# Adjunctive Damage Model to Describe the Interaction of Different Defect Types in Textile Composites on the Strain-Rate-Dependent Material Behaviour

^{*}

*J. Compos. Sci.*

**2023**,

*7*(9), 365; https://doi.org/10.3390/jcs7090365 (registering DOI)

## Abstract

**:**

## 1. Introduction

_{as}layer structure under uniaxial loading was investigated in [16]. During the injection moulding process, the authors introduced air into the liquid matrix via a bypass, resulting in void volume contents between 2.5% and 8.8%. Under both tensile–tensile and compression–compression fatigue, a decrease in lifetime was demonstrated for the porous material.

## 2. Materials and Methods

#### 2.1. Materials and Pre-Damaged Methods

#### 2.2. Adjunctive Damage Model

#### 2.3. Parameter Identification

## 3. Results and Discussion

#### Model Validation

## 4. Conclusions and Summary

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Selected micrographs of nominally void-free (

**a**), with low void content (

**b**) and with higher void content (

**c**) GF-NCF/EP test specimens.

**Figure 2.**Principle representation of homogeneously distributed manufacturing and operational defects.

**Figure 4.**Comparison of representative strain-rate-dependent stress-strain-curves from experimentally determined and computationally generated data for nominally defect-free GF-MAG/EP composites for parameter identification.

**Figure 5.**Comparison of representative stress-strain curves determined experimentally and with the identified parameters calculated stress-strain curves of nominally defect-free, porous and pre-fatigued GF-MAG/EP- composites at the reference strain rate.

**Figure 6.**Validation of the ASM for additional strain rates for nominal defect-free GF-NCF/EP-composites for strain rates of $0.04$ s${}^{-1}$, $0.4$ s${}^{-1}$ and 40 s${}^{-1}$.

**Figure 7.**Validation of the strain-rate-dependent stress-strain curves of porous GF-NCF/EP-composites calculated with the ASM.

**Figure 8.**Validation of the material behaviour of defective GF-NCF/EP-composites with separately and simultaneously existing operational defects ${D}_{cy}=0.29$ and manufacturing defects with ${V}_{P}=1.43\%$ (

**a**) and ${V}_{P}=2.9\%$ (

**b**).

Void Content | Max. Injection Pressure | Vacuum | Holding Pressure | Degassing |
---|---|---|---|---|

0.01 ± 0.01% | 3 | −1 | 3 | Yes |

1.43 ± 0.65% | 0.5 | −0.4 | 0 | No |

2.9 ± 0.9% | 1 | −0.2 | 0 | No |

**Table 2.**Identified model parameters for the description of the strain-rate-dependent material behaviour of nominally defect-free GF-NCF/EP-composites.

Parameter | 90° | 45° | 0° |
---|---|---|---|

${E}_{\alpha}^{0,ref}$ in GPa | 8.4 | 12.4 | 18.9 |

${\dot{\epsilon}}^{ref}$ in ${s}^{-1}$ | 0.0004 | 0.0004 | 0.0004 |

${A}_{\alpha}^{E}$ | 0.02 | 0.01 | 0.02 |

${\xi}_{\alpha}$ | 2.24 | 0.2 | 0.06 |

${\lambda}_{\alpha}$ | 1.12 | 1 | 1.7 |

${\kappa}_{\alpha}$ | 10 | 11 | 9.8 |

${D}_{\alpha}^{0}$ | 0.17 | 0.001 | 0 |

${D}_{\alpha}^{\omega}$ | 0 | 0 | 0 |

**Table 3.**Identified model parameters for the description of the strain-rate-dependent material behaviour of defective GF-NCF/EP-composites.

Defect Parameter | Defect Measure | 90° | 45° | 0° |
---|---|---|---|---|

${D}_{\alpha}^{0}$ | ${V}_{P}=1.43\%$ | 0.21 | 0.025 | 0.039 |

${D}_{\alpha}^{0}$ | ${V}_{P}=2.9\%$ | 0.22 | 0.04 | 0.046 |

${D}_{\alpha}^{\omega}$ | ${D}_{cy}=0.29$ | 0.1 | -/- ^{1} | -/- |

${D}_{\alpha}^{\omega}$ | ${D}_{cy}=0.42$ | 0.17 | -/- | -/- |

^{1}not yet determined.

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**MDPI and ACS Style**

Protz, R.; Koch, I.; Gude, M.
Adjunctive Damage Model to Describe the Interaction of Different Defect Types in Textile Composites on the Strain-Rate-Dependent Material Behaviour. *J. Compos. Sci.* **2023**, *7*, 365.
https://doi.org/10.3390/jcs7090365

**AMA Style**

Protz R, Koch I, Gude M.
Adjunctive Damage Model to Describe the Interaction of Different Defect Types in Textile Composites on the Strain-Rate-Dependent Material Behaviour. *Journal of Composites Science*. 2023; 7(9):365.
https://doi.org/10.3390/jcs7090365

**Chicago/Turabian Style**

Protz, Richard, Ilja Koch, and Maik Gude.
2023. "Adjunctive Damage Model to Describe the Interaction of Different Defect Types in Textile Composites on the Strain-Rate-Dependent Material Behaviour" *Journal of Composites Science* 7, no. 9: 365.
https://doi.org/10.3390/jcs7090365