# Study on Dynamic Mechanical Properties of Carbon Fiber-Reinforced Polymer Laminates at Ultra-Low Temperatures

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## Abstract

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## 1. Introduction

## 2. Experiment

#### 2.1. Experimental Platform

#### 2.2. Material Preparation and Experimental Scheme

_{2s}. Then, vacuum package the mold containing prepreg. Finally, push the mold into the autoclave and cure it according to the specific curing curve (the maximum curing temperature is $180\xb0\mathrm{C}$, and the maximum pressure is $0.6\mathrm{MPa}$ in the autoclave). Some studies have pointed out that the laminate samples used in dynamic compression experiments are cylinders or cuboids, which has little influence on the final experimental results, but the length–diameter ratio is suitable in the range of $0.5~2.0$. Considering the processing difficulty, the thickness of the original laminates, and the diameter of the Hopkinson pressure bar, the dynamic compression sample is finally processed into a cuboid of $10\mathrm{mm}\times 10\mathrm{mm}\times 8\mathrm{mm}$, and the surface of each sample needs to be polished to ensure it is smooth and parallel. According to the requirements of the composite material three-point bending test standard GB/T1449-2005 [27] and considering the small size of the cryogenic box and the support of the Hopkinson bending bar, the dynamic bending sample is finally processed into a cuboid of $60\mathrm{mm}\times 10\mathrm{mm}\times 2\mathrm{mm}$. The shapes of the two samples are shown in Figure 2.

## 3. Simulation

#### 3.1. Low-Temperature Dynamic Constitutive Model

#### 3.2. Failure Criterion and Damage Evolution

#### 3.3. Bilinear Cohesive Zone Model for Interface

#### 3.4. Finite Element Modeling

## 4. Results and Discussion

#### 4.1. Dynamic Compression Experimental Results

#### 4.2. Dynamic Bending Experimental Results

#### 4.3. Numerical Prediction Results

#### 4.3.1. Numerical Prediction Results of Dynamic Compression

#### 4.3.2. Numerical Prediction Results of Dynamic Bending

## 5. Conclusions

- We independently designed the observable cryogenic box and improved the Hopkinson bending bar. Based on the SHPB device, we set up an ultra-low temperature dynamic experimental platform with a synchronous observation function; the dynamic mechanical properties of CFRP laminates at ultra-low temperatures were tested, and the damage evolution process was observed simultaneously.
- The experimental results are as follows: CFRP laminates exhibit a noticeable strain rate effect during dynamic compression; the compression strength and modulus increase linearly with the increase in strain rate and show a quadratic function variation trend of first increasing and then decreasing with the increase in temperature. The damage degree of the dynamic bending sample increases obviously with the increase in impact velocity and decreases first and then increases with the decrease in temperature, and the damage degree is minimum at $-80\mathbb{C}$.
- Based on the ultra-low temperature dynamic constitutive, failure criterion, and interlayer interface damage constitutive of CFRP laminates, a numerical prediction model was established to predict the mechanical properties and damage evolution process of the dynamic compression and bending of CFRP laminates at ultra-low temperatures. The predicted results of the relationship between the dynamic mechanical properties and strain rate and temperature agree with the experimental results. The FEA results of the damage evolution process of CFRP laminates are basically consistent with the experimental observations.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Ultra-low temperature dynamic experimental platform with synchronous observation function.

**Figure 3.**Finite element model. (

**a**) Hopkinson pressure bar and dynamic compression sample. (

**b**) Hopkinson bending bar and dynamic bending sample.

**Figure 5.**The dynamic compression samples of CFRP laminates: (

**a**) the damage evolution process captured by high-speed camera and corresponding DIC analysis results during compression at a $1200/\mathrm{s}$ strain rate; (

**b**) the final damage morphology at different temperatures and strain rates.

**Figure 6.**Stress–strain curves of the dynamic compression samples at different strain rates and temperatures: (

**a**) room temperature; (

**b**) $-80\xb0\mathrm{C}$; (

**c**) $-180\xb0\mathrm{C}$; (

**d**) $800/\mathrm{s}$ strain rate; (

**e**) $1200/\mathrm{s}$ strain rate; (

**f**) $1600/\mathrm{s}$ strain rate.

**Figure 7.**The relationship between mechanical properties of the dynamic compression sample and strain rate and temperature: (

**a**) compression strength–strain rate, (

**b**) compression modulus–strain rate, (

**c**) compression strength–temperature, (

**d**) compression modulus–temperature.

**Figure 9.**The damage evolution process captured by high-speed camera of the dynamic bending samples of CFRP laminates at different temperatures and impact velocities.

**Figure 10.**Optical microscope image of the fracture position after dynamic impact at different temperatures.

**Figure 11.**Load–displacement curves of the dynamic bending samples at different temperatures and $10\mathrm{m}/\mathrm{s}$ impact velocity.

**Figure 12.**The FEA results of dynamic compression samples of CFRP laminates under 1600⁄s strain rate compression: (

**a**) strain nephogram, (

**b**) stress nephogram.

**Figure 13.**The stress nephogram of the FEA results of the dynamic bending sample applied at the impact velocity of $8.5\mathrm{m}/\mathrm{s}$.

**Table 1.**Static material properties of single-layer plate at room temperature [7].

Modulus | ${\mathit{E}}_{1}$ | ${\mathit{E}}_{2}\text{}=\text{}{\mathit{E}}_{3}$ | ${\mathit{G}}_{12}\text{}=\text{}{\mathit{G}}_{13}$ | ${\mathit{G}}_{23}$ | ${\mathit{v}}_{12}\text{}=\text{}{\mathit{v}}_{13}$ | ${\mathit{v}}_{23}$ |
---|---|---|---|---|---|---|

$138\mathrm{GPa}$ | $7\mathrm{GPa}$ | $4.8\mathrm{GPa}$ | $3.8\mathrm{GPa}$ | $0.3$ | $0.35$ | |

Strength | ${\mathit{X}}_{\mathit{t}}$ | ${\mathit{X}}_{\mathit{c}}$ | ${\mathit{Y}}_{\mathit{t}}$ | ${\mathit{Y}}_{\mathit{c}}$ | ${\mathit{S}}_{\mathbf{12}}\mathbf{=}{\mathit{S}}_{\mathbf{23}}\mathbf{=}{\mathit{S}}_{\mathbf{13}}$ | |

$2500\mathrm{MPa}$ | $800\mathrm{MPa}$ | $80\mathrm{MPa}$ | $150\mathrm{MPa}$ | $110\mathrm{MPa}$ | ||

Fracture toughness | ${\mathit{W}}_{\mathit{f}\mathit{t}}$ | ${\mathit{W}}_{\mathit{f}\mathit{c}}$ | ${\mathit{W}}_{\mathit{m}\mathit{t}}$ | ${\mathit{W}}_{\mathit{m}\mathit{c}}$ | ||

$12.5\mathrm{N}/\mathrm{mm}$ | $12.5\mathrm{N}/\mathrm{mm}$ | $0.1\mathrm{N}/\mathrm{mm}$ | $0.1\mathrm{N}/\mathrm{mm}$ |

**Table 2.**Tensile properties of single-layer plate at different temperatures [7].

Samples | Temperature | Modulus $\left(\mathbf{G}\mathbf{P}\mathbf{a}\right)$ | Strength $\left(\mathbf{M}\mathbf{P}\mathbf{a}\right)$ |
---|---|---|---|

$0\xb0$ | $\mathrm{RT}$ | $150$ | $2181$ |

$173\mathrm{K}$ | $138$ | $1867$ | |

$77\mathrm{K}$ | $139$ | $1828$ | |

$90\xb0$ | $\mathrm{RT}$ | $8.8$ | $56.6$ |

$173\mathrm{K}$ | $11.3$ | $55.6$ | |

$77\mathrm{K}$ | $15.4$ | $53.2$ |

**Table 3.**The strength of the single-layer plate in different directions and the corresponding material parameters at $0.001/s$ reference strain rate.

${\mathit{\sigma}}_{0}$ | $\mathbf{A}$ | $\mathit{n}$ | |
---|---|---|---|

Fiber direction | $800\mathrm{Mpa}$ | $2.04$ | $0.41$ |

Transverse direction | $150\mathrm{Mpa}$ | $4.65$ | $0.22$ |

Thickness direction | $150\mathrm{Mpa}$ | $0.11$ | $0.50$ |

${\mathit{K}}_{\mathit{n}}\text{}=\text{}{\mathit{K}}_{\mathit{s}}\text{}=\text{}{\mathit{K}}_{\mathit{t}}$ | ${\mathit{\sigma}}_{\mathit{n}}^{0}$ | ${\mathit{\tau}}_{\mathit{s}}^{0}={\mathit{\tau}}_{\mathit{t}}^{0}$ | ${\mathit{G}}_{\mathit{n}}^{\mathit{C}}$ | ${\mathit{G}}_{\mathit{s}}^{\mathit{C}}$ | ${\mathit{\eta}}_{\mathit{B}\mathit{K}}$ |
---|---|---|---|---|---|

$1\times {10}^{6}\mathrm{N}/{\mathrm{mm}}^{2}$ | $45\mathrm{MPa}$ | $60\mathrm{MPa}$ | $1\mathrm{N}/\mathrm{mm}$ | $1.5\mathrm{N}/\mathrm{mm}$ | $1$ |

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## Share and Cite

**MDPI and ACS Style**

Zhao, W.; Lin, S.; Wang, W.; Yang, Y.; Yan, X.; Yang, H. Study on Dynamic Mechanical Properties of Carbon Fiber-Reinforced Polymer Laminates at Ultra-Low Temperatures. *Materials* **2023**, *16*, 2654.
https://doi.org/10.3390/ma16072654

**AMA Style**

Zhao W, Lin S, Wang W, Yang Y, Yan X, Yang H. Study on Dynamic Mechanical Properties of Carbon Fiber-Reinforced Polymer Laminates at Ultra-Low Temperatures. *Materials*. 2023; 16(7):2654.
https://doi.org/10.3390/ma16072654

**Chicago/Turabian Style**

Zhao, Wenhao, Sanchun Lin, Wenfeng Wang, Yifan Yang, Xuan Yan, and Heng Yang. 2023. "Study on Dynamic Mechanical Properties of Carbon Fiber-Reinforced Polymer Laminates at Ultra-Low Temperatures" *Materials* 16, no. 7: 2654.
https://doi.org/10.3390/ma16072654