# Experimental and Finite Element Research on the Failure Mechanism of C/C Composite Joint Structures under Out-of-Plane Loading

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials and Configuration

#### 2.2. Procedures

## 3. Results and Discussion

#### 3.1. Failure Mode

#### 3.2. Numerical Simulation

**x**direction, ${Y}_{T}\text{}\mathrm{and}\text{}{Y}_{C}$ are the tensile and compressive strengths in the

**y**direction, and ${\mathrm{S}}_{12}$ is the in-plane shear strength (Table 1).

_{1}, E

_{2}, G

_{12}, ν1

_{2}, ν

_{21}are the parameters given in Table 1, ${d}_{f}\text{}\mathrm{and}\text{}{d}_{m}$ are damage variables derived from ${d}_{f}^{t},{d}_{m}^{t},{d}_{f}^{c},{d}_{m}^{c},$ and ${d}_{s}$ is the shear damage variable expressed as ${d}_{s}=1-(1-{d}_{f}^{t})(1-{d}_{m}^{t})(1-{d}_{f}^{c})(1-{d}_{m}^{t})(1-{d}_{f}^{t}),D=1-((1-{d}_{f}^{})(1-{d}_{m}^{})\text{}{\nu}_{12}{\nu}_{21})$.

#### 3.3. Progressive Damage

#### 3.4. Finite Element Prediction

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Common in-plane failure modes of bolt joint structures: (

**a**) tensile failure, (

**b**) splitting failure, (

**c**) shear failure, and (

**d**) extrusion failure.

**Figure 2.**Common out-of-plane failure modes of (

**a**) single plate bolt joint structure and (

**b**) a double plate bolt joint structure.

**Figure 3.**Layer structure of the C/C composites (

**a**) and braiding pattern of the pre-fabricated part (

**b**).

**Figure 8.**Failure morphology of the (

**a**) top and bottom surfaces and the (

**b**) side of the lower lap plate.

RT | 600 °C | 800 °C | RT | 600 °C | 800 °C | ||
---|---|---|---|---|---|---|---|

Density (g/cm^{3}) | 1.65 | Tensile strength ${X}_{t}$ (MPa) | 260 | 263 | 271.3 | ||

Coefficient of thermal expansion (10–6/°C) | 0.19 | Compression strength ${X}_{c}$ (MPa) | 176 | 212 | 224 | ||

Elastic modulus ${E}_{11}$ (GPa) | 85 | 92.5 | 95 | Tensile strength ${Y}_{t}$ (MPa) | 260 | 263 | 271.3 |

Elastic modulus ${E}_{22}$ (GPa) | 85 | 92.5 | 95 | Compression strength ${Y}_{c}$ (MPa) | 176 | 212 | 224 |

Elastic modulus ${E}_{33}$ (GPa) | 21 | 13 | 10.3 | Tensile strength ${Z}_{t}$ (MPa) | 78.6 | 80.2 | 84.9 |

Shear modulus ${G}_{12}$ (GPa) | 20 | 25.7 | 27.6 | Compression strength ${Z}_{C}$ (MPa) | 326 | 350 | 358 |

Shear modulus ${G}_{13}={G}_{23}$ (GPa) | 4 | 6.1 | 6.8 | Shear strength ${S}_{12}$ (MPa) | 43 | 51 | 54.5 |

Poisson ratio ${\nu}_{12}$ | 0.035 | Shear strength ${S}_{13}={S}_{23}$ (MPa) | 11 | 16.4 | 18.2 | ||

Poisson ratio ${\nu}_{13}$=${\nu}_{23}$ | 0.032 |

Temperature | ${\mathit{t}}_{\mathit{n}}^{0}\left(\mathbf{N}/\mathbf{m}\mathbf{m}\right)$ | ${\mathit{t}}_{\mathit{s}}^{0}\left(\mathbf{N}/\mathbf{m}\mathbf{m}\right)$ | ${\mathit{t}}_{\mathit{t}}^{0}\left(\mathbf{N}/\mathbf{m}\mathbf{m}\right)$ | ${\mathit{G}}^{\mathit{C}}$ (mJ/mm^{2}) |
---|---|---|---|---|

RT | 20.2 | 13 | 13 | 0.3 |

600 °C | 21.3 | 13.8 | 13.8 | 0.32 |

800 °C | 21.7 | 14 | 14 | 0.33 |

Hexagon Bolt Joint (N) | Countersunk Bolt Joint (N) | ||||
---|---|---|---|---|---|

600 °C | 800 °C | 600 °C | 800 °C | ||

Experiment | 1 | 7155 | 8028 | 7294 | 8186 |

2 | 7134 | 8396 | 7302 | 8296 | |

Simulation | 7648 | 8405 | 7890 | 8508 |

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**MDPI and ACS Style**

Zhang, Y.; Zhou, Z.; Tan, Z.
Experimental and Finite Element Research on the Failure Mechanism of C/C Composite Joint Structures under Out-of-Plane Loading. *Materials* **2019**, *12*, 2922.
https://doi.org/10.3390/ma12182922

**AMA Style**

Zhang Y, Zhou Z, Tan Z.
Experimental and Finite Element Research on the Failure Mechanism of C/C Composite Joint Structures under Out-of-Plane Loading. *Materials*. 2019; 12(18):2922.
https://doi.org/10.3390/ma12182922

**Chicago/Turabian Style**

Zhang, Yanfeng, Zhengong Zhou, and Zhiyong Tan.
2019. "Experimental and Finite Element Research on the Failure Mechanism of C/C Composite Joint Structures under Out-of-Plane Loading" *Materials* 12, no. 18: 2922.
https://doi.org/10.3390/ma12182922