# Analysis of the Parameters Affecting the Stiffness of Short Sisal Fiber Biocomposites Manufactured by Compression-Molding

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{3}, i.e., significantly lower than that of the synthetical fibers, and the main tensile properties, determined by a single fiber tensile test, were as follows: Young modulus E

_{f}= 37 GPa, tensile strength σ

_{f,R}= 685 MPa and tensile strain ε

_{f,R}= 1.7%.

_{m}= 1.05 g/cm

^{3}, tensile strength σ

_{m,R}is about 50 MPa, Young E

_{m}modulus = 2.7 GPa, and tensile stress strain ε

_{m,R}= 4%.

#### 2.2. Manufacturing

^{3}).

#### 2.3. Mechanical Tests

_{R}, and Young’s modulus, E, of the biocomposite analyzed along with the same mechanical characteristic of the constituent materials, fibers and matrix.

#### 2.4. Methods

_{f}= 0.35, indicated presence of about 500 short fibers or portions of short sisal fibers, with an average diameter of 0.2 mm and an average length of 4 mm. Each fiber interacted with the matrix by means of a bonded type relationship, which indicated perfect fiber–matrix adhesion. The meshes ensured convergence of the solutions. On average, the number of quadratic, three-dimensional, tetrahedral elements used was 2.5 million.

_{f}= 0.35, the manufacture of which is described in Paragraph 2.2, the RVE had to take into account every feature that characterized the tested samples. In particular, the orientation of the short sisal fibers, which was random at the end of the mixing phase, was subsequently altered by the final manufacturing phase, i.e., compression-molding. During this phase, since the thickness of the specimen was less than the maximum length of the fiber, a given percentage of the fiber lost its random orientation and tended to align itself with the lamination plane (x-y), resulting in a lower directionality in the direction of compression, i.e., the direction z in Figure 3. This aspect was taken into account by means of an orientation distribution assessment of the RVE of type 0.35 in the x direction and 0.35 in the y direction, against 0.3 in the z direction; see the coordinate system in Figure 3. This specific orientation distribution was determined by exploring the effect of different levels of reductions in the orientation of the fibers in the z-axis on the Young’s modulus and comparing the results with the experimental ones.

_{f}, differed from each other by less than 1%.

_{f}= 0.35.

_{f}= 0.35 and orientation distribution, i.e., 0.35 in the x and y directions and 0.3 in the z direction; however, these were two very different models, as can be deduced visually from Figure 4, since every generation run produced dissimilar outcomes. The results, in terms of the E of the biocomposite, between the two RVEs differed by less than 0.2%; this demonstrated that the model had incorporated a sufficient number of fibers or portions of fibers to guarantee a stable result.

_{f}= 0.35, was E = 5.37 ± 0.06 GPa; see Table 1. The numerically calculated Young’s modulus value was 5.5 GPa, i.e., 3% higher than that experimental one, due to the absence of curvature in the fibers. Significant difficulties were encountered when making a RVE characterized simultaneously by V

_{f}= 0.35 and by fibers with nonzero curvature. The influence of the average curvature of the fibers on a RVE with V

_{f}= 0.1 was then analyzed. It was found that even small undulations, i.e., similar to those found in the specimens, caused a reduction in stiffness of between 3% and 5%. Such a result is therefore compatible with the difference between the estimate of Young’s modulus calculated by the numerical model and the experimental value.

_{f}values between 0.1 and 0.35 showed linear variation of Young’s modulus. This result agrees perfectly with the results of the numerical models presented here, as shown in Section 3.1.

## 3. Results

#### 3.1. Influence of the Fiber Volume Fraction

_{f}. In order to analyze the influence of this parameter, RVEs were made with the following values: 0.1, 0.15, 0.2, 0.25, 0.3, 0.35. The other parameters were kept constant, i.e., fiber length 4 mm, straight fibers and orientation distribution of type 0.35 in the x direction, 0.35 in the y direction and 0.3 in the z direction. In accordance with [29], a maximum fiber volume fraction of 0.35 corresponds to the maximum tensile strength. As such, higher fiber volume fractions are not used in the practical applications. A 3D transparent view of the six different RVEs is shown in Figure 6.

_{f}) curve; see the graph in Figure 7.

_{m}is the Young modulus of matrix k, given by:

#### 3.2. Influence of the Average Length of the Fibers

#### 3.3. Influence of Fiber Orientation

_{f}value of 0.35, as well as a biocomposites thickness of 3.5 mm and a fiber length of 4 ± 2 mm, the influence of the distribution/orientation of the fibers on the stiffness of the composite in the x-y plane was analyzed by considering four RVEs with the following fiber orientation distributions: dx = dy = dz = 0.33, dx = dy = 0.35 and dz = 0.3, dx = dy = 0.375 and dz = 0.25, dx = dy = 0.4 and dz = 0.2, where dx, dy and dz represent, respectively, the probability of having a fiber oriented along directions x, y and z. For details, refer to [38]. A 3D transparent image of the four RVEs is shown in Figure 10.

#### 3.4. Influence of the Curvature of the Fibers

_{f}= 0.1, taking into account the difficulties in generating RVEs characterized simultaneously by large V

_{f}and nonlinear fibers. Further studies are in progress seeking to implement RVE with a higher fiber volume fraction. RVEs were made with the following curvature factors of the fibers: 0.75 and 1.5; see Figure 12. In DIGIMAT, curved inclusions are swept geometries, where the sweep path is a random Bezier curve and the sweep section is a circle. The Bezier curve that was used as sweep path had 11 control points. The first control point was always fixed, while the 10 remaining control points were generated incrementally, with each one being placed at a random distance and orientation relative to the previous one. The curvature factor governed the maximum acceptable change in orientation from one control point to the next; this could range from 0 (which resulted in a straight beam) to 10. This is more a measure of the tortuosity of the fibers than of the actual curvature; for details refer to [38].

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Short optimized sisal fibers, (

**b**) the double mold and hydraulic press used in the compression-molding operation.

**Figure 2.**SEM micrographs of the fracture surfaces of the biocomposite subjected to static tensile loading.

**Figure 3.**RVE of an epoxy short sisal fiber biocomposite having Vf = 0.35: (

**a**) 3D view, (

**b**) 3D view of the mesh.

**Figure 4.**3D transparent view of two different RVEs of an epoxy short sisal fiber biocomposite with V

_{f}= 0.35, as used for the validation of the numerical model: (

**a**) first generation run, (

**b**) second generation run.

**Figure 5.**Results of the numerical simulation of simple tensile loading in the x direction for an epoxy short sisal fiber composite with V

_{f}= 0.35. Map of displacements in x-direction (numerical values represent displacements in meters).

**Figure 6.**RVE of epoxy-short sisal fiber composites with variable V

_{f}: (

**a**) 0.1, (

**b**) 0.15, (

**c**) 0.2, (

**d**) 0.25, (

**e**) 0.3, (

**f**) 0.35.

**Figure 8.**RVE of epoxy resin-short sisal fiber composites with V

_{f}= 0.35 and variable mean fiber length: (

**a**) 1 mm, (

**b**) 4 mm, (

**c**) 8 mm.

**Figure 9.**Graph of the resulting Young’s modulus of the composite as the average length of the short sisal fibers varied.

**Figure 10.**RVE of epoxy resin-short sisal fiber composites with V

_{f}= 0.35 and variable orientation distribution: (

**a**) dx = dy = dz = 0.33, (

**b**) dx = dy = 0.35 and dz = 0.3, (

**c**) dx = dy = 0.375 and dz = 0.25, (

**d**) dx = dy = 0.4 and dz = 0.2.

**Figure 11.**Graph of the resulting Young’s modulus of the composite in the x-y plane as the distribution of the orientation of the fibers varied.

**Figure 12.**RVE of epoxy resin-short sisal fiber composites with V

_{f}= 0.1 and variable mean fiber curvature: (

**a**) 0.75, (

**b**) 1.

**Figure 13.**Graph of the Young’s modulus of the composite as the mean curvature factor of the fibers varied in an RVE with V

_{f}= 0.1.

Material | σ_{R} [MPa] | E [GPa] |
---|---|---|

Sisal fibers | 685 | 37 |

Green epoxy | 50 | 2.7 |

Green epoxy-sisal biocomposite with V_{f} = 0.35 | 35 | 5.37 |

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**MDPI and ACS Style**

Pantano, A.; Militello, C.; Bongiorno, F.; Zuccarello, B.
Analysis of the Parameters Affecting the Stiffness of Short Sisal Fiber Biocomposites Manufactured by Compression-Molding. *Polymers* **2022**, *14*, 154.
https://doi.org/10.3390/polym14010154

**AMA Style**

Pantano A, Militello C, Bongiorno F, Zuccarello B.
Analysis of the Parameters Affecting the Stiffness of Short Sisal Fiber Biocomposites Manufactured by Compression-Molding. *Polymers*. 2022; 14(1):154.
https://doi.org/10.3390/polym14010154

**Chicago/Turabian Style**

Pantano, Antonio, Carmelo Militello, Francesco Bongiorno, and Bernardo Zuccarello.
2022. "Analysis of the Parameters Affecting the Stiffness of Short Sisal Fiber Biocomposites Manufactured by Compression-Molding" *Polymers* 14, no. 1: 154.
https://doi.org/10.3390/polym14010154