# Determining Material Data for Welding Simulation of Presshardened Steel

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## Abstract

**:**

## 1. Introduction

- flow stress ${k}_{F}$;
- elastic modulus E and Poisson ratio $\nu $;
- coefficient of thermal expansion $\alpha $;
- specific electrical resistance ${\rho}_{el}$;
- mass density $\rho $;
- specific heat capacity ${c}_{p}$/specific entropy $h$; and
- specific thermal conductivity $\lambda $.

## 2. Materials and Methods

#### 2.1. Experimental

#### 2.1.1. Test Procedure

#### 2.1.2. Data Processing

#### 2.2. Numerical Material Simulation

#### 2.3. Resistance Spot Welding Simulation and Welding Experiments

## 3. Results and Discussion

#### 3.1. Flow Stress

#### 3.2. Physical Properties

#### 3.2.1. Elastic Modulus and Poisson Ratio

#### 3.2.2. Coefficient of Thermal Expansion

#### 3.2.3. Specific Electric Resistance

#### 3.2.4. Mass Density

#### 3.2.5. Specific Heat Capacity

#### 3.2.6. Specific Thermal Conductivity

#### 3.3. Data Application in Resistance Spot Welding

_{4}or A

_{S}is considered to be sufficient to form a joint across the sheet metals’ surfaces. The experimentally observed nugget growth curve lies well in between both criteria. In Figure 14, melting is only assumed when the temperature A

_{S}is surpassed, which explains the seemingly too-small nugget in the picture. It shall also be noted that the computed electrode indentation depth and shape conform very well with the experiment. By comparison of the sheet thicknesses on the left border of Figure 14, it is assured that the relative scaling of FEA and the macrosection is correct.

#### 3.4. Tabular Data

## 4. Conclusions

- Data on the flow stress of 22MnB5 was measured and converted to stress–strain data for test temperatures ranging from ${T}_{\phi}=293\mathrm{K}$ to ${T}_{\phi}=1473\mathrm{K}$.
- Flow stress data is provided by means of flow parameters for the tested temperatures according to the Hockett–Sherby model.
- Physical material property data of 22MnB5 as a function of temperature has been computed using material simulation software. The data was critically reviewed considering literature data.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Flow stress curves of 22MnB5 after rapid heating from heat-treated state; * artificial curves.

**Figure 14.**Macrosection of weld nugget in comparison to computed result, the latter half-translucent; temperature profile is in K, gray surface represents melt.

**Table 1.**Computed phase-transformation temperatures of 22MnB5; quasi-static according to [24], and rapid heating.

Quantity | $\dot{\mathit{T}}\approx 0\mathbf{K}{\mathbf{s}}^{-1}$ | $\dot{\mathit{T}}=1\mathbf{k}\mathbf{K}{\mathbf{s}}^{-1}$ |
---|---|---|

${\mathit{A}}_{\mathit{c}3}/\mathit{K}$ | 1153 | 1213 |

${\mathit{A}}_{\mathit{c}1}/\mathit{K}$ | 993 | 1068 |

**Table 2.**Hockett–Sherby flow stress parameters of 22MnB5 after rapid heating from martensitic state.

${\mathit{T}}_{\mathit{\phi}}/\mathbf{K}$ | ${\mathit{k}}_{\mathit{f},0}/\mathbf{M}\mathbf{P}\mathbf{a}$ | ${\mathit{k}}_{\mathit{f},\mathit{s}}/\mathbf{M}\mathbf{P}\mathbf{a}$ | $\mathit{m}/1$ | $\mathit{P}/1$ |
---|---|---|---|---|

293 | 1066 | 1488 | 87 | 0.885 |

673 | 680 | 844 | 8934 | 1.533 |

773 | 432 | 529 | 818 | 1.11 |

873 | 298 | 368 | 134.5 | 0.82 |

973 | 147 | 196 | 90.5 | 0.83 |

1073 | 97 | 248 | 1 | 0.52 |

1173 | 79.5 | 180 | 1 | 0.515 |

1273 | 39 | 100 | 2 | 0.605 |

1373 | 25 | 74.3 | 2.6 | 0.663 |

1473 | 17.5 | 43.5 | 3 | 0.615 |

$\mathit{T}/\mathbf{K}$ | $\mathit{E}/\mathbf{G}\mathbf{P}\mathbf{a}$ | $\mathit{\nu}/1$ | $\mathit{T}/\mathbf{K}$ | $\mathit{\alpha}/{10}^{-5}{\mathbf{K}}^{-1}$ | $\mathit{T}/\mathbf{K}$ | ${\mathit{\rho}}_{\mathit{e}\mathit{l}}/\mathsf{\mu}\mathsf{\Omega}\mathbf{m}$ |
---|---|---|---|---|---|---|

273.15 | 211.804 | 0.290 | 293.15 | 1.256 | 273.15 | 0.214 |

505.05 | 198.693 | 0.298 | 460.98 | 1.307 | 458.96 | 0.340 |

744.51 | 179.279 | 0.307 | 595.73 | 1.348 | 651.12 | 0.506 |

935.80 | 151.383 | 0.315 | 762.56 | 1.398 | 840.70 | 0.742 |

1068.15 | 128.226 | 0.320 | 917.37 | 1.442 | 1027.97 | 1.020 |

1213.15 | 113.060 | 0.347 | 1068.15 | 1.485 | 1068.15 | 1.082 |

1426.11 | 91.707 | 0.360 | 1213.15 | 1.160 | 1132.22 | 1.122 |

1669.15 | 65.859 | 0.375 | 1322.89 | 1.280 | 1244.72 | 1.156 |

1831.15 | 1.470 | 0.450 | 1437.27 | 1.380 | 1402.63 | 1.201 |

3273.15 | 1.470 | 0.450 | 1567.51 | 1.469 | 1570.86 | 1.238 |

1669.15 | 1.525 | 1669.15 | 1.254 | |||

1831.15 | 2.416 | 1831.15 | 1.402 | |||

1966.85 | 2.504 | 3273.15 | 1.604 | |||

2192.90 | 2.646 | |||||

2426.40 | 2.777 | |||||

2708.93 | 2.919 | |||||

2989.43 | 3.036 | |||||

3273.15 | 3.133 |

$\mathit{T}/\mathbf{K}$ | $\mathsf{\rho}/\mathbf{k}\mathbf{g}{\mathbf{m}}^{-3}$ | $\mathit{T}/\mathbf{K}$ | $\mathbf{h}/\mathbf{M}\mathbf{J}{\mathbf{m}}^{-3}$ | $\mathit{T}/\mathbf{K}$ | $\mathit{\lambda}/\mathbf{W}{\mathbf{m}}^{-1}{\mathbf{K}}^{-1}$ |
---|---|---|---|---|---|

273.15 | 7815 | 273.15 | 0 | 273.15 | 45.738 |

408.21 | 7775 | 433.92 | 591 | 343.92 | 46.153 |

589.77 | 7717 | 637.68 | 1441 | 425.87 | 45.807 |

798.48 | 7643 | 735.55 | 1911 | 534.21 | 44.244 |

946.10 | 7588 | 851.72 | 2529 | 662.40 | 41.172 |

1068.15 | 7541 | 951.01 | 3150 | 854.26 | 35.678 |

1213.15 | 7560 | 1019.39 | 3652 | 956.06 | 33.161 |

1372.11 | 7475 | 1103.25 | 4163 | 1051.18 | 31.402 |

1566.58 | 7373 | 1213.15 | 4795 | 1150.47 | 29.447 |

1669.15 | 7322 | 1470.95 | 5921 | 1211.79 | 28.152 |

1831.15 | 6947 | 1669.15 | 6838 | 1407.03 | 30.473 |

2092.03 | 6722 | 1831.15 | 9110 | 1608.95 | 32.917 |

2539.46 | 6320 | 2022.07 | 9952 | 1669.15 | 33.700 |

3273.72 | 5625 | 2336.66 | 11,239 | 1831.15 | 100.000 |

2701.79 | 12,521 | 3273.15 | 120.000 | ||

3001.71 | 13,405 | ||||

3273.15 | 14,090 |

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**MDPI and ACS Style**

Kaars, J.; Mayr, P.; Koppe, K.
Determining Material Data for Welding Simulation of Presshardened Steel. *Metals* **2018**, *8*, 740.
https://doi.org/10.3390/met8100740

**AMA Style**

Kaars J, Mayr P, Koppe K.
Determining Material Data for Welding Simulation of Presshardened Steel. *Metals*. 2018; 8(10):740.
https://doi.org/10.3390/met8100740

**Chicago/Turabian Style**

Kaars, Jonny, Peter Mayr, and Kurt Koppe.
2018. "Determining Material Data for Welding Simulation of Presshardened Steel" *Metals* 8, no. 10: 740.
https://doi.org/10.3390/met8100740