# Delamination Effect on the Buckling Behaviour of Carbon–Epoxy Composite Typical Aeronautical Panels

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Eigenvalue Buckling Analysis

#### 2.2. SMXB Approach

## 3. Test Case

_{4s}, with 32 layers each of 0.165 mm thickness. The panel was made of a Carbon Fibre/Epoxy resin material system, whereby properties were evaluated using an experimental campaign based on the principal ASTM test standards, performed at the National Research Council of Italy by using an MTS test machine. The mechanical properties are listed in Table 2.

#### FEM Model

## 4. Results and Discussion

#### 4.1. CD1–CD4 Configurations

#### 4.2. CD5–CD8 Configurations

#### 4.3. CD9–CD10 Configurations

#### 4.4. CD11–CD16 Configurations

#### 4.5. CD1–CD16 Configuration Comparison

## 5. Conclusions

- The depth of the delamination influences the local buckling and damage propagation but does not affect the stiffness of the panel or the overall compressive behaviour.
- The lower the radius of the initial delamination, the higher the propagation velocity, even if the triggering occurs later.
- If the delamination initiation load is close to the overall buckling load of the panel, no damage propagation is observed.
- By increasing the thickness of the panel and the stringers by 1.32 mm, corresponding to eight layers (quasi-isotropic, symmetrical and balanced layup sequence), the stiffness of the panel significantly changes, including damage propagation.
- With the same geometric parameters, by reducing the width of the bay, the overall stiffness of the panel will not vary significantly, while the propagation of the damage will be completely different.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Out-of-plane displacement contour plot: (1) buckling of circular delamination, (2) buckling of the skin, (3) global buckling including stringers and (4) delamination initiation, with (

**a**) CD1, (

**b**) CD2, (

**c**) CD3 and (

**d**) CD4.

**Figure 6.**CD1–CD4 configurations: (

**a**) delaminated area vs. load curves; (

**b**) delamination evolution at final analyses load (pink represent the delaminated area).

**Figure 7.**Out-of-plane displacement contour plot: (1) buckling of circular delamination, (2) buckling of the skin, (3) global buckling including stringers and (4) delamination initiation, with (

**a**) CD5, (

**b**) CD6, (

**c**) CD7 and (

**d**) CD8.

**Figure 8.**CD5–CD8 configurations: (

**a**) delaminated area vs. load curves; (

**b**) delamination evolution at final analyses load (pink represent the delaminated area).

**Figure 9.**Out-of-plane displacement contour plot: (1) buckling of circular delamination, (2) buckling of the skin, (3) global buckling including stringers and (4) delamination initiation, with (

**a**) CD9 and (

**b**) CD10.

**Figure 10.**CD9–CD10 configurations: (

**a**) delaminated area vs. load curves; (

**b**) delamination evolution at final analyses load (pink represent the delaminated area).

**Figure 11.**Out-of-plane displacement contour plot: (1) buckling of circular delamination, (2) buckling of the skin, (3) global buckling including stringers and (4) delamination initiation, with (

**a**) CD11, (

**b**) CD12, (

**c**) CD13, (

**d**) CD14, (

**e**) CD15 and (

**f**) CD16.

**Figure 12.**CD11–CD16 configurations: (

**a**) delaminated area vs. load curves; (

**b**) delamination evolution at final analyses load (pink represent the delaminated area).

**Figure 13.**Delaminated area vs. load and load vs. displacement charts. Comparison against CD1, CD5, CD9 and CD11 configurations.

**Figure 14.**Delaminated area vs. load and load vs. displacement charts. Comparison against CD3, CD7, CD10 and CD12 configurations.

**Figure 15.**Delaminated area vs. load and load vs. displacement charts. Comparison against CD2, CD6 and CD15 configurations.

**Figure 16.**Delaminated area vs. load and load vs. displacement charts. Comparison against CD4, CD8 and CD16 configurations.

Configuration ID | e | f | g | n | m | Delamination Depth | Skin Layup | Foot Stringer Layup |
---|---|---|---|---|---|---|---|---|

CD1 | 48 | 176 | 40 | 2.64 | 2.64 | 0.33 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{2s} |

CD2 | 48 | 176 | 40 | 2.64 | 2.64 | 0.66 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{2s} |

CD3 | 48 | 176 | 30 | 2.64 | 2.64 | 0.33 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{2s} |

CD4 | 48 | 176 | 30 | 2.64 | 2.64 | 0.66 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{2s} |

CD5 | 48 | 176 | 40 | 3.96 | 3.96 | 0.33 | [(45°, 0°,90°, −45°)]_{3s} | [(45°, 0°,90°, −45°)]_{3s} |

CD6 | 48 | 176 | 40 | 3.96 | 3.96 | 0.66 | [(45°, 0°,90°, −45°)]_{3s} | [(45°, 0°,90°, −45°)]_{3s} |

CD7 | 48 | 176 | 30 | 3.96 | 3.96 | 0.33 | [(45°, 0°,90°, −45°)]_{3s} | [(45°, 0°,90°, −45°)]_{3s} |

CD8 | 48 | 176 | 30 | 3.96 | 3.96 | 0.66 | [(45°, 0°,90°, −45°)]_{3s} | [(45°, 0°,90°, −45°)]_{3s} |

CD9 | 63 | 146 | 40 | 2.64 | 2.64 | 0.33 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{2s} |

CD10 | 63 | 146 | 30 | 2.64 | 2.64 | 0.33 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{2s} |

CD11 | 63 | 146 | 40 | 2.64 | 3.96 | 0.33 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{3s} |

CD12 | 63 | 146 | 30 | 2.64 | 3.96 | 0.33 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{3s} |

CD13 | 63 | 146 | 40 | 2.64 | 3.96 | 0.495 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{3s} |

CD14 | 63 | 146 | 30 | 2.64 | 3.96 | 0.495 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{3s} |

CD15 | 63 | 146 | 40 | 2.64 | 3.96 | 0.66 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{3s} |

CD16 | 63 | 146 | 30 | 2.64 | 3.96 | 0.66 | [(45°, 0°,90°, −45°)]_{2s} | [(45°, 0°,90°, −45°)]_{3s} |

Carbon Fibre/Epoxy Resin Material Properties | ||
---|---|---|

Property | Value | Description |

${\mathrm{E}}_{11}$ | $122,000\mathrm{MPa}$ | Young’s modulus in the fibres’ direction |

${\mathrm{E}}_{22}={\mathrm{E}}_{33}$ | $6265\mathrm{MPa}$ | Young’s modulus in the transverse directions |

${\mathrm{G}}_{12}={\mathrm{G}}_{13}$ | $4649\mathrm{MPa}$ | Shear modulus in the 1–2 and 1–3 planes |

${\mathrm{G}}_{23}$ | $4649\mathrm{MPa}$ | Shear modulus in the 2–3 plane |

${\mathsf{\nu}}_{12}={\mathsf{\nu}}_{13}$ | $0.3008$ | Poisson’s ratio in the 1–2 and 1–3 planes |

${\mathsf{\nu}}_{23}$ | $0.02$ | Poisson’s ratio in the 2–3 plane |

GIc | 180 J/m^{2} | Mode I critical energy release rate |

GIIc = GIIIc | 1900 J/m^{2} | Mode II and Mode III critical strain energy release rate |

${\mathrm{t}}_{\mathrm{h}}$ | $0.165\mathrm{mm}$ | Ply thickness |

Configuration ID | Stiffness | Buckling Circular Delamination | Buckling Skin | Buckling Stringer | Delamination Initiation |
---|---|---|---|---|---|

CD1 | 281,094 N/mm | 3.7 kN 0.013 mm | 83.3 kN 0.296 mm | 123.3 kN 0.439 mm | 108 kN 0.4 mm |

CD2 | 281,060 N/mm | 21.4 kN 0.076 mm | 76.9 kN 0.274 mm | 122.9 kN 0.437 mm | 136.2 kN 0.525 mm |

CD3 | 281,097 N/mm | 6.5 kN 0.023 mm | 86.5 kN 0.308 mm | 124.6 kN 0.4432 mm | 111.6 kN 0.4125 |

CD4 | 281,060 N/mm | 38.2 kN 0.136 mm | 82.3 kN 0.293 mm | 121.5 kN 0.433 mm | 136.2 kN 0.412 mm |

Configuration ID | Stiffness | Buckling Circular Delamination | Buckling Skin | Buckling Stringer | Delamination Initiation |
---|---|---|---|---|---|

CD5 | 399,172 N/mm | 5.28 kN 0.013 mm | 264 kN 0.661 mm | 264.3 kN 0.661 mm | 200 kN 0.506 mm |

CD6 | 399,105 N/mm | 30.7 kN 0.077 mm | 255.1 kN 0.639 mm | 259.3 kN 0.649 mm | 178.4 kN 0.45 mm |

CD7 | 399,176 N/mm | 9.2 kN 0.023 mm | 262.3 kN 0.657 mm | 262.3 kN 0.657 mm | 200.8 kN 0.5065 mm |

CD8 | 399,109 N/mm | 53.7 kN 0.134 mm | 257.7 kN 0.646 mm | 257.7 kN 0.6457 mm | 193.7 kN 0.4875 mm |

Configuration ID | Stiffness | Buckling Circular Delamination | Buckling Skin | Buckling Stringer | Delamination Initiation |
---|---|---|---|---|---|

CD9 | 278,843 N/mm | 3.93 kN 0.014 mm | 106 kN 0.380 mm | 112.87 kN 0.405 mm | 119.4 kN 0.0444 mm |

CD10 | 278,841 N/mm | 6.96 kN 0.0249 mm | 109.3 kN 0.392 mm | 112.3 kN 0.4026 mm | 117.7 kN 0.434 mm |

Configuration ID | Stiffness | Buckling Circular Delamination | Buckling Skin | Buckling Stringer | Delamination Initiation |
---|---|---|---|---|---|

CD11 | 305,413 N/mm | 4.31 kN 0.014 mm | 125.4 kN 0.4107 mm | 183.7 kN 0.6014 mm | 133.3 kN 0.4437 mm |

CD12 | 305,414 N/mm | 7.61 kN 0.025 mm | 130.3 kN 0.427 mm | 184.4 kN 0.6039 mm | 133.8 kN 0.4437 mm |

CD13 | 304,877 N/mm | 14.3 kN 0.047 mm | 124.18 kN 0.4073 mm | 183.1 kN 0.6006 mm | 113.4 kN 0.375 mm |

CD14 | 305,054 N/mm | 25.1 kN 0.082 mm | 130.8 kN 0.429 mm | 184.2 kN 0.6039 mm | 119.4 kN 0.3937 mm |

CD15 | 304,902 N/mm | 24.9 kN 0.082 mm | 119 kN 0.3907 mm | 183 kN 0.6002 mm | 131.6 kN 0.4375 mm |

CD16 | 304,905 N/mm | 43.7 kN 0.1434 mm | 126.8 kN 0.4158 mm | 183.7 kN 0.6025 mm | 141 kN 0.4687 mm |

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**MDPI and ACS Style**

Riccio, A.; Castaldo, R.; Palumbo, C.; Russo, A. Delamination Effect on the Buckling Behaviour of Carbon–Epoxy Composite Typical Aeronautical Panels. *Appl. Sci.* **2023**, *13*, 4358.
https://doi.org/10.3390/app13074358

**AMA Style**

Riccio A, Castaldo R, Palumbo C, Russo A. Delamination Effect on the Buckling Behaviour of Carbon–Epoxy Composite Typical Aeronautical Panels. *Applied Sciences*. 2023; 13(7):4358.
https://doi.org/10.3390/app13074358

**Chicago/Turabian Style**

Riccio, Aniello, Rossana Castaldo, Concetta Palumbo, and Angela Russo. 2023. "Delamination Effect on the Buckling Behaviour of Carbon–Epoxy Composite Typical Aeronautical Panels" *Applied Sciences* 13, no. 7: 4358.
https://doi.org/10.3390/app13074358