# Investigation into the Effect of Interlock Volume on SPR Strength

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## Abstract

**:**

## 1. Introduction

#### Current Research

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Methods

## 3. Results and Discussion

^{2}values. The product of the X and Y interlocks, known as the interlock area, represented by the X–Y rectangle in Figure 1, was also plotted to capture the interlock in a single metric. However, this also resulted in large variations around the mean regression line, which is linear in nature due to the assumption that the pull-out strength of the joint could be calculated using the interlocks by the shear punch force, ${F}_{max}$, as seen in Equation (2).

^{2}value was improved from approximately 0.55 for the X and Y interlocks to around 0.6 for the X*Y area. However, the Volumelock achieved an R

^{2}value of 0.88, a significant improvement. Figure 9 shows the linear regression line of the X interlock with max load, including 95% confidence bands, accounting for the standard deviation of both the measurement and the max load. This results in a variance from the bands of ±0.38 kN if this line is used to predict the strength of joints.

^{3}, or a specific energy absorption of 774.32 J/g. The volume captured by the rivet head in the top sheet remained relatively consistent across the range of lower Volumelocks, allowing a fair comparison to be drawn between them. The regression line intersects the axis at (0,0) because the gradient is the specific energy absorption, meaning zero mass is unable to absorb energy. Further work should be conducted to understand the relationship at higher Volumelock values when the failure mode changes, as this study only focused on the failure mode of tail pull-out.

^{3}and a standard deviation of 4.82 does result in noticeable variations. The data points and regression line can be seen in Figure 13. The data points fit well with the regression line, showing that the max load can be predicted from Volumelock with a 95% certainty that the prediction will be within ±0.26 kN, or within 5% of the mean strength from the dataset in this study.

## 4. Conclusions

- This study resulted in a new measurement method for cross-section analysis that is potentially capable of predicting tensile test joint strength with enough accuracy to remove the need for conducting extensive physical tensile testing.
- The measurement technique represents a new way of optimising joint parameter choice through a single measurement, improving on current measurement and prediction techniques in terms of accuracy and precision.
- The relationships between joint performance and Volumelock measurement were investigated and found to be a function of specific energy absorption, which in turn is a function of the material and geometry constants of the tested samples. This opens up the possibility for future work to calculate values useful to car body designers and joining engineers without the need for extensive physical strength testing.
- Further work should be conducted to fully understand the effect of geometry and material on the relationship between Volumelock and joint strength.
- In this initial work we have only begun to explore what might be achieved using this new approach, and we encourage other researchers to help us further develop this interesting new method for the wider benefit of the joining community.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Test ID | Rivet | Nominal Rivet Length (mm) | Die | Die Depth (mm) | Avg X Interlock (mm) | Standard Deviation X interlock | Avg Y Interlock (mm) | Standard Deviation Y Interlock | Avg Volumelock (mm^{3}) | Standard Deviation Volumelock | Avg Max Load (kN) | Standard Deviation Max Load | Avg Total Energy Absorbed (J) | Standard Deviation Energy Absorbed | Calculated Shear Punch Force (kN) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | K50A42AH00 | 8.5 | DG10-100 | 1 | 0.719 | 0.0572 | 1.11 | 0.079 | 25.3 | 1.80 | 5.10 | 0.131 | 44.9 | 2.29 | 3.74 |

2 | K50A42AH00 | 8.5 | DG10-120 | 1.2 | 0.620 | 0.0560 | 1.27 | 0.029 | 26.2 | 2.11 | 5.21 | 0.115 | 54.4 | 2.66 | 4.17 |

3 | K50A42AH00 | 8.5 | DG10-140 | 1.4 | 0.620 | 0.0231 | 1.33 | 0.178 | 27.7 | 1.30 | 5.37 | 0.109 | 60.0 | 2.62 | 4.37 |

4 | C50D42AH00 | 8.5 | DG10-160 | 1.6 | 0.680 | 0.0862 | 1.47 | 0.211 | 31.6 | 3.45 | 5.77 | 0.241 | 76.5 | 6.07 | 4.92 |

5 | K50M42AH00 | 8.5 | DG10-180 | 1.8 | 0.780 | 0.0578 | 1.57 | 0.301 | 38.0 | 2.19 | 5.93 | 0.241 | 80.5 | 3.98 | 5.41 |

6 | K50742AH00 | 8.5 | DG10-200 | 2 | 0.790 | 0.1467 | 1.95 | 0.640 | 40.7 | 4.47 | 5.89 | 0.136 | 76.6 | 3.26 | 6.74 |

7 | K50842AH00 | 8.5 | DG10-220 | 2.2 | 0.800 | 0.0374 | 2.46 | 0.283 | 38.1 | 1.10 | 6.04 | 0.109 | 80.2 | 3.34 | 8.53 |

8 | K50A42AH00 | 6.5 | DG10-200 | 2 | 0.537 | 0.0612 | 1.07 | 0.119 | 11.8 | 1.15 | 3.85 | 0.079 | 16.3 | 0.61 | 3.44 |

9 | K50A42AH00 | 7 | DG10-200 | 2 | 0.590 | 0.0762 | 1.24 | 0.187 | 17.5 | 1.67 | 4.51 | 0.069 | 32.4 | 0.75 | 4.04 |

10 | K50A42AH00 | 7.5 | DG10-200 | 2 | 0.420 | 0.0967 | 1.22 | 0.172 | 15.3 | 3.20 | 4.85 | 0.179 | 40.9 | 3.87 | 3.76 |

11 | K50A42AH00 | 8 | DG10-200 | 2 | 0.610 | 0.0581 | 1.57 | 0.224 | 27.0 | 1.78 | 5.50 | 0.168 | 65.2 | 0.86 | 5.14 |

## Appendix B

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**Figure 1.**SPR cross section: Left side—conventional X–Y interlock measurement; Right side—Arealock measurement.

**Figure 3.**Cross-tension test configuration [5].

**Figure 8.**Comparative percentage increase in cross-section measurements and strength measurements for Stacks 9 and 11 (

**a**) and 5 and 7 (

**b**).

Top Sheet | Bottom Sheet | |||
---|---|---|---|---|

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

Stack 1 | AA5754 H111 | 3.0 | AA5754 H111 | 3.0 |

Test ID | Rivet Type | Rivet Length (mm) | DG Die Cavity (Diameter ) | DG Die Cavity (Depth) | Insertion Force (kN) | Insertion Velocity (mm/s) |
---|---|---|---|---|---|---|

1 | K50A42AH00 | 8.5 | 10 | 100 | 70.96 | 340 |

2 | K50A42AH00 | 8.5 | 10 | 120 | 72.40 | 340 |

3 | K50A42AH00 | 8.5 | 10 | 140 | 73.80 | 340 |

4 | K50A42AH00 | 8.5 | 10 | 160 | 72.28 | 330 |

5 | K50A42AH00 | 8.5 | 10 | 180 | 64.14 | 300 |

6 | K50A42AH00 | 8.5 | 10 | 200 | 53.62 | 270 |

7 | K50A42AH00 | 8.5 | 10 | 220 | 50.30 | 260 |

8 | C50D42AH00 | 6.5 | 10 | 200 | 46.7 | 230 |

9 | K50742AH00 | 7.0 | 10 | 200 | 50.66 | 250 |

10 | K50M42AH00 | 7.5 | 10 | 200 | 52.38 | 260 |

11 | K50842AH00 | 8.0 | 10 | 200 | 53.80 | 270 |

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**MDPI and ACS Style**

Jepps, L.; Briskham, P.; Sims, N.; Susmel, L.
Investigation into the Effect of Interlock Volume on SPR Strength. *Materials* **2023**, *16*, 2747.
https://doi.org/10.3390/ma16072747

**AMA Style**

Jepps L, Briskham P, Sims N, Susmel L.
Investigation into the Effect of Interlock Volume on SPR Strength. *Materials*. 2023; 16(7):2747.
https://doi.org/10.3390/ma16072747

**Chicago/Turabian Style**

Jepps, Lewis, Paul Briskham, Neil Sims, and Luca Susmel.
2023. "Investigation into the Effect of Interlock Volume on SPR Strength" *Materials* 16, no. 7: 2747.
https://doi.org/10.3390/ma16072747