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TWENTY-THIRD INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS (ICCM23)
MICROMECHANICS OF HYBRID COMPOSITE LAMINA WITH
NATURAL AND SYNTHETIC FIBRES
Nenglong Yang1, Zhenmin Zou1, Prasad Potluri2, 3 and Kali Babu Katnam1, 2 *
1 Department of Mechanical, Aerospace and Civil Engineering, The University of Manchester, UK
2 Northwest Composites Centre, The University of Manchester, UK
3 Department of Materials, The University of Manchester, UK
*Corresponding author (Kali-Babu.Katnam@manchester.ac.uk)
Keywords: Fibre hybrid composites, RVE modelling, Homogenisation, Micro-stress fields
ABSTRACT
This study investigates the effect of intra-laminar fibre hybridisation on the homogenised lamina
properties and micro-stress fields, with an emphasis on natural and synthetic fibre combinations. A
representative volume element (RVE) approach, considering random fibre distributions, is employed to
study unidirectional flax/E-glass/epoxy composite laminae. The results indicate that intra-laminar
hybridisation with natural and synthetic fibre combinations can offer opportunities to tailor the
homogenised lamina properties, especially to vary the effective density and thus achieve high specific
properties. In addition, it is shown that the intra-laminar hybridisation can significantly alter the micro-
stress and strain fields, potentially affecting intra-laminar damage mechanisms.
1 INTRODUCTION
In recent years, the growing awareness of environmental protection and sustainability has motivated
the use of natural fibres as reinforcements in fibre-reinforced polymer materials to replace synthetic
fibres. The rising market demand for more sustainable, recyclable and biodegradable materials is
expected to continue in the coming years [1]. Natural fibre-reinforced composites (NFRCs) are being
increasingly used in secondary structural applications, such as in automotive components (e.g., door
panels, dashboards and seats), construction materials (e.g., pipes, wall and roof panels) and sports
equipment (e.g., bicycle racks, tennis rackets and golf clubs) [2, 3]. The market growth of NFRCs is
attributed to their desirable factors, such as high specific strength and stiffness, low cost and production
energy, non-toxicity and biodegradability. However, NFRCs have certain disadvantages, such as low
durability, high moisture absorption, low thermal stability, variation in mechanical properties and
dimensional instability, which could significantly influence the structural integrity and reliability of
NFRC-based structural components and thus are major hurdles to their use in primary structural
applications. To address some of these limitations, natural and synthetic fibres can be combined to
produce natural fibre-based hybrid composites (NFHCs), such as inter-laminar (with different single
fibre-based laminae) or intra-laminar (with more than one fibre-based laminae) hybrid laminate [4].
Many experimental studies have been conducted to investigate the mechanical behaviour of NFHCs
[5-16]. In these studies, E-glass fibres are the most commonly used synthetic fibres added to NFRCs.
For instance, flax [5, 6], hemp [7, 8], sisal [9, 10], basalt [11-13] and jute [14, 15] have all been
hybridised with E-glass fibres. Zhang et al. [5] experimentally investigated the effect of fibre volume
fraction and inter-laminar hybridisation on the tensile properties of unidirectional flax/E-glass
composites and showed that the tensile strength and failure strain of laminates can be improved with
increased E-glass fibre content, but with no considerable effect on the tensile modulus. Moreover, the
interlaminar shear strength and fracture toughness were enhanced with inter-laminar hybridisation. In
the experimental study of hemp/E-glass composites, Prashanth et al. [15] reported that the inter-laminar
hybridisation of hemp fibre-based laminates with E-glass fibres resulted in enhancing the mechanical
properties (tensile, flexural and impact responses) when compared to those of the hemp FRCs. Similarly,
Abd El-baky et al. [16] reported that increasing the E-glass fibre content improved the mechanical
properties of flax/E-glass composites. Experimental studies on the inter-laminar hybridisation of basalt
fibre-based laminates with E-glass fibres [11-13] showed that the addition of E-glass fibres to basalt
composites decreases the overall density as well as the tensile and flexural moduli of the laminates.
Nenglong Yang, Zhenmin Zou, Prasad Potluri and Kali Babu Katnam
Furthermore, the impact strength of basalt/E-glass laminates was found to be higher than that of both
basalt fibre-based and E-glass fibre-based laminates [12]. The literature thus indicates that NFHCs can
potentially replace conventional composites with synergistic effects on the mechanical properties of
laminates, and that these material properties are significantly influenced by a range of factors, including
fibre and matrix types, fibre volume fractions, fibre orientation, stacking sequence, and matrix-fibre
interfacial adhesion.
Although several experimental studies in the literature have reported on the inter-laminar
hybridisation of natural fibre-based laminates with synthetic fibres, no studies have been conducted on
intra-laminar hybridisation [17]. A few experimental studies have investigated the intra-laminar
hybridisation of synthetic fibre-based laminates [18-20]. Moreover, several computational studies have
investigated the mechanical behaviour of synthetic/synthetic fibre hybrid composite laminates, such as
the inter-laminar hybridisation of Kevlar fibre-based laminates with E-glass [21], carbon fibre-based
woven laminates with Dyneema [22], carbon fibre-based laminates with Kevlar [23], and on the intra-
laminar hybridisation of carbon fibre-based laminae with E-glass [24, 25]. These studies have mostly
been based on the computational micromechanics of composites using representative volume element
(RVE) models [26] with periodic boundary conditions [27]. However, no computational studies have
been reported on the intra-laminar hybridisation of natural fibre-based laminates. In this regard, a
computational study has been conducted to focus on the intra-laminar hybridisation of natural fibre-
based laminae with synthetic fibres to understand the effect of fibre hybridisation on the homogenised
lamina properties as well as intra-laminar micro-stress fields. A RVE model has been developed in the
current study to investigate flax/E-glass intra-laminar hybrid composite laminae and implemented using
Python and ABAQUS/Standard.
2 MICROMECHANICAL RVE MODEL
A 3D RVE model is developed for fibre hybrid unidirectional laminae. In this model, both the
synthetic fibres and matrix within the lamina are considered to be continuous, homogeneous, isotropic
and defect-free. However, the natural fibres are considered to be transversely isotropic. Additionally,
the fibres are assumed to possess circular cross-sections. A perfect matrix-fibre interface is also assumed
for both fibre types. Considering a random fibre distribution within the hybrid lamina, the microstructure
of the RVE is generated using the random sequential expansion (RSE) algorithm [28]. The RSE
algorithm is modified to populate both synthetic and natural fibres and achieve target fibre volume
fractions. The modified algorithm ensures that the large fibres are placed first within the RVE domain,
creating enough space to accommodate the small fibres and reaching the targeted volume fractions for
both fibre types. The modified algorithm also ensures geometric periodicity at the boundaries of the
RVE (i.e., when a fibre contacts the boundary of the model, the portion of the fibre beyond the boundary
is also placed on the opposite boundary) to apply period boundary conditions. In the current study, the
RVE model is applied to study unidirectional flax/E-glass/epoxy hybrid composite laminae. Considering
that the total fibre volume fraction is fixed at 0.6, the individual fibre volume fractions are varied and
different microstructures are generated. Representative microstructure for each combination of fibre
volume fractions for the flax/E-glass/epoxy lamina are shown in Fig. 1, where the flax fibre volume
fraction, the E-glass fibre volume fraction and the matrix volume fraction are denoted by
,
and
, respectively.
Using Python and ABAQUS/Standard, the RVE model is implemented within the framework
of the finite element method. The micro-stress/strain fields and the homogenised material
properties are obtained by imposing displacement-based periodic boundary conditions. The
material properties and the fibre diameters used in the RVE models are given in Table 1. The RVE
size is selected by considering the large fibre diameter as the characteristic length of the micro-
constituents. To ensure that the RVE is sufficiently large compared to the fibre diameters, the
length and width of the RVE (the dimensions perpendicular to the fibre direction) are 15 times the
diameter of the large fibre. For the flax-/E-glass/epoxy hybrid lamina, as the flax fibres are assumed to
be circular with a diameter of 30 m, the length (and width) of the RVE used is 450 m. Because of the
unidirectional fibres, a small value (of the order of the radius of the small fibre) is used for the thickness
of the RVE (along the fibre direction). The matrix and the fibres are modelled using C3D8R and C3D6
elements, respectively. A mesh convergence study is conducted to determine the average element size
of the RVE. An element size of 1/8 of the radius of the small fibre (i.e., ~0.9375 m for the flax/E-
glass/epoxy lamina) is used to mesh the RVEs, with only one element along the thickness direction.
Table 1: The properties of the constituents [4, 29-34] and the fibre diameters used in the RVEs.
Constituent
(GPa)
(GPa)
(GPa)
(GPa)
Density
(
g/cm
)
Diameter
(
m
)
E-glass
73
73
30.4
30.4
0.2
0.2
2.5
15
Flax
54.1
7
3
2
0.3
0.75
1.4 – 1.5
30
Epoxy
2.55
2.55
0.94
0.94
0.35
0.35
1.15
-
Figure 1: Representative microstructures generated by using the modified RSE algorithm for the
RVE model of the flax/E-glass/epoxy lamina with different fibre volume fractions (
,
,
):
(a) (0.48, 0.12, 0.40), (b) (0.36, 0.24, 0.40), (c) (0.24, 0.36, 0.40), and (d) (0.12, 0.48, 0.40).
The RVE model is used, and the homogenised lamina properties are obtained by volume averaging
the micro-stress fields using the procedure in Li and Sitnikova [35]. This procedure employs six key
degrees of freedom (kdofs) to impose the macro-stress state (with six independent components). Using
the kdofs, which are implemented in ABAQUS with six reference nodes, six loading cases are
considered (i.e., three normal and three shear loading cases). The reference nodes are used to apply
generalised forces (which are related to the volume average of the microscopic stress components or the
macroscopic stress components) or generalised displacements (which are related to the volume average
of the microscopic strain components or the macroscopic strain components) [35]. Either the generalised
nodal forces are applied to obtain the generalised nodal displacements or the generalised nodal
displacements are applied to obtain the generalised nodal forces. When the generalised nodal forces are
applied to the RVE, the homogenisation procedure with the six loading cases provides the compliance
matrix, which can be used to obtain the homogenised engineering constants for the hybrid lamina. The
generalised nodal displacements at each reference point are proportional to the six macroscopic strain
components (ˆ,ˆ,ˆ,ˆ,ˆ,ˆ), which are connected to the periodic boundary conditions. The
subscripts 1, 2 and 3 are associated with the material principal directions, i.e., the longitudinal and
transverse directions. Similarly, the generalised nodal forces at each reference point are proportional to
the six macroscopic stress components (ˆ,ˆ,ˆ,ˆ,ˆ,ˆ). In this study, six generalised forces
are individually applied, representing the six loading cases, and the corresponding generalised
displacements and then the compliance matrix are obtained from the RVE models. The generalised
forces (,,,,,) at the reference points are linked to the six macroscopic stresses
(ˆ,ˆ,ˆ,ˆ,ˆ,ˆ) and the volume of the RVE () via energy equivalence [35] as in Eq. 1.
=ˆ
(,= 1, 2, 3)
(1)
Nenglong Yang, Zhenmin Zou, Prasad Potluri and Kali Babu Katnam
To determine the homogenised lamina properties, the six loading cases are analysed individually
(i.e., for each macroscopic stress component) using the RVE model. For the first loading case, the
generalised force is applied only, with a magnitude equal to the volume of the RVE, i.e., . From
Eq. 1, it represents the uni-axial tensile loading case with the corresponding macroscopic stress
component, ˆ = 1. Using the corresponding generalised displacement, the homogenised properties
(
, , ) can then be obtained using Eq. 2 [35]. The remaining homogenised properties are
obtained similarly for the other loading cases, and the complete set of homogenised properties (
,
,
,
,
,
,, , ) can be determined.
=ˆ
ˆ
=1
ˆ
; =ˆ
ˆ
; =ˆ
ˆ (2)
3 MECHANICAL BEHAVIOUR OF FIBRE HYBRID COMPOSITE LAMINA
The RVE modelling approach and the homogenisation procedure presented in Sec. 2 are applied to
the flax/E-glass/epoxy laminae with different fibre volume fractions. In addition, flax/epoxy and E-
glass/epoxy laminae are also analysed to validate the RVE model with analytical models applicable to
non-hybrid unidirectional laminae (with only one fibre type as the reinforcing constituent) for estimating
the homogenised lamina properties. A sanity check, as described by Li and Sitnikova [35], is initially
performed by assigning the material properties of the fibre to be the same as the matrix and analysing
the RVE for the six independent loading conditions. The sanity check is done to verify whether the
model can produce the desired output in the simplest case [35], including the imposed periodic boundary
and loading conditions.
3.1 Hybrid lamina: Homogenised properties
To validate the RVE model, non-hybrid unidirectional laminae, i.e., E-glass/epoxy and
flax/epoxy unidirectional laminae, are first analysed, considering a fibre volume fraction of 0.6.
Five different microstructures are analysed, and the average homogenised properties are obtained.
The average homogenised lamina properties of E-glass/epoxy are given in Table 2 and are
compared with the analytical estimations obtained using the Chamis, Halpin-Tsai and Mori-Tanaka
models [36-38]. Similarly, the average homogenised properties of flax/epoxy unidirectional lamina are
given in Table 3. The comparison shows that a good agreement for the longitudinal modulus (
)
and the major Poisson’s ratio (), while a considerable error for the other properties. In comparison
with the RVE data, the Chamis equations [36] are found to predict the homogenised properties of the E-
glass/epoxy lamina with low relative error, while the Halpin-Tsai equations [37] are seen to be the more
accurate in predicting the properties of the flax/epoxy lamina. Overall, the comparisons in Tables 2 and
3 validate the RVE model. The standard deviation of the homogenised properties obtained from the
RVE models shows that the homogenised properties are not dependent on the microstructure, thus, the
size of the RVE used is appropriate.
Table 2: The comparison of the homogenised properties of E-glass/epoxy unidirectional lamina
(with a fibre volume fraction of 0.6) obtained from the RVE model and the Chamis, Halpin-Tsai
and Mori-Tanaka analytical models.
RVE
Chamis [36]
Halpin-Tsai [37]
Mori-Tanaka [38]
Estimation
Error %
Estimation
Error %
Estimation
Error %
(GPa)
44.76 ± 0.02
44.82
0.1
44.82
0.1
44.84
0.2
0.25 ± 0.00
0.26
3.9
0.26
3.9
0.25
0.0
(GPa)
10.70 ± 0.23
10.10
5.8
12.14
12.6
7.58
34.1
(GPa)
4.24 ± 0.05
3.79
11.2
3.64
15.2
3.39
22.3
(GPa)
3.95 ± 0.08
3.79
4.1
3.64
8.2
2.98
28.0
Table 3: The comparison of the homogenised properties of flax/epoxy unidirectional lamina (with
a fibre volume fraction of 0.6) obtained from the RVE model and the Chamis, Halpin-Tsai and
Mori-Tanaka analytical models.
RVE
Chamis [36]
Halpin-Tsai [37]
Mori-Tanaka [38]
Estimation
Error %
Estimation
Error %
Estimation
Error %
(GPa)
33.44 ± 0.04
33.48
0.1
33.48
0.1
33.48
0.1
0.32 ± 0.01
0.32
0.0
0.32
0.0
0.32
0.0
(GPa)
4.79 ± 0.23
5.02
4.7
4.75
0.8
4.02
17.5
(GPa)
1.83 ± 0.00
2.01
9.4
1.83
0.0
1.80
1.7
(GPa)
1.51 ± 0.13
1.60
5.8
1.47
2.7
1.44
4.7
The average homogenised properties of the flax/E-glass/epoxy lamina are obtained from five
different microstructures for each combination of fibre volume fractions and presented in Table 4. It can
be seen that the homogenised properties of the flax/E-glass laminae with different hybrid volume
fractions within the homogenised properties of the flax/epoxy lamina (lower bound) and the E-
glass/epoxy lamina (upper bound) as expected. It is observed that the longitudinal modulus (
) of the
flax/E-glass/epoxy lamina decreases with higher flax fibre volume content. A similar trend is observed
for the transverse modulus (
), the in-plane and transverse shear moduli (
and
) and the major
Poisson’s ratio (). To account for the effect of the increasing volume fraction of low density flax
fibres on the effective density () of the flax/E-glass/epoxy, the homogenised specific properties are
obtained and given in Table 5. The specific longitudinal modulus (
) and the major Poisson’s ratio
() of the flax/E-glass/epoxy lamina are increased with higher flax fibre volume content.
Table 4: The homogenised properties for the flax/E-glass/epoxy lamina with varying flax and E-
glass fibre volume fractions (and with a total fibre volume fraction of 0.6).
(
,
,
)
(GPa)
(GPa)
(GPa)
(GPa)
(g/cm
)
(0.60, 0.00, 0.40)
33.44 ± 0.04
0.32 ± 0.02
4.79 ± 0.23
1.83 ± 0.00
1.51 ± 0.13
1.33
(0.48, 0.12, 0.40)
35.84 ± 0.00
0.30 ± 0.00
5.40 ± 0.01
2.13 ± 0.01
1.70 ± 0.00
1.46
(0.36, 0.24, 0.40)
37.95 ± 0.00
0.29 ± 0.00
6.28 ± 0.08
2.49 ± 0.03
2.02 ± 0.02
1.58
(0.24, 0.36, 0.40)
40.31 ± 0.00
0.27 ± 0.00
7.47 ± 0.11
2.95 ± 0.03
2.45 ± 0.02
1.71
(0.12, 0.48, 0.40)
42.42 ± 0.00
0.26 ± 0.00
8.91 ± 0.06
3.54 ± 0.03
3.05 ± 0.04
1.83
(0.00, 0.60, 0.40)
44.76 ± 0.02
0.25 ± 0.00
10.7 ± 0.22
4.24 ± 0.05
3.95 ± 0.08
1.96
Table 5: The specific homogenised properties of the flax/E-glass/epoxy lamina with varying flax
and E-glass fibre volume fractions (and with a total fibre volume fraction of 0.6).
(
,
,
)
/
(GPa. cm
/g)
/
(
cm/g
)
/
(GPa. cm
/g)
/
(GPa. cm
/g)
/
(GPa. cm
/g)
(0.60, 0.00, 0.40)
25.14
0.24
3.60
1.38
1.14
(0.48, 0.12, 0.40)
24.62
0.21
3.71
1.46
1.17
(0.36, 0.24, 0.40)
23.99
0.18
3.97
1.57
1.28
(0.24, 0.36, 0.40)
23.60
0.16
4.37
1.73
1.43
(0.12, 0.48, 0.40)
23.13
0.14
4.86
1.93
1.66
(0.00, 0.60, 0.40)
22.84
0.13
5.46
2.16
2.02
Nenglong Yang, Zhenmin Zou, Prasad Potluri and Kali Babu Katnam
3.2 Micro-stress fields: The effect of fibre hybridisation
To show the effect of fibre hybridisation on the intra-laminar matrix stresses, the von Mises stress
distribution within the matrix is presented in Figs. 2-3. In Fig. 2, the von Mises stress distribution
is normalised and shown for the flax/epoxy lamina, with
,
,
=(0.60, 0.0, 0.40), for the
six loading conditions (i.e., unit macro stress components, i.e., ˆ = 1 MPa). As can be seen in Figs.
2a-2f, where the fibres are removed, and only the matrix is shown, the von Mises matrix stress
amplification is induced under the two in-plane shear loading cases (3.65 MPa and 3.80 MPa under ˆ
and ˆ, respectively), while the highest matrix stress amplification is observed under the transverse
shear loading (5.04 MPa under ˆ). Similarly, the von Mises matrix stress amplifications are shown in
Figs. 3a-3f for the six loading cases for the flax/E-glass/epoxy lamina with
,
,
=
(0.48, 0.12, 0.40). In comparison with the von Mises matrix stress amplification in the flax/epoxy
lamina, with an E-glass fibre volume fraction of 0.12, the von Mises matrix stress amplification is
considerably higher under the two in-plane shear loading cases (14.24 MPa and 15.04 MPa under ˆ
and ˆ , respectively), which are higher than the matrix stress amplification obtained under the
transverse shear loading (7.96 MPa under ˆ). Similarly, under the transverse tensile loading cases
(ˆ), the von Mises matrix stress amplification is ~2.05 MPa for the flax/epoxy lamina, while it is
considerably higher (4.09 MPa) for the flax/E-glass/epoxy lamina (see Figs. 2b and 3b). These von
Mises matrix stress distributions indicate that the combination of the fibre volume fractions influences
the intra-laminar micro-stress fields. As the modulus of E-glass fibres is higher than that of the flax
fibres, the stress amplifications induced are higher with increasing E-glass fibre content, and such
localised stress concentrations could thus influence intra-laminar damage mechanisms.
Figure 2: The von Mises stress fields in the matrix of the flax/epoxy lamina with
,
,
=
(0.60, 0.0, 0.40) under the six independent loading cases (the unit macro-stress components, in
MPa): (a) ˆ = 1, (b) ˆ = 1, (c) ˆ = 1, (d) ˆ = 1, (e) ˆ = 1, and (f) ˆ = 1.
Figure 3: The von Mises stress fields in the matrix of the flax/E-glass/epoxy lamina with
,
,
=(0.48, 0.12, 0.40) under the six independent loading cases (the unit macro-stress
components, in MPa): (a) ˆ = 1, (b) ˆ = 1, (c) ˆ = 1, (d) ˆ = 1, (e) ˆ = 1, and (f) ˆ = 1.
Figure 4: The reversed cumulative volume % of the matrix versus the von Mises stress
amplification factor (SAF) for the flax/E-glass/epoxy lamina with varying fibre volume fractions
under the six loading cases: (a) ˆ = 1, (b) ˆ = 1, (c) ˆ = 1, (d) ˆ = 1, (e) ˆ = 1, and (f)
ˆ = 1.
Nenglong Yang, Zhenmin Zou, Prasad Potluri and Kali Babu Katnam
Using the RVEs, the effect of the microstructure on the von Mises matrix stress amplification factor
(SAF) of flax/E-glass laminae is further investigated. For each combination of fibre volume fractions,
the micro-stress fields are obtained considering five different microstructures. As a sufficiently large
RVE size is used, the variation in the microstructure is observed to have a negligible effect on the RVE
response. For the flax/E-glass/epoxy laminae, each combination of fibre volume fractions is considered,
and the reversed cumulative distribution plots are obtained by using the matrix volume percentage and
SAF. For the six loading cases, the reversed cumulative distribution data are shown in Fig. 4, with five
different combinations of fibre volume fractions. It can be seen that the reversed cumulative distributions
are sensitive to the fibre volume fraction of E-glass fibres as higher SAFs are induced with increasing
E-glass fibre content. As shown in Fig. 4a, under the longitudinal tensile loading case, the reverse
cumulative distribution is insensitive to the E-glass fibre volume fraction. In contrast, for the other five
loadings (transverse tensile, in-plane shear and transverse shear) conditions, the matrix stress
distribution is considerably influenced by the E-glass fibre content. In general, this suggests that the
fibre content of synthetic fibres (with relatively high modulus) can alter matrix stress distributions,
which can also affect fibre-matrix interface shear and normal stresses in fibre hybrid laminae with
natural and synthetic fibres.
4 CONCLUSIONS
In this work, a representative volume element (RVE) model is developed for hybrid unidirectional
lamina with natural and synthetic fibres. The microstructure of the RVEs are generated using a modified
RSE algorithm. The RVE model is employed to investigate the homogenised lamina properties of and
the micro-stress fields in the flax/E-glass/epoxy hybrid laminae with different combinations of fibre
volume fractions. The RVE model has been validated against existing analytical models by comparing
the homogenised lamina properties. The results show that the intra-laminar fibre hybridisation of the E-
glass/epoxy lamina with flax fibres can be used to alter the homogenised properties. With an increasing
flax fibre content, the effective density can be varied, and thus the specific lamina properties be tailored.
Moreover, the von Mises matrix stress fields show that the matrix stress concentrations in the flax/epoxy
lamina are relatively lower compared to the flax/E-glass/epoxy hybrid lamina, and the matrix stress
concentrations are increased with increasing E-glass fibre content. In general, the developed RVE can
be employed to study intra-laminar fibre hybrid laminae with natural and synthetic fibres, and the effect
of such fibre hybridisation can be analysed to tailor hybrid composites and achieve desirable properties.
ACKNOWLEDGEMENTS
The authors acknowledge the financial support of University of Manchester and Engineering and
Physical Sciences Research Council (EPSRC) [Grant Number: EP/T517823/1]. The authors also
acknowledge the use of the Computer Shared Facility 3 at The University of Manchester.
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