# A Strain Rate Dependent Damage Model for Evaluating the Dynamic Response of CFRTP Laminates with Different Stacking Sequence

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## Abstract

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## 1. Introduction

^{−5}s

^{−1}to 1 s

^{−1}and 100 s

^{−1}to 2500 s

^{−1}, respectively. Chen et al. [6] showed the failure strain of PEEK composites increased apparently with the strain rate increasing from 0.001 s

^{−1}to 1000 s

^{−1}. Ou et al. [7] investigated the effect of strain rate on the mechanical properties and failure patterns of GFRP and reported that tensile strength, maximum strain and toughness increase with increasing strain rates from 1/600 s

^{−1}to 160 s

^{−1}. The authors previous research also revealed that the strain rate sensitivity of CFRTP laminates was obvious from strain rate 2 × 10

^{−4}s

^{−1}to 2200 s

^{−1}[8]. The strain rate sensitivity was one of the key factors an accurate assessment of composite tensile strength and fracture toughness under dynamic loadings [9,10].

## 2. Strain Rate Relate Dependent Material Model

#### 2.1. Constitute Model

#### 2.2. Damage Initiation Model

#### 2.3. Damage Evolution Model

#### 2.4. Model Implementation

## 3. Experimental Method

## 4. Model Validation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Comparison of experimental results and simulation results (

**a**) contact force; (

**b**) experimental failure pattern; (

**c**) SSD and SRD (

**d**) SSI and SRD (

**e**) SSI and SRI simulation result.

**Figure 7.**Comparison of experimental results and simulation results (

**a**) contact force; (

**b**) experimental failure pattern; (

**c**) SSD and SRD (

**d**) SSI and SRD (

**e**) SSI and SRI simulation result.

**Figure 8.**Comparison of experimental results and simulation results (

**a**) contact force; (

**b**) experimental failure pattern; (

**c**) SSD and SRD (

**d**) SSI and SRD (

**e**) SSI and SRI simulation result.

Elastic Parameter | Strength Parameter | Fracture Energy | Strain Rate Parameter | ||||||
---|---|---|---|---|---|---|---|---|---|

(GPa) | (MPa) | (N/mm) | |||||||

${E}_{11}$ | 42.9 | ${\sigma}_{11}^{f,t}$ | 850 | ${\sigma}_{12}^{f}$ | 105 | ${G}_{1}$ | 0.3 | ${m}_{1}^{e}$ | 0.005 |

${E}_{22}$ | 4.5 | ${\sigma}_{11}^{f,c}$ | 350 | ${\sigma}_{23}^{f}$ | 105 | ${G}_{2}$ | 0.2 | ${m}_{2}^{e}$ | 0.064 |

${E}_{33}$ | 4.5 | ${\sigma}_{22}^{f,t}$ | 260 | ${\sigma}_{13}^{f}$ | 105 | ${G}_{3}$ | 0.2 | ${m}_{3}^{e}$ | 0.032 |

${E}_{12}$ | 1.2 | ${\sigma}_{22}^{f,c}$ | 275 | ${m}_{1}^{s}$ | 0.003 | ||||

${E}_{23}$ | 1.2 | ${\sigma}_{33}^{f,t}$ | 260 | ${m}_{2}^{s}$ | 0.042 | ||||

${E}_{31}$ | 1.2 | ${\sigma}_{33}^{f,c}$ | 275 | ${m}_{3}^{s}$ | 0.027 |

Elastic Parameter | Strength Parameter | Fracture Energy | Strain Rate Parameter | ||||||
---|---|---|---|---|---|---|---|---|---|

(GPa) | (MPa) | (N/mm) | |||||||

${E}_{11}$ | 115 | ${\sigma}_{11}^{f,t}$ | 1524 | ${\sigma}_{12}^{f}$ | 210 | ${G}_{1}$ | 0.9 | ${m}_{1}^{e}$ | 0.001 |

${E}_{22}$ | 10.5 | ${\sigma}_{11}^{f,c}$ | 945 | ${\sigma}_{23}^{f}$ | 210 | ${G}_{2}$ | 0.6 | ${m}_{2}^{e}$ | 0.018 |

${E}_{33}$ | 10.5 | ${\sigma}_{22}^{f,t}$ | 615 | ${\sigma}_{13}^{f}$ | 210 | ${G}_{3}$ | 0.6 | ${m}_{3}^{e}$ | 0.024 |

${E}_{12}$ | 6.2 | ${\sigma}_{22}^{f,c}$ | 425 | ${m}_{1}^{s}$ | 0.001 | ||||

${E}_{23}$ | 6.2 | ${\sigma}_{33}^{f,t}$ | 615 | ${m}_{2}^{s}$ | 0.012 | ||||

${E}_{31}$ | 6.2 | ${\sigma}_{33}^{f,c}$ | 425 | ${m}_{3}^{s}$ | 0.014 |

Impact Energy (J) | Experiment (N) | SSD and SRD (N) | Error (%) | SSI and SRD (N) | Error (%) | SSI and SRI (N) | Error (%) | |
---|---|---|---|---|---|---|---|---|

QI | 10 | 3203 | 3200 | 0.1% | 3581 | 11.8% | 3408 | 6.4% |

AP | 3 | 3525 | 3423 | 2.9% | 3412 | 3.2% | 3396 | 3.7% |

6 | 5158 | 5416 | 5% | 4759 | 7.7% | 4727 | 8.4% |

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**MDPI and ACS Style**

Zhang, Y.; Liu, B.
A Strain Rate Dependent Damage Model for Evaluating the Dynamic Response of CFRTP Laminates with Different Stacking Sequence. *Electronics* **2022**, *11*, 3728.
https://doi.org/10.3390/electronics11223728

**AMA Style**

Zhang Y, Liu B.
A Strain Rate Dependent Damage Model for Evaluating the Dynamic Response of CFRTP Laminates with Different Stacking Sequence. *Electronics*. 2022; 11(22):3728.
https://doi.org/10.3390/electronics11223728

**Chicago/Turabian Style**

Zhang, Yiben, and Bo Liu.
2022. "A Strain Rate Dependent Damage Model for Evaluating the Dynamic Response of CFRTP Laminates with Different Stacking Sequence" *Electronics* 11, no. 22: 3728.
https://doi.org/10.3390/electronics11223728