Analytical study of strength and failure behaviour of plain weave fabric
composites made of twisted yarns
N.K. Naik*, R. Kuchibhotla
Department of Aerospace Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
Abstract
A two-dimensional analytical method is presented for the failure behaviour of plain weave fabric composites made of twisted yarns. The
studies have been carried out on laminates with different con®gurations under on-axis uni-axial tensile loading. The cross-sectional area of
the yarn was taken to be elliptical and the yarn path was taken to be sinusoidal. Different stages of failure are considered in the analysis. It has
been observed that there is no signi®cant reduction in tensile strength properties of plain weave fabric composites as a result of twisting of
yarns. For E-glass yarns, twisting of yarns up to 58, can facilitate ease of fabrication without signi®cantly compromising the strength
properties of the woven fabric composites.
Keywords: A. Fabrics/textiles; B. Strength; C. Analytical modelling; C. Damage mechanics
1. Introduction
Advanced textile structural composites are ®nding
increasing use for many high performance applications
during last one decade. Textile techniques such as twodimensional (2D) and three-dimensional (3D) weaving,
braiding, knitting and through-the-thickness stitching have
assisted in enhancing the performance of textile composite
structures. Such composites are characterised by enhanced
through-the-thickness elastic and strength properties,
impact/fracture resistance, damage tolerance and dimensional stability. Additionally, textile structural composites
are associated with near-net-shape and cost effective manufacturing processes. For high in-plane speci®c stiffness and
high in-plane speci®c strength applications, 2D woven
fabric (WF) composites can be the competitors to laminated
composites made of unidirectional (UD) layers. To derive
the maximum bene®ts of the textile structural composites,
an improved understanding of the detailed structure of the
reinforcement with the advances in fabric formation techniques is essential.
The textile structural composites are made using the
woven, braided, knitted or stitched preforms. The textile
preforms are planar or 3D. The special feature of the textile
preforms is the signi®cant reinforcement interconnectivity
between adjacent planes of reinforcements. This interconnectivity provides additional interface strength to
supplement the relatively weak ®bre/resin interface. The
interconnectivity is mainly in the plane of the preform for
the planar textile preforms. Such materials are known as 2D
textile preforms. The 3D textile preforms for the structural
composites are fully integrated continuous reinforcement
assemblies having multi-axial in-plane and out-of-plane
reinforcement orientations. Formation of different textile
preforms is an important stage in composites technology.
WFs are produced by the process of weaving in which the
fabric is formed by interlacing warp and ®ll strands/yarns.
Knitted preforms are made by interlooping whereas braided
preforms are made by intertwining. One of the important
requirements of the reinforcing elements during preform
preparation is the lateral cohesion. For this reason, the
twisted yarns are used for preparing the textile preforms
rather than the straight strands.
Twisted yarns are normally used for increasing the lateral
cohesion of the ®laments and also for ease of handling. By
twisting yarns, possible micro damages within the yarn can
be localised, leading to possible increase in the failure
strength of the yarn. For this reason, twisted yarns are
normally used for making textile preforms, especially for
698
Nomenclature
a
yarn width
aij
extensional compliance matrix
axt, ayt as shown in Fig. 4
Aij
extensional stiffness matrix
E, G, n elastic properties
g
inter-yarn gap
h
maximum yarn thickness
hm
matrix thickness
ht
fabric thickness
HL
lamina thickness
l
sub-element, element, section dimensions
L
unit cell dimensions
nx, ny, nz number of sub-elements, elements, sections
in the x-, y-, z-directions
Å
Q
transformed reduced stiffness matrix
R
radius of yarn
S
shear strength
Vf
®bre volume fraction
x, y, z cartesian coordinates
XT, YT tensile strength
zxi …x; y†; i ˆ 1±4 yarn shape parameters
zyi …y†; i ˆ 1±4 yarn shape parameters
a
angle of twist for the yarn
1
normal strain
1p
pre-strain
s
normal stress
s x
load per unit area in x-direction
q…x†; q…y† local off-axis angle of the undulated yarn
t
shear stress
Superscripts
el
refers to element
nl
non-linear
o
overall properties
s
quantities of strand
sec
refers to section
sel
refers to sub-element
y
quantities of yarn
Subscripts
f, F
quantities in ®ll direction
L
longitudinal axis of the ®bre
T
transverse axis of the ®bre
w, W quantities in warp direction
1,2
local coordinates
x, y
global coordinates
E-glass reinforcements. Twisting of yarns may lead to possible reduction in ultimate failure strain. But twisting of yarns
may be unavoidable for engineering reasons.
The objective of the present work is to study the failure
behaviour of plain weave fabric laminates made of twisted
yarns (Fig. 1). This requires the knowledge of mechanical
behaviour of twisted yarns along with the effect of laminate
con®guration made of WF layers.
There are many research papers on the mechanical
behaviour of the WF composites under in-plane on-axis
uni-axial tensile loading [1±44]. But these studies are
based on WF composites made using straight strands. The
mechanical behaviour of straight strands is very similar to
the mechanical behaviour of UD composites and is well
understood. The mechanical behaviour of twisted yarns is
signi®cantly different. This in turn, can effect the mechanical behaviour of WF composites made of twisted yarns.
2. Mechanical behaviour of twisted impregnated yarns
Twisting of yarns introduces lateral cohesion leading to
ease of handling of the yarns during preform fabrication.
Studies are available on the mechanical behaviour of
twisted impregnated yarns [45±48]. An analytical method
is presented in Ref. [47] for predicting the elastic properties
of twisted impregnated yarns made of long unbroken ®laments. In this analysis, varying degree of twist in ®laments
at different radii of the yarn and possible migration and
microbuckling of ®laments are considered. The effects of
twist angle and the extent of migration and microbuckling
on the elastic properties and the pre-straining of the yarn are
presented.
An analytical method is presented for the prediction of
longitudinal and transverse tensile strengths of twisted
impregnated yarns in Ref. [48]. It has been observed that
the transverse tensile strength of twisted impregnated yarns
can increase compared to that of corresponding impregnated
strands. This is because of the lateral pressure generated
during twisting. Effective transverse tensile strength of the
twisted impregnated yarns varies as a function of radial
position of the yarn (Fig. 2). Near the periphery, there is a
marginal increase in the effective transverse tensile strength
whereas the increase is signi®cant near the centre of the
twisted impregnated yarns. Even though there is reduction
in the mean longitudinal tensile strength of the twisted
impregnated yarns compared to those of corresponding
impregnated strands, the reduction is marginal. Considering
possible increase in transverse tensile strength, reduction in
longitudinal tensile strength and pre-straining of the ®laments, optimum twist angle should be provided. Further,
it has been observed that the variation of the shear strength
as a function of radial position is marginal for different twist
angles. Shear strength of twisted impregnated yarns can be
taken to be equal to the shear strength of the corresponding
straight impregnated strands.
Variation of effective transverse tensile strength, YTy as a
function of radial position at sections is shown in Fig. 2.
This ®gure is based on circular cross-sectional area for the
twisted yarn. A linear variation of the transverse tensile
strength as a function of radial position is assumed in the
699
Fig. 1. Idealised representation of 2D orthogonal plain weave fabric composite made using twisted yarns.
present study. Elastic and strength properties of the twisted
impregnated yarns are presented in Table 1 for E-glass/
epoxy. The pre-strain, 1 p introduced in the ®laments during
twisting of yarns is also presented. As the twist angle
increases, pre-strain in the ®laments increases. In the present
study, the yarn cross-section is taken as an ellipse with
minor axis-to-major axis ratio ˆ 0.8
3. Lamina geometry
For the evaluation of the mechanical behaviour of
plain weave fabric composites, mathematical representa-
tion of lamina geometry is essential. The mathematical
shape functions used were either linear, circular or sinusoidal functions [1±4,9,22]. Earlier studies were based
on WF composites made of straight strands. For such
materials, strand thickness-to-strand width ratio is low.
It is in the practical range of 0.05±0.1. Such fabrics can
be tightly woven with very small value of inter-strand
gap. Inter-strand gap-to-strand width ratio can be in the
range of 0.0±0.1.
Twisted yarns are characterised by near circular crosssectional area. For typical twisted yarns, yarn thicknessto-yarn width ratio (h/a) can be in the range of 0.6±1.0
with a possible elliptical cross-sectional area. For such
700
Fig. 2. Variation of effective transverse tensile strength, Y yT as a function of
radial position at sections.
fabrics, the ratio inter-yarn gap-to-yarn width (g/a) would
be higher.
For the present study, yarn cross-sections are considered
to be elliptical with major axis along the width and minor
axis along the thickness of the yarn. Sinusoidal functions are
considered for the yarn path along the loading direction.
Typical requirements for the mathematical shape functions for modelling the geometry of the plain weave fabric
lamina are:
1. The yarn cross-section and yarn undulation should be
exactly simulated.
2. Possible inter-yarn gap should be considered.
3. The interface contact between the warp and ®ll yarns
should be maintained.
4. The undulation angle at a given cross-section of the yarn
should be the same.
5. The yarn should be continuous and there should not be
any abrupt change in the slope of the yarn along its
length.
Considering the above aspects, mathematical expressions
have been presented in our earlier work [22] for plain weave
fabric lamina made of straight strands.
The objective of the present study is to de®ne the geometry of the 2D orthogonal plain weave fabric lamina made
of twisted yarns for the prediction of thermo mechanical
behaviour. For this, the elliptical cross-section of the yarn
and the sinusoidal path of the yarn are used. Hence, the
interface contact between the warp and ®ll yarns cannot
be maintained throughout. As such, with twisted yarns,
there may not be interface contact between the warp and
the ®ll yarns throughout. But the actual cross-sectional area
is considered. Yarn undulation is exactly simulated along
the loading direction whereas only the equivalent area is
considered with respect to transverse direction.
As can be seen, the yarn cross-sectional area, yarn
undulation along the loading direction and realistic interyarn gap are the important requirements for the accurate
prediction of thermo mechanical behaviour. Even though
there is geometrical inconsistency with respect to the transverse direction, it would not affect the predicted thermo
mechanical properties.
3.1. Lamina geometry: elliptical cross-section
Representative unit cells of the plain weave fabric lamina
made of twisted yarns are shown in Fig. 3. The crosssections with respect to warp and ®ll directions are
presented in Fig. 4.
The expressions for the shape functions to de®ne the
geometrical unit cell are as follows:
In the Y±Z plane, i.e. along the warp direction (Fig. 4),
h
zy1 …y† ˆ 2 f
2
"
2y
12
af
2 #1=2
zy2 …y† ˆ 2zy1 …y†
zy3 …y† ˆ
yˆ0!^
yˆ0!^
af
2
af
2
hf
py
cos
af 1 gf
2
zy4 …y† ˆ hw 1 zy3 …y†
Table 1
Elastic and strength properties of twisted impregnated yarns: E-glass/epoxy, Vfy ˆ 0:7 (Yarn diameter ˆ 1 mm: Shear strength of the yarn, Sy ˆ 39:7 MPa:
Y yT values are at r=R ˆ 0: The quantities in the bracket are at r=R ˆ 1)
a (8)
E yL (GPa)
E yT (GPa)
G yLT (GPa)
G yTT (GPa)
n yLT
n yTT
X yT (MPa)
Y yT (MPa)
1 p (%)
0
2
5
10
51.50
51.31
50.32
47.13
17.70
17.70
17.67
17.59
5.85
5.85
5.86
5.90
6.67
6.67
6.67
6.66
0.313
0.313
0.315
0.320
0.327
0.327
0.326
0.322
1397
1395
1385
1348
27.9 (27.9)
28.2 (27.9)
30.6 (27.9)
38.8 (27.9)
±
0.061
0.380
1.543
701
Fig. 3. Representative unit cells of the plain weave fabric lamina made of
twisted yarns.
In the X±Z plane, i.e. along the ®ll direction (Fig. 4),
2 #1=2
"
hw
2x
zx1 …x; y† ˆ
2hy1 …y†
12
aw
2
a
xˆ0!^ w
2
2 #1=2
"
hw
2x
2hy1 …y†
zx2 …x; y† ˆ 2
12
aw
2
a
xˆ0!^ w
2
Fig. 4. Cross-sections of plain weave fabric lamina made of twisted yarns.
hy1 …y† ˆ
hf
2 zy3 …y†
2
hy2 …y† ˆ
hf
2 zy2 …y†
2
If zx2 …x; y† 2 zx3 …x; y† # 0 then zx2 …x; y† ˆ zx3 …x; y†:
The local undulation angle of the ®ll yarn at any crosssection along its length is given by:
h
px
2 hy2 …y†
zx3 …x; y† ˆ 2 w cos
aw 1 gw
2
a
yˆ0!^ f
2
qf …x† ˆ tan21
hw
px
1 hy2 …y† 2 hf
zx4 …x; y† ˆ 2
cos
aw 1 gw
2
a
yˆ0!^ f
2
and the warp yarn at any cross-section along its length is
d
‰zx …x; y†Š
dx 3
phw
px
ˆ tan21
sin
…aw 1 gw †
2…aw 1 gw †
702
given by:
d
‰zy …y†Š
dy 3
phf
py
21
sin
ˆ tan
…af 1 gf †
2…af 1 gf †
qw …y† ˆ tan21
4. Laminate geometry
A laminate is formed by stacking individual layers one
over the other. In multi-directional laminates made of UD
layers, a variety of laminate con®gurations can be obtained
by varying the orientation angle of individual layers. On the
other hand, in the case of WF laminates, different stacking
patterns can be obtained even without considering the orientations of individual layers as a variable [22]. One of the
typical WF laminate con®gurations is to maintain the same
warp and ®ll directions for all layers. This laminate con®guration is similar to UD composite consisting of many
layers.
In the case of WF laminates with aligned warp and ®ll
directions, different laminate con®gurations are obtained by
shifting the adjacent layers in such a way that the yarns of
one layer are not in-phase with the yarns of the adjacent
layers. The shift of one layer with respect to the adjacent
layer can be in warp and/or ®ll directions.
In an actual laminate, the relative movements of the
fabric layers are affected by friction between fabric layers,
local departure in yarn perpendicularity, possible variation
of number of counts from place to place in the fabric and
constraints on the relative lateral movement of the layers
during lamination. Hence, an actual laminate would have
scattered zones of different combinations of shift [22].
The idealised cases of laminate on-axis shapes are shown
in Fig. 5. In con®guration-1 (C1), there is no relative shift
between adjacent layers, i.e. each layer is exactly stacked
over the adjacent layer. All the layers are in-phase. Such a
con®guration is termed as aligned con®guration. In con®guration-2 (C2), the adjacent layers are shifted with
respect to each other by a distance of …a 1 g†=2 both in the
®ll and the warp directions. In this case adjacent layers are
out-of-phase. Such a con®guration is also termed as bridged
con®guration.
As can be seen from Figs. 3±5, the WFs consist of interlacing regions in which both the warp and ®ll yarns are
present and the gap regions where either warp or ®ll yarns
are present. In the case of C1, for the WF laminate as a
whole, clear interlacing regions and gap regions can be
seen. In the case of C2, gap region of one layer is bridged
by the interlacing region of the adjacent layer.
In an actual WF laminate, the shift of different layers with
respect to the adjacent layers would be random. Based on
the photo micrographic studies and the predictions obtained
using analytical models in the case of WF laminates made of
straight strands, it has been shown that the predictions based
on C2 con®guration match well with the experimental data
[15,23].
5. Analysis
The stress and failure analysis of the geometrical representative unit cell is based on volume averaging method. A
geometrical representative unit cell for a typical plain weave
fabric lamina made of twisted yarns is shown in Fig. 3.
Fig. 5. Representative unit cells for different laminate con®gurations-for analysis.
703
Fig. 6. Plain weave fabric lamina made of twisted yarns: unit cell idealised, parallel-series scheme.
Based on similarity, unit cell for analysis is identi®ed. The
unit cell is discretised into sections perpendicular to the
loading direction. Loading is assumed to be along the ®ll
direction. The sections are further discretised into elements
(Fig. 6). The elements are further discretised into subelements.
It may be noted that an element consists of three types of
regions: longitudinal (®ll) yarn, transverse (warp) yarn and
pure matrix. As has been explained earlier, effective transverse tensile strength of the twisted impregnated yarn varies
as a function of radial position of the yarn. To take this
aspect into account, the longitudinal and transverse yarn
regions are further subdivided into sub-elements. Subelements are obtained by discretising the longitudinal and
transverse yarn regions along the thickness directions with
the same longitudinal and transverse dimensions.
It may be noted that the longitudinal and the transverse
sub-element properties are derived from the properties of
the twisted impregnated yarns. Based on the discretisation,
length, width and thickness of the sub-elements are known.
Matrix sub-element/region properties are taken to be those
of bulk matrix. Based on these, the element properties are
derived as explained later.
5.1. Stress and failure analysis
The discretisation scheme is shown in Fig. 6.
The strain for the elements in the loading direction is the
same as that for the corresponding section by the iso-strain
assumption at the section level.
el
sec
1sel
x ˆ 1x ˆ 1 x
In the transverse direction, the assumption is made that all
the elements have the same strain as the corresponding
section. Also, the transverse strain for a section is the
same as the average transverse strain for the unit cell.
el
sec
1sel
y ˆ 1y ˆ 1 y ˆ 1y
The extensional stiffness matrix for each sub-element is
equal to its transformed reduced stiffness matrix.
h i
sel
Asel
ˆ ‰QŠ
ij
The element and section extensional stiffness matrices are
obtained as:
nz h
h i
i
1 X
Asel
Ael
ij ˆ
ij lz
Lz nˆ1
h
ny h
i
i
1 X
ˆ
Asec
Ael
ij
ij ly
Ly nˆ1
The extensional compliance matrix of the section is,
h i h
i21
ˆ Asec
asec
ij
ij
The extensional compliance matrix of the unit cell/WF
704
laminate is,
‰aij Š ˆ
nx h
i
1 X
l
asec
Lx nˆ1 ij x
The transverse strain of the unit cell/WF laminate is,
1y ˆ a21 s x
Here, s x is load per unit area.
The longitudinal strain of the section is,
1sec
x ˆ
sec
s x 2 Asec
12 1y
sec
A11
The longitudinal strain of the unit cell/WF laminate is,
1x ˆ
nx
1 X
1sec l
Lx nˆ1 x x
The sub-element stress is,
sel
sel sel
s xsel ˆ Asel
11 1x 1 A12 1y
Fig. 7. Stress±strain behaviour for plain weave fabric laminates made of
twisted yarns: E-glass/epoxy, a ˆ 08; linear analysis.
The ®ll sub-element stresses in the local co-ordinates:
s 1sel ˆ cos2 …qf …x††s xsel
5.1.1. Non-linear analysis
Because of the undulation of the yarns, each sub-element
is off-axis with respect to loading direction. Considering this
aspect, possible non-linear behaviour of each sub-element is
considered as follows [49]:
s 2sel ˆ sin2 …qf …x††s xsel
sel
tsel
12 ˆ sin…qf …x††cos…qf …x††s x
The above expressions are based on linear analysis.
The stresses obtained from the above equations in each
sub-element are compared with the permissible stress
values. If the induced stress in any sub-element exceeds
the permissible limit, that particular sub-element is treated
as failed and does not contribute to further load sharing.
Generally, it is observed that the failure takes place in a
section with longitudinal yarns at an angle with respect to
the loading direction. Hence, in such sub-elements, the early
modes of failure would be shear failure and transverse
failure. The ultimate failure would take place when the
®bres break. Hence ®bre strain/twisted yarn strain/section
strain was monitored during loading. The effective permissible twisted yarn strain would be the ®bre strain
minus pre-strain due to twisting. When the section strain/
®bre strain exceeds the permissible strain, the section is
supposed to have failed indicating the failure of unit cell/
WF laminate.
1nl
x ˆ Sxx …u…x††s x …u…x†† 1
‰1 2 cos…4u…x††Š2
S5555 …s x …u…x†††3
64
For E-glass/epoxy, S5555 ˆ 37 £ 1029 MPa23 at Vfs ˆ 0:46:
And, Sxx is the compliance element.
sel
sec
It may be noted that s x ˆ s xsel ; 1nl
and
x ˆ 1x ˆ 1x
u…x† ˆ qf …x†:
The sub-element/section strains in local coordinates,
2
nl
1nl
1 ˆ cos …qf …x††1x
This value of induced strain is compared with the permissible strain of the twisted yarn/section.
6. Results and discussion
Predicted strength properties of the plain weave fabric
Table 2
Predicted strength properties of plain weave fabric laminates made of twisted yarns: E-glass/epoxy, Vfo ˆ 0:44; h=a ˆ 0:8; g=a ˆ 0:2 (linear analysis)
a (8)
0
2
5
10
WTI (MPa)
WTC (MPa)
FTI(FSI) (MPa)
PMBFI (MPa)
XT (MPa)
1 x (%)
C1
C2
C1
C2
C1
C2
C1
C2
C1
C2
C1
C2
15
15
15
15
22
22
21
19
47
48
49
52
29
29
30
33
25(32)
25(32)
25(31)
23(32)
29(31)
29(31)
27(31)
25(31)
119
119
119
119
120
120
120
121
227
224
209
155
262
258
240
178
3.73
3.68
3.44
2.53
3.85
3.80
3.55
2.60
705
Fig. 8. Stress±strain behaviour for plain weave fabric laminates made of
twisted yarns: E-glass/epoxy, a ˆ 28; linear analysis.
Fig. 10. Stress±strain behaviour for plain weave fabric laminates made of
twisted yarns: E-glass/epoxy, a ˆ 108; linear analysis.
composites made of twisted yarns using linear analysis are
presented in Table 2 and in Figs. 7±12. Failure strength and
strain data are presented for both C1 and C2 cases with
different twist angles. Different stages of failure like warp
transverse failure initiation (WTI), complete failure of
warp (WTC), ®ll transverse failure initiation (FTI), ®ll
shear failure initiation (FSI), pure matrix block failure
initiation (PMBFI) and the ®bre breakage, i.e. the ultimate
tensile failure (XT) have been monitored. In Figs. 7±10,
WTI, PMBFI and XT have been indicated by `a', `d' and
`e', respectively.
It can be seen that warp transverse failure initiation is
the ®rst mode of failure. Because of the higher undulation angle, ®ll transverse failure and ®ll shear failure
also take place early. The next failure is the failure of
Fig. 9. Stress±strain behaviour for plain weave fabric laminates made of
twisted yarns: E-glass/epoxy, a ˆ 58; linear analysis.
Fig. 11. Stress±strain behaviour for plain weave fabric laminates made of
twisted yarns: E-glass/epoxy, con®guration C1, linear analysis.
706
Table 3
Predicted strength properties of plain weave fabric laminates made of twisted yarns: E-glass/epoxy, Vfo ˆ 0:44; h=a ˆ 0:8; g=a ˆ 0:2 (non-linear analysis)
a (8)
0
2
5
10
WTI (MPa)
WTC (MPa)
FTI(FSI) (MPa)
PMBFI (MPa)
1 x (%)
XT (MPa)
C1
C2
C1
C2
C1
C2
C1
C2
C1
C2
C1
C2
15
15
15
15
22
22
21
19
47
48
49
52
29
29
30
33
25(32)
25(32)
25(31)
23(32)
29(31)
28(31)
27(31)
26(31)
118.4
118.4
118.6
±
120
120
120
±
131.2
131.0
129.4
118.6
121.2
120.6
120.4
113.2
1.91
1.91
1.85
±
2.03
2.02
2.03
±
pure matrix block. Failure of the pure matrix block
would lead to the disintegration of the composite. Effectively, this can be treated as the failure of the WF
composite. But the ®bres can still be intact. The ®bres
break when the ultimate strain exceeds the permissible
strain limit inside the section. This is the ultimate failure
of the WF composite.
In Table 2, 1 x is the failure strain of the plain weave
fabric laminates made of twisted yarns during tensile
loading along warp or ®ll directions. As the angle of
twist of the yarn increases, the ultimate failure strength
and the ultimate failure strain decrease. This is because
of the higher pre-strain within the yarn as the twist
angle increases. This can be seen from Table 1. The
ultimate strength and ultimate strain predictions for C2
are higher than for C1. This is because of the bridging effect
in the case of C2. The weaker gap regions of one layer are
bridged by the stronger interlacing regions of the adjacent
layer for C2.
For twist angles of the yarn, say up to 58, the variation in
ultimate strength and ultimate strain values is not signi®cant
compared to those of corresponding straight strand. Since
twisting of E-glass yarns is an engineering requirement for
facilitating ease of preform fabrication, the yarns can be
twisted optimally without reducing the strength values
signi®cantly.
Because of higher h/a ratio in the case of plain weave
fabric composites made of twisted yarns, the strength properties are lower compared to the WF composites with
lower h/a ratio and cross-ply laminates [23]. From Figs.
11 and 12, it can be seen that the stress±strain behaviour
is nearly identical for different angles of twist.
Predicted strength properties using the non-linear analysis are presented in Table 3. As expected the ultimate
strength and ultimate strain are lower in this case compared
to the predictions based on linear analysis. This is because
of higher strain state within the sections.
The difference in behaviour between the predictions
using linear analysis and non-linear analysis is seen only
after pure matrix block failure. As indicated earlier, failure
of pure matrix block leads to the disintegration of WF
composites. Effectively, the corresponding stress can be
taken to be practical strength value for the WF composites.
From this point of view, both linear and non-linear analysis
give identical results.
7. Conclusions
A 2D analytical method is presented for the failure
behaviour of plain weave fabric composites made of twisted
yarns. The studies have been carried out under uni-axial
on-axis tensile loading. Twisting of yarns, especially for
E-glass composites, is an engineering requirement for
facilitating ease of preform fabrication. Based on this, the
following conclusions are derived:
Fig. 12. Stress±strain behaviour for plain weave fabric laminates made of
twisted yarns: E-glass/epoxy, con®guration C2, linear analysis.
1. The twisted yarn thickness-to-width ratio would be higher
compared to the straight strand thickness-to-width ratio.
2. The variation in tensile strength properties for plain
weave fabric composites as a result of twisting of yarns
is not signi®cant up to an optimum angle of twist.
707
3. E-glass yarns can be twisted up to 58 so as to facilitate
ease of preform fabrication without compromising on
the tensile strength properties of plain weave fabric
composites signi®cantly.
Acknowledgements
This work was supported by the Structures Panel,
Aeronautics Research and Development Board and ISROIIT(B) Space Technology Cell.
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