Keywords

1 Introduction

At present, the research on the residual strength of corroded pipeline is generally based on the finite element simulation results. Irregular defect shapes have caused great distress to the research of corroded pipeline. Through a series of assumptions and simplifications of corrosion defects, some scholars [1] transformed irregular corrosion defect shapes into a regular square, circular and other shapes. Researchers [2,3,4] have realized the decrease in the pressurized bearing capacity of pipeline subjected to external loads by using finite element simulation technology.

Mondal [5] proposed that for corroded pipeline, it is impossible to simulate the influence of corrosion cracking and crack propagation on the pressurized bearing capacity of pipeline by using standard finite element modeling technology. It is recommended to use fracture mechanics to calculate the residual strength of corroded pipeline containing corrosion defects or crack-like defects. Lu et al. [6] studied the residual strength of pressurized equipment with structural defects and proposed to establish a finite element defect component model. The surface of the outer wall of the pipeline to the defect surface is modeled in a smooth way to prevent stress concentration. Bai et al. [7] studied the bearing capacity of pipeline subjected to axial force, pressure and bending moment, and proposed that different loading sequences had different effects on the bearing capacity of pipeline. The loading sequence of the first pressure and then the final axial force and bending moment of the thick-walled pipe has a greater impact than other loading sequences.

Based on the research results of Bai et al. [7], this paper will study the ultimate bearing capacity of corroded pipeline by applying pressure first and then applying axial force or bending moment to corroded pipeline.

2 The Finite Element Model

2.1 Modeling

In order to reduce the time of calculation, the shell element is used to model the finite element pipeline, and the symmetrical boundary of the finite element software is used to establish the model of a quarter of corroded pipeline. As shown in Fig. 1, the mesh size of the non-defect area is 1 mm, and the mesh size of the defect area is 3 mm.

Fig. 1.
figure 1

The FE model of a quarter of corroded pipeline

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In this paper, the simplified rectangular defect shape is used as the corrosion defect of the pipeline. and the fluid cavity simulation technology is used. The cavity is defined by specifying the surface that completely surrounds the cavity and is associated with the node called the cavity reference node.

2.2 Verify the Finite Element Model

The material parameters and size parameters of the corroded pipeline are selected from the paper of Oh et al. [8], as shown in Tables 1 and 2.

According to the numerical simulation results, the stress curve of the most unfavorable element at the defect is drawn, as shown in Fig. 2. The red dotted line is the ultimate tensile strength of the pipeline material 563.8MPa, and the black dotted line is the pressure value 24.09MPa when the ultimate tensile strength is reached by simulation. This value has an error of 0.864% (0.21MPa) with the value 24.3MPa obtained by Oh et al. [8]. Mondal et al. [2] carried out a numerical analysis of the test pipeline, and the simulation value was 24.47MPa, which had a 0.69% (0.17MPa) error with the test value in Oh et al. [8]. The simulation results obtained in this paper are more conservative than those of Mondal et al. [2] but also have high accuracy, which is conducive to the analysis of the bearing capacity of corroded pipeline during operation.

Table 1. The parameter of material [8]
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Table 2. The dimensions of corroded pipe [8]
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Fig. 2.
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Burst pressure predicted by finite element model

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3 Interaction Curve of Ultimate Bearing Capacity of Corroded Pipeline

According to the defect size specification in ASME B31G [9], the shallow defect pipeline (d/t = 0.25) and deeply defect pipeline (d/t = 0.75) were designed on the basis of the intact pipeline, and the size is shown in Table 3. The material parameters in Xu [10] are selected. The stress-strain curve of the pipeline is shown in Fig. 3, and the ductile damage parameters of the material are shown in Table 4.

Table 3. The three dimensions of corroded pipeline [9]
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Fig. 3.
figure 3

The stress-strain curve [10]

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Table 4. The parameter of ductile damage [10]
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As shown in Fig. 4, the axial force is positive for the axial compressive force, the bending moment is positive for the defect on the compression side. The pressure, axial force and bending moment ultimate bearing capacity of corroded pipeline are obtained by simulation.

As shown in Fig. 4 (a), the curved surface shape is like an ellipse. With the increase of pressure, the axial force and bending moment values first decrease and then increase, and finally decrease. This is because the low pressure increases the bearing capacity of the pipeline. However, with the increase of pressure, the pipeline is easier to enter the yield stage., damage occurs in advance, and the ultimate bearing capacity of the pipeline gradually decreases. As shown in Fig. 4 (b), the axial force and bending moment ultimate bearing capacity curves of the intact pipeline are symmetrical along the M = 0 MPa line. With the increase of pressure, the ultimate bearing capacity of axial force decreases gradually, while the ultimate bearing capacity of bending moment increases first and then decreases. As shown in Fig. 4 (c), the existence of defects weakens the enhancement effect of pressure on the ultimate bearing capacity of pipeline, and also reduces the ultimate bearing capacity of pressure, axial force and bending moment of pipeline, and increases the decrease rate of the ultimate bearing capacity of axial force and bending moment of corroded pipeline under higher pressure, making pipeline more easier to damage.

As shown in Fig. 4 (e), with the increase of pressure, the ultimate bearing capacity of corroded pipeline gradually decreases, and the existence of deeply defects greatly affects the ultimate bearing capacity of corroded pipeline. As shown in Fig. 4 (d) and Fig. 4 (f), the N-M interaction curve of the corroded pipeline is not symmetrical along the M = 0 MPa line. Due to the interaction between axial force and bending moment, the ultimate bearing capacity of the pipeline subjected to axial force and bending moment will be greater than the ultimate bearing capacity of the pipeline under a single axial force or bending moment. The existence of defects reduces the ultimate bearing capacity of the pipeline under a single load. With the increase of pressure, the interaction curve of axial force and bending moment of corroded pipeline gradually flattened. As the defect depth increases, the ellipticity of the interaction curve increases, and the second-order effect of the pipeline gradually decreases.

Fig. 4.
figure 4

Interaction of pressure, axial force and bending moment for corroded pipeline

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4 The Failure Mode of Corroded Pipeline

Based on the ductile damage parameters of metals, the failure modes of corroded pipeline subjected to axial compressive force and bending moment are studied in this paper. Fig. 5 is the deformation diagram of the corroded pipeline subjected to axial compressive force and bending moment. The corroded pipeline is first destroyed at the defect, and the crack develops circumferentially along the pipeline.

Fig. 5.
figure 5

The deformation of corroded pipeline subjected to axial force and bending moment predicted by numerical simulation

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5 Conclusion

Based on the ductile damage parameters of the material, the ultimate bearing capacity of the corroded pipeline was simulated by the fluid cavity simulation technology. Finally, the interaction surface and curve of the ultimate bearing capacity of the corroded pipeline with different defect depths were obtained.

The results show that low axial force can improve the bending moment bearing capacity of shallow corroded pipeline, while for deeply corroded pipeline, it only accelerates the damage to pipeline. The ultimate bearing capacity of corroded pipeline with different defect depths is affected by pressure. Under low pressure, the axial force and bending moment bearing capacity of the intact or shallow corroded pipeline will increase, and the area contained in the corresponding N-M interaction curve will increase. The pipeline is more likely to be damaged at the location of corrosion defect, and the cracks develop along the circumferential direction.