# Buckling Analysis of CNT-Reinforced Polymer Composite Beam Using Experimental and Analytical Methods

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## Abstract

**:**

## 1. Introduction

## 2. Production of Materials

## 3. Analytical Methods

#### 3.1. Effective Properties of CNTRC

#### 3.2. Governing Equations of CNTRC

_{i}(i = 0, 1, 2) is the mass moment of inertia given by:

_{1}, c

_{2}, c

_{3}and c

_{4}.

## 4. Experimental Program

#### 4.1. Tensile Test

#### 4.2. Compressive Test

#### 4.3. Buckling Test

## 5. Results

## 6. Conclusions

- The experimental outcomes indicated that adding CNT can improve a composite’s mechanical performance by up to 0.3%;
- The developed analytical model and the previously presented experimental results exhibited great agreement;
- The average load-carrying capacity for the clamped–clamped boundary condition was 268% higher in the CNT samples and 282% higher in the NEAT samples compared to the simple–simple condition. Therefore, the supporting conditions of the samples caused the capacity and load–displacement curves of buckling behavior to change;
- The damage modes that occurred after compression and buckling were intense fiber breakage. In other words, in all buckling tests, it was observed that the damage initiated with micro cracks and showed progressive damage in the form of fiber rupture.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Carbon Fiber | Epoxy Matrix | CNT | |
---|---|---|---|

E_{11} (GPa) | 230 | 2.72 | 500 |

E_{22} (GPa) | 15 | 2.72 | 500 |

E_{33} (GPa) | 15 | 2.72 | 500 |

ʋ_{12} | 0.28 | 0.3 | 0.26 |

ʋ_{13} | 0.28 | 0.3 | 0.26 |

ʋ_{23} | 0.28 | 0.3 | 0.26 |

G_{12} (GPa) | 15 | 1.18 | |

G_{13} (GPa) | 15 | 1.18 | |

G_{23} (GPa) | 15 | 1.18 |

Sample | Young’s Moduli (GPa) | |
---|---|---|

Experimental | Analytical | |

0.0%wt CNT | 12.18 | 14.48 |

0.3%wt CNT | 13.42 | 16.18 |

0% | 0.3% | |
---|---|---|

Experimental | 933 | 1036 |

Analytical | 947 | 1102 |

0% | 0.3% | |
---|---|---|

Experimental | 3572 | 3817 |

Analytical | 3593 | 3899 |

Sample | Maximum Load (N) | Rate of Increase (%) | Maximum Displacement (mm) |
---|---|---|---|

NEAT1 | 15,816.18 | — | 2.51 |

NEAT2 | 15,506.25 | — | 2.65 |

CNT1 | 16,771.16 | 6 and 8.10 | 2.46 |

CNT2 | 17,812.36 | 12.10 and 14.80 | 2.64 |

Sample | Maximum Load (N) | Rate of Increase (%) | Maximum Displacement (mm) |
---|---|---|---|

NEAT1 | 922.20 | — | 5.48 |

NEAT2 | 945.28 | — | 6.73 |

CNT1 | 1040.44 | 12.8 and 10 | 6.30 |

CNT2 | 1031.68 | 11.8 and 9.1 | 6.35 |

Sample | Maximum Load (N) | Rate of Increase (%) | Maximum Displacement (mm) |
---|---|---|---|

NEAT1 | 3516.02 | — | 3.88 |

NEAT2 | 3629.42 | — | 4.11 |

CNT1 | 3825.80 | 8.8 and 5.4 | 4.02 |

CNT2 | 3808.21 | 8.3 and 4.9 | 4.13 |

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## Share and Cite

**MDPI and ACS Style**

Madenci, E.; Özkılıç, Y.O.; Aksoylu, C.; Asyraf, M.R.M.; Syamsir, A.; Supian, A.B.M.; Mamaev, N.
Buckling Analysis of CNT-Reinforced Polymer Composite Beam Using Experimental and Analytical Methods. *Materials* **2023**, *16*, 614.
https://doi.org/10.3390/ma16020614

**AMA Style**

Madenci E, Özkılıç YO, Aksoylu C, Asyraf MRM, Syamsir A, Supian ABM, Mamaev N.
Buckling Analysis of CNT-Reinforced Polymer Composite Beam Using Experimental and Analytical Methods. *Materials*. 2023; 16(2):614.
https://doi.org/10.3390/ma16020614

**Chicago/Turabian Style**

Madenci, Emrah, Yasin Onuralp Özkılıç, Ceyhun Aksoylu, Muhammad Rizal Muhammad Asyraf, Agusril Syamsir, Abu Bakar Mohd Supian, and Nicolay Mamaev.
2023. "Buckling Analysis of CNT-Reinforced Polymer Composite Beam Using Experimental and Analytical Methods" *Materials* 16, no. 2: 614.
https://doi.org/10.3390/ma16020614