Stiffness properties of intraply woven hybrid composites by numerical homogenisation

Abstract

Hybrid fabrics represent a rapidly emerging branch of reinforcements for composite materials. A justified use of these textiles requires good understanding of their behaviour and their modelling tools. Hybrid composites have significant strain differences amongst their phases. The lack of information on the applicability of the homogenisation methods in finite element and mesomechanical models in predicting the mechanical properties of Intraply Woven hybrid Composites (IWHC) has provided the motivation for this study. The emphasis was put on developing FE model, while investigating other meso-mechanical models concerning their efficiency, accuracy, applicability and limitations. Results were obtained from FEA and meso-mechanical models. Tensile testing was conducted to characterise the properties and mechanisms of failure for different carbon content hybrid composites. Published (publisher's copy) Peer Reviewed

Full text

Page 1

University of East London Institutional Repository: http://roar.uel.ac.uk

This paper is made available online in accordance with publisher policies. Please
scroll down to view the document itself. Please refer to the repository record for this
item and our policy information available from the repository home page for further
information.

Author(s): Saidpour, Hossein; Oscar, Quentin
Title: Stiffness properties of intraply woven hybrid composites by numerical
homogenisation
Year of publication: 2006
Citation: Saidpour, Hossein; Oscar, Q. (2006) ‘Stiffness properties of intraply woven
hybrid composites by numerical homogenisation’ Proceedings of Advances in
Computing and Technology, (AC&T) The School of Computing and Technology 1st
Annual Conference, University of East London, pp.184-195
Link to published version:
http://www.uel.ac.uk/act/proceedings/documents/ACT06Proceeding.pdf

Page 2

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


184
STIFFNESS PROPERTIES OF INTRAPLY WOVEN HYBRID
COMPOSITES BY NUMERICAL HOMOGENISATION

Hossein Saidpour, Quentin Oscar
Design and Manufacturing Research Group
S.H.Saidpour@uel.ac.uk

Abstract: Hybrid fabrics represent a rapidly emerging branch of reinforcements for composite
materials. A justified use of these textiles requires good understanding of their behaviour and their
modelling tools. Hybrid composites have significant strain differences amongst their phases. The lack
of information on the applicability of the homogenisation methods in finite element and meso-
mechanical models in predicting the mechanical properties of Intraply Woven hybrid Composites
(IWHC) has provided the motivation for this study. The emphasis was put on developing FE model,
while investigating other meso-mechanical models concerning their efficiency, accuracy, applicability
and limitations. Results were obtained from FEA and meso-mechanical models. Tensile testing was
conducted to characterise the properties and mechanisms of failure for different carbon content hybrid
composites.


1. Introduction

Carbon composite materials show high
specific strength and stiffness. However,
since they comprise brittle fibres in a brittle
matrix, they can be susceptible to impact
damage. Attempts to improve the carbon
performance have included modifications to
fibre-matrix interface, [1] the fabrics, [2]
and the fibres. The use of hybrid composites
is another direction, [3]. Hybrid composites
include fibres of different types in
reinforcement; hence it becomes possible to
combine the advantages of the different
fibres while simultaneously attenuating their
less desirable qualities.
Hybrid composites can be classified into two
main categories: interply and intraply
structures. There has been significant work
dedicated to study the mechanical behaviour
and properties of unidirectional and cross
ply intraply hybrid composites [4]. However
the case of intraply woven hybrid
composites and the effect of their
constituent’s contents and type of fibre
intermingling have not been considered
satisfactorily in the literature. Therefore it is
vital to further the understanding of the
behaviour of intraply
composites and their modes of damage
under different loading conditions. This will
assist the designer in selecting the most
appropriate material
applications.
Hybrid composites have significant strain
differences amongst their phases. The lack
of information on the applicability of the
homogenisation methods in finite element
and meso-mechanical models in predicting
the mechanical properties of Intraply Woven
hybrid Composites (IWHC) has provided
the motivation for this study. Emphasis in
this study has been put on developing FEM,
while investigating other meso-mechanical
models concerning
accuracy, applicability and limitations.
Varieties of models are available in the
literature for modelling the mechanical
behaviour of textile composites. The
majority are still based on laminate theory
and orientation averaging techniques (the
latter sometimes referred to as fabric
woven hybrid
for specific
their efficiency,

Page 3

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


185
geometry models). Most of the orientation
averaging schemes assume the existence of a
constant stress or strain state throughout the
material unit cell, which overemphasises the
role of the matrix or the fibre: reinforcement
on the overall behaviour. Consequently,
predictions carries out using iso-stress/strain
models may have
associated with them. In addition, they do
not allow the prediction of failure. Therefore
these models can only provide a very rough
estimate of internal stresses, and hence
cannot be used for damage and strength
analysis.
In recent models, Inclusion models were
applied on models of short fibres and
particle-reinforced composites, as well as
models for polycrystalline materials in
metals applications. The Inclusion model
was extended towards modelling knitted
fabrics reinforced composites by Huysmans
et al, [5]. Their results showed that the
model is efficient and can be used for a
variety of composite materials (UD, random
fibre mats, knits, weaves and braids) and
solved major shortcomings found in
orientation averaging models. Inclusion
models also abandon the iso-stress/strain
assumption and allow the prediction of
stiffness and failure with good accuracy.
The model computational efficiency and
ability in principle to be applied on other
woven fabrics architecture gave it a good
interest. While the method of cells predicts
the micro stress field within the unit cell of a
composite material using energy principles,
and originates from the work of Aboudi and
Chen et al, [6]. They were the first to
propose a mechanistic solution (using the
complementary variational principle) as
opposed to the orientation averaging
schemes. Such models have been applied up
to now to composites reinforced with 2D
and 3D weaves and braids. The prediction of
internal stress fields is a unique capability of
significant errors
the cell method, which sets it apart from
everything else available up to now. The
ability of cell models to predict stresses
inside the material gives them a unique
advantage. These models showed that they
could accurately predict the engineering
constants and failure progression in a
composite material.
On the other hand, Finite Element models
(FEM) with different levels of detail and
idealisations have been considered in
literature, [7]. FEM can provide estimates of
the internal stress/strain fields with moderate
to good accuracy, which allows some of
them to be used for progressive damage
analysis. The potential of the FE method can
be fully accomplished by using a geometry
development tools incorporated with the FE
code. Geometrical pre-processor such as
WiseTex developed by Lomov et al, [8], has
been developed for textile architectures,
proved to be a powerful tool making a 3D
visualisation of 2D woven and braided unit
cells, with an initiative and user-friendly
graphical editor to define the weaving or
braiding pattern.
Geometrical models representing the unit
cell of IWHC hybrids and their parent textile
reinforced composites have been built using
the geometrical characterisation data derived
from experiments using Wisetex modeller,
the output of the latter has been transferred
to the Inclusion and Cell modelling codes.
FE models were built using Ideas-8
modelling task and by importing the
geometrical data from Wisetex. In an
integration on the modelling methodology of
woven hybrid composites Photo-grametry
technique (strain-mapping)
implemented on a small unit cell of the
woven fabric composite to provide useful
information regarding damage initiation,
damage propagation, compare strain results
obtained using FE strain distribution with
the strain mapping results and to identify the
were

Page 4

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


186
special problems occurring when measuring
small areas.

2. FE modelling of woven fabric
composites

Woven fabrics usually present orthogonal
interlaced yarns (warp and weft) and the
distribution of the fibres in the yarns and of
the yarns in the composites may be
considered regular. This allows us to apply
homogenisation theories for the periodic
media both to the different yarns using the
Meso-mechanical model and to the fabric
using simple averaging method proposed by
Theocaris and Stavroulakis, [9]. Theocaris
proposed a simplified analysis to estimate
the effective properties of woven fabric
composites using
technique and by treating the fabric as a
series of cross-ply laminates and by
applying a 2D plane strain analysis on their
model. Kawabata et al, [10] developed a
finite deformation theory to characterise the
uni-axial, bi-axial, and shear deformation
behaviour of a plain weave fabric. Mean
while Kalidini, [11] computed the accuracy
of his (helix) FE idealised geometrical
model for the yarns using planner boundary
conditions with an analytical model (the
weighted averaging model) based on an
averaged iso-strress
assumption, [12]. Results showed that
although the local stresses and strains
computed with this helix model gain more
insight on the internal stress distribution of
complex braids, it remains an idealisation of
the real structure and is therefore not
necessary superior to analytical approach for
strength predictions.
Whitcomb et al., [13], looked at intrinsic
model parameters like the solid model type
of the yarns and the numerical integration
order. They performed FE three-dimensional
strain analysis to predict the elastic
simple averaging
and iso-strain
properties of a of a plain weave unit cell.
The effective material properties and strain
distribution caused large normal and shear
strain concentrations, which might lead to
earlier damage initiation than the one, which
could occur in unidirectional or cross-ply
laminates. They have also been active in the
development of micro-macro approaches
using sub-modelling and sub-structuring
techniques to improve the computational
efficiency. Similarly Tan et al, [14]
proposed a three-dimensional sub modelling
techniques using a three-dimensional macro
and micro blocks for predicting the linear
elastic property of woven fabric unit cells.
Meso-mechanical and numerical studies
were carried out for four types of woven
fabric unit cells. Results showed good
agreement between Meso-mechanical and
FE model and that the number of elements
in the FE model doesn’t affect the effective
stiffness constants significantly, but the
boundary conditions does, however the
values for the FE model was 50% larger
than those predicted by the Meso-
mechanical model and the reason for that is
that the FE model runs under the Iso-strain
condition, which gave upper bound while
the presented Meso-mechanical models, are
developed under the Iso stress conditions,
which gave a lower bound.

3. Experimental
details
3.1. Materials used

In order to study the effect of varying fibre
content ratio in intraply woven hybrid
composites, carbon
hybridised with aramid yarns (A) in
symmetric twill 2/2 fabrics having the same
end/picks count of 6.0±0.3 per cm and
different carbon content (Table 1 and
figure1).
and numerical
(C) yarns were

Page 5

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


187
Table 1: Different combination of materials used, with different carbon content

SAMPLES
C %
(WARP)
C %
(WEFT)
C%
(TOTAL)
VF
%
Inter
yarn
porosity
FABRIC
WEIGHT
(g/m2)

00 and
900
directions
Y
Y
Y
Y
Y
Y
Y
Tensile in
Bias
direction
(450)
Y
N
N
Y
N
N
Y
AE
examination
A
C17
C33
C50
C66
C83
C
0.00
17.00
33.00
50.00
66.00
83.00
100.00
0.00
66.00
66.00
50.00
66.00
66.00
100.00
0.00
18.60 44.90 37.00
22.80 46.10 35.70
22.60 46.00 35.00
32.00 48.50 33.10
37.00 49.70 31.70
52.0 53.00 28.30
44.10 35.90 152.60
188.70
196.10
195.60
211.00
218.40
238.60
Y
N
N
Y
N
N
Y



Figure 1: Codes used to name the different hybrid fabrics used

Rütapox SL-L20 matrix resin system was
used to produce composite plates. The wet
lay up method was used to laminate the
samples. All samples consisted of 8 layers
of fabric, with a total thickness of 2 mm.
The fibre volume fraction varied in the
range of 44 to 53%. A detailed examination
was performed using optical microscopy in
order to characterise the different parameters
of the fabric geometry used in this
investigation (Table 2).

3.2 Tensile test procedure

The effective stiffness properties and
compliance matrices in the hybrid
composites were determined experimentally
using the method proposed by Gommers et
al., [15] and Wachueux [16]. All the results
(table 3) were normalised to 45% fibre
volume fraction, while no scaling was done
for the ultimate strain, since it was not

sensitive to fibre volume fraction in the
range of (10 % variation).
Tensile tests were carried out according to
ISO standards [17, 18] in 2 different
orientations (0o, bias) on woven fabric
samples. The results were used to derive the
in-plane stiffness matrix for the composites
and therefore predict the in-plane stiffness
properties of IWHC. The longitudinal
tensile test on all hybrids and their parent
composites was carried out on the Zwick
146641 machine.
microscopy was used to characterise the
mechanism of damage in fractured samples
after tensile loading.
The experimental results were used as an
input to build the yarn and fabric geometries
using the WiseTex geometric modeller.
Geometry data (yarn packing density, fabric
volume fraction in the composite, fabric
weight were
Scanning electron
obtained.

Page 6

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


188

Table 2: Materials specification. Geometrical and mechanical characteristics
Fabric parameters
Weave
Ends/picks, 1/cm
Yarns
Yams commercial code
Manufacturer
Linear density, tex
Yarn width, mm
Yarn thickness, mm
Fibres
Filament diameter, µm
Number of the filaments in the yarn
Fibre density, g/cm3
Filament tensile modulus, longitudinal, GPa
Filament tensile modulus, transverse, GPa
Filament shear modulus, longitudinal, GPa
Filament shear modulus, transverse, GPa
Filament Poisson’s ratio, longitudinal/ transverse
Resin
Tensile modulus, GPa
Poisson ratio
Tensile strength, MPa
Ultimate strain, %
Flexure strength, MPa
Impregnated yarns
Yarn’s packing density, %
Impregnated yarns tensile modulus, longitudinal, GPa
Impregnated yarns tensile modulus, transverse, GPa
Impregnated yarns shear modulus, longitudinal, GPa
Impregnated yams shear modulus, transverse, GPa
Impregnated yarns Poisson’s ratio, longitudinal
Impregnated yams Poisson’s ratio, transverse

3.3. Building the FE geometry for the
IWHC and their parent composites

FEM geometry has an important role on the
results obtained from the numerical
simulation. In this study I-DEAS-CAD
Solid modeller was used to generate a three-
dimensional solid model. The model has the
potential to repeat itself in all the three
directions under different loading
conditions. Therefore it will be possible to
Carbon yarns
twill 2/2
6.0

HTA/HTS 200
Tenax
200
1.80
0.13

7
3000
1.77
238
28
23.5
10.76
0.3

1.578
0.33
40.68±2.32
3.62±0.49
125

73.9
176.2
9.69
4.92
3.45
0.30
0.368
Aramid Yarns

Kevlar 49
Du Pont
128
1.61
0.12

15.8
1131
1.45
119
7
6.3
2.69
0.3

68.9
82.72
4.88
2.89
1.80
0.30
0.35
incorporate different damage criterions.
However due to the complicated geometrical
details in modelling, the geometry was
established at the yarn level. Contacts
between dissimilar materials (yarns, resin or
matrix) were assumed to be perfect, i.e.
displacement and traction are continuous
and thermal contact resistance is negligible.
No defects or voids were incorporated in the
model. The yarns were assumed to have
regular distribution in the fabric, hence

Page 7

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


189
eliminating the nesting effect found in
stacked laminates. In contrast to the plain
weave, twill weave has its symmetry along
the diagonal axis of the whole unit cell,
therefore a whole unit cell were used rather
than the quarter cell used in plain weaves.
In this study, the yarns were constructed
from straight and sinusoidal shape function
and have lenticular cross-section, the warp
and fill bundles were assumed to be
geometrically identical, the cross-section is
kept constant, in other words, the entire cut
sections orthogonal to the global x- and y-
axes have the same fibre bundles cross-
sections. To obtain the yarn shape function,
a systematic procedure using optical
microscopy has been used to obtain a 3D
geometric characterisation of the woven
hybrid composite. Interpolation method was
used to obtain the best fitting line equation
(equation 1) and (Figure 2).



Figure 2: C50 hybrid cross-section, before
interpolating the best fitting line to obtain
the yarn shape function.
Y (x)=ht/2*(1-Cos (PI*x / Lf))

Where:

Lf is fibre undulation length, and ht is
lamina thickness
The 3D solid models for both the warp and
weft volumes (Yarns) were developed then
re-oriented to construct
Subtracting yarns volume from a whole
rectangular block created matrix pockets
(Figure 3).

[1]
the fabric.


Figure 3: FEM of a repeating unit cell of
a twill weave hybrid fabric reinforced
composite (resin pockets are subtracted
from the image), also allowing to attach to
the unit cell local coordinate system.

The meshing process was generated
carefully after partitioning the part into
volumes representing the different materials
in the unit cell. Holger Thom and Hirai et al
[21, 22] examined several meshes of yarns,
showing that longitudinal modulus can be
influenced slightly by mesh size. In this
study, the model used a total of 410,000
elements. Automatic mesh generation using
three-dimensional solid parabolic element
with 10 nodes, four faces, with 3 DOF was
used to mesh the geometry. Refined mesh
was generated using map-meshing technique
at the sharp edges to avoid element’s
distortion. Filaments were assumed to
follow a parallel path to the middle line of
the yarn, and to have regular distribution in
the yarns, hence it was possible to calculate
yarn’s effective stiffness properties using the
inclusion model. The mechanical properties
then were assigned to the elements.
For a general unit cell, the boundary
condition has to be completely periodic.
This means that displacement on one side of
the unit cell should be followed by a similar

Page 8

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


190
displacement on the opposite side plus or
minus some constant. Chapman, [19] and
Carvelli et al [20] applied periodic boundary
conditions on a plain weave fabric
composites unit cell
equations (CE) on the opposite faces.
However since twill weave unit cell model
has larger unit cell size compared to a plain
weave unit cell, this would increase number
of DOF. This resulted in technical
difficulties prevented us from applying these
boundary conditions due to increase in
computational efficiency, mapping identical
mesh on opposite faces, and applying
constraint equation CE automatically on
opposite faces.
Simplified conditions for the extreme
condition case (free
symmetrically stacked laminate) allowed us
to solve the model and to get strain
distribution fields. These conditions were
specified as follows:
An axial displacement ux (Xmax, y, z) applied
to the unit cell (along the warp fibres) at the
Xmax plane, allowing
contractions in the y and z directions.
using constrain
surface on a
Poisson's ratio
(Xmax, y, z)

The displacements on each of the other 5
faces were represented as:
(Xo, y, z) u=0
(x, Ymax, z) v=free
(x, Y0, z) v=0
(x, y, Zmax) w=0
(x, y, Zo) w=const (CDOF2)

Where u, v, and w are the displacements in
the x, y, and z respectively. A simplified
analysis using simple averaging technique
for a homogeneous material was used in this
study to obtain the effective stiffness
properties for our unit cell. The effective
(overall) composite stiffness relates the
u=Xmax *
x ε
homogenised stress within the material unit
cell to the average strain over the unit cell.
Six different loading conditions were
applied on to the unit cell to calculate stress
averaging on the unit cell for each loading
case. The average stresses were obtained by
volumetric averaging of the effective unit
cell’s stresses over the unit cell volume
Ne
e
V
V∑
=
1
C is the effective (overall)
composite stiffness, <
σ> average stress on
an element,
V Volume of element,V Total
e
e
>< >=<
1
σσ
,
Where:
c
e
e
volume of the FE model,
elements in FE model.

4. Results and discussion

Geometrical models representing the unit
cell of IWHC and their parent textile
reinforced composites have been built using
the geometrical characterisation data (table
2) derived from experiments using Wisetex
modeller the output of the latter has been
transferred to the Inclusion and Cell
modelling codes. FE models were built
using Ideas-8 modelling task and by
importing the geometrical data from
Wisetex. The experimental and numerical
findings are presented in Figure 3. Poissons
ratio (v0) was calculated using the inclusion
model. All strength and stiffens results were
normalised to a 45% fibre volume fraction.
Longitudinal tensile results show a trend in
stiffness properties increasing with the
increase in carbon content in the hybrid
composite (Figure 4). The highest value was
at the carbon composites (49.42 GPa), with
its highest standard deviation (3.81 Gpa)
among other composites. This could be due
to carbon composites
processing; especially to voids created in the
wet lay up laminating. Stress strain curve
e
N Number of
sensitivity to

Page 9

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


191
showed linear behaviour up to samples
breakage. Samples showed different modes
of failure represented by Aramid fibres
ductile breakage and looping (Figure 5a),

carbon fibres brittle breakage (Figure 5c),
while the C50 hybrid composite showed
mixed mode of damage (Figure 5b).

Figure 4: Experimental and analytical stiffness (Young Moduli) for different carbon
content hybrid composites


5a 5b 5c
Figure 5a, 5b and 5c: Different modes of failure in the aramid, C50, Carbon composites
(5a, 5b, and 5c) tensile tested samples in 0o direction of loading



Matrix debris was found surrounding the
deformed fibres. This indicates that the
aramid fibres suffered substantial extension
where energy has been absorbed in this form
of damage. Poor bonding were observed at
the fibres and their surrounding matrix. Also
aramid fibres reduced in diameter and pulled
out. While Carbon tensile samples under

Page 10

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


192
longitudinal
interface
transverse de bonding for the fibres in weft
and a brittle fibre breakage for the fibres in
warp with some extent of fibre pullout
(Figure 5c). Mixed failure was found in the
hybrid composites (Figure 5b).
The Bias tensile samples showed high
deformation areas; where the sample
narrowed significantly in the width at the
central region (Figure 6). Also the
composites showed high strain to failure
(over 9.5%) in carbon composite compared

tensile loading,
represented
showed
by failure the
to 0.9% in the 0o tensile tested samples.
While stiffness and strength properties
showed high anisotropy in all composites.
Young’s Moduli values were at their highest
in the warp and weft directions (due to
materials symmetry) but lowest values in
materials bias direction. Non-linearity has
been characterised in the stress-strain curve
in all composites tested in the longitudinal
tensile and the Bias directions. This is
caused by de-laminations and matrix failure
in carbon, while aramid composites suffered
fibres buckling in addition to that failure.

Figure 6: Carbon and aramid 45o tensile tested samples showed narrowing in sample’s
width. A microscopic image for the thickness of a failed carbon composite tested in
tensile along the Bias direction (45o) revealed inter-laminar fractures

Stiffness properties showed high anisotropy
in all composites (table 3). Young Moduli
were at their highest values at the warp and
weft directions (due to materials symmetry)
but at their lowest values in materials bias

Table 4: Poissons ratio using FEA, inclusion and cell models

Composite zy yz
A 0.397 0.058
C50 0.402 0.043
C 0.406 0.036
A 0.386 0.045
C50 0.393 0.034
model
C 0.373 0.029
A 0.369 0.045
C50 0.374 0.033
model
C 0.371 0.029

direction. While in plane shear moduli and
Poisson constants reached their maximum
values at a 45o off axis orientation and they
were at their lowest values in warp and weft
directions (table 4).
yx
0.058
0.043
0.036
0.045
0.035
0.029
0.045
0.034
0.029
xy
0.401
0.410
0.416
0.386
0.394
0.373
0.369
0.370
0.371
xz
0.036
0.027
0.023
0.035
0.030
0.028
0.039
0.034
0.031
zx
0.036
0.027
0.023
0.035
0.031
0.028
0.039
0.036
0.031
FEA
Inclusion
Cell
Inter-
laminar
fractures

Page 11

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


193
The reasons for any deviations from the
experimental results can be considered as
follows:
By considering homogenised
properties we neglected
progressive micro-mechanical
events (matrix cracking, fibre breakage, and
de bonding), this
overestimation of the predicted elastic
prosperities. Part of the error in the FE
model can be attributed to the inaccuracies
in yarn’s shape description, especially in the
out of plane co-ordinates of the paths.
Despite this, it is clear that the yarn mesh in
the FE model is capable of predicting the
anisotropic behaviour of woven fabric
composites, which also indicates that
geometrical aspects like yarns shape, yarns
cross section, and orientation are of a
secondary importance
behaviour of hybrid composites.
Meso-mechanical results using the inclusion
model have been affected by disregarding
the ?factor effects described by Huysman.
This value depends on materials physical
properties and yarns
recommended value
π
plain weave glass fabric) has been used in
our calculation. Calibration procedure would
be recommended to obtain accurate value to
be used for this type of reinforcement.
However, since the aim of this study is to
validate the applicability of the generic
inclusion method applicability to predict
IWHC mechanical properties, only an
evaluation of the results would be needed to
achieve these aims.
These errors could be attributed to
difficulties in describing the geometry and
the properties of the constituents of the
textile correctly. On the other hand, the
fibres manufacturer
transversal fibres
properties have been obtained from different
literature resources. Such assumptions could
yarns
yarn’s
damage
the
resulted in an
in the tensile
curvature.
(calibrated on a
A
2/
did
properties.
not provide
Fibres
contribute in the relative error in our
predictions.
A draw back of the boundary conditions
applied in our FEM is that it did not
consider the far
(periodic boundary conditions). Periodic
displacements boundary conditions are to be
applied using constraint equations on pairs
of nodes lying on the opposite unit cell
faces, with the simulation tool available in
IDEAS-8 this can be time consuming task.
In addition their presence would increase the
number of degrees of freedom associated
with face’s nodes and make to solve almost
impossible. Therefore
periodic boundary conditions cannot be
considered a generic method due to the
difficulties associated in applying them. A
draw back from using these simplified
boundary conditions could develop reaction
forces at nodes caused by the direct force
application, leading
stresses, which results in misleading stress
values. However FE methods, still allows
the prediction of the effective stiffness
properties using non-periodic boundary
conditions, using the prescribed procedure
in section (4.1). Further work would be
needed to implement these boundary
conditions by developing a program
associated with IDEAS-8 to generate
automatically pairs of corresponding nodes
on opposite faces then coupling them with
the appropriate constraint equations. This
would improve the calculated stress and
strain fields in the unit cell.

5 Conclusions

FE model for the IWHC showed that it
could be a useful to estimate the composite
behaviour, it allows consideration of non-
periodic boundary conditions, and moreover
it would give more insight view on the
internal stress and strain distribution in
fields displacement
applying these
to high-localised

Page 12

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


194
IWHC. However the difference in results for
different mechanical properties, are caused
by loss in geometrical details and due to
simplifications made in applied boundary
conditions. Stiffness properties showed high
anisotropy in all
dominated elastic properties (e.g. on-axis
moduli) are predicted with an acceptable
accuracy but matrix-dominated behaviour,
like shear properties are predicted with
significant errors. Damage analysis using FE
and photo-grametry strain mapping showed
similarity in the strain repetitive patterns and
values. Strain analysis was useful in
predicting probability of strain to failure
initiation in IWHC and in locating their
locations in the unit cell. The damage
analysis was supported by SEM and AE
monitoring, which agreed with our FE
analysis.

6. Acknowledgment

The investigation was supported by EPSRC
grant (00314736). The authors are grateful
to Mr. Roger Price (Intergals Technologies)
for the valuable industrial support. A
significant proportion of the work was
conducted in the Department MTM,
K.U.Leuven as part of a European Marie
Curie grant (HPMT-CT-2000-00030).

6. References

1. Kessler A and Bledzki AK. Low velocity
impact behaviour of glass/epoxy cross-ply
laminates with different fibre treatments.
Polymer Composites 1999; 20 (2): 269-278

2. Kim JK and Leung and Lee SWR, Hirai
Y. Impact performance of a woven fabric
CFRP laminate. Polymer and Polymer
composites 1996; 4 (8): 549-61

composites. Fibre
3. Jang BZ, Chen LC, Hwang LR, Hawkes
JE and Zee RH. The response of fibre
composites to impact loading. Polymeric
composites 1990; 11 (3): 144-157

4. Chamis CC, Lark RF and Sinclair JH.
Mechanical Property Characterisation of
Intraply Hybrid Composites. Test methods
and design allowable for fibrous composites,
ASTM STP 734, Chamis C. C., Ed.,
American Society for testing and materials,
1981, pp. 261-280

5. Huysmans G. Unified Meso-mechanical
models for textile composites, PhD. Thesis,
K.U.Leuven, 2000

6. Chen D. and Chang S. Analysis of
composite materials: A Meso-mechanical
approach. Reinforced
Composites 1993; 12, 1323-1338

7. Huysmans G, Gommers B. and Verpoest
I. A binary finite element model for the
effective stiffness prediction of warp-
knitted-fabric composites. In: Hudgkinson
J. (editor). Proceedings
International Conference: On Deformation
and Fracture of Composites. Manchester
1997. pp. 309

8. Lomov SV, Huysmans G, Luo Y, Parnas
RS, Prodromou A, Verpoest I and Phelan
FR. Textile composites:
strategies. Composites Part A: Applied
Science and Manufacturing 2001; 32 (10),
1379-1394

9. Theocaris PS and Stavroulakis GE. The
effective elastics moduli of plane-weave
woven fabric composites by numerical
homogenisation. Reinforced
Composites1997; 16 (18), 1675-1691

Plastics and
of the 4th
modelling
Plastic

Page 13

Advances in Computing and Technology,
The School of Computing and Technology 1st Annual Conference, 2006


195
10. Kawabata S, Niwa M and Kawai.
Textile Institute Feb.1973; 64, 20-62

11. Kalidindi SR and Franco E. Numerical
evaluation of isostrain and weighted-average
models for elastic
three-dimensional composites, Composite
science and technology 1997, 57, p. 293-305

12. Kregers AF and Teters GA. Use of
averaging methods
viscoelastic properties
reinforced composites.
composite materials 1979; 4, 377-383

13. Whitcomb J and Tang X. Routine
three-dimensional analysis
composites. In: Proc. 12th Int. Conf. on
Composite Materials (ICCM-12), Paris
(France), 1999

14. Tan P, Tong L and Steven GP. 3D
modelling technique for predicting the linear
elastic property of opened-packing woven
fabric unit cells. Composite structures 1997;
1 (38), 261-271

15. Gommers B, Verpoest I and Van Houtte
P. Determination of
Properties of Composite materials by
Tensile testing I and II, accepted by the
journal of Composite materials 1997

16. Wachuex R. In-plane mechanical
Evaluation and damage characterisation of










moduli of
to detrmine
of
Mechanics
the
spatially
of
of woven
the Mechanical
glass woven fabric Laminates, EUPOCO
master thesis dissertation,
Universitiet-Leuven, 1996

17. ISO 527-5: 1997
Determination of tensile properties for
unidirectional fibre
composites

18. ISO-14129: 1997 (E), Fibre-reinforced
plastic composites-Determination of the in-
plane shear stress/shear strain response,
including the in-plane shear modulus and
strength, by the 45± tension test method

19. Carvelli V, Poggi C. Homogenisation
procedure for numerical analysis of woven
fabric composites. Composites Part A 2001;
32, 1425-1432

20. Borovkov AI. Effective mechanical
properties of the fibrous composites,
Moskou:VINITI, 1985

21. Holger Thom. FEA Modelling of plain
weave composites. Composite Materials
1999; 33 (16), 1491-1510

22. Huysmans G, Verpoest I and Van Houtte
P. A Poly-inclusion approach for the elastic
modelling of knitted fabric composites. Acta
Materialia 1998; 46, 3003



Katholieke
(E), Plastic-
reinforced plastic