# Three-Dimensional Finite Element Modelling of Sheet Metal Forming for the Manufacture of Pipe Components: Symmetry Considerations

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Finite Element Model (FEM)

#### 2.2. Materials

#### 2.3. Boundary Conditions (Constraints, Load, and Contacts Definition)

## 3. Results and Discussion

#### 3.1. Residual Stress and Plastic Strain Distribution

#### 3.2. Pipe Dimension Analysis

#### 3.3. Modelling Validation (Roudness and Symmetry of Curvature Simulation vs. Real Data/Symmetry from Middle Plane)

## 4. Conclusions

- This model makes it possible to predict dimensions of the tube with the input parameters of the three-roll bending process. In this paper, parameter selection is based on the technical data of the three-roll bending process currently used;
- The residual stress and plastic deformation through the thickness of the plate are estimated, and the final dimensions of the tube are discussed. The minimum residual stress was in the vicinity of the neutral fiber (value 40 MPa), with a symmetrical distribution of the equivalent plastic strain and von Mises stress, with a maximum value of 130.6 MPa;
- Finally, validation of the FEM simulation is carried out experimentally. This comparison showed that the numerical and experimental results agree, with a shape error of 1.95% in the experimental case and 2.3% for the simulation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Roll-bending process at different steps: (

**a**) initial bending position; (

**b**) initial roll-bending; (

**c**) 25% of the roll-bending process; (

**d**) 50% of the roll-bending process; (

**e**) 75% of the roll-bending process; (

**f**) obtained pipe.

**Figure 9.**(

**a**) Distribution of equivalent plastic strain along the sheet thickness which is bent. (

**b**) Corresponding graph along the sheet thickness from node 59079 to 78945.

**Figure 10.**(

**a**) Distribution of equivalent von Mises stress over a section of bend along the sheet thickness. (

**b**) Corresponding graph along the sheet thickness from node 59079 to 78945.

**Figure 13.**Curvature of the pipe obtained from the sensor, on left denoted by (

**a**) after first pre-bending and right give by (

**b**) at the end of the bending process.

Diameter | 3800 mm |

Length | 4000 mm |

Thickness | 22 mm |

Weight of the component | 116.620 TN |

Capacity | 607 × 10^{6} mm^{3} |

Materials of the component | SA-516 Gr.70N |

Yield strength (MPa) | 805 |

Young’s modulus (GPa) | 200 |

Density/(Kg/mm^{3}) | 7.83 × 10^{−6} |

Poisson ratio | 0.29 |

Mesh | No. of Elements | Average Radius Error % | Effective Stress (GPa) | Effective Plastic Strain | Relative CPU Time (mins) |
---|---|---|---|---|---|

Coarse | 3560 | 1.85 | 0.832 | 1.43 × 10^{−2} | 300 |

Normal | 8898 | 1.72 | 0.837 | 1.50 × 10^{−2} | 420 |

Fine | 17,796 | 1.71 | 0.838 | 1.51 × 10^{−2} | 830 |

Desired Radius (mm) | Obtained Radius (mm) | Average Radius Error (%) | Shape Error (mm) | ||
---|---|---|---|---|---|

First Bending | End of Bending | ||||

Experimental | 1900 | 1927 | 1920 | 1.2 | 1.95 |

FEM | 1900 | 1932.6 | 1934 | 1.7 | 2.30 |

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**MDPI and ACS Style**

Bhujangrao, T.; Veiga, F.; Penalva, M.; Costas, A.; Ruiz, C.
Three-Dimensional Finite Element Modelling of Sheet Metal Forming for the Manufacture of Pipe Components: Symmetry Considerations. *Symmetry* **2022**, *14*, 228.
https://doi.org/10.3390/sym14020228

**AMA Style**

Bhujangrao T, Veiga F, Penalva M, Costas A, Ruiz C.
Three-Dimensional Finite Element Modelling of Sheet Metal Forming for the Manufacture of Pipe Components: Symmetry Considerations. *Symmetry*. 2022; 14(2):228.
https://doi.org/10.3390/sym14020228

**Chicago/Turabian Style**

Bhujangrao, Trunal, Fernando Veiga, Mariluz Penalva, Adriana Costas, and Cristina Ruiz.
2022. "Three-Dimensional Finite Element Modelling of Sheet Metal Forming for the Manufacture of Pipe Components: Symmetry Considerations" *Symmetry* 14, no. 2: 228.
https://doi.org/10.3390/sym14020228