# Theoretical and Experimental Analysis of a New Process for Forming Flanges on Hollow Parts

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{pi}, and a base 5. The material can flow freely in a radial direction until it comes into contact with the limit ring—until then, the flange has a variable thickness, and the die cavity is not filled completely. Since the flange diameter cannot be increased, the filling of the die cavity continues, resulting in a uniform thickness of the flange. After filling the closed die cavity with the material being deformed, the volume of the impression is increased by using the limit ring with a bigger inside diameter. After that, the extrusion process is continued as previously in order to increase the flange diameter.

^{2}K [6]. The heat exchange coefficient with the environment was equal to 0.02 kW/m

^{2}K. The initial temperature of the billet and tools was 20 °C. The punch velocity was set equal to 50 mm/min. Experiments were performed with the Instron 1000 HDX testing machine using the tools shown in Figure 2. To prevent uncontrolled movement of the die in the opposite direction to the punch movement, the die and base were clamped between two additional plates with the usage of screws.

_{pi}of the rings ranged from 23 to 56 mm and was changed every 3 mm. The outside diameter D

_{z}of individual rings was maintained constant at 70 mm. Numerical results were then used to determine the values of forces at which the die cavity was filled when using limit rings with different inside diameters. Experimental tests were carried out under the same conditions as those applied in the numerical analysis. Analyzed parameters are given in Table 1. The results were compared with those obtained in radial extrusion without rings [5,6].

## 3. Results and Discussion

- σ
_{max}is the maximum principal stress, - σ
_{HMH}is the reduced stress according to the Huber–Mises–Hencky hypothesis, - ε is the strain,
- C is the material constant.

_{1}almost coincides with that of circumferential stresses. For the analyzed case of principal stresses, the planes of the highest shear stresses (88.73 MPa) are oriented at an angle of ±45° relative to the first principal direction (Figure 9). As a result, the flange begins to crack in these planes, which is confirmed by the experimental results (Figure 6b).

_{p}expressed in mm (Equation (9)). The objective function described by Equation (10) is then defined, and the least-squares method is used to determine the coefficients a and b, thus yielding Equation (11) that is plotted as a red straight line in Figure 10. Given the above, it can be stated that the maximum incremental extrusion force for forming a flange with a given diameter can be roughly determined using the obtained equation.

- D
_{p}is the inside diameter of the limit ring, - F(D
_{p}) is the force as a function of limit ring diameter, - a, b are coefficients,
- Ω
_{F}is the objective function, - F
_{i}is the value of force at i-th measurement (Table 3).

## 4. Conclusions

- the incremental radial extrusion process for hollow parts makes it possible to form flanges with their diameter bigger by 30% than that of flanges produced by extrusion without the use of rings;
- due to the favorable stress pattern, the proposed method makes it possible to produce flanges with uniform thickness, which cannot be done by the extrusion process without rings wherein the flange thickness decreases with the distance from the workpiece axis;
- due to the use of rings for limiting a free radial flow of material in flange extrusion, three-axial compressive stresses occur in the flange during filling of the closed die cavity, which is desired in terms of cracking;
- flange cracking occurs in the plane of maximum shear stresses; this plane is oriented at an angle of ±45° relative to the direction of the maximum principal stress, this direction being similar to that of circumferential stresses; in the performed research, the crack always occur in the same direction;
- the maximum forming forces increase almost linearly with increasing flange diameter.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic design of incremental radial extrusion of flange: 1—punch, 2—billet, 3—die, 4—ring, 5—base.

**Figure 6.**Hollow part with a flange produced by (

**a**) incremental radial extrusion—crack formation, (

**b**) incremental radial extrusion—visible crack, (

**c**) radial extrusion without rings—visible crack.

**Figure 8.**Distribution of (

**a**) the normalized Cockcroft–Latham ductile fracture criterion and (

**b**) circumferential stresses in a 59.5 mm diameter flange.

**Figure 9.**Stress pattern at the point located on the flank of a flange with a diameter at which cracking occurs.

**Table 1.**Analyzed parameters of incremental radial extrusion of the flange (denotations according to Figure 1).

D (mm) | g (mm) | l (mm) | R (mm) | h (mm) | D_{pi} (mm) | D_{z} (mm) |
---|---|---|---|---|---|---|

20 | 3 | 80 | 1 | 3 | 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56 | 70 |

**Table 2.**Values of stress components at the point located on the flank of a flange with a diameter at which cracking occurs (denotations according to Figure 9).

σ_{x}(MPa) | σ_{y}(MPa) | σ_{z}(MPa) | τ_{xy}(MPa) | τ_{xz}(MPa) | τ_{yz}(MPa) | σ_{1}(MPa) | σ_{2}(MPa) | σ_{3}(MPa) |

171.60 | −4.74 | 10.51 | −7.71 | 0.25 | 2.74 | 171.93 | 10.98 | −5.54 |

α_{1}(°) | β_{1}(°) | γ_{1}(°) | α_{2}(°) | β_{2}(°) | γ_{2}(°) | α_{3}(°) | β_{3}(°) | γ_{3}(°) |

2.49 | 92.49 | 89.95 | 89.62 | 80.29 | 9.71 | 92.47 | 169.97 | 80.28 |

**Table 3.**Maximum extrusion force versus inside diameter of the ring (denotations according to Figure 1).

Measurement No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

D_{pi}(mm) | 23 | 26 | 29 | 32 | 35 | 38 | 41 | 44 | 47 | 50 | 53 | 56 |

F_{i}(kN) | 85 | 89 | 92 | 96 | 101 | 106 | 111 | 117.5 | 124 | 131 | 137 | 142 |

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**MDPI and ACS Style**

Winiarski, G.; Gontarz, A.; Samołyk, G.
Theoretical and Experimental Analysis of a New Process for Forming Flanges on Hollow Parts. *Materials* **2020**, *13*, 4088.
https://doi.org/10.3390/ma13184088

**AMA Style**

Winiarski G, Gontarz A, Samołyk G.
Theoretical and Experimental Analysis of a New Process for Forming Flanges on Hollow Parts. *Materials*. 2020; 13(18):4088.
https://doi.org/10.3390/ma13184088

**Chicago/Turabian Style**

Winiarski, Grzegorz, Andrzej Gontarz, and Grzegorz Samołyk.
2020. "Theoretical and Experimental Analysis of a New Process for Forming Flanges on Hollow Parts" *Materials* 13, no. 18: 4088.
https://doi.org/10.3390/ma13184088