# A Useful Manufacturing Guide for Rotary Piercing Seamless Pipe by ALE Method

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Simulations of Seamless Pipe Manufacturing Process by ALE Numerical Simulation Method

#### 2.1. Material Models Selection

#### 2.2. Workpiece and Tools Geometry

#### 2.3. ALE Keywords and Mesh

#### 2.4. Mesh Sensitivity Study

#### 2.5. Results and Validation

## 3. Sensitivity Analysis by Considering the Effect of Velocity, the Temperature, and the Maximum Plug Diameter

#### 3.1. Selection of Scenarios

#### 3.2. Results and Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

(a) general | ||

ALE | Arbitrary Lagrangian–Eulerian | |

D/t | Pipe outer dimeter to thickness ratio | |

FEM | Finite element method | |

FSI | Fluid structure interactions | |

ID | Pipe inner diameter | |

OD | Pipe outer diameter | |

(b) software | ||

Software name | Developer | City and Country |

AFDEX 3D | Metal Forming Research Corporation (MFRC) | WingsTower A1208, Jinju-si 52818, Korea |

LS-DYNA | Livermore Software Technology (LST) | ANSYS, Inc. Southpointe 2600 Ansys Drive Canonsburg, PA 15317 USA |

METAFOR | University of Liège, Aerospace and Mechanical Engineering | Place du 20 Août 7, 4000 Liège, Belgium |

MSC-SuperForm | MSC Software Corporation | 4675 MacArthur Court Newport Beach, CA 92660 USA |

ProCAST | Pacific Engineering Systems International (Pacific ESI) | 277-279 Broadway Glebe, New South Wales, 2037 Australia |

QForm | Quantorform Ltd. | 2-nd Yuzhnoportovyy Proyezd, 16/2, 115088, Moscow, Russia |

Simufact Forming | MSC Software Corporation | 4675 MacArthur Court Newport Beach, CA 92660 USA |

## Nomenclature

${f}_{h}\left({\epsilon}_{eff}^{p}\right)$ | Hardening function |

${E}_{p}$ | Plastic hardening modulus |

${s}_{ij}$ | Deviatoric stress |

${\overline{s}}_{ij}^{n+1}$ | Trial deviatoric stress |

$\beta $ | Strain rate effects parameter |

${\delta}_{ij}$ | Kronecker delta |

${\epsilon}_{eff}^{p}$ | Effective plastic strain |

${\dot{\epsilon}}_{ij}$ | Strain rate tensor |

${\dot{\epsilon}}_{ij}^{\prime}$ | Deviatoric strain |

$\varphi $ | von Mises flow rule |

${\sigma}_{Y}$ | Yield stress |

${\sigma}_{0}$ | Initial yield stress |

${\sigma}_{ij}$ | Cauchy stress tensor |

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**Figure 1.**Mesh used in finite element analysis (

**a**) Original shape of element; (

**b**) Severe deformed shape of element, adapted from [31] with permission from Elsevier publisher.

**Figure 2.**Stress–strain curves of Plasticine at room temperature reproduced from reference [47] with permission from author.

**Figure 6.**Solid material deforms and translates inside the fixed mesh, reproduced from reference [50] with permission from author.

**Figure 11.**Side cross-sectional view shows Lode parameter and frontal cross-section views at different locations.

**Figure 13.**Rotary piercing with different maximum plug diameters with (

**a**) plug diameter = 27 mm, (

**b**) plug diameter = 30 mm, (

**c**) plug diameter = 33 mm.

**Figure 14.**Pipe average diameter versus maximum plug diameter (Note: ALE = arbitrary Lagrangian–Eulerian, ID = inner diameter, OD = outer diameter).

**Figure 16.**Stress contour plots of (

**a**) scenario No. 4, (

**b**) scenario No. 12, and (

**c**) scenario No. 60 (Note: T = material temperature, V = velocity, and PD

_{max}= maximum plug diameter).

**Figure 18.**Effect of material temperature on maximum von Mises stress at V = 5 mm/s (Note: PD

_{max}= maximum plug diameter).

**Figure 21.**Interpolations of the coefficients of the proposed equation (

**a**) C

_{00}, (

**b**) C

_{10}, (

**c**) C

_{01}, (

**d**) C

_{20}, (

**e**) C

_{02}, (

**f**) C

_{11}, (

**g**) C

_{21}, (

**h**) C

_{12}, (

**i**) C

_{30}, and (

**j**) C

_{03.}

Property | Unit | Value |
---|---|---|

Density | kg/m^{3} | 1800 |

Young’s Modulus | MPa | 42.5 |

Yield Stress | MPa | 0.18 |

Poisson’s ratio | - | 0.434 |

Parameter | Value | Parameter | Value |
---|---|---|---|

Initial workpiece diameter (mm) | 45 | Distance between roll axes (mm) | 330 |

Minimum roll gap (mm) | 38 | Feed angle (°) | 9 |

Maximum plug diameter (mm) | 33 | Entrance face angle (°) | 3.5 |

Plug advance (mm) | 25 | Exit face angle (°) | 3 |

Guide shoe diameter (mm) | 47 | Workpiece velocity (mm/s) | 5 |

Parameter | Description | Value |
---|---|---|

NQUAD | Number of quadrature points | 3 |

CTYPE | Coupling type | 4 |

DIREC | Coupling direction | 2 |

PFAC | Penalty factor | 0.1 |

FRCMIN | Minimum volume fraction for coupling activation | 0.4 |

ILEAK | Leakage control | 2 |

PLEAK | Leakage control penalty factor | 0.1 |

PFACMM | Mass-based penalty stiffness factor | 3 |

SN | T | V | PD_{max} | SN | T | V | PD_{max} | SN | T | V | PD_{max} |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 5 | 27 | 21 | 5 | 30 | 27 | 41 | 15 | 15 | 27 |

2 | 0 | 5 | 30 | 22 | 5 | 30 | 30 | 42 | 15 | 15 | 30 |

3 | 0 | 5 | 33 | 23 | 5 | 30 | 33 | 43 | 15 | 15 | 33 |

4 | 0 | 5 | 37 | 24 | 5 | 30 | 37 | 44 | 15 | 15 | 37 |

5 | 0 | 15 | 27 | 25 | 10 | 5 | 27 | 45 | 15 | 30 | 27 |

6 | 0 | 15 | 30 | 26 | 10 | 5 | 30 | 46 | 15 | 30 | 30 |

7 | 0 | 15 | 33 | 27 | 10 | 5 | 33 | 47 | 15 | 30 | 33 |

8 | 0 | 15 | 37 | 28 | 10 | 5 | 37 | 48 | 15 | 30 | 37 |

9 | 0 | 30 | 27 | 29 | 10 | 15 | 27 | 49 | 20 | 5 | 27 |

10 | 0 | 30 | 30 | 30 | 10 | 15 | 30 | 50 | 20 | 5 | 30 |

11 | 0 | 30 | 33 | 31 | 10 | 15 | 33 | 51 | 20 | 5 | 33 |

12 | 0 | 30 | 37 | 32 | 10 | 15 | 37 | 52 | 20 | 5 | 37 |

13 | 5 | 5 | 27 | 33 | 10 | 30 | 27 | 53 | 20 | 15 | 27 |

14 | 5 | 5 | 30 | 34 | 10 | 30 | 30 | 54 | 20 | 15 | 30 |

15 | 5 | 5 | 33 | 35 | 10 | 30 | 33 | 55 | 20 | 15 | 33 |

16 | 5 | 5 | 37 | 36 | 10 | 30 | 37 | 56 | 20 | 15 | 37 |

17 | 5 | 15 | 27 | 37 | 15 | 5 | 27 | 57 | 20 | 30 | 27 |

18 | 5 | 15 | 30 | 38 | 15 | 5 | 30 | 58 | 20 | 30 | 30 |

19 | 5 | 15 | 33 | 39 | 15 | 5 | 33 | 59 | 20 | 30 | 33 |

20 | 5 | 15 | 37 | 40 | 15 | 5 | 37 | 60 | 20 | 30 | 37 |

_{max}= maximum plug diameter (mm).

Surface | C | Value | C | Value |
---|---|---|---|---|

V = 5 mm/s | C_{00} | −13.45 | C_{11} | 0.02057 |

C_{10} | 2.82 | C_{21} | −0.0002623 | |

C_{01} | −0.6224 | C_{12} | 0.0001563 | |

C_{20} | −0.1031 | C_{30} | 0.001158 | |

C_{02} | −0.003655 | C_{03} | −0.0002983 | |

V = 15 mm/s | C_{00} | 54.73 | C_{11} | 0.05132 |

C_{10} | −3.005 | C_{21} | −0.0007234 | |

C_{01} | −1.154 | C_{12} | 0.0002157 | |

C_{20} | 0.06465 | C_{30} | −0.0004516 | |

C_{02} | −0.005454 | C_{03} | −0.00033 | |

V = 30 mm/s | C_{00} | −28.33 | C_{11} | 0.06595 |

C_{10} | 5.272 | C_{21} | −0.0009622 | |

C_{01} | −1.391 | C_{12} | 0.0003002 | |

C_{20} | −0.2039 | C_{30} | 0.002417 | |

C_{02} | −0.008803 | C_{03} | −0.0003383 |

Surface | Goodness of Fit | Value |
---|---|---|

V = 5 mm/s | SSE | 0.01303 |

R^{2} | 0.9999 | |

Adjusted R^{2} | 0.9998 | |

RMSE | 0.0361 | |

V = 15 mm/s | SSE | 0.01488 |

R^{2} | 0.9999 | |

Adjusted R^{2} | 0.9998 | |

RMSE | 0.03585 | |

V = 30 mm/s | SSE | 0.4139 |

R^{2} | 0.9998 | |

Adjusted R^{2} | 0.9995 | |

RMSE | 0.06434 |

^{2}= coefficient of determination, and RMSE = root mean square error.

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## Share and Cite

**MDPI and ACS Style**

Topa, A.; Cerik, B.C.; Kim, D.K. A Useful Manufacturing Guide for Rotary Piercing Seamless Pipe by ALE Method. *J. Mar. Sci. Eng.* **2020**, *8*, 756.
https://doi.org/10.3390/jmse8100756

**AMA Style**

Topa A, Cerik BC, Kim DK. A Useful Manufacturing Guide for Rotary Piercing Seamless Pipe by ALE Method. *Journal of Marine Science and Engineering*. 2020; 8(10):756.
https://doi.org/10.3390/jmse8100756

**Chicago/Turabian Style**

Topa, Ameen, Burak Can Cerik, and Do Kyun Kim. 2020. "A Useful Manufacturing Guide for Rotary Piercing Seamless Pipe by ALE Method" *Journal of Marine Science and Engineering* 8, no. 10: 756.
https://doi.org/10.3390/jmse8100756