# 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

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**ABSTRACT:**A micromechanical approach for predicting the overall elastic behavior, as well as thermal expansion coefficients, of composite materials is presented. The approach is based on modeling the composites with regular arrays of unit material cells, construct ing a possible stress pattern for a considered representative cell, and then minimizing the complementary energy of the representative cell under given average stresses. The proce dure is concise in concept, theoretically adaptable, and easy to conduct. Applications to unidirectionally fiber-reinforced composites and to some particulate composites are given. Good agreement with known theoretical/experimental results are shown.Journal of Reinforced Plastics and Composites 01/1993; 12(12):1323-1338. · 0.90 Impact Factor -
##### Article: Low velocity impact behavior of glass/epoxy cross‐ply laminates with different fiber treatments

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**ABSTRACT:**This paper deals with the influence of the fiber/matrix adhesion quality on the impact behavior of cross-ply glass/epoxy laminates. Glass fibers with two different treatments (one to promote and one to prevent adhesion to the matrix) were embedded in epoxy matrix systems and subjected to low velocity impacts at energies below perforation energy. It will be shown that the laminates with good fiber/matrix adhesion are significantely more damage resistant than the plates with poor adhesion. It will be pointed out that the composites with the more brittle matrix system show the lower damage resistance. For all materials, the absorbed energy correlates well with the amount of impact induced damage. Furthermore, an experimental/mathematical model is introduced that gives the possibility of predicting the maximum deflection and maximum force for any given impact energy. Only one experiment is needed for each material to identify the model parameters. These parameters describe the real material behavior and can be used as characteristic values to classify materials with respect to their impact stiffness and damage resistance.Polymer Composites 04/2004; 20(2):269 - 278. · 1.48 Impact Factor - SourceAvailable from: Valter Carvelli[Show abstract] [Hide abstract]

**ABSTRACT:**The paper presents a procedure for the numerical evaluation of the mechanical properties of woven fabric laminates. Woven fabrics usually present orthogonal interlaced yarns (warp and weft) and distribution of the fibers in the yarns and of the yarns in the composite may be considered regular. This allows us to apply the homogenization theory for periodic media both to the yarn and to the fabric. Three-dimensional finite element models are used in two steps to predict both the stiffness and the strength of woven fabric laminates. The model includes all the important parameters that influence the mechanical behavior: the lamina thickness, the yarn orientation, the fiber volume fraction and the mechanical characteristics of the components. The capabilities of the numerical model were verified studying the elastic behavior of a woven fabric laminate available in the literature and the ultimate strength of a glass fabric laminate experimentally investigated. The procedure, that can be implemented into commercial finite element codes, appears to be an efficient tool for the design of textile composites.Composites Part A Applied Science and Manufacturing 01/2001; · 2.74 Impact Factor

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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

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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,

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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

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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

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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.

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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

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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

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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

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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

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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

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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

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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).

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