# Characterisation of the Anisotropic Thermoelastic Properties of Natural Fibres for Composite Reinforcement

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Composite Production

#### 2.3. Thermal and Mechanical Testing

_{g}), the temperature dependence of their modulus and the coefficient of thermal expansion. A TA Instruments Q800 dynamic mechanical analyser (TA Instruments, New Castle, DE, USA) was used to determine the storage modulus, loss modulus and the Tan Delta of the composites over a range of temperatures. Samples were tested in the deformation mode using a three-point bending clamp (TA Instruments, New Castle, DE, USA) with a preload of 0.1 N and a frequency of 1 Hz. Samples were heated from −50 °C to 150 °C at a rate of 3 °C/min. A TA Instruments Q400E thermomechanical analysis machine (TA Instruments, New Castle, DE, USA) was used to determine the matrix glass transition temperature and the thermal expansion, coefficient of the natural fibre composites. A macro expansion probe was used to allow a large contact area of the sample to be tested. The composites were tested over a range of different fibre orientations (0°, 25°, 45°, 65°, 90°).

#### 2.4. Composite Fibre Volume Fraction

## 3. Results

#### 3.1. Composite Fibre Volume Fraction

#### 3.2. Composite and Fibre Modulus

_{g}), is clearly visible between 70 °C–90 °C. It can be seen over the whole temperature range, that the composites of Young’s modulus decrease as the off-axis loading angle increases. It is also interesting to note that the transverse stiffness of some of the composites loaded at higher off-axis angles is lower than the epoxy resin at temperatures below the matrix T

_{g}. This is an indication of the likely probability of low transverse stiffness of the flax and sisal fibre. The longitudinal fibre modulus E

_{f1}can be obtained at any temperature from the composite longitudinal moduli (E

_{C0}) and the epoxy matrix modulus (E

_{m}) using the well-known Voigt model (also known as the linear rule of mixtures) using the equation below:

_{f}and V

_{m}are the volume fractions of the fibre and the matrix, respectively. It should be noted that the properties of the composites and epoxy matrix change by orders of magnitude in the region of T

_{g}. These large changes can give unexpected results from the micromechanical equations used in this work; and so, we have restricted the temperatures for the micromechanical analysis to the range of −50 °C to +50 °C. The results for the longitudinal fibre moduli of flax and sisal fibres obtained from Equation (1) are compared with the epoxy matrix modulus in Figure 3a. It can be seen that the axial stiffness of both of these fibres is considerably greater than the stiffness of the epoxy matrix; and hence, as observed in the introduction, it can be expected that these fibres will give a considerable reinforcement effect in the composite longitudinal direction. It is further noted that the values obtained for the room temperature fibre moduli of flax and sisal are in good agreement with the values previously reported from single fibre tensile testing.

_{f2}can be obtained at any temperature from the composite longitudinal moduli (E

_{c90}) and the epoxy matrix modulus (E

_{m}) using the well-known Reuss model (also known as the inverse rule of mixtures) using the equation below:

_{f2}for both fibres are significantly lower than the modulus of the epoxy matrix across the whole temperature range. The transverse modulus of the sisal fibres is only approximately 50% of that of the matrix. The flax fibre transverse modulus is even lower with values of only 30% of that of the epoxy matrix. Figure 3b clearly illustrates a major weakness in the application of these natural fibres as a composite reinforcement, in that they provide no reinforcement of the polymer matrix in the transverse direction. On the contrary, these fibres have an anti-reinforcement effect in the transverse direction and result in a composite with a lower transverse modulus than the matrix polymer alone.

_{f1}/E

_{f2}for the flax and sisal fibres, and compares them with some other reinforcement fibres [22]. It can be seen that both sisal and flax are highly anisotropic in their mechanical performance. The flax fibres have a modulus ratio from 55–80 across the temperature range studied, and can be seen to have a level of anisotropy comparable with pitch carbon fibre. The sisal fibres have a considerably lower level of anisotropy, with a modulus ratio of approximately 17. This is lower than most carbon and aramid fibres, but still highly anisotropic in comparison with glass fibres.

_{Cθ}) from Figure 1 and Figure 2 can also be used to obtain values for the composite shear modulus G

_{C12}, which can then be used to obtain a value for the fibre shear modulus G

_{f12}. The mechanics concerning the coordinate system transformations can be applied, leading to the well-known relationship between off-axis modulus and the principal properties of a unidirectional composite ply [12]:

_{C12}by using the curve fitting Equation (3) with the experimental results taken from Figure 2 at various temperatures. An example is shown in Figure 5 for the flax and sisal composite moduli obtained at 25 °C.

_{f12}can then be obtained at any temperature from the composite moduli (G

_{C12}) and the epoxy matrix shear modulus (G

_{m}), also using the well-known Reuss model:

#### 3.3. Composite and Fibre Thermal Expansion

_{g}), the thermal strain is low but as the temperature increases towards T

_{g}, the thermal strain increases, and above T

_{g}, the thermal strain is significantly high. The temperature region of this change of slope is indicative of the polymer (matrix) T

_{g}which, in both cases, can be seen to be in the range of 70 °C to 90 °C (similar to the values obtained by DMA). It can further be noted from these figures, that when loading at 90°, the thermal strain of the composite is approximately the same as the resin thermal strain. At fibre orientation angles, the composite thermal strain is very low and a change in slope at T

_{g}becomes quite indistinct. Interestingly, when the flax composites are at 0° fibre orientation, the thermal strain turns negative, above the matrix T

_{g}temperature. From the results, it can be concluded that the composite thermal strain decreases as the fibre orientation decreases from 90° to 0°.

_{f1}) can be obtained using a rearrangement of the well-established Schapery [23] equation:

_{C1}and α

_{m}are the longitudinal coefficient of thermal expansion (CTE) of the composite and the linear CTE of matrix [17]. There is not, as yet, a universally applicable micromechanical model or equation for predicting the transverse CTE of composites; and so, we have compared the results from the published methods of both Chamberlain [24] and Chamis [25]. The rearrangement of the equation from Chamis gives the following expression for the transverse CTE (α

_{f2}) of the fibres:

_{C2}is the transverse CTE of the composite and F is the fibre packing factor with a value of 0.785 for the square packing [24].

_{f2}in comparison to the Chamis equation. The sisal fibres appear to have a slightly smaller transverse CTE compared to flax fibres over the −50 °C to +50 °C temperature range. In both cases, the fibre transverse CTE is of the same order of magnitude as the epoxy matrix CTE, which is probably a reflection of the thermal response of the amorphous polymeric components of these fibres. An overall summary of the temperature dependence of the various thermomechanical parameters obtained for sisal and flax fibres in this study is shown in Table 1. It should be noted that the values of α

_{f2}in Table 1 are an average of the values obtained using Equations (6) and (7).

#### 3.4. Implications for Natural Fibre Performance as a Composite Reinforcement

_{f2}for flax and sisal is very close to that of the polymer matrix, implies a similar lack of any interfacial radial compressive stress to the interfacial stress transfer capability in composites using these fibres. In fact, if, as appears to be the case at some points in Figure 8, α

_{f2}is greater than the CTE of the polymer matrix, this could result in an interface under radial tension, which could be very weak.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Optical micrographs of polished cross sections of natural fibre epoxy composites: (

**a**) Flax fibre composites; (

**b**) Sisal fibre composites.

**Figure 2.**Results of dynamic mechanical analysis (DMA) of epoxy matrix and composites at various loading angles: (

**a**) Flax fibre composites; (

**b**) Sisal fibre composites.

**Figure 3.**Comparison of the fibre and resin moduli: (

**a**) Fibre longitudinal modulus; (

**b**) Fibre transverse modulus.

**Figure 5.**The composite modulus at various loading angles compared to values fitted using Equation (3).

**Figure 7.**Results of TMA of epoxy matrix composites at various loading angles: (

**a**) Flax fibre composites; (

**b**) Sisal fibre composites.

**Figure 8.**Comparison of resin and fibre coefficients of thermal expansion: (

**a**) Flax fibres; (

**b**) Sisal fibres.

Flax | Sisal | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

−50 °C | −25 °C | 0 °C | 25 °C | 50 °C | −50 °C | −25 °C | 0 °C | 25 °C | 50 °C | |

E_{1f} (GPa) | 69.8 | 67.6 | 65.7 | 62.5 | 60.2 | 25.0 | 24.6 | 23.3 | 21.9 | 21.1 |

E_{2f} (GPa) | 1.3 | 1.2 | 1.1 | 1.0 | 0.75 | 1.9 | 1.8 | 1.7 | 1.6 | 1.3 |

G_{12} (GPa) | 2.1 | 1.8 | 1.5 | 1.4 | 1.1 | 1.1 | 1.0 | 1.1 | 1.1 | 1.1 |

α_{1f}(µm/m °C) | −6.0 | −6.9 | −7.1 | −8.0 | −6.9 | −3.3 | −4.6 | −7.4 | −3.9 | −4.0 |

α_{2f}(µm/m °C) | 48.0 | 68.1 | 68.4 | 82.7 | 65.2 | 33.2 | 54.7 | 70.0 | 79.1 | 76.8 |

**Table 2.**Comparison of reinforcement fibre thermoelastic properties at room temperatures [22].

E-Glass | Carbon | Aramid | Flax | Sisal | |
---|---|---|---|---|---|

E_{f1} (GPa) | 77 | 220 | 152 | 62.5 | 21.9 |

E_{f2} (GPa) | 68 | 14 | 4.2 | 1.0 | 1.6 |

G_{f12} (GPa) | 30 | 14 | 2.9 | 1.4 | 1.1 |

α_{f1} (µm/m °C) | 5 | −0.4 | 3.6 | −8.0 | −3.9 |

α_{f2} (µm/m °C) | 5 | 18 | 77 | 83 | 80 |

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**MDPI and ACS Style**

Thomason, J.; Yang, L.; Gentles, F.
Characterisation of the Anisotropic Thermoelastic Properties of Natural Fibres for Composite Reinforcement. *Fibers* **2017**, *5*, 36.
https://doi.org/10.3390/fib5040036

**AMA Style**

Thomason J, Yang L, Gentles F.
Characterisation of the Anisotropic Thermoelastic Properties of Natural Fibres for Composite Reinforcement. *Fibers*. 2017; 5(4):36.
https://doi.org/10.3390/fib5040036

**Chicago/Turabian Style**

Thomason, James, Liu Yang, and Fiona Gentles.
2017. "Characterisation of the Anisotropic Thermoelastic Properties of Natural Fibres for Composite Reinforcement" *Fibers* 5, no. 4: 36.
https://doi.org/10.3390/fib5040036