# Modeling the Stiffness of Coupled and Uncoupled Recycled Cotton Fibers Reinforced Polypropylene Composites

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and methods

#### 2.1. Materials

#### 2.2. Cotton Flocks Treatment and Composites Preparation

^{®}(Duisburg, Germany). The coupled composites added a 6 wt% of MAPP at the same time than the other phases. The process took 10 min, at 185 °C and at a speed of 80 rpm. Coupled and uncoupled composites with CF contents ranging from 20 to 50 wt% were prepared. The obtained blends were cut down to 8 mm pellets able to be mold injected. These pellets were stored for 24 h in an oven at 80 °C to eliminate the humidity.

#### 2.3. Composite and Standard Specimen Preparation

^{−2}and the maintaining pressure was 37.5 kg/cm

^{−2}. A steel mold with a cavity in the shape of the standard specimen was used, and at least ten specimens for every one of the composite formulations were obtained.

#### 2.4. Mechanical Test

#### 2.5. Morphologic Analysis of the Reinforcements

## 3. Results and Discussion

#### 3.1. Young’s Modulus of the Composites

_{t}

^{C}) reinforced with CF contents ranging from 20 to 50 wt%. The table also shows the tensile strength of the composites (σ

_{t}

^{C}), the percentage of reinforcement in weight (W

^{F}), and its volume fraction (V

^{F}).

#### 3.2. Neat Contribution of the Reinforcements

_{t}

^{C}, E

_{t}

^{F}, and E

_{t}

^{M}are the Young’s moduli of the composite, reinforcement, and matrix, respectively. V

^{F}represents the reinforcement volume fraction, and ƞ

_{e}is a modulus efficiency factor that equalizes the contribution of the reinforcements to the Young’s modulus of the composite. This efficiency factor is seldom presented as a length efficiency factor times an orientation efficiency factor (ƞ

_{e}= ƞ

_{l}· ƞ

_{o}). At the exception of the intrinsic Young’s modulus of the reinforcements and the modulus efficiency factor, the rest of the values can be easily obtained during the tensile test of the composites. Clearly, the RoM can only be used if the Young’s modulus of the composite evolves linearly against reinforcement content.

_{e}·E

_{t}

^{F}in the RoM. Thus, the RoM can be rearranged to account for such neat contribution as:

#### 3.3. Micromechanics Analysis of the Young’s Modulus

_{e}·E

_{t}

^{F}. While it is possible to measure the intrinsic Young’s modulus of the fibers, and more so in the case of the strands, some authors defend the use of micromechanics methods as an alternative [11,37,38]. In addition, a high number of experiments are necessary due to the foreseeable standard deviations of the mechanical properties of natural fiber reinforcements. Thus, the Hirsh model was proposed as a means to evaluate the intrinsic Young’s modulus of CF.

_{e}was evaluated at 0.49 ± 0.04, a value similar to HS. Finally, SGW showed the highest values for ƞ

_{e}, with a mean of 0.56 ± 0.02.

^{F}and r

^{F}are the reinforcement mean weighed length and radius, respectively. The Poisson’s ratio of the matrix is represented by ν and µ is a coefficient of the stress concentration rate at the end of the fibers. The Poisson ratio was 0.36, as found in the literature [22]. The orientation factor η

_{o}was obtained from η

_{o}= η

_{l}/η

_{e}. Table 3 shows the obtained values.

#### 3.4. Effect of the Morphology of the Reinforcements

^{11}and E

^{22}are the longitudinal and transversal elastic modulus, calculated by the Halpin–Tsai equations [11]:

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Workflow of the research, including the production of cotton flock byproducts, composite mixing and material testing.

**Figure 2.**Young’s modulus of the coupled and uncoupled CF-PP composites against reinforcement content.

**Figure 4.**Correlation between the experimental Young’s moduli of the composites and the computed ones by using the Tsai and Pagano model in combination with Halpin and Tsai equations: (

**A**) Unweighted correlation; (

**B**) correlation line adding the condition of such line going through the origin.

**Table 1.**Young’s modulus and tensile strength of the cotton fiber (CF)/polypropylene (PP) composites.

0%MAPP | 6%MAPP | ||||
---|---|---|---|---|---|

W^{F} | V^{F} | E_{t}^{C} (GPa) | σ_{t}^{C} (MPa) | E_{t}^{C} (GPa) | σ_{t}^{C} (MPa) |

0 | 0 | 1.5 ± 0.1 | 27.6 ± 0.5 | 1.5 ± 0.1 | 27.6 ± 0.5 |

20% | 0.131 | 3.2 ± 0.1 | 35.0 ± 0.5 | 3.3 ± 0.1 | 41.7 ± 0.7 |

30% | 0.205 | 3.9 ± 0.2 | 38.2 ± 0.8 | 3.9 ± 0.1 | 47.1 ±0.7 |

40% | 0.287 | 4.7 ± 0.2 | 41.7 ± 0.8 | 4.8 ± 0.2 | 53.6 ± 1.0 |

50% | 0.376 | 5.6 ± 0.2 | 45.4 ± 1.1 | 5.4 ± 0.2 | 58.3 ± 1.2 |

**Table 2.**Young’s moduli of stone groundwood, hemp strands, and glass fiber reinforced polypropylene coupled composites.

SGW | HS | ONPF | GF | |
---|---|---|---|---|

20% | 2.7 ± 0.1 | 2.8 ± 0.1 | 2.8 ± 0.1 | 4.1 ± 0.1 |

30% | 3.5 ± 0.1 | 3.8 ± 0.1 | 3.8 ± 0.1 | 5.7 ± 0.1 |

40% | 4.3 ± 0.1 | 5.2 ± 0.1 | 4.2 ± 0.1 | 7.7 ± 0.1 |

50% | 5.2 ± 0.1 | 6.3 ± 0.1 | 5.3 ± 0.1 | - |

V^{F} | E_{t}^{F} (GPa) | ƞ_{e} | ƞ_{l} | ƞ_{o} | α_{o} |
---|---|---|---|---|---|

0.131 | 31.48 | 0.52 | 0.89 | 0.58 | 48.8 |

0.205 | 28.06 | 0.47 | 0.89 | 0.53 | 53.3 |

0.287 | 26.48 | 0.45 | 0.89 | 0.51 | 55.1 |

0.376 | 25.46 | 0.45 | 0.90 | 0.49 | 56.2 |

Mean | 27.87 ± 2.63 | 0.47 ± 0.03 | 0.89 ± 0.01 | 0.53 ± 0.04 | 53.3 ± 3.3 |

**Table 4.**Theoretical Young’s moduli of the composites computed by using the Tsai and Pagano model in combination with Halpin andTsai equations.

Experimental | Tsai-Pagano | Error (GPa) | Error (%) | |||||
---|---|---|---|---|---|---|---|---|

V^{F} | 0% MAPP | 6% MAPP | 0% MAPP | 6% MAPP | 0% MAPP | 6% MAPP | 0% MAPP | 6% MAPP |

0.131 | 3.2 | 3.3 | 2.9 | 2.9 | 0.3 | 0.4 | 9.4 | 12.1 |

0.205 | 3.9 | 3.9 | 3.7 | 3.7 | 0.2 | 0.2 | 5.1 | 5.1 |

0.287 | 4.7 | 4.8 | 4.7 | 4.6 | 0 | 0.2 | 0 | 4.2 |

0.376 | 5.6 | 5.4 | 5.8 | 5.7 | –0.2 | –0.3 | –3.6 | –5.6 |

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## Share and Cite

**MDPI and ACS Style**

Serra, A.; Tarrés, Q.; Chamorro, M.-À.; Soler, J.; Mutjé, P.; Espinach, F.X.; Vilaseca, F.
Modeling the Stiffness of Coupled and Uncoupled Recycled Cotton Fibers Reinforced Polypropylene Composites. *Polymers* **2019**, *11*, 1725.
https://doi.org/10.3390/polym11101725

**AMA Style**

Serra A, Tarrés Q, Chamorro M-À, Soler J, Mutjé P, Espinach FX, Vilaseca F.
Modeling the Stiffness of Coupled and Uncoupled Recycled Cotton Fibers Reinforced Polypropylene Composites. *Polymers*. 2019; 11(10):1725.
https://doi.org/10.3390/polym11101725

**Chicago/Turabian Style**

Serra, Albert, Quim Tarrés, Miquel-Àngel Chamorro, Jordi Soler, Pere Mutjé, Francesc X. Espinach, and Fabiola Vilaseca.
2019. "Modeling the Stiffness of Coupled and Uncoupled Recycled Cotton Fibers Reinforced Polypropylene Composites" *Polymers* 11, no. 10: 1725.
https://doi.org/10.3390/polym11101725