# Optimization of Resistance Spot Welding with Inserted Strips via FEM and Response Surface Methodology

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Finite Element Modeling

#### 2.1. Model Construction

#### 2.1.1. Geometrical Model

#### 2.1.2. Boundary Condition

^{−2}K

^{−1}and 1.5 × 10

^{4}Wm

^{−2}K

^{−1}, respectively.

#### 2.1.3. Material Properties and Welding Parameters

#### 2.1.4. Contact Resistance Model

_{S}and T

_{0}are the contact super temperature and the bulk temperature at the interfaces, respectively, and L is the Lorentz constant of iron (about 2.0 × 10

^{−8}(V/°C)

^{2}). In the present computations, T

_{S}at the sheet/sheet interface was specified to be the solidus of steel (1500 °C), and that at the electrode/sheet interface to be the melting point of the electrodes (1084 °C).

#### 2.1.5. Computational Procedure

#### 2.2. Temperature History

#### 2.3. Weld Formation Process

#### 2.4. Electrode Surface Temperature

#### 2.5. Validation of Simulated Results

## 3. Results and Discussions

#### 3.1. Development of Regression Model

#### 3.1.1. Second-Order Regression Equation

_{0}is the response of the central point, and a

_{i}, a

_{ii}, and a

_{ij}are regression coefficients of respective linear, squared, and interaction model terms.

#### 3.1.2. Design of Experiment

#### 3.1.3. Regression Models

#### 3.2. Effect of Process Parameters on the Responses

#### 3.2.1. Electrode Tip Temperature

#### 3.2.2. Weld Diameter

#### 3.2.3. Strip Temperature

#### 3.3. Determination of the Process Window for a Preferable Strip

#### 3.4. Experiment Validation

## 4. Conclusions

- (1)
- The inserted strips would lead to earlier weld initiation of weld and bigger final weld size in both diameter and thickness, and meanwhile lower electrode surface temperature.
- (2)
- Strip thickness showed a negative effect on the electrode tip temperature, while the increase of strip resistivity led to a first-down-then-up electrode tip temperature. Both the strip thickness and the resistivity showed a positive effect on the weld diameter and the maximum strip temperature.
- (3)
- A graphical optimization suggested a Cu55Ni45 strip with thickness of 0.12 mm for a 0.4 mm steel sheet.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Temperature (°C) | Young’s Modulus (GPa) | Electrical Resistivity (Ω·m × 10 ^{−7}) | Specific Heat (J·kg ^{−1}·K^{−1}) | Thermal Expansion Coefficient (K ^{−1} × 10^{−5}) |
---|---|---|---|---|

21 | 124 | 0.264 | 397.75 | 1.66 |

93 | 105 | 0.300 | 401.93 | 1.67 |

204 | 93 | 0.399 | 418.68 | 1.71 |

316 | 83 | 0.505 | 431.24 | 1.75 |

427 | 55 | 0.619 | 439.61 | 1.78 |

538 | 39 | 0.699 | 452.17 | 1.84 |

649 | 25 | 0.800 | 464.73 | 1.85 |

732 | - | - | 477.30 | - |

760 | 16 | 0.898 | - | 1.89 |

774 | - | - | - | - |

799 | - | - | - | - |

871 | 14 | 0.948 | - | 1.93 |

982 | 7 | 0.998 | - | - |

Temperature (°C) | Yield Strength (MPa) | Electrical Resistivity (Ω·m × 10 ^{−7}) | Specific Heat (J·kg ^{−1}·K^{−1}) | Thermal Expansion Coefficient (K ^{−1} × 10^{−5}) |
---|---|---|---|---|

21 | 188 | 1.42 | 443.8 | 1.1 |

93 | 178 | 1.86 | 452.2 | 1.15 |

204 | - | 2.67 | 510.8 | 1.22 |

316 | 140 | 3.76 | 564 | 1.3 |

427 | 122 | 4.95 | 611.3 | 1.35 |

538 | - | 6.48 | 661.5 | 1.4 |

649 | 75.8 | 8.18 | 762 | 1.46 |

732 | - | - | 1004.8 | - |

760 | 13.8 | 10.1 | 2386.5 | 1.4 |

774 | - | 11.2 | 1189.1 | 1.35 |

799 | - | 11.8 | - | 1.35 |

871 | 188 | 1.42 | 443.8 | 1.1 |

1093 | 178 | 1.86 | 452.2 | 1.15 |

Temperature (°C) | Young’s Modulus (GPa) | Electrical Resistivity (Ω·m × 10 ^{−7}) | Specific Heat (J·kg ^{−1}·K^{−1}) | Thermal Expansion Coefficient (K ^{−1} × 10^{−5}) |
---|---|---|---|---|

21 | 200 | 7.2 | 412 | 1.4 |

93 | - | 7.7 | 445 | - |

204 | - | 8.5 | 502 | - |

316 | - | 9.3 | 551 | - |

427 | - | 10.1 | 622 | - |

538 | 147 | 10.7 | 858 | 1.8 |

649 | - | 11.3 | 876 | - |

760 | - | 11.9 | 889 | - |

871 | 100 | 12.4 | 657 | 1.83 |

982 | - | 13.5 | 643 | - |

1093 | 50 | 15.0 | 690 | 1.86 |

1204 | - | 16.4 | 711 | - |

1755 | 15 | - | - | 1.9 |

Source | Sum of Squares | df | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|

Model | 39,900.97 | 7 | 5700.139 | 106.679 | <0.0001 | significant |

A-A | 1021.73 | 1 | 1021.726 | 19.122 | 0.0006 | |

B-B | 24,934.92 | 1 | 24,934.923 | 466.660 | <0.0001 | |

C-C | 3595.16 | 1 | 3595.162 | 67.284 | <0.0001 | |

D-D | 7773.95 | 1 | 7773.949 | 145.490 | <0.0001 | |

AB | 719.82 | 1 | 719.820 | 13.472 | 0.0025 | |

A^{2} | 194.26 | 1 | 194.260 | 3.636 | 0.0773 | |

C^{2} | 3645.55 | 1 | 3645.548 | 68.227 | <0.0001 | |

Residual | 748.06 | 14 | 53.433 | |||

Cor Total | 40649.03 | 21 | ||||

R-Squared = 0.9816 | Adj R-Squared = 0.9724 | |||||

Pred R-Squared = 0.9551 | Adeq Precision = 40.2028 |

Source | Sum of Squares | df | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|

Model | 28.02 | 7 | 4.003 | 22.612 | <0.0001 | significant |

A-A | 7.33 | 1 | 7.326 | 41.386 | <0.0001 | |

B-B | 3.29 | 1 | 3.294 | 18.609 | 0.0007 | |

C-C | 2.08 | 1 | 2.082 | 11.759 | 0.0041 | |

D-D | 7.57 | 1 | 7.573 | 42.781 | <0.0001 | |

AD | 4.00 | 1 | 4.003 | 22.613 | 0.0003 | |

CD | 1.25 | 1 | 1.250 | 7.060 | 0.0188 | |

D^{2} | 2.65 | 1 | 2.653 | 14.987 | 0.0017 | |

Residual | 2.48 | 14 | 0.177 | |||

Cor Total | 30.50 | 21 | ||||

R-Squared = 0.9187 | Adj R-Squared = 0.8781 | |||||

Pred R-Squared = 0.7943 | Adeq Precision = 18.3722 |

Source | Sum of Squares | df | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|---|

Model | 926,739.32 | 7 | 132,391.332 | 253.237 | <0.0001 | significant |

A-A | 633,080.32 | 1 | 633,080.315 | 1210.953 | <0.0001 | |

B-B | 91,660.70 | 1 | 91,660.700 | 175.328 | <0.0001 | |

C-C | 153,993.21 | 1 | 153,993.206 | 294.557 | <0.0001 | |

D-D | 18,474.23 | 1 | 18,474.231 | 35.337 | <0.0001 | |

AC | 8660.82 | 1 | 8660.821 | 16.566 | 0.0011 | |

A^{2} | 2394.08 | 1 | 2394.079 | 4.579 | 0.0505 | |

C^{2} | 4758.75 | 1 | 4758.748 | 9.103 | 0.0092 | |

Residual | 7319.13 | 14 | 522.795 | |||

Cor Total | 934,058.45 | 21 | ||||

R-Squared = 0.9922 | Adj R-Squared = 0.9882 | |||||

Pred R-Squared = 0.9809 | Adeq Precision = 49.7324 |

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**Figure 3.**Calculated temperature histories in resistance spot welding of a 0.40 mm SAE1004 steel (results are presented for different levels of penetration in the steel sheet, ranging from 0 mm (faying interface) to 0.4 mm (electrode surface)), (

**a**) without strip and (

**b**) with a 0.10 mm AISI304 strip.

**Figure 4.**Comparison of weld formation process of (

**a**) without strip and (

**b**) with a 0.10 mm AISI304 strip.

**Figure 5.**Comparison of (

**a**) time-dependent electrode tip temperature and (

**b**) temperature distribution of the symmetrical axis at the final moment of welding stage without strip and with a 0.10 mm AISI304 strip [4]. Reprinted with permission.

**Figure 6.**Comparison of calculated result and experimental result, (

**a**) with a 0.10 mm AISI304 steel strip and (

**b**) without strip [4]. Reprinted with permission.

**Figure 8.**Perturbation plot showing the effect of the four factors on the electrode tip temperature (strip thickness (

**A**), welding current (

**B**), strip resistivity (

**C**), and sheet thickness (

**D**)).

**Figure 9.**(

**a**) Response surface and (

**b**) contour plot showing the effect of factor A and C on the electrode tip temperature at B = 0 and D = −1.

**Figure 10.**Perturbation plot showing the effect of the four factors on the weld diameter (strip thickness (

**A**), welding current (

**B**), strip resistivity (

**C**), and sheet thickness (

**D**)).

**Figure 11.**(

**a**) Response surface and (

**b**) contour plot showing the effect of factor A and C on the weld diameter at B = 0 and D = −1.

**Figure 12.**Perturbation plot showing the effect of the four factors on the strip temperature (strip thickness (

**A**), welding current (

**B**), strip resistivity (

**C**), and sheet thickness (

**D**)).

**Figure 13.**(

**a**) Response surface and (

**b**) contour plot showing the effect of factor A and C on the strip temperature at B = 0 and D = −1.

**Figure 15.**Comparison of (

**a**) electrode surface profiles and (

**b**) electrode surface diameter during electrode wear test [4]. Reprinted with permission.

**Figure 16.**Cross-sections of the electrodes used after 600 welds, (

**a**) no strip; (

**b**) 0.10 mm AISI304 strip; and (

**c**) optimized strip [4]. Reprinted with permission.

Welding Parameters | Value |
---|---|

Electrode diameter (mm) | 5 |

Electrode force (kN) | 1.8 |

Welding current (kA) | 5.7 |

Squeeze time (ms) | 200 |

Weld time (ms) | 160 |

Hold time (ms) | 100 |

Notation | Factor | Level | ||
---|---|---|---|---|

−1 | 0 | 1 | ||

A | Strip thickness (mm) | 0.05 | 0.1 | 0.15 |

B | Weld current (kA) | 5.0 | 5.5 | 6.0 |

C | Strip resistivity (μΩ·m) | 0.3 | 0.55 | 0.8 |

D | Sheet thickness (mm) | 0.4 | 0.6 | 0.8 |

No. | Factors | Tip Temperature (°C) | Weld Diameter (mm) | Strip Temperature (°C) | |||
---|---|---|---|---|---|---|---|

A | B | C | D | ||||

1 | 0 | 1 | 1 | 1 | 684.3 | 4.55 | 1263 |

2 | −1 | 0 | 0 | −1 | 645.3 | 0.89 | 911.5 |

3 | −1 | 0 | 1 | 0 | 659.3 | 3.93 | 935.5 |

4 | 1 | 0 | 1 | 0 | 640.9 | 4.52 | 1399 |

5 | 1 | 1 | 0 | 1 | 604 | 4.6 | 1338 |

6 | 1 | −1 | −1 | 0 | 587.9 | 3.92 | 1079 |

7 | −1 | 0 | −1 | 1 | 606.9 | 3.93 | 773.5 |

8 | 1 | 0 | −1 | −1 | 637.9 | 3.6 | 1167 |

9 | −1 | −1 | 0 | −1 | 600.2 | 0 | 839.8 |

10 | 0 | 1 | 1 | −1 | 725 | 4.31 | 1317 |

11 | −1 | −1 | 1 | 0 | 613.5 | 3.4 | 859 |

12 | 1 | 1 | 0 | −1 | 664.4 | 4.49 | 1479 |

13 | 0 | −1 | 1 | −1 | 648 | 3.56 | 1164 |

14 | −1 | 1 | 0 | 1 | 649.6 | 4.36 | 927.6 |

15 | 0 | 1 | −1 | 0 | 679.9 | 4.28 | 1083 |

16 | 1 | −1 | 0 | 0 | 567.4 | 4.26 | 1257 |

17 | 0 | 0 | −1 | −1 | 649.8 | 1.93 | 1014 |

18 | 0 | −1 | −1 | 1 | 557.4 | 3.69 | 857.7 |

19 | 0 | −1 | 0 | 1 | 552.7 | 3.97 | 994.6 |

20 | −1 | 1 | −1 | 0 | 688.2 | 4.09 | 894 |

21 | 1 | 0 | 1 | 1 | 640.9 | 4.52 | 1399 |

22 | 0 | 0 | 0 | 0 | 624.8 | 4.27 | 1158 |

Response | R-Squared | Adj R-Squared | F-Value | p-Value | Response Equation |
---|---|---|---|---|---|

Electrode TipTemperature (°C) | 0.9816 | 0.9724 | 106.679 | <0.0001 | $\begin{array}{ll}TipTemperature& =619.54-8.54A+42.32b+16.76C-24.11D\\ & -10.24AB-6.28{A}^{2}+27.60{C}^{2}\end{array}$ |

WeldDiameter (mm) | 0.9187 | 0.8781 | 22.612 | <0.0001 | $\begin{array}{ll}WeldDiameter& =4.15+0.76A+0.51B+0.40C+0.74D\\ & -0.77AD-0.43CD-0.73{D}^{2}\end{array}$ |

StripTemperature (°C) | 0.9922 | 0.9882 | 253.237 | <0.0001 | $\begin{array}{ll}StripTemperature& =1129.72+212.65A+84.38B+104.88C\\ & -37.88D+35.69AC-20.04{A}^{2}-31.07{C}^{2}\end{array}$ |

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## Share and Cite

**MDPI and ACS Style**

Zhao, Y.; Wang, W.; Wei, X.
Optimization of Resistance Spot Welding with Inserted Strips via FEM and Response Surface Methodology. *Materials* **2021**, *14*, 7489.
https://doi.org/10.3390/ma14237489

**AMA Style**

Zhao Y, Wang W, Wei X.
Optimization of Resistance Spot Welding with Inserted Strips via FEM and Response Surface Methodology. *Materials*. 2021; 14(23):7489.
https://doi.org/10.3390/ma14237489

**Chicago/Turabian Style**

Zhao, Yangyang, Wurong Wang, and Xicheng Wei.
2021. "Optimization of Resistance Spot Welding with Inserted Strips via FEM and Response Surface Methodology" *Materials* 14, no. 23: 7489.
https://doi.org/10.3390/ma14237489