# Selection of Constitutive Material Model for the Finite Element Simulation of Pressure-Assisted Single-Point Incremental Forming

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Work

_{i}= 0.7 mm and a diameter of D = 285 mm, the forming diameter is d = 180 mm, form height is h = 50 mm, and forming angle is α = 45°. To assure accuracy, all experiments and measurements were repeated three times, and the average of the results was calculated. Due to the high manganese content of this tool, its resistance to wear is exceptional. Figure 2 depicts the utilised forming tool, whereas Table 1 outlines its elemental composition.

#### 2.2. FE Modelling Work

^{3}, while its Poisson’s ratio and modulus of elasticity are 0.29 and 207 GPa, respectively. The material plastic behaviour obtained from experimental tensile tests was inputted to the model as tabulated values of plastic stress–strain paired values. Three material damage models were considered, namely the Gurson–Tvergaard–Needleman (GTN) damage model, ductile damage model, and fracture-forming-limit damage (FFLD) model. The GTN yield function is defined as in Equation (1).

_{eq}and σ

_{m}are the equivalent von Mises stress and hydrostatic stress, respectively. q

_{1}, q

_{2}, and q

_{3}are the material parameters, and σ

_{y}is the flow/yield stress of the material. The volume void fraction is modified to f

^{∗}due to the accelerating effects of the void coalescence as follows:

_{f}are the critical void volume fraction at the onset of voids coalescence and the critical void volume fraction at the onset of failure, respectively. The change in the void volume fraction is due to the enlargement of existing voids and the nucleation of new voids. Thus, the rate of change in the void volume fraction is expressed as a sum of the rate of growth of existing voids (f

_{G}) and the rate of void nucleation (f

_{N}) and can be defined as in Equations (3) and (4).

_{N}represents the mean nucleation strain with a standard deviation of S

_{N}, and f

_{N}is the void volume fraction of the nucleating voids. The DP600 steel parameters for the GTN model were collected from the literature [40] as detailed in Table 2.

_{h}) and the equivalent von Mises stress (σ

_{eq}) as defined by equation 5. The experimentally measured values of the fracture initiation strain at different triaxialities [41] are depicted in Figure 6; the associated data were inputted to the model as tabulated values, and a strain rate of 1 s

^{−1}was considered to be a suitable average value for incremental-forming processes [42]. The aforementioned fracture strain represents the start or onset of material damage (strain at the start of fracture), which is followed by material damage evolution. A generalised model that relates triaxiality to equivalent initial fracture strain (${\overline{\epsilon}}_{0}^{pl}$) is depicted in Equation (6), with C

_{1}and C

_{2}as the material constants, and η

_{0}is generally approximated to be 0.333 [43].

_{f}), effective plastic displacement (u

^{pl}), and yield stress (σ

_{y}) as detailed in Equation (7). The fracture energy for the DP600 steel was reported as 106 MJ/m

^{2}. Compared with the extrapolated stress–strain relation following damage initiation, stresses during the damage evolution are softened or reduced by a factor of 1-D. To capture the residual load-carrying capability of a cracked ductile material, a postpeak softening component of the stress–strain curve is usually included in the modelling work.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**Typical stress–strain curve showing strain hardening and softening post damage initiation.

**Figure 11.**Blank deformation and deformed mesh over various stages (initial stage on left and final stage on right) of PA-SPIF.

**Figure 12.**von Mises stress distribution for FFLD material model at (

**a**) no fluid pressure, (

**b**) pressure 0.2 bar, and (

**c**) pressure 0.4 bar.

**Figure 13.**von Mises stress distribution for GTN material model at (

**a**) no fluid pressure, (

**b**) pressure 0.2 bar, and (

**c**) pressure 0.4 bar. Predicted fracture regions are marked with red arrow.

**Figure 14.**von Mises stress distribution for DD material model at (

**a**) no fluid pressure, (

**b**) pressure 0.2 bar and (

**c**) pressure 0.4 bar.

**Figure 15.**Thickness spatial variation at end of process as predicted by simulation using (

**a**) GTN material model, (

**b**) FFLD model, and (

**c**) DD material model for different pressure settings.

**Figure 16.**Variation from CAD at end of process as predicted by simulation using (

**a**) GTN material model, (

**b**) FFLD model, and (

**c**) DD model for different pressure settings.

Tool elemental composition (wt.%) | Al | Fe | Ni | Mn | Cu | Zn | Pb | Sn |

5.0 | 2.0 | 1.0 | 2.5 | 60 | 22 | 0.20 | 0.20 | |

Oil physical Properties | Density (gr/cm³) | Viscosity (mm²/s)at 40 °C | Flash point (°C) | |||||

0.92 | 6 | 310 | ||||||

Workpiece elemental composition (wt.%) | C | Mn | Si | Cr | Al | Ni | P | Cu |

0.116 | 1.545 | 0.289 | 0.634 | 0.042 | 0.041 | 0.029 | 0.019 |

**Table 2.**GTN model parameters [40].

q_{1} | q_{2} | q_{3} | f_{0} | f_{c} | f_{f} | f_{N} | S_{N} | ε_{N} |
---|---|---|---|---|---|---|---|---|

1.5 | 1 | 2.25 | 0.008 | 0.15 | 0.25 | 0.00062 | 0.1283 | 0.5421 |

**Table 3.**Comparison of experimental and numerical results of various material models at different pressure settings.

Axial Depth (mm) | Experimental Results | FFLD | GTN | DD | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

0.0 bar | 0.2 bar | 0.4 bar | 0.0 bar | 0.2 bar | 0.4 bar | 0.0 bar | 0.2 bar | 0.4 bar | 0.0 bar | 0.2 bar | 0.4 bar | |

Variation from CAD (mm) | ||||||||||||

20 | 1.4 | 1.11 | 1.03 | 1.39 | 1.12 | 1.01 | 1.42 | 1.21 | 1.05 | 1.38 | 1.06 | 0.99 |

30 | 1.1 | 0.96 | 0.88 | 1.16 | 0.95 | 0.86 | 1.17 | 1.04 | 0.89 | 1.13 | 0.93 | 0.86 |

40 | 1.01 | 0.88 | 0.83 | 0.99 | 0.86 | 0.81 | 1.10 | 0.92 | 0.84 | 0.94 | 0.86 | 0.83 |

Thickness (mm) | ||||||||||||

10 | 0.56 | 0.52 | 0.47 | 0.56 | 0.51 | 0.46 | 0.51 | 0.50 | 0.44 | 0.53 | 0.50 | 0.44 |

20 | 0.48 | 0.44 | 0.38 | 0.47 | 0.43 | 0.37 | 0.44 | 0.41 | 0.36 | 0.46 | 0.41 | 0.36 |

30 | 0.47 | 0.44 | 0.39 | 0.46 | 0.43 | 0.38 | 0.45 | 0.40 | 0.37 | 0.47 | 0.42 | 0.39 |

40 | 0.47 | 0.46 | 0.41 | 0.47 | 0.45 | 0.40 | 0.46 | 0.44 | 0.37 | 0.45 | 0.43 | 0.38 |

Material Model | |||
---|---|---|---|

Characteristics | FFLD | DD | GTN |

No-fracture prediction | Yes | Yes | No |

Thickness discrepancy up to (%) | 3 | 6 | 10 |

Variation from CAD up to (%) | 10 | 16 | 21 |

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**MDPI and ACS Style**

Abdelhafeez Hassan, A.; Küçüktürk, G.; Yazgin, H.V.; Gürün, H.; Kaya, D.
Selection of Constitutive Material Model for the Finite Element Simulation of Pressure-Assisted Single-Point Incremental Forming. *Machines* **2022**, *10*, 941.
https://doi.org/10.3390/machines10100941

**AMA Style**

Abdelhafeez Hassan A, Küçüktürk G, Yazgin HV, Gürün H, Kaya D.
Selection of Constitutive Material Model for the Finite Element Simulation of Pressure-Assisted Single-Point Incremental Forming. *Machines*. 2022; 10(10):941.
https://doi.org/10.3390/machines10100941

**Chicago/Turabian Style**

Abdelhafeez Hassan, Ali, Gökhan Küçüktürk, Hurcan Volkan Yazgin, Hakan Gürün, and Duran Kaya.
2022. "Selection of Constitutive Material Model for the Finite Element Simulation of Pressure-Assisted Single-Point Incremental Forming" *Machines* 10, no. 10: 941.
https://doi.org/10.3390/machines10100941