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;

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