Springback Coefficient Research of API X60 Pipe with Dent Defect
Abstract
:1. Introduction
2. Material
3. Parametric Finite Element Analysis
3.1. Finite Element Model
3.2. Load Model and Boundary Condition
- (1)
- The indenter was applied with a displacement load to simulate the extrusion of the pipe by an external object.
- (2)
- The indenter was applied with a reverse displacement load to simulate the process of removing the external object after the pipe was dented.
- (3)
- An internal pressure was assigned to the inner surface of the pipe to simulate the dented pipe under normal operation.
- (4)
- The internal pressure was released to evaluate the residual dent depth and observe the springback phenomenon.
3.3. Plug-In Program
3.4. FE Model Verification
4. Results and Discussion
4.1. Pipe Wall Thickness
4.2. Internal Pressure
4.3. Indenter Size
4.4. Dent Location
5. Significance Analysis of Influential Factors
5.1. Orthogonal Design
5.2. Grey Correlation Degree Calculation
5.3. Significance Analysis
6. Nonlinear Regression Analysis
6.1. Formula of Springback Coefficient after Pressurization
6.2. Formula of Springback Coefficient after De-Pressurization
7. Conclusions
- (1)
- To quickly and accurately establish an FE model of a dented pipe and to automate the simulation and analysis, ABAQUS secondary development technology was introduced. The plug-in interface for the parametric modeling and analysis of a dented pipe was programmed using RSG of ABAQUS, whose corresponding kernel script was compiled to cascade with it. This method avoids repeated modeling, saves time and energy, and effectively improves the automation of the simulation analysis process.
- (2)
- After pressurization, a thicker wall thickness led to larger springback coefficient. A larger internal pressure led to greater springback. The springback coefficient increased with increasing indenter size and dent depth. The closer the dent was to the bottom of the pipeline, the smaller the springback coefficient. Therefore, a dent at the top of the pipe should be of most concern in the evaluation of a dent, where the dent springs back most fully.
- (3)
- After de-pressurization, the springback coefficient decreased with increasing dent depth, wall thickness, indenter size, and dent location. However, the springback coefficient increased with increasing internal pressure. The springback coefficients were concentrated between 1.1 and 1.5. Therefore, the literature [9,11] values of the springback coefficient without internal pressure of 1.43 are not very accurate.
- (4)
- The effects of the influential factors on the springback coefficient were obtained by a combination of an orthogonal experimental design and the Grey correlation. For the springback coefficient after pressurization, the order of importance of the influential factors from largest to smallest was the dent location, dent depth, internal pressure, wall thickness, and indenter size. For the springback coefficient after de-pressurization, the order of importance of the influential factors from largest to smallest was the internal pressure, dent depth, wall thickness, indenter size, and dent location.
- (5)
- Quantitative expressions of the springback coefficient and influence factors were fit using a nonlinear regression method, which provides a reference for the calculation of springback of dented pipes.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
D | outside diameter of pipe (mm) |
t | wall thickness of pipe (mm) |
P | internal pressure of pipe (MPa) |
a | short axis of ellipsoidal indenter (mm) |
b | long axis of the ellipsoidal indenter (mm) |
β | dent location (°) |
d | dent depth before pressurizing (mm) |
dp | dent depth after pressurizing (mm) |
dr | dent depth after releasing pressure (mm) |
Hp | springback coefficient after pressurizing |
Hr | springback coefficient after releasing pressure |
E | Young’s modulus (MPa) |
α | undetermined coefficient |
δ | undetermined coefficient |
γ | undetermined coefficient |
ς | undetermined coefficient |
τ | undetermined coefficient |
υ | undetermined coefficient |
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Yield Stress | True Ultimate Tensile Stress | Young’s Modulus | Poisson’s Ratio |
---|---|---|---|
451 MPa | 660 MPa | 2 × 105 MPa | 0.3 |
Factors | 1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|---|
Levels | Wall Thickness (mm) | Internal Pressure (MPa) | Indenter Size a/b | Dent Location (°) | Ratio of Dent Depth to Pipe Diameter | |
1 | 6.9 | 2 | 0.1 | 0 | 0.04 | |
2 | 7.7 | 4 | 0.3 | 30 | 0.06 | |
3 | 8.5 | 6 | 0.5 | 60 | 0.08 | |
4 | 9.3 | 8 | 0.7 | 90 | 0.1 |
Number | Influence Factors | Springback Coefficient | ||||
---|---|---|---|---|---|---|
Wall Thickness (mm) | Internal Pressure (MPa) | Indenter Size a/b | Dent Location (°) | Ratio of Dent Depth to Pipe Diameter | ||
1 | 6.9 | 2 | 0.1 | 0 | 0.04 | 0.185 |
2 | 6.9 | 4 | 0.3 | 30 | 0.06 | 0.315 |
3 | 6.9 | 6 | 0.5 | 60 | 0.08 | 0.457 |
4 | 6.9 | 8 | 0.7 | 90 | 0.1 | 0.475 |
5 | 7.7 | 2 | 0.3 | 60 | 0.1 | 0.620 |
6 | 7.7 | 4 | 0.1 | 90 | 0.08 | 0.648 |
7 | 7.7 | 6 | 0.7 | 0 | 0.06 | 0.368 |
8 | 7.7 | 8 | 0.5 | 30 | 0.04 | 0.258 |
9 | 8.5 | 2 | 0.5 | 90 | 0.06 | 0.725 |
10 | 8.5 | 4 | 0.7 | 60 | 0.04 | 0.508 |
11 | 8.5 | 6 | 0.1 | 30 | 0.1 | 0.368 |
12 | 8.5 | 8 | 0.3 | 0 | 0.08 | 0.328 |
13 | 9.3 | 2 | 0.7 | 30 | 0.08 | 0.568 |
14 | 9.3 | 4 | 0.5 | 0 | 0.1 | 0.553 |
15 | 9.3 | 6 | 0.3 | 90 | 0.04 | 0.567 |
16 | 9.3 | 8 | 0.1 | 60 | 0.06 | 0.358 |
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Zhang, P.; Huang, Y.; Wu, Y. Springback Coefficient Research of API X60 Pipe with Dent Defect. Energies 2018, 11, 3213. https://doi.org/10.3390/en11113213
Zhang P, Huang Y, Wu Y. Springback Coefficient Research of API X60 Pipe with Dent Defect. Energies. 2018; 11(11):3213. https://doi.org/10.3390/en11113213
Chicago/Turabian StyleZhang, Peng, Yunfei Huang, and Ying Wu. 2018. "Springback Coefficient Research of API X60 Pipe with Dent Defect" Energies 11, no. 11: 3213. https://doi.org/10.3390/en11113213