JCOMA 635

Composites: Part A 31 (2000) 299–308

www.elsevier.com/locate/compositesa

Shear deformation and micromechanics of woven fabrics

U. Mohammed, C. Lekakou*, L. Dong, M.G. Bader
School of Mechanical and Materials Engineering, University of Surrey, Guildford, Surrey GU2 5XH, UK
Received 11 December 1998; received in revised form 1 September 1999; accepted 13 September 1999

Abstract
This paper includes an experimental study and a mathematical analysis of the shear deformation of woven fabrics by using picture-frame
type shear testing. Four types of weaves were tested and compared: a loose plain weave, a tight plain weave, a twill and a satin weave. The
locking shear angle was determined both in picture-frame tests and manual shear tests. The experimental data presented for each fabric
include curves of shear load–shear stress as a function of either the shear angle or the shear rate, and measured locking shear angles. The
shear deformation data were analysed by following elasticity principles and taking into account the effects of fibre inextensibility. A
microstructural analysis was carried out in all four fabrics to investigate the shear locking on the basis of a geometrical approach and the
maximum packing fibre fraction. q 2000 Elsevier Science Ltd. All rights reserved.
Keywords: A. Fabrics; Shear; B. Elasticity; C. Micromechanics

1. Introduction perfect shear testing equipment. As a result, most of the

proposed methods are only suitable for low shear angles.
Woven fabrics have been used in the production of An early test adopted in the textile industry is the Kawabata
composite products due to ease of handling, the variety of evaluation system for fabrics (KES-F) [2–5] in which a
woven patterns available and the relative stability of their sample of fabric, usually 200 × 50 mm; is clamped along
pattern and shape during lay up. In the manufacture of the two opposite long edges and is sheared by moving one
components of complex shape, the fabrics are draped onto of the clamped edges at a constant speed (see Fig. 1(a)).
a mould surface of varying geometric complexity resulting During shear the clamped edges are kept apart by a tension,
in changes in the fibre orientation, local fibre fraction and usually of 10 N/m width, applied on the fabric. This type of
porosity. This leads to variations of the local permeability test is similar to a type of manual shear testing which is
throughout the fabric, which will affect resin infiltration, as usually applied to determine manually the ‘locking shear
well as to inhomogeneities in the mechanical properties of angle’ of fabrics [6].
the composite product. Hu and Zhang [3] analysed the stresses developed in a
Shearing of fabrics is a major deformation mode during KES test and concluded that, due to the presence of corners
draping [1]. This involves mainly in-plane rotation of the and the presence of both tensile and shear stresses, the speci-
fibre bundles at the cross-overs of the weave, but also fibre men is not subjected to pure and uniform shear. A finite
slip and fibre buckling. Good draping involves the fitting of element analysis yielded a distribution of shear stress
a fabric over a surface without wrinkling and tearing. along the clamping direction, where the shear stress varied
Wrinkling is attributed to buckling of the fibre bundles from zero at the corners to a maximum in the middle of the
and occurs when the fabric is sheared locally past a limit specimen. This was compared to the conventional shear test
angle defined as the ‘locking angle’ of the fabric. for a stiff material, which involved the application of torque
There has been a considerable amount of work in the area on a cylindrical specimen, resulting in a pure shear mode of
of textiles to develop prototype tests and apparatus for the deformation.
determination of the shear properties of fabrics. Buckling of The second type of shear test for textiles is the FAST test
fabrics during shear has been a major problem in designing [7–11] (see Fig. 1(b)) which employs the bias extension
principle for measuring shear. The principle is also used
* Corresponding author. Tel.: 11-483-300-800 ext. 2411; fax: 11-483-
to derive the in-plane shear response of ^45 laminates in
259-508. polymer composites [12]. However, when this test is applied
E-mail address: c.lekakou@surrey.ac.uk (C. Lekakou). to fabrics or composites under processing conditions,
1359-835X/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved.
PII: S1359-835 X( 99)00 081-0
300 U. Mohammed et al. / Composites: Part A 31 (2000) 299–308

Fig. 1. (a) KES-F shear test; (b) FAST shear test; and (c) picture frame shear test.

shearing is non-uniform throughout the specimen due to the satin weave. In each case, shear curves are presented and
distortion of width uniformity [13]. analysed. A material model including theory of elasticity
Another type of proposed shear test for fabrics involves and the effects of fibre inextensibility is applied to the
the shearing of a fabric specimen, usually 200 × 200 mm; analysis of shear data. Data of locking shear angle for all
held within a picture hinged frame [13–16] (see Fig. 1(c)). the weaves are presented from both manual shear tests and
Two diagonally opposite corners of the picture frame are the picture frame experiments. With the aid of micro-
pulled apart at a constant rate in a tensile testing machine. If structural analysis, a geometrical analysis of the shear of
it is assumed that the fabric is inextensible in the two fibre the unit cell of each weave is carried out, aiming at predict-
directions, there is only in-plane shear before wrinkling ing the shear-locking angle. The predictions are then
starts. It has been suggested [16] not to clamp individual compared with the experimental data.
fibre bundles in the frame but to let their ends rotate freely;
otherwise it has been observed [16] that fibres bend
severely, slip out of the clamping frame or stretch to form
2. Materials
an S during deformation.
The elastic behaviour model is often used to describe the Four E-glass woven fabrics were tested: a loose plain
shear deformation of fabrics before wrinkling. Many inves- weave (LPW), a tight plain weave (TPW), a twill weave
tigators use the shear tests to calculate the shear rigidity of
the fabric [4,9,14,17]. The shear modulus of fabrics calcu-
lated from such tests has been used as input data for finite
element, elastic solid mechanics simulations of draping
[18,19]. The elasticity theory has also been adopted in
micromechanical analyses [20,21].
The purpose of this study is to present shear deformation
data of fabrics from picture frame experiments for different
types of weaves, namely two plain weaves, a twill and a

Table 1
Specifications of the tested woven fabrics

Weave type LPW TPW TWILL 5HSW

Coding Basket weave Y0212 Y0185 Y0227

Thickness (mm) 0.58 0.48 0.28 0.23

Areal density (kg m 22) 0.529 0.546 0.331 0.297
Ends/10 mm 1.1 6.7 11.8 22.4
Picks/10 mm 1.2 6.3 11.8 21.3
Fig. 2. Set up of the picture frame shear testing as carried out in this study.
 U. Mohammed et al. / Composites: Part A 31 (2000) 299–308 301

each fabric specimen an orthogonal grid of 20 × 20 was

marked with a marker pen. The picture frame was mounted
onto a LLoyd Instruments T30K tensile testing machine,
with a 5 kN load cell, and held in orthogonal shape (see
Fig. 2). The fabric was placed on the pins of the frame
arms, where each arm had 20 homogeneously distributed
thin pins. The fabric was held on the frame in such a way
as to allow rotation of the fibre bundles around the pins.
[16]. The testing machine was then set in tensile mode at
a constant crosshead speed. Various crosshead speeds were
Fig. 3. Geometrical analysis of the picture frame. tried in the range of 5–100 mm/min.
The fabric deformation was followed during the test both
visually and via a digital camera which could take photo-
(TWILL) and a 5 harness satin weave (5HSW), supplied by graphs at regular intervals as frequently as every 3 s. The
Fothergill Engineered Fabrics Ltd. Table 1 presents the purpose of this was to identify the moment when the first
features of the tested fabrics. All four fabrics might be wrinkles would appear in order to determine the shear-
considered approximately isotropic in the two in-plane locking angle. The shear-locking angle was also determined
directions. by shearing a fabric specimen manually until wrinkling
appeared.
Fig. 3 illustrates the geometry of the picture frame experi-
3. Experimental procedures and analysis of the shear ment. The LLoyd Instruments machine in tensile mode
test measures the tensile force, Fx, and the extension, 2Dl. The
tensile force can be translated into shear components, Fs by
The picture-frame type of shear test (Fig. 1(c)) has been the relation
employed in this study. An orthorhombic frame of 200 ×
200 mm was constructed with freely movable arms [16]. On Fs ˆ Fx =2 cos a=2† 1†
Assuming that the thickness, H, of the fabric does not
change during shear before wrinkling occurs and the shear
stress t s is homogeneous, then before the locking shear
angle has been reached
ts ˆ Fs = LH† 2†
From the geometry of Fig. 3, it follows:
H1 ˆ h1 1 Dl 3†
and
L cos p=4† 1 Dl
cos a=2† ˆ 4†
L
The shear angle, g (see Fig. 3), is expressed as
g ˆ p=2 2 a 5†
and the rate of change of shear angle is given by the relation
dg d Dl†
ˆ 2‰L sin p=4 2 g=2†Š21 6†
dt dt
where dg=dt is in rad/s and d 2Dl†=dt is the crosshead speed
of the tensile testing machine.

4. Shear test results

Figs. 4(a)–7(a) present the results of the shear tests in the

form of applied Instron load versus shear angle, g (as
defined in Section 3), for the LPW, the TPW, the twill and
Fig. 4. Shear test curves for the loose plain weave fabric (LPW) at different the satin, respectively, at different crosshead speeds of the
crosshead speeds of the tensile testing machine. tensile testing machine, namely 5, 10, 50 and 100 mm/min.
302 U. Mohammed et al. / Composites: Part A 31 (2000) 299–308

Fig. 6. Shear test curves for the twill fabric (TWILL) at different crosshead
speeds of the tensile testing machine.
Fig. 5. Shear test curves for the tight plain weave fabric (TPW) at different
crosshead speeds of the tensile testing machine.
fabrics at a crosshead speed of 5 mm/min. As can be seen
The effect of the crosshead speed on the two plain weaves the satin weave is easily deformed with minimum amount of
(Figs. 4(a) and 5(a)) may be considered to be small, within shear, as expected. The LPW displays a little higher initial
the experimental error of the testing. The effect of the cross- rigidity due to the regular yarn crossovers, but can reach
head speed is more pronounced on the twill and the satin large deformations without excessive shear energy require-
weave (Figs. 6(a) and 7(a)), although no consistent trend of ments due its large open pores and the absence of shear
the load with the crosshead speed is obvious for the range of locking. The TPW is the most difficult to deform in shear
crosshead speeds used. It must be mentioned that the twill and is associated with early wrinkling.
and satin weaves were very difficult to handle and lay on the Table 2 presents the data of the shear-locking angle from
picture frame, which must have increased the experimental both the picture frame shear test and the manual shear test.
error and might account for the observed differences in the The agreement between the two tests for the TPW, the twill
above load-deformation curves. Inconsistent trends in the and the satin weave is very good. In the case of the LPW the
load-deformation curves at different crosshead speeds of shear-locking angle in the picture frame test is larger by 78
the tensile testing machine were also observed in some of than that from the manual shear test (without smoothing).
the data of McGuinness and O’Bradaigh [16]. Figs. 4(b)– This is probably due to the pronounced difference between
7(b) present the results of the shear tests in the form of the free rotation of the bundles at the pins in the picture
applied total load, Fx, versus rate of shear, determined by frame, and possibly even slip, and the firm clamping of
Eq. (6). In this case, there is a clear trend where the shear the two opposite edges of fabric in the manual test. It
curves move to the right, i.e. to higher shear rates, as the seems that this difference was enlarged due to the looseness
crosshead speed increases for all tested fabrics. of the weave.
The load data were translated into mean shear stress However, during the manual shear test experiments it was
values along the fibre direction and Fig. 8 displays shear realised that it was possible to achieve much higher shear-
stress versus shear angle curves for the four tested woven locking angles if the wrinkles were smoothed out. So
 U. Mohammed et al. / Composites: Part A 31 (2000) 299–308 303

illustrated in Fig. 8, is considered to be represented by

non-linear elastic mechanical behaviour, polynomial curve
fitting has been used in the regression analysis of the
experimental points for each fabric, namely:
LPW: basket weave
ts ˆ 0:1241g3 1 622:71g 7†
TPW:
ts ˆ 0:0028g5 2 2:7694g3 1 2588:1g 8†
TWILL:
ts ˆ 0:587g3 1 569:23g 9†
5HSW:
ts ˆ 0:4718g3 1 115:43g 10†
All polynomial shear curves described by relations (7)–
(10) are symmetric about the origin. t s represents a measure
of shear stress along the directions of the fibres in the fabric
which are non-orthogonal during shear. However, it is
possible to assume that the fibre directions are approxi-
mately orthogonal at small shear strains, 1 12, and determine
an initial, Secant, in-plane, shear modulus, E12, for each
fabric at 112 ˆ 1% :
LPW: E12 ˆ 35 kPa;
TLW: E12 ˆ 148 kPa;
Fig. 7. Shear test curves for the 5 harness satin weave fabric (5HSW) at TWILL: E12 ˆ 32 kPa; and
different crosshead speeds of the tensile testing machine. 5HSW: E12 ˆ 6:6 kPa:
For higher shear strains a mathematical analysis on the
manual smoothing was applied, the level of which must
basis of elasticity theory follows. In this analysis, x denotes
have been subjective, and the results are also presented in
position in a fixed, Eulerian, orthogonal frame of reference
Table 2. Smoothing must be associated with fabric stretch-
and X denotes position in an embedded material, orthogonal
ing and fibre slipping. In the diaphragm forming [22–23] of
frame following the material deformation. The deformation
fibre reinforced thermoplastics, the rubber diaphragm plays
gradient tensor is given by
an equivalent role in the elimination of wrinkles by exerting
membrane tensile stresses. 2X
Fˆ 11†
2x
5. Elasticity analysis of the shear deformation of fabrics where from the picture-frame experiment
x1 ˆ cos g=2†X1 1 sin g=2†X2 12†
If the response of the fabrics in shear deformation,
x2 ˆ sin g=2†X1 1 cos g=2†X2 13†
The strain tensor 1 is then given by
1ˆ 1
2 I 2 FT F† 14†
where I is the unit tensor (whose diagonal elements are unity
and non-diagonal elements are zero) and F T is the transpose
of matrix F. Relation (14) can be written in two dimensional
form as follows:
" # " #
111 112 1 1 2 sec g sec g tan g
2
ˆ 15†
121 122 2 sec g tan g 1 2 sec2 g
Fig. 8. A comparison of the shear behaviour of the four tested woven
fabrics. The Cauchy stress tensor s associated with the fixed
304 U. Mohammed et al. / Composites: Part A 31 (2000) 299–308

Table 2
Values of the maximum shear angle above which wrinkling appears

Fabric Picture-frame test (8) Manual test (8) Manual test 1 smoothing (8)

Basket weave (LPW) 61 54 70

Tight plain weave (TPW) 10 9 38
Twill weave (TWILL) 25 24 40
Satin weave (5HSW) 26 25 45

frame of reference x is then given by the equation (basket weave), and for the satin (5HSW) and twill (TWILL)
X weaves up to g ˆ 258: The analysis was not applied to the
s ˆ 2pI 1 2E1 1 Ti Fii ^ Fii 16†
TPW, because it wrinkled very early at g ˆ 108:
where p is an arbitrary hydrostatic pressure to satisfy the The measured shear stress, t s, in Fig. 8 has been analysed
incompressibility constraint, E is the modulus matrix and into the orthogonal components of the Cauchy stress tensor
the last term in Eq. (16) denotes the yarn extensibility limit s11 ˆ s22 ˆ ts sin g=2† 21†
in the fibre directions Fii. Qiu and Pence [24] wrote the last
term with the aid of a standard reinforcing model as s12 ˆ s21 ˆ ts cos g=2† 22†
X 0
s ˆ 2pI 1 2E1 1 ti f C11 †Fii ^ Fii 17† where each fabric is considered symmetric and balanced in
the two in-plane directions.
where ti is a material parameter for each fibre direction ti ˆ
By also taking into account Eqs. (15)–(20) and the
0 corresponds to neo-Hookean material response and
geometry of the picture-frame experiment in Fig. 3, it
ti ! / corresponds to totally inextensible fibre yarns)
follows:
and (C11) 1/2 is the stretch in the fibre direction Fii and an
element of the matrix C: f 0 C11 † ˆ f 0 C22 † ˆ sec4 g 1 sin2 g sec4 g 2 1 23†
C ˆ FT F 18† " #
X 1 sin g
0
f (C11) is the first derivative of f(C11) where from the Fii × Fii ˆ 24†
sin g 1
standard reinforcing model [24]
f C11 † ˆ 1
2 C11 2 1†2 19† s12 ˆ s21 ˆ E12 sec g tan g 1 t sin g
and  sec4 g 1 sin2 g sec4 g 2 1† ˆ f 12 g† 25†
f 0 C11 † ˆ C11 2 1† 20† and
Eqs. (11)–(20) have been used for the analysis of the s11 ˆ s22 ˆ E11 1 2 sec2 g†
experimental data of Fig. 8. The analysis has been applied
before the limit of shear locking and wrinkling of fabric. 1 ti sec4 g 1 sin2 g sec4 g 2 1† ˆ f 11 g† 26†
Since, according to Table 2 and Fig. 8, the LPW, did not
wrinkle within the range of experimental data presented in A regression analysis was carried out to determine E11,
Fig. 8 whereas the satin (5HSW) and twill (TWILL) weaves E12 and ti from the data of s 12 and s 11 as functions of g . Fig.
wrinkled around a shear angle, g , of 258, the theoretical 9 demonstrates the applied linear data fitting when s 12 is
analysis was applied to the whole data range for the LPW plotted against the function f12(g ) for the LPW (basket
weave), twill (TWILL) and satin (5HSW). Table 3 presents
the determined values for the moduli and the material para-
meter ti from the regression analysis of the experimental
data for the three investigated fabrics. Figs. 10–12 illustrate
the agreement between the experimental data (relations (21)

Table 3
Values for E11, E12 and ti determined from the regression analysis of the data
of shear deformation of a loose plain weave (LPW), a twill (TWILL) and a
5 harness satin (weave)

Fabric E11 (kPa) E12 (kPa) ti (kPa)

LPW 13 20 0.050
TWILL 35 31 17
Fig. 9. Fitting of the experimental shear data according to Eqs. (22) and (25) 5HSW 31 12 12
for the loose plain weave, the twill and the satin weave.
 U. Mohammed et al. / Composites: Part A 31 (2000) 299–308 305

bundles and the structure is compressed in-plane to the

maximum fibre fraction, sometimes also involving
compression of the bundles.
In plain weaves, it is assumed that the maximum shear
angle at shear locking is associated with the disappearance
of the macropores between fibre yarns. This is consistent
with the analysis of the shear locking effect in plain weaves
by Prodromou and Chen [15] although they defined and
considered slightly different geometric parameters from
Fig. 10. Experimental data and predictions of the shear stress (in-plane,
orthogonal directions) versus shear angle for the loose plain (basket) weave. the parameters of this study. Fig. 14 represents the basic
cell in a plain weave: parameters to be considered in this
study include the height, h, the dimensions of the original
and (22)) and the predictions (according to Eqs. (25) and macropore, w and t, and the yarn width, W. The shear-
(26) and the determined values in Table 3), when the shear locking angle is given by
stress s 12 is plotted against the shear angle.
g ˆ p=2 2 arcsin h=w† 2 arcsin h=t† 27†
The values of the determined parameters in Table 3 cover
a wide range of shear data up to fabric wrinkling and not just The aim is to minimise h at the maximum shear-locking
initial small strains covered by the Secant modulus at a angle.
strain of 1%. These constant values of Table 3 can then be Regarding the maximum shear angle at wrinkling for the
employed in the elasticity analysis for each fabric for large plain weaves in Table 2, it was observed that wrinkling in
strains before wrinkling. The non-linear nature of the the picture-frame test appeared before the macropores
experimental data and the predicted curves of the shear closed, something that was particularly obvious in the
stress s 12 versus shear angle in Figs. 10–12 is due mainly case of TPW. This fabric was particularly stiff to in-plane
to the change of the angle between the fibre directions shear due to strong “anchoring” of fibre yarns at the cross-
during shear. over points. For the plain weaves shear locking at micro-
structural level occurred in the manual shear test in which
the fabric was also stretched during manual smoothing.
6. Microstructural analysis of the shear locking effect According to the microstructural data, at the maximum
shear-locking angle measured by the manual shear test
The next step after investigating shear deformation of (with smoothing) for both tested plain weaves it is
fabrics in terms of mechanical testing is to study the wrink-
h=W ˆ 0:08 for LPW and TPW:
ling phenomenon. Wrinkling is associated with the level of
the compressive stresses which develop during the shearing The 5 harness satin and the twill weaves seemed to shear
of fabrics, the thickness of fabric, its stiffness and its micro- easily and it was considered that wrinkling in the picture-
structure. External tensile stresses during draping, as a result frame test was associated with shear locking at micro-
of manual smoothing of fabric for example, counteract the structural level. If wc and tc are the dimensions of the
compressive stresses and reduce wrinkling. unsheared unit cell of the satin weave, wctc changes during
At microstructural level, wrinkling of a fabric during shear (see Fig. 14(b)) due mainly to the compression of the
shear is associated with the maximum locking shear. fibre yarns by a maximum compression ratio CR ˆ 64%;
Fig. 13 illustrates the microstructural changes during shear according to the micrographs in Fig. 13. By assuming that
for the TPW, the 5-harness satin and the twill when each of the maximum packing fibre volume fraction in the locked
these fabrics is undergoing shear from the unsheared state to shear state is V f ;max ˆ 0:65
a maximum shear angle. The aim of this section is to devise
tan g ˆ f =g 28†
a procedure for the prediction of the locking shear angle. At
lock, it is considered that there are no macro-pores between where
g ˆ tc CR 29†

Vfo wc
f ˆ 2 wc 30†
Vf;max CR
where Vfo and Vf, max are the initial (unsheared state) and
maximum packing volume fractions, respectively, and CR
is the maximum compression ratio of the fibre yarn.
Relations (28)–(30) lead to the prediction of a locking
Fig. 11. Experimental data and predictions of the shear stress (in-plane, shear angle of 258 which agrees with the experimental data
orthogonal directions) versus shear angle for the twill weave. of Table 2 for 5HSW. If the same relations are applied to the
306 U. Mohammed et al. / Composites: Part A 31 (2000) 299–308

TWILL with CR ˆ 0:58 (see Fig. 13 and 14(b)) and

assumed V f ;max ˆ 0:63; a locking shear angle of 248 is
predicted which again agrees with the experimental data
of Table 2 for TWILL.

7. Conclusions

Fig. 12. Experimental data and predictions of the shear stress (in-plane, This paper included a study of the shear deformation of
orthogonal directions) versus shear angle for the satin weave. fabrics covering both mechanical and microstructural
aspects. Mechanical testing involved shear testing in

Fig. 13. Microstructural changes in fabrics during shear: (a) unsheared state; and (b) locking shear angle.
 U. Mohammed et al. / Composites: Part A 31 (2000) 299–308 307

and the twill reached intermediate shear-locking angles,

around 258. The TPW was the most difficult to shear and
wrinkled easily before it reached the shear-locking angle at
microstructural level. However, with manual smoothing of
fabric during shear it was possible to delay wrinkling to
higher shear angles for all fabrics.
A microstructural analysis was carried out with the aim of
investigating and predicting the shear locking effect at
microstructural level. In the case of plain weaves, shear
locking was concluded to occur when the in-plane macro-
pores between fibre yarns were reduced to a specified extent
in comparison with the bundle width. In the case of satin and
twill weaves, shear locking was concluded to occur when
the maximum packing fibre fraction was reached and after
the fibre yarns were compressed to an extent specified in the
microstructural analysis of each sheared fabric.

Fig. 14. (a) Basic cell in a plain weave as considered in the microstructural References
analysis of shear deformation. (b) Unit cell in unsheared and sheared state
as considered in the analysis of the shear locking effect for the satin weave [1] Potter KD. The influence of accurate stretch data for reinforcements
and the twill weave. on the production of complex structural mouldings. Composites
1970;10:161–7.
[2] Kawabata S. The standardisation and analysis of hand evaluation, 2.
picture-frame type of experiments. The non-linear curves of Japan: HESC, The Textile Machinery Society of Japan, 1980.
shear stress in the fibre direction versus shear angle were [3] Hu J-L, Zhang Y-T. The KES shear test for fabrics. Textile Research
fitted with polynomial functions which are symmetric about Journal 1997;67(9):654–64.
the origin. No clear trend has been concluded for the depen- [4] Yu JZ, Cai Z, Ko FK. Formability of textile preforms for composite
applications. Part 1: characterisation experiments. Composites
dence of the elastic shear deformation curves on the cross- Manufacturing 1994;5(2):113–22.
head speed of the tensile testing machine. On the contrary, [5] Kothari VK, Tandon SK. Shear behaviour of woven fabrics. Textile
when the mechanical testing data were plotted in the form of Research Journal 1989;March:142–50.
shear stress as a function of shear rate, there was an obvious [6] Andrews P, Paton R, Wang J. In: Scott ML, editor. The drape forming
and consistent trend in all fabrics for the viscous shear of a rudder tip preform, Proceedings of the ICCM-11, Gold Coast
Australia, IV. Melbourne: Australian Composites Structures Society,
curves to move to higher shear as the crosshead speed was 1997. p. 411–21.
increased. [7] Ly NG, Tester DH, Buckenham P, Rocznoik AF, Adriaanson AL,
A mathematical elasticity analysis was applied to the data Scaybrook F, De Jong S. Simple instruments for quality control by
of shear mechanical testing. The aim was to evaluate the finishers and taylors. Textile Research Journal 1991;61:402.
orthogonal, in-plane, shear and normal stresses as a function [8] Yick K-L, Chen KPS, Dhingra RC, How YL. Comparison of mechan-
ical properties of shirting materials measured on the KES-F and FAST
of shear angle when taking into account the effects of instruments. Textile Research Journal 1996;66(10):622–33.
changing fibre directions on the strain tensor and the effects [9] Buckenham P. Bias-extension measurements on woven fabrics.
of constraints in yarn extensibility. The modelling in combi- Journal of the Textile Institute 1997;88(1):33–40.
nation with data fitting yielded values for the moduli and the [10] Boisse P, Buet K, Gasser A, Hanklar S, Launay J. Biaxial mechanical
inextensibility parameter for the three types of weave (plain, behaviour of textile composite reinforcements. Mecanique
Industrielle et Materiaux 1997;50(3):140–4.
satin and twill) before wrinkling. From that it was concluded [11] Boisse P, Barr M. Experimental study of biaxial behaviour in fabrics
that the yarn inextensibility plays an important role in the Comptes Rendus de l Academie de Sciences, Serie II. Mecanique
elasticity analysis of the satin and twill fabrics. The shear Physique Chimie Astronomie 1996;323(8):503–9.
stress varies non-linearly with shear angle due mainly to the [12] ASTM D3518 Standard test method for in-plane shear response of
change of the angle between the fibre directions during polymer matrix composite materials by tensile test of a ^45 of
laminate, 1994;14.01:151–7.
shear and its effects on the values of orthogonal stress and [13] McGuinness GB, O’Bradaigh CM. Development of rheological
strain. models for forming flows and picture-frame shear testing of fabric
Relatively good agreement was reached between the reinforced thermoplastic sheets. Journal of Non-Newtonian Fluid
picture frame test and the manual shear test (without fabric Mechanics 1997;73:1–28.
smoothing) used in the determination of the maximum shear [14] Gelin JC, Cherouat A, Boisse P, Sabhi H. Manufacture of thin compo-
site structures by the RTM process: a numerical simulation of the
angle before wrinkling occurred in each fabric. The LPW shaping operation. Composites Science and Technology
was easily sheared without wrinkling. The five harness satin 1996;56:711–8.
weave had the lowest initial shear modulus. Both the satin [15] Prodromou AG, Chen J. On the relationship between shear angle and
308 U. Mohammed et al. / Composites: Part A 31 (2000) 299–308

wrinkling of textile composite preforms. Composites Part A predicted moduli and stresses in plain weave composites. Journal of
1997;28A:491–503. Composite Materials 1995;29(16):2134–59.
[16] McGuinness GB, O’Bradaigh CM. Characterisation of thermoplastic [21] Vandeurzen Ph, Ivens J, Verpoest I. A three-dimensional micro-
composite melts in rhombus-shear: the picture-frame experiment. mechanical analysis of woven fabric composites. II: elastic analysis.
Composites Part A 1998;29A:115–32. Composites Science and Technology 1996;56:1317–27.
[17] Potturi P, Atkinson J, Porat I. A robotic flexible test syetem (FTS) for [22] Delaloye S, Niedermeier M. Optimisation of the diaphragm forming
fabrics. Mechatronics 1995;5(2/3):245–78. process for continuous fibre-reinforced advanced thermoplastic
[18] Boisse P, Cherouat A, Gelin JC, Sabhi H. Experimental study and composites. Composites Manufacturing 1995;6(3/4):135–44.
finite element simulation of a glass fibre fabric shaping process. [23] O’Bradaigh CM, McGuinness GB, Pipes RB. Numerical analysis of
Polymer Composites 1995;16(1):83–95. stresses and deformations in composite materials sheet forming:
[19] Mohammed U, Lekakou C, Bader MG. In: Visconti IC, editor. central indentation of a circular sheet. Composites Manufacturing
Mathematical and experimental studies of the draping of woven 1993;4(2):67–83.
fabrics in resin transfer moulding (RTM), Proceedings of ECCM-8, [24] Qiu GY, Pence TJ. Remarks on the behaviour of simple directionally
2. Abington, UK: Woodhead, 1998. p. 683–90. reinforced incompressible non-linearly elastic solids. Journal of
[20] Chapman C, Whitcomb J. Effect of assumed tow architecture on Elasticity 1997;49:1–30.