# A Finite Element Study to Investigate the Mechanical Behaviour of Unidirectional Recycled Carbon Fibre/Glass Fibre–Reinforced Epoxy Composites

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Their Behaviour

#### 2.1. Recycled Composites

^{f}) 40 wt% and 60 wt%. The resin combined with its hardener in a 2:1 ratio occupies the composite’s remaining volume (V

^{r}). The recycled composites possess a uniform structure throughout the lamina. The composite types maintained a UD fibre orientation (0°) and continuous (uniform length from end to end) and long (105 ± 2 mm) fibres.

#### 2.2. Recycled Composite Damage Behaviour

## 3. Finite Element Methodology

#### 3.1. Recycled Composite Assumption

#### 3.2. Elastoplastic Material Model for Recycled Composites

#### 3.3. Continuum Ductile Damage Model for Recycled Composites

#### 3.4. Numerical Material Modeling

#### 3.5. Modelling, Loads and Boundary Conditions

#### 3.5.1. Tensile Test Model

_{1}, B

_{1}, C

_{1}, X

_{1}, C

_{2}, B

_{2}and A

_{2}, and five cells, which were A

_{1}–B

_{1}, B

_{1}–C

_{1}, C

_{1}–C

_{2}, C

_{2}–B

_{2}and B

_{2}–A

_{2}, in that order (see Figure 5).

_{1}to C

_{1}and C

_{2}to A

_{2}with 4080 elements. These are the cells experiencing the least stress. The maximum stress will be experienced within the cell C

_{1}–C

_{2}, leading to damage at X

_{1}(expected point). A very fine mesh was created with 8160 elements, covering the sensitive area. An explicit mesh with linear geometric order was used, with full integration eliminating the hourglass effect throughout the sample.

_{1}–B

_{1}, restricting free movements in terms of displacement (U) and rotation (UR) in all three (x,y,z) axes (U1 = U2 = U3 = UR1 = UR2 = UR3 = 0). Similar restrictions were applied to cell B

_{2}–A

_{2}at the opposite end (U1 = U3 = UR1 = UR2 = UR3 = 0), but allowing displacement (U2) in the direction parallel to the applied force (y-axis). This particular condition was assigned to the sample via a separately created reference point (RP) at point A

_{2}. The cells occupying the space between points B

_{2}and A

_{1}were couples to the created RP. During the numerical TT simulation, the applied displacement (U2) will pull the cells uniaxially at RP and evenly distribute the force within the respective cells below.

#### 3.5.2. Impact Test Model

_{3}, B

_{3}, C

_{3}, X

_{2}, C

_{4}, B

_{4}and A

_{4,}and five cells, which were A

_{3}–B

_{3}, B

_{3}–C

_{3}, C

_{3}–C

_{4}, C

_{4}–B

_{4}and B

_{4}–A

_{4}, in that order (see Figure 6). The parts (sample and hammer) were then assembled by placing the hammer tip above X

_{2}, maintaining a small gap between the parts.

_{3}to C

_{3}and C

_{4}to A

_{4}. The points cover four cells that were not exposed directly to impact, making it a less sensitive area. The hammer hits perpendicular to the middle cell at point X

_{2}. This sensitive region of the sample experiences heavy damage, leading to a break. A very fine mesh with 63,800 elements was created at the middle cell C

_{3}–C

_{4}. An explicit mesh with linear geometric order was used throughout the sample. Full integration was used at the impact cell C

_{3}–C

_{4}, but reduced integrations were adopted at cells with no direct contact with the hammer in order to reduce the complexity. The hourglass was blocked from the entire model.

_{3}and B

_{4}. The displacement in all three (x,y,z) axes (U1 = U2 = U3 = 0) was restricted at the pinned edges. The hammer was defined as a rigid body by creating constraints. A normal mesh with 1786 elements was created for the hammer. A reference point (RP) was created at the centre of the hammer to apply uniform velocity perpendicular to the sample. Furthermore, contact modelling was implemented. The hammer (moving part) was adjusted until its surface fully covered the sample’s surface (inert part) during impact. The datum planes were used as a guideline to align the parts. After fixing the positions, surfaces were created using designated cells. An explicit contact-based interaction was created to assign the surfaces. First, a frictionless contact was created on the surfaces. Then, for the numerical IT, a tangential behaviour was created on the surfaces, with a 0.3 friction coefficient, followed by creating a normal behaviour with hard contact for the hammer to hit the sample, due to the applied velocity.

## 4. Results and Discussion

#### 4.1. Numerical Input Parameters

#### 4.2. Numerical Tensile Test Results

_{2}(see Figure 5). As the tensile strength of the rGF/EP and rCF/EP samples increased, the displacement to failure also increased, with an increase in strain rate to failure. Initially, multiple estimations were made to fracture the samples within the defined time step. A lower displacement failed to damage the samples, and higher values exceeded the experimental time frame, resulting in errors. Finally, the optimal values of the applied displacement are as follows: 0.55 mm (40% rGF/EP), 0.67 mm (60% rGF/EP), 1.05 mm (40% rCF/EP), 1.15 mm (60% rCF/EP) and 2 mm (EP). It can be observed that the fibreless EP samples required a higher displacement to failure, indicating the longer strain rate to failure.

#### 4.3. Numerical Impact Test Results

^{2}, and the numerical case is 25 kJ/m

^{2}. However, the difference between 40 and 60% rCF/EP in the experimental case is 3.63 kJ/m

^{2}, and in the numerical case is 37.7 kJ/m

^{2}. Such a poor energy difference between 40 and 60% rCF/EP experimental IT can be related to previously mentioned defects, such as the poor wettability of rCF to reinforce with EP, as the energy pattern in other composite types seems to fall within a comparable order. However, the char-based defects on rGF/EP were reflected less. Overall, based on the energy variations in rGF/EP and rCF/EP, it can be concluded that the numerically observed energies are reliable in all composite types, and are defect-free.

^{2}, and by 60% rCF/EP is 120.46 kJ/m

^{2}. Meanwhile, Caminero et al. 2016 [54] tested UD 66% vCF/EP using unnotched charpy IT and noticed a 189.01 kJ/m

^{2}internal energy. The study highlighted that, among various multidirectional vCF/EP laminates, the UD laminate possesses a high performance under impact and flexural testing. In addition, when comparing the energy absorbed by 40% rGF/EP, which is 1.4 kJ or 33.49 kJ/m

^{2}, and 60% rGF/EP, which is 2.4 kJ or 59.31 kJ/m

^{2}, to a similar study, Bazli et al. 2019 [55] tested UD 70.5% vGF/EP composites under unnotched charpy IT, which resulted in 5.6–7.1 kJ depending on the exposed temperature. The study also highlighted that UD vGF/EP displayed a higher performance in flexural and impact modes compared to a woven and randomly oriented fibre arrangement.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Sample fracture after experimental TT: (

**a**) 100% EP; (

**b**) 40% rGF/EP; (

**c**) 60% rGF/EP; (

**d**) 40% rCF/EP; (

**e**) 60% rCF/EP; and after IT: (

**f**) E-EP; (

**g**) 40% rGF/EP; (

**h**) 60% rGF/EP; (

**i**) 40% rCF/EP; (

**j**) 60% rCF/EP.

**Figure 7.**Fractured samples after numerical TT: (

**a**) 100% EP; (

**b**) 40% rGF/EP; (

**c**) 60% rGF/EP; (

**d**) 40% rCF/EP; (

**e**) 60% rCF/EP.

**Figure 9.**Comparing the experimental and numerical SS curves of rGF/EP composites: (

**a**) SS curves of 60% rGF/EP; (

**b**) SS curves of 40% rGF/EP.

**Figure 10.**Comparing experimental and numerical SS curves of rCF/EP composites: (

**a**) SS curves of 60% rCF/EP; (

**b**) SS curves of 40% rCF/EP.

**Figure 12.**Numerical IT results using von Mises stress distribution: (

**a**) 60% rCF/EP; (

**b**) 40% rCF/EP; (

**c**) 60% rGF/EP; (

**d**) 40% rGF/EP; (

**e**) 100% EP.

**Figure 13.**Internal energy observed by the composites after numerical IT: (

**a**) 60% rCF/EP; (

**b**) 40% rCF/EP; (

**c**) 60% rGF/EP; (

**d**) 40% rGF/EP; (

**e**) 100% EP.

**Table 1.**Experimental results of the compression moulded recycled composites [31].

Composite RECIPES | V^{f}(wt%) | V^{r}(wt%) | Tensile Strength (MPa) | Young Modulus (GPa) | Impact Strength (kJ/m ^{2}) | Fracture Strain (No Unit) | Density (g/cm ^{3}) |
---|---|---|---|---|---|---|---|

rCF/EP | 60 ± 2 | 40 ± 2 | 235.70 | 60.80 | 53.61 | 0.00683 | 1.52 |

40 ± 2 | 60 ± 2 | 210.34 | 45.28 | 49.98 | 0.00827 | 1.64 | |

rGF/EP | 60 ± 2 | 40 ± 2 | 114.58 | 30.72 | 41.05 | 0.00272 | 1.77 |

40 ± 2 | 60 ± 2 | 65.42 | 27.37 | 18.99 | 0.00156 | 1.85 | |

EP | 0 | 100 | 39.46 | 2.16 | 35.18 | 0.05810 | 1.45 |

Composite Types | Young Modulus (MPa) | Yield Point | Ultimate Point | Fracture Strain | Poisson Ratio | ||
---|---|---|---|---|---|---|---|

Stress (MPa) | Strain (No Unit) | Stress (MPa) | Strain (No Unit) | ||||

60% rCF | 13,262 | 55.8332 | 0.00421 | 246.529 | 0.02151 | 0.00683 | 0.3 |

40% rCF | 11,103 | 45.8554 | 0.00413 | 181.254 | 0.01952 | 0.00827 | 0.3 |

60% rGF | 10,921.3 | 26.4294 | 0.00242 | 120.598 | 0.01321 | 0.00272 | 0.25 |

40% rGF | 9011.50 | 22.0782 | 0.00245 | 83.16 | 0.01077 | 0.00156 | 0.25 |

100% EP | 2004.46 | 10.1626 | 0.00507 | 41.7633 | 0.02825 | 0.05810 | 0.3 |

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**MDPI and ACS Style**

Karuppannan Gopalraj, S.; Kärki, T.
A Finite Element Study to Investigate the Mechanical Behaviour of Unidirectional Recycled Carbon Fibre/Glass Fibre–Reinforced Epoxy Composites. *Polymers* **2021**, *13*, 3192.
https://doi.org/10.3390/polym13183192

**AMA Style**

Karuppannan Gopalraj S, Kärki T.
A Finite Element Study to Investigate the Mechanical Behaviour of Unidirectional Recycled Carbon Fibre/Glass Fibre–Reinforced Epoxy Composites. *Polymers*. 2021; 13(18):3192.
https://doi.org/10.3390/polym13183192

**Chicago/Turabian Style**

Karuppannan Gopalraj, Sankar, and Timo Kärki.
2021. "A Finite Element Study to Investigate the Mechanical Behaviour of Unidirectional Recycled Carbon Fibre/Glass Fibre–Reinforced Epoxy Composites" *Polymers* 13, no. 18: 3192.
https://doi.org/10.3390/polym13183192