figure.5 Schematic diagram of two cracks

The crack location on the double crack elbow is shown in Figure 5. The two cracks are arranged on the inside and outside of the elbow along the axial direction. The crack spacing is 2 mm, 4 mm, 6 mm, 8 mm, 10 mm, 12 mm, 14 mm, 16 mm, 18 mm, 22 mm, 30 mm respectively. The crack length is 50 mm and the depth is 10 mm.

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Effect of crack on elbow strength

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Effect of single crack on elbow

The influence of single crack with different sizes on the strength of elbow is different, that is to say, the stress concentration at the corresponding position of elbow caused by different crack length and depth is different; the influence of the same crack on elbow under different load conditions is also different. The location of crack stress sampling points is shown in Figure 6.

The strength calculation results of the elbow are shown in Figure 7. It can be seen from Figure 7 that the maximum stress value of the inner surface (the area where end face 1 is located) of the inner side of the elbow is 87.71 MPa, and the stress value of the outer side (the area where position 2 is located) of the inner surface of the corresponding elbow is 67.26 MPa. The stress on the inner surface of the elbow from end face 1 to end face 2 increases first and then decreases gradually. The minimum stress on the outer surface of the elbow (location 4) and its vicinity is 21.08 MPa. The degree of stress concentration and the gradient of stress change in the inner side of elbow are greater than that in the outer side.

The variation rule of the stress on the elbow with single crack (located on the outer surface) with the crack length is shown in Figure 8. The change rule of stress on the axial section of single crack with different length (located on the outer surface) is shown in Figure 9.

Fig.6 Schematic diagram of crack stress sampling point

Fig.7 Stress distribution on the longitudinal section of elbow

Fig.8 Variation trend of stress on elbow with single crack (located on outer surface) with crack length

Fig.9 Stress distribution on axial section of single crack with different length (located on the outer surface)

When the ratio of crack length to depth L / h is less than 1, the stress at the crack end is the maximum stress on the elbow, at this time, the possibility of crack continuing to expand is relatively large; when l / h is more than 1, the maximum stress at the crack bottom is the maximum stress on the elbow; when 1 < L / h ≤ 5 When l / H > 5, the maximum stress at the bottom of the crack increases with the length of the crack, and the maximum stress at the end of the crack increases very slowly. The minimum stress on the crack decreases with the increase of crack length. The greater the crack length is, the greater the maximum stress value around the crack is. As shown in Fig. 7, the maximum stress on the outer surface of the non cracked elbow is 21.08 MPa, and the maximum stress on the defective elbow is 43.43-95.43 MPa. The defect increases the stress on the outer surface of the elbow by 2.06-4.52 times. With the increase of crack length, the gradient of stress on the crack also increases.

The variation of stress on the elbow with single crack (located on the inner surface) with the crack length is shown in Figure 10. When l / h is less than 1, the stress at the end of the crack is the maximum stress on the elbow, and the possibility of the crack to continue to expand is relatively large; when l / h is greater than 1, the maximum stress at the bottom of the crack is the maximum stress on the elbow; when 1 < L / h ≤ 5, the maximum stress at the bottom of the defect increases rapidly with the increase of the crack length; when l / h is greater than 10 With the increase of crack length, the maximum stress at the bottom and the end of the crack gradually increases, but its increasing range is relatively small, and the minimum stress on the crack gradually decreases with the increase of crack depth.

Fig.10 Variation trend of stress on elbow with single crack (located on inner surface) with crack length

Fig.11 Stress distribution on axial section of single crack with different length (located on inner surface)

The change rule of stress on the axial section of single crack with different length (located on the inner surface) is shown in Figure 11. The greater the crack length is, the greater the maximum stress value around the crack is. According to the previous analysis, the maximum stress on the inner surface of the crack free elbow is 87.71 MPa, and the maximum stress on the defective elbow is 174.8-283.3 MPa. The defect increases the stress on the outer surface of the elbow by 1.99-3.23 times. When l / h ≤ 1, the stress from the crack edge to the center of the crack bottom decreases gradually, and the stress at the center of the crack bottom is the smallest; when l / H > 1, the stress from the crack end to the crack bottom decreases first and then increases, and the maximum stress at the crack bottom is greater than the maximum stress at the crack end. The increase of the maximum stress at the crack tip is smaller than that at the crack bottom.

The variation rule of stress on the elbow with single crack (located on the outer surface) with crack depth is shown in Figure 12. The maximum stress at the bottom of the crack is the maximum stress near the crack. With the increase of the crack depth, the maximum stress at the end of the crack gradually increases. The maximum stress at the bottom of the crack is smaller than that at the end of the crack, and the difference between the maximum stress at the bottom of the crack and the maximum stress at the end decreases with the increase of the crack depth. The minimum stress near the crack decreases with the increase of crack depth.

Fig.12 Variation trend of stress on elbow with single crack (located on outer surface) with crack depth

The distribution of stress on the axial section of single crack (located on the outer surface) with different depth is shown in Figure 13. The greater the crack depth is, the greater the maximum stress value around the crack is. According to the previous analysis, the maximum stress on the outer surface of the crack free elbow is 21.08 MPa, and the maximum stress on the defective elbow is 57.44-151.1 MPa. The defect increases the stress on the outer surface of the elbow by 2.72-7.17 times. When l / h ＜ 5 / 3, the stress distribution from the end to the bottom of the crack first decreases and then increases; when l / h ＞ 5 / 3, the stress from the end to the bottom of the crack gradually increases, and the stress at the bottom of the crack is always greater than the maximum stress at the end of the crack.

Fig.13 Stress distribution on axial section of single crack (located on outer surface) with different depth

The variation of stress on the elbow with single crack (located on the inner surface) with crack depth is shown in Figure 14. When l / h ＞ 2.5, the maximum stress at the bottom of the crack defect is the maximum stress on the elbow. At this time, the maximum stress at the end and bottom of the crack gradually increases with the increase of the crack depth; when l / h ＜ 2.5 At the same time, the maximum stress at the bottom of the defect decreases with the increase of the depth of the defect. At this time, the maximum stress at the end of the crack increases with the increase of the depth of the crack and is greater than the maximum stress at the bottom. The minimum stress on the crack increases with the increase of crack depth.

Fig.14 Variation trend of stress on elbow with single crack (located on inner surface) with crack depth

The change rule of stress on the axial section of single crack (located on the inner surface) with different depth is shown in Figure 15. The greater the crack depth is, the greater the maximum stress value around the crack is. According to the previous analysis, the maximum stress on the inner surface of the crack free elbow is 87.71 MPa, and the maximum stress on the cracked elbow is 186.2-304.8 MPa. The defect increases the stress on the outer surface of the elbow by 2.12-3.47 times. With the increase of crack depth, the more inhomogeneous the stress distribution on the crack is, the more likely the crack will continue to grow.

Fig.15 Stress distribution on axial section of single crack (located on inner surface) with different depth

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Effect of double cracks on elbow strength

The influence of two cracks with different spacing on the strength of the elbow is different, that is to say, the stress concentration at the corresponding position of the elbow caused by different spacing of cracks is also different. When the distance between two cracks is different, the weakening degree of the bearing capacity of the pipeline is also different.

The variation rule of the stress on the elbow with double cracks (located on the inner surface) with the crack spacing is shown in Figure 16. The maximum stress of adjacent crack decreases with the increase of crack spacing. When the distance between two cracks is less than or equal to 8 mm, the range of stress reduction is relatively large, and the maximum stress difference is 78.4 MPa; when the distance between two cracks is more than 8 mm, the range of stress reduction is relatively small, and the maximum stress difference is 15 MPa; when the distance between two cracks is less than or equal to 14 mm When the distance between two cracks is more than 14 mm, the maximum stress at the bottom of the crack is greater than that at the end of the crack. The minimum stress on the crack remains unchanged with the increase of crack spacing, and the maximum stress difference is 1.15mpa.

Fig.16 Variation trend of stress on double crack (located on inner surface) elbow with crack spacing

Fig.17 Stress distribution on axial section of double cracks (located on inner surface) with different spacing

The change rule of stress on the axial section of double cracks with different spacing (located on the inner surface) is shown in Figure 17. The larger the distance between two cracks is, the smaller the maximum stress value around the cracks is. According to the previous analysis, the maximum stress on the inner surface of the cracked elbow is 87.71 MPa, and the maximum stress on the cracked elbow is 268.5-361.9 MPa. The defects increase the stress on the outer surface of the elbow by 3.06-4.12 times. The stress in the middle of two cracks decreases with the increase of crack spacing, which shows that the interaction between cracks decreases with the increase of crack spacing. With the increase of crack spacing, the difference of stress value between two ends of crack becomes smaller and smaller.

The variation rule of the stress on the elbow with double cracks (located on the outer surface) with the crack spacing is shown in Figure 18. When the distance between two cracks is less than 10 mm, the maximum stress at the adjacent part of the defect is greater than the maximum stress at the bottom of the defect, and decreases gradually with the increase of the distance between cracks; when the distance between cracks is 10-14 mm, the maximum stress at the adjacent part of the crack is the same as the maximum stress at the bottom of the crack; when the distance between cracks is more than 14 mm At the same time, the maximum stress at the bottom of the crack is greater than that at the adjacent position of the crack, and increases with the increase of the crack spacing. With the increase of crack spacing, the maximum stress fluctuates in a certain range, and the maximum value is always less than the maximum stress in the crack adjacent position. The minimum stress on the crack fluctuates in a certain range with the increase of crack spacing, and the maximum stress difference is 0.36 MPa.

Fig.18 Variation trend of stress on double crack (located on the outer surface) elbow with crack spacing

Fig.19 Stress distribution on axial section of double cracks (located on the outer surface) with different spacing

The change rule of stress on the axial section of double cracks with different spacing (located on the outer surface) is shown in Figure 19. The larger the distance between two cracks is, the smaller the maximum stress around the cracks is. According to the previous analysis, the maximum stress on the outer surface of the crack free elbow is 21.08 MPa, and the maximum stress on the cracked elbow is 86.69-122.9 MPa. The defects increase the stress on the outer surface of the elbow by 4.11-5.83 times. When the crack spacing is equal to 30 mm, the stress in the middle of the gap between the two defects is 21.29 MPa, which is 0.21 MPa higher than the stress on the outer surface of the elbow without crack. Therefore, when the crack spacing is more than 30 mm, the interaction between cracks can be ignored.

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Conclusion

- (1) For elbows with a single crack, when the crack depth is fixed, the greater the crack length is, the greater the maximum stress the crack bears, and the stress distribution tends to be uniform.
- (2) For elbows with a single crack, when the crack length is fixed, the maximum stress of the crack is smaller with the increase of the crack depth.
- (3) For elbows with two cracks, the larger the crack spacing is, the smaller the superposition effect of stress between cracks is. The difference of defect spacing makes the stress gradient near the defect different, and the smaller the defect spacing is, the greater the stress gradient is.

Source: Network Arrangement – China Stainless Steel Elbow Manufacturer – Yaang Pipe Industry Co., Limited (www.ugsteelmill.com)

(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless steel products, including Super Duplex Stainless Steel Flanges, Stainless Steel Flanges, Stainless Steel Pipe Fittings, Stainless Steel Pipe. Yaang products are widely used in Shipbuilding, Nuclear power, Marine engineering, Petroleum, Chemical, Mining, Sewage treatment, Natural gas and Pressure vessels and other industries.)

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