# Calibration of the Flow Curve Up to Large Strain Range by Incremental Sheet Forming Coupled with FEM Simulation

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## Abstract

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## 1. Introduction

## 2. Experiments

#### 2.1. Material Properties

_{T}, m, and c are the parameters of the proposed equation, and m is a dependent parameter calculated as follows:

_{T}and c in the Kim–Tuan model are calculated using the curve fitting tool, which is available on some optimization packages such as Excel or MATLAB. The Kim–Tuan equation can be easily reduced to the Swift equation when ${\sigma}_{0}$ is ignored and c is infinity. In addition, this equation can be simplified to the Voce equation when the parameter $m$ is zero.

#### 2.2. ISF Experiment

#### 2.3. Forming Force Measurement

## 3. Finite Element Simulation

#### 3.1. The Associated Flow Rule with Mixed Hardening

#### 3.2. Calibration of Stress–Strain Curve Up to Large Strain Range

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Dimensions of tensile test specimen. (

**b**) Stress–strain curves of the AL5052-O sheet for three different orientations.

**Figure 3.**(

**a**) Forming set up for incremental sheet forming. (

**b**) Two-wing star toolpath. (

**c**) Fracture happening for the two-wing star toolpath (bottom-up view).

**Figure 4.**(

**a**) Forming force Fz in the first and second depth increment. (

**b**) Forming force Fz in whole forming process.

**Figure 6.**(

**a**) The formed part after 3rd depth increment in the FEM. (

**b**) Force Fz prediction by FEM using stress–strain curve in uniform deformation range.

**Figure 9.**(

**a**) Force prediction for the first three forming steps with the increment strain of $\left({\epsilon}_{u}+0.05\right)$. (

**b**) Best-fitted trial stress–trial strain in large strain range.

**Figure 10.**(

**a**) Fracture prediction by FEM with the best-fitted trial stress–trial strain curve. (

**b**) Comparison of the experimental force and force prediction by FEM with different hardening equations.

Direction | 0$\xb0$ | $45\xb0$ | $90\xb0$ |
---|---|---|---|

Young’s modulus [GPa] | 73.2 | 71.2 | 74.1 |

Yield stress [MPa] | 183.3 | 172.5 | 173.6 |

Ultimate tensile strength [MPa] | 229.8 | 216.6 | 220.1 |

Elongation [%] | 11.0 | 13.6 | 10.5 |

R-value | 0.758 | 0.646 | 0.863 |

K_{T} | 131.580 | 124.809 | 124.268 |

m | 0.271 | 0.278 | 0.251 |

c | 61.163 | 75.433 | 69.521 |

Yield Function Hill48 | |||
---|---|---|---|

F | G | H | N |

0.4996 | 0.5688 | 0.4312 | 1.2244 |

Increment | Experimental (N) | FEM Using the Fitted Curve (N) | FEM Using Voce Curve (N) |
---|---|---|---|

15th | 1050.3 | 1065.73 | 956.39 |

20th | 1095.97 | 1104.38 | 766.37 |

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**MDPI and ACS Style**

Kim, Y.-S.; Tuan, P.-Q.; Xiao, X.; Kim, J.-j. Calibration of the Flow Curve Up to Large Strain Range by Incremental Sheet Forming Coupled with FEM Simulation. *Metals* **2022**, *12*, 252.
https://doi.org/10.3390/met12020252

**AMA Style**

Kim Y-S, Tuan P-Q, Xiao X, Kim J-j. Calibration of the Flow Curve Up to Large Strain Range by Incremental Sheet Forming Coupled with FEM Simulation. *Metals*. 2022; 12(2):252.
https://doi.org/10.3390/met12020252

**Chicago/Turabian Style**

Kim, Young-Suk, Pham-Quoc Tuan, Xiao Xiao, and Jin-jae Kim. 2022. "Calibration of the Flow Curve Up to Large Strain Range by Incremental Sheet Forming Coupled with FEM Simulation" *Metals* 12, no. 2: 252.
https://doi.org/10.3390/met12020252