Abstract: considers what are the researches carried

Abstract:  As the
increasing demand of the use of ultralight spacecraft structures using woven
fibre composites is put interest in the research of predicting mechanical
behaviour of the woven fibre composites made of one or two plies. Lightness
associated with the symmetrical and balanced properties made the material very
much suitable for the weight sensitive applications. In this paper, initially
it provides the general overview of the thin woven fibre composite material
which is going to focus to have a better understanding and to familiarise with
the terminology. Then, the paper considers what are the researches carried on
up to now, to predict the mechanical behaviour of the woven fibre composites
especially for one and two plies. Also, this paper stating the theory and
equations involved in predicting the mechanical behaviour, available
experimental support to validate the research carried on the micromechanical
modelling and discuss the limitations and shortcomings of the methodologies
used in the previous researches.

Keywords:
 Classical lamination theory; Woven
fibre composites; Mechanical behaviour; Non-linear bending; Micromechanical modelling;

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1.   
Introduction

The use of ultralight spacecraft structures using polymer
films and ultrathin composite fibre materials is most trending in the
aeronautic industry. There are various researches carried on the ultralight
space structures associated with advanced packaging techniques. This technique
was often enthused by origami techniques (Caltec, 2015). The current curiosity
on this technique are in applications of solar collectors and antenna
structures.

In aeronautic applications, the textile composites are
used over other alternatives due to their high mechanical properties. Thin
woven fibre composite materials are anticipated to use in ultra-thin deployable
structures popularly because of their symmetrical and balanced properties.

There are several studies on thin-walled tubular booms in
the current trend using carbon fibre composites. It is very effective to use
these in the mechanism of deployable structures as the stored strain energy
release will provides efficient operation. These structures made of thin-walled
composite materials have quite a lot of benefits over the structures which are
having mechanical joints. They are having high strength to weight ratio, they can
be made of several range of shapes at low cost due to lesser number of
components and behave insensitive to friction.

This paper presents an introduction to the thin woven
fibre composites, background to the study, equations involved, the summary of
what are the researches carried on the thin woven fibre composites in the
application of aerospace and specifically on the behaviour of bending, the methodology
they had chosen and analyse the results obtained through the proposed
methodology. And finally, the conclusion.

2.      
Papers reviewed

2.1  
General

The fibre composite material is generally incorporated
with two components as fibre and matrix. Fibre is the main constituent which
contributed to the mechanical properties of composites and the matrix usually
resin, is to support and protect the fibres while transferring load between the
broken fibres (Jones, 1999).

Obviously, the fibres are weak in bending due to its’
high length to diameter ratio and therefore it is more flexible perpendicular
to the fibre direction. So, the woven nature is increasing its’ bending stiffness
in the composite material (Jones, 1999).
The woven fibre in the sense, having two fibre bundles which called as yarns
weaved one over another in both warp and weft direction. The properties of this
is depended on the pattern of weave and number of fibres used in each direction
(Soykasap, 2005).

Figure 1: Plain weave fibre

As the woven fibre composites are predicted to use in the
ultra-thin deployable structures is mainly due to its’ high strength to weight
ratio. So, the thin woven in the sense is especially considering one and two
plies woven fibres in these weight sensitive applications.

2.2  
Background

Over the years, to predict the behaviour of laminate
composites, the Classical Lamination Theory is used with certain assumptions. The
theory doesn’t account the non-uniform interlaminar stresses which causing
failure (free edge delamination) in the composite laminate and signifies some
of the stresses even those are not actually exists (Jones, 1999). CLT is postulating
the following assumptions (Jones, 1999):

·        
The plate is to be considered as thin and has
uniform thickness over.

·        
Only considered the in-plane stresses of the
laminate

·        
Neglecting the through thickness shear strains

·        
Assuming elastic approach i.e. the fibre bundles
obeys Hook’s law

·        
Considers the laminate constructed of
orthotropic sheets. It is symmetrical about the middle surface

Now from the researches it has been shown that the CLT
has enough accuracy in predicting the in-plane properties of thin laminates but
directly using the CLT to estimate the properties of thin woven fibre
composites of one and two plies end up with high error percentage. Through the
experiments carried out on thin woven composites it has been clearly stated
that CLT disagree with this. The CLT overestimate the maximum bending stress up
to 200% and the bending stiffness up to 400% (Soykasap, 2005).

Rather than going with the complicated finite element
modelling to predict the bending properties, it is advantageous to introduce a
factor that accounting the causes of the error in a simple way. Some
researchers focused on possible causes to the above error percentage and
contribution of each causes to the error margin and introduced a modification
factor to reduce the error margin (Herath & Mallikarachchi,
2016).
This approach is a simplified method to predict the bending properties with a
certain accuracy and even though this wouldn’t predict the failure load of the
composites accurately.

2.3  
Equations involved

Fibre volume fraction can be expressed as follows

(1)

The longitudinal modulus, transverse modulus, shear
modulus and Poisson’s ratio of the yarn can be calculated using the rule of
mixture and fibre volume fraction as follows (Jones, 1999) (Soykasap,
2005)

(2)

(3)

(4)

(5)

In the above equations subscript ‘f’ refers the fibre and
subscript ‘m’ refers matrix.

ABD (6 x 6) stiffness matrix is showing the relation in
between the applied loads and the associated strains as follows

2.4  
Research overview

2.4.1 Unit cell
geometry

As a sequential pattern of weaving geometry can be
observed all over the surface of the woven fibre composite, a particular
repetitive cell can be represented as unit cell. At microscopic scale yarns
consisting of thousands of fibres where they can’t be modelled individually.
So, each yarn is modelled based on hypo-elastic approach since each fibre in
the yarn can slide with respect to each other (Badel, Maire,
Vidal-Salle, & Boisse). Initially yarns
were modelled as curved shape beams with equivalent rectangular cross section
and constraint along the centreline (Mallikarachchi, 2012). As it didn’t record
the Poisson’s effect in an acceptable accuracy, many models were analysed and
here the researcher modelled the beam with fourth root of a sine wave.

Overview

Soykasap (2005) carried out the research on the topic of
‘Micromechanical Models for Bending Behaviour of Woven Composites’. This paper
was focused on the micromechanical models for bending behaviour of woven fibre
composites. Before this research, many finite element models were developed in
relevance to this.

Fujita (1992) and Dano (2000) studied the in-plane
properties of woven composites using beam element, Benarcyk and Arnold (2003)
used three-dimentional repeating unit cell model and Page (2004) developed two-dimensional
finite element model to study damage properties (Soykasap,
2005).

Plain weave style T300/LTM45 composite was taken as the
sample for the modelling. Material properties of a single yarn was estimated
using fibre volume fraction and rule of mixture.

This study was considered the interaction between the
fibre bundles and the matrix and carried out geometrically non-linear analysis to
predict and analyse the behaviour of the one, two and three plies woven fibre
composites.

This research is concluded that, for one ply woven
composite CLT overestimates both bending stiffness and minimum bend radius by a
factor of 3.9 and 2 respectively, and it was observed 82% and 33% difference
for two ply woven composite and 6.6% and 0.7% difference in bending stiffness
and minimum bend radius values respectively (Soykasap, 2005).

According to the research of Soykasap (2005), in the case
of three ply woven composite, the material behaves as almost homogeneous and
all the deviation in the estimated values is much occurs for one and two plies
woven composite. Therefore Mallikarachchi (2012) was focused on the
micromechanical modelling of two ply plain style woven carbon fibre composite
to analyse the bending behaviour for small strains. A homogenized analyse was
carried out by neglecting the geometrical non-linear effects. Modelling
technique was assumed periodic boundary conditions to an assembly of
transversely isotropic three-dimensional yarns and computed the 6 x 6 ABD
matrix. This paper concluded that even though 9% difference in bending
stiffness with experimental comparison, prediction of the axial stiffness and
Poisson’s effect with solid elements are having better accuracy (Mallikarachchi, 2012).

The experiments were carried out to predict the bending
behaviour of the thin woven fibre composites. From these experiments, it was
noticed that the bending behaviour is not a linear as we expected earlier. It
is showing a substantial reduction in its bending stiffness when going for high
curvature bends (Yapa & Mallikarachchi, 2017). Yapa &
Mallikarachchu (2017) modelled a homogenised Kirchhoff plate one-dimensional
unit cell with equivalent rectangular cross section. This model is not
correctly representing the resin interface at the crossover points, it failed
to estimate shear modulus and Poisson’s effect accurately.

Meanwhile, a homogenized Kirchhoff plate model with an
assembly of transversely isotropic three-dimensional beam elements was captured
the linear response of single ply triaxial woven fabric composites accurately
thus neglecting the geometric non-linear effects. The fabric in the sense means
woven tows in three directions, at 0 degrees and ±60 degrees and it impregnate
with resin like a general composite (Kueh & Pellegrino).

Apart from these, there are several other researches
carried on the woven composites. One is, introducing three-dimensional mesoscopic
finite element analysis to determine the macroscopic mechanical behaviour and
also determined the deformed geometry of the reinforcement (Badel, Maire,
Vidal-Salle, & Boisse).

Further, there are several analytical models on plain woven
fabrics considering the yarn section at crossover, the shape of the yarn, the
contact condition at thread crossover and the set of yarn at mesoscopic scale (Bilbao,
Soulat, Hivet, Launay, & Gasser, 2008).

Other research was focused on to develop an optical
measurement based cantilever test to predict the bending behaviour of woven
fabric because already existing standard tests are not adequate. The research
concluded that, prediction of the bending behaviour from the proposed method is
not possible by only considering yarns properties (Bilbao,
Soulat, Hivet, Launay, & Gasser, 2008).

There is a possibility to associate semi discrete method
which is based on the specific finite elements made of discrete number of
components that is proposed by (Hamila, Boisse, & Chatel) to bending stiffness
such as taken into account in three node plate or shell elements (Hamila,
Boisse, & Chatel).

Tensile and shear deformation of the woven fabrics was
investigated the applicability of elastic theory using modelling technique (Ramgulam,
Potluri, & Ciurezu). Further study should be carried out in
this research to include the effects of contact area and large shear
deformation modelling considering yarns transverse flattening.

There are several researches focused on the forming of
woven composites. Vanclooster, Lomov and Verpoest compare an explicit finite
element method and kinematic mapping scheme for simulations with the
experimental results. The main aim of this study was a kinematic mapping
algorithm can be used to investigate the complexity of the woven composites
behaviour. And the research concluded that, due to initial conditions during
forming this approach fails (Vanclooster, Lomov, &
Verpoest).

3. Conclusion

Due to increasing popularity of the use of thin woven
fibre composites in the ultra-thin deployable structure, this research is going
to focus on the micromechanical modelling to predict non-linear bending behaviour
of thin woven fibre composite materials. After studied the previous researches,
it is noted that bending behaviour is a non-linear for the thin woven fibre
composites