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

^{1}

^{2}

^{*}

## 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

- Buckley, J.D.; Edie, D.D. Carbon-Carbon Materials and Composites; Noyes Publications: New Jersey, NJ, USA, 1993. [Google Scholar]
- Li, T.Q.; Xu, Z.H.; Hu, Z.J.; Yang, X.G. Application of a high thermal conductivity C/C composite in a heat-redistribution thermal protection system. Carbon
**2010**, 48, 924–925. [Google Scholar] [CrossRef] - Scarponi, C. Carbon-carbon composites in aerospace engineering. In Advanced Composite Materials for Aerospace Engineering; Woodhead Publishing: Sawston/Cambridge, UK, 2016; pp. 385–412. [Google Scholar]
- Chowdhury, P.; Sehitoglu, H.; Rateick, R. Damage tolerance of carbon-carbon composites in aerospace application. Carbon
**2018**, 126, 382–393. [Google Scholar] [CrossRef] - Lachaud, J.; Aspa, Y.; Vignoles, G.L.; Goyheneche, J.M. 3D modeling of thermochemical ablation in carbon-based material: Effect of anisotropy on surface roughness onset. In Proceedings of the 10th ISMSE & the 8th ICPMSE, Collioure, France, 19–23 June 2006; European Space Agency: Paris, France, 2006. [Google Scholar]
- Kumar, S.; Kushwaha, J.; Mondal, S.; Kumar, A.; Jain, R.K.; Devi, G.R. Fabrication and ablation testing of 4D C/C composite at 10 MW/m
^{2}heat flux under a plasma arc heater. Mater. Sci. Eng. A**2013**, 566, 102–111. [Google Scholar] [CrossRef] - Xiao, Y.; Ishikawa, T. Bearing strength and failure behavior of bolted composite joints (Part I: Experimental investigation). Compos. Sci. Technol.
**2005**, 65, 1022–1031. [Google Scholar] [CrossRef] - Guo, S.; Morishima, R. Numerical analysis and experiment of composite sandwich T-joints subjected to pulling load. Compos. Struct.
**2011**, 94, 229–238. [Google Scholar] [CrossRef] - Stocchi, C.; Robinson, P.; Pinho, S.T. A detailed finite element investigation of composite bolted joints with countersunk fasteners. Compos. Part A
**2013**, 52, 143–150. [Google Scholar] [CrossRef] - Gray, P.J.; McCarthy, C.T. A highly efficient user-defined finite element for load distribution analysis of large-scale bolted composite structures. Compos. Sci. Technol.
**2011**, 71, 1517–1527. [Google Scholar] [CrossRef][Green Version] - Olmedo, A.; Santiuste, C. On the prediction of bolted single-lap composite joints. Compos. Struct.
**2012**, 94, 2110–2117. [Google Scholar] [CrossRef][Green Version] - Olmedo, A.; Santiuste, C.; Barbero, E. An analytical model for the secondary bending prediction in single-lap composite bolted-joints. Compos. Struct.
**2014**, 111, 354–361. [Google Scholar] [CrossRef] - Sharos, P.A.; Egan, B.; McCarthy, C.T. An analytical model for strength prediction in multi-bolt composite joints at various loading rates. Compos. Struct.
**2014**, 116, 300–310. [Google Scholar] [CrossRef] - McCarthy, M.A.; McCarthy, C.T.; Lawlor, V.P.; Stanley, W.F. Three-dimensional finite element analysis of single-bolt, single-lap composite bolted joints: Part I—Model development and validation. Compos. Struct.
**2005**, 71, 140–158. [Google Scholar] [CrossRef] - McCarthy, M.A.; Lawlor, V.P.; Stanley, W.F.; McCarthy, C.T. Bolt-hole clearance effects and strength criteria in single-bolt, single-lap, composite bolted joints. Compos. Sci. Technol.
**2002**, 62, 1415–1431. [Google Scholar] [CrossRef] - McCarthy, M.A.; McCarthy, C.T.; Padhi, G.S. A simple method for determining the effects of bolt–hole clearance on load distribution in single-column multi-bolt composite joints. Compos. Struct.
**2006**, 73, 78–87. [Google Scholar] [CrossRef] - Gray, P.J.; McCarthy, C.T. A global bolted joint model for finite element analysis of load distributions in multi-bolt composite joints. Compos. Part B
**2010**, 41, 317–325. [Google Scholar] [CrossRef] - Feo, L.; Marra, G.; Mosallam, A.S. Stress analysis of multi-bolted joints for FRP pultruded composite structures. Compos. Struct.
**2012**, 94, 3769–3780. [Google Scholar] [CrossRef] - Karakuzu, R.; Taylak, N.; Icten, B.M.; Aktas, M. Effects of geometric parameters on failure behavior in laminated composite plates with two parallel pin-loaded holes. Compos. Struct.
**2008**, 85, 1–9. [Google Scholar] [CrossRef] - Atas, A.; Mohamed, G.F.; Soutis, C. Effect of clamping force on the delamination onset and growth in bolted composite laminates. Compos. Struct.
**2012**, 94, 548–552. [Google Scholar] [CrossRef] - Khashaba, U.A.; Sebaey, T.A.; Alnefaie, K.A. Failure and reliability analysis of pinned-joints composite laminates: Effects of stacking sequences. Compos. Part B
**2013**, 45, 1694–1703. [Google Scholar] [CrossRef] - Wang, H.Q.; Cao, J.; Feng, J.C. Brazing mechanism and infiltration strengthening of CC composites to TiAl alloys joint. Scripta Mater.
**2010**, 63, 859–862. [Google Scholar] [CrossRef] - Sharma, R.; Mahajan, P.; Mittal, R.K. Elastic modulus of 3D carbon/carbon composite using image-based finite element simulations and experiments. Compos. Struct.
**2013**, 98, 69–78. [Google Scholar] [CrossRef] - Cheng, J.; Li, H.J.; Zhang, S.Y.; Xue, L.Z.; Luo, W.F.; Li, W. Failure behavior investigation of a unidirectional carbon–carbon composite. Mater. Des.
**2014**, 55, 846–850. [Google Scholar] [CrossRef] - Bruneton, E.; Narcy, B.; Oberlin, A. Carbon-carbon composites prepared by a rapid densification process I: Synthesis and physico-chemical data. Carbon
**1997**, 35, 1593–1598. [Google Scholar] [CrossRef] - Westwood, M.E.; Webster, J.D.; Day, R.J.; Hayes, F.H.; Taylor, R. Oxidation protection for carbon fibre composites. J. Mater. Sci.
**1996**, 31, 1389–1397. [Google Scholar] [CrossRef] - Golecki, I.; Morris, R.C.; Narasimhan, D.; Clements, N. Rapid densification of porous carbon–carbon composites by thermal-gradient chemical vapor infiltration. Appl. Phys. Lett.
**1995**, 66, 2334–2336. [Google Scholar] [CrossRef] - Delhaès, P.; Trinquecoste, M.; Lines, J.F.; Cosculluela, A.; Goyheneche, J.M.; Couzi, M. Chemical vapor infiltration of C/C composites: Fast densification processes and matrix characterizations. Carbon
**2005**, 43, 681–691. [Google Scholar] [CrossRef] - Fang, H.T.; Zhu, J.C.; Yin, Z.D.; Jeon, J.H.; Hahn, Y.D. A Si-Mo fused slurry coating for oxidation protection of carbon-carbon composites. J. Mater. Sci. Lett.
**2001**, 20, 175–177. [Google Scholar] [CrossRef] - Delhaes, P. Chemical vapor deposition and infiltration processes of carbon materials. Carbon
**2002**, 40, 641–657. [Google Scholar] [CrossRef] - Hashin, Z. Failure Criteria for Unidirectional Fiber Composites. J. Appl. Mech.
**1980**, 47, 329–334. [Google Scholar] [CrossRef] - Tang, Y.L.; Zhou, Z.G.; Pan, S.D.; Xiong, J.; Guo, Y. Mechanical property and failure mechanism of 3D Carbon–Carbon braided composites bolted joints under unidirectional tensile loading. Mater. Des.
**2015**, 65, 243–253. [Google Scholar] [CrossRef] - Coelho, A.M.G.; Mottram, J.T. Numerical Evaluation of Pin-Bearing Strength for the Design of Bolted Connections of Pultruded FRP Material. J. Compos. Constr.
**2017**, 21, 04017027. [Google Scholar] [CrossRef][Green Version] - Harper, P.W.; Hallett, S.R. Cohesive zone length in numerical simulations of composite delamination. Eng. Fract. Mech.
**2008**, 75, 4774–4792. [Google Scholar] [CrossRef][Green Version]

**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 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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