# Investigation of the Deformation Behaviour and Resulting Ply Thicknesses of Multilayered Fibre–Metal Laminates

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{®}CFR-TP PA6 CF60-01, Dallas, TX, USA) and Al-5754 aluminium alloy sheets were used in the experiments. Table 1 provides the chemical composition of the Al-5754 used in this study. The plies were bonded to each other using an adhesive layer based on polyolefin, i.e., Cox 391 (nolax AG, Sempach, Switzerland) with a thickness of 0.1 mm. The two lay-ups of multilayered FML used in this study are shown in Figure 1 and their details are given in Table 2. Figure 2 shows the manufacturing steps, including schematic illustrations of the adhesion and forming processes. Due to the different thermal conductivity of the individual layers, laminates were equipped with internal thermocouples in a preliminary study in order to determine a correlation between the external temperature profiles and the temperatures occurring in the laminate for all manufacturing steps.

## 3. Finite-Element Analysis

## 4. Results and Discussion

^{2}from 0.87 to 0.97 when a temperature-dependent friction coefficient is implemented.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Micrograph of lay-up L2 and (

**b**) finite-element model and meshing system (dimensions in mm).

**Figure 6.**Influence of the Coulomb coefficient factor on inter-ply slippage. (

**a**) µ = 0.01, (

**b**) µ = 0.1, and (

**c**) µ = 0.2.

**Figure 7.**Influence of the inter-ply Coulomb coefficient on the α angle. (

**a**) µ = 0.01, (

**b**) µ = 0.1, and (

**c**) µ = 0.2.

**Figure 9.**Delamination at the metal–polymer interface. (

**a**) Final product with L1 and (

**b**) semi-deformed profile with L2 at the forming load of 10 kN.

**Figure 10.**Predicted delamination at the metal–polymer interface in a semi-deformed profile with L2 in the middle forming stages.

**Figure 12.**Measured and predicted thickness of CFRP plies at the head radius. (

**a**) Constant friction coefficient. (

**b**) Temperature-dependent friction coefficient.

Si | Fe | Cu | Mn | Mg | Cr | Zn | Ti | Al |
---|---|---|---|---|---|---|---|---|

0.4 | 0.4 | 0.1 | 0.5 | 3.0 | 0.3 | 0.2 | 0.15 | Balance |

Lay-Up | Dimensions (mm) | Mesh Size of M Plies in the Simulations (mm) |
---|---|---|

L1 [M/C]s | [1.0/0.5]s | 0.25 |

L2 [(M/C)2]s | [(1.0/0.5)2]s | 0.25 |

Temperature (°C) | Thermal Conductivity (J/kg·°C) | Heat Capacity (W/m·°C) | Elastic Modulus (GPa) |
---|---|---|---|

50 | 140.0 | 0.93 | 69.0 |

100 | 145.0 | 0.96 | 68.0 |

150 | 150.0 | 0.975 | 65.0 |

200 | 154.0 | 0.99 | 63.0 |

250 | 157.0 | 1.00 | 60.0 |

$\mathit{A}$ | ${\mathit{m}}_{1}$ | ${\mathit{m}}_{2}$ | ${\mathit{m}}_{3}$ | ${\mathit{m}}_{4}$ |
---|---|---|---|---|

335.92 | −0.00167 | 0.10085 | −0.00058 | 0.0 |

Strain Rate (s^{–1}) | Temperature (°C) | $\mathbf{Stress}\mathbf{Coefficient}({\mathit{\sigma}}^{*};\mathbf{MPa})$ |
---|---|---|

$8.5\times {10}^{-4}$ | 21.5 | 118.8 |

$8.5\times {10}^{-3}$ | 132.0 | |

$8.5\times {10}^{-2}$ | 138.6 | |

$8.5\times {10}^{-4}$ | 50 | 87.1 |

$8.5\times {10}^{-3}$ | 94.3 | |

$8.5\times {10}^{-2}$ | 101.6 | |

$8.5\times {10}^{-4}$ | 75 | 70.6 |

$8.5\times {10}^{-3}$ | 77.2 | |

$8.5\times {10}^{-2}$ | 79.6 | |

$8.5\times {10}^{-4}$ | 100 | 58.7 |

$8.5\times {10}^{-3}$ | 62.9 | |

$8.5\times {10}^{-2}$ | 64.8 | |

$8.5\times {10}^{-4}$ | 150 | 16.6 |

$8.5\times {10}^{-3}$ | 14.9 | |

$8.5\times {10}^{-2}$ | 13.1 |

**Table 6.**Measured and predicted thickness of the deformed multilayered FML (constant friction coefficient).

Lay-Up | Ply | Thickness at P1 (micron) | Thickness at P2 (micron) | Thickness at P3 (micron) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | ||

L1 | CFRP | 822 | 971 | 18.1 | 832 | 955 | 14.8 | 881 | 970 | 10.0 |

CFRP1 | 430 | 454 | 5.5 | 440 | 445 | 1.1 | 514 | 513 | 0.4 | |

L2 | CFRP2 | 832 | 960 | 15.3 | 737 | 940 | 27.6 | 903 | 1002 | 11.0 |

CFRP3 | 509 | 506 | 0.6 | 472 | 495 | 4.7 | 530 | 537 | 1.4 |

**Table 7.**Measured and predicted thickness of the deformed multilayered FML (temperature-dependent friction coefficient).

Lay-Up | Ply | Thickness at P1 (micron) | Thickness at P2 (micron) | Thickness at P3 (micron) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | Measured | Predicted | Error (%) | ||

L1 | CFRP | 822 | 836 | 1.7 | 832 | 833 | 0.1 | 881 | 875 | 0.7 |

CFRP1 | 430 | 416 | 3.2 | 440 | 435 | 1.1 | 514 | 505 | 1.7 | |

L2 | CFRP2 | 832 | 860 | 3.3 | 737 | 714 | 3.1 | 903 | 920 | 1.9 |

CFRP3 | 509 | 520 | 2.1 | 472 | 495 | 4.8 | 530 | 528 | 0.4 |

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**MDPI and ACS Style**

Irani, M.; Kuhtz, M.; Zapf, M.; Ullmann, M.; Hornig, A.; Gude, M.; Prahl, U.
Investigation of the Deformation Behaviour and Resulting Ply Thicknesses of Multilayered Fibre–Metal Laminates. *J. Compos. Sci.* **2021**, *5*, 176.
https://doi.org/10.3390/jcs5070176

**AMA Style**

Irani M, Kuhtz M, Zapf M, Ullmann M, Hornig A, Gude M, Prahl U.
Investigation of the Deformation Behaviour and Resulting Ply Thicknesses of Multilayered Fibre–Metal Laminates. *Journal of Composites Science*. 2021; 5(7):176.
https://doi.org/10.3390/jcs5070176

**Chicago/Turabian Style**

Irani, Missam, Moritz Kuhtz, Mathias Zapf, Madlen Ullmann, Andreas Hornig, Maik Gude, and Ulrich Prahl.
2021. "Investigation of the Deformation Behaviour and Resulting Ply Thicknesses of Multilayered Fibre–Metal Laminates" *Journal of Composites Science* 5, no. 7: 176.
https://doi.org/10.3390/jcs5070176