an experimental study of in-plane large shear deformation of woven fabric composite

COMPOSITES

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Composites Science and Technology 67 (2007) 252–261

SCIENCE ANDTECHNOLOGY

An experimental study of in-plane large shear deformationof woven fabric composite

B. Zhu a, T.X. Yu a,*, X.M. Tao b

a Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kongb Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received 10 June 2006; accepted 2 August 2006Available online 4 October 2006

Abstract

Textile composites used as structural components have attracted more and more attention due to their superior properties and effi-cient stamping operations. However, formability of textile composite sheets, restricted by failure mechanisms such as wrinkling, remainsas a crucial and challenging issue. Although in stamping of real parts, wrinkling depends on many factors, this paper mainly focuses onthe in-plane characterization of pure shear deformation and its contribution to wrinkling. A comprehensive experimental study on wovenfabric composites is presented. Modified picture frame tests were conducted up to wrinkling. The effect of test conditions was investi-gated, and the reduction of yarn width was found to be a key for wrinkling. The onset of wrinkling was determined by a densificationmethod and by a laser scanning technique. Moreover, the cross-sectional profiles of fabric samples during the test were traced, helping tobuild up a theoretical model of the composite sheets during their large shear deformation.� 2006 Elsevier Ltd. All rights reserved.

Keywords: A. Textile composites; B. Non-linear behavior; C. Buckling; Picture frame test

1. Introduction

Compared with traditional metals and laminated com-posites, textile composites have many advantages due totheir high specific stiffness, high strength, low weight, niceintegral performance, low thermal expansion and goodcorrosion resistance. Most important is that, textile com-posites are more flexible than metals and possess a highcapacity to conform to complicated contours; therefore,they are particularly suitable for manufacturing compo-nents with complex shape. Reductions in costs of materialforming can be achieved through highly efficient stampingoperations [1,2]. Stamping, which deforms a flat sheet intoa particular shape in a relatively high processing tempera-ture with a pair of punch and die, is a very cheap processwith a cycle of only seconds regardless of the size of theparts.

0266-3538/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compscitech.2006.08.011

* Corresponding author. Tel.: +852 2358 8652; fax: +852 2358 1543.E-mail address: [email protected] (T.X. Yu).

However, formability of textile composite sheet,restricted by corresponding failures especially wrinkling[3], is a crucial and challenging problem for stamping oper-ations. In-plane characterization experiments have con-firmed that wrinkling of the woven fabric will occur whenthe critical shear angle, named the ‘‘locking angle’’, betweenthe warp and weft yarns is reached. These wrinkles havepotential to induce numerous processing and strength prob-lems [4]. In the real stamping operations, due to the com-pression, compaction and friction, wrinkles usually occurwell before the locking angle is reached; however, the shearstill predominates the deformation mode of the material aswell as wrinkling, so a comprehensive study of the in-planeshear characteristic will benefit the further understanding ofthe formability of textile composite sheets under stamping.

Most of textile composites, currently used in structuralcomponents that have to carry substantial working loads,are woven composite sheets made from glass fiber or car-bon fiber. Because of this, woven fabric reinforced compos-ites have been more widely investigated in recent years.

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B. Zhu et al. / Composites Science and Technology 67 (2007) 252–261 253

2. Previous studies

The mechanical properties and deformation mecha-nisms of woven fabric composite have been experimentallyinvestigated and generally understood by a number ofresearchers through pure shear test approaches [5]. The‘‘picture frame’’ test (Fig. 1) is one of the fundamentalmethods to characterize the in-plane shear behaviour oftextile composites [6,7]. A square textile fabric is clampedinto a fixture with four arms connected by four hinges.Since the arms can rotate freely at the hinges, the anglebetween two groups of yarns varies, thus resulting in a pureshear deformation of the fabric under an external diagonaltensile load.

To normalize test data from different picture frame set-ups, Peng et al. [8] proposed a general formula through anenergy approach, which states that at the same shear angle,the consumed external energy in the same area of deformedregion is the same and equals to the work done by theexternal load:

Pp¼ L2

fabric=Lframe

l2fabric=lframe

ð1Þ

where P and p are diagonal tensile forces, respectively; L

and l are referred to Fig. 1. It should be noted that Eq.(1) is only valid under the same loading rate. In the caseof rate-dependent shear behaviour, a more general resultwas reported by McGuinness and Bradaigh [9].

Lussier and Chen [10] conducted a series of pure shearcharacterization experiments on plain woven composites.They analyzed the detailed stages that may occur duringthe large shear deformation, and made correspondingphysical explanations. The influence of temperature in therange from 20 to 190 �C on shear behaviour was also stud-ied. The distribution of temperature on the sample duringstamping was measured using a FLIR Systems infraredcamera. The tensile and shear properties were likewisestudied by other researchers [11,12].

In-plane shear deformation is limited by local wrinkling,when yarns reach the so-called ‘‘locking angle’’. This lock-ing angle has been experimentally measured and analyti-cally modelled by many researchers [13–15]. Prodromouand Chen [13] used a pin-joint model, namely, yarns arepinned together at points of intersection or joints, whilethe yarns are assumed to be longitudinally inextensible

Fig. 1. Set-up of picture frame test.

and transversely incompressible, free to rotate, but not totranslate. It is proposed that the minimum possible valuefor the locking angle occurs when the gap between yarnsreaches zero. According to a purely geometrical relation,the locking angle, hc, is given by

hc ¼ arcsinw

wþ g0

ð2Þ

where w is the yarn width, and g0 is the initial gap widthbetween yarns.

In order to evaluate the formability of various textilefabric preforms, Yu et al. [16] conducted characterizationexperiments. The conclusion shows that loading rate andprocessing time are significant for composites duringstamping, which was also studied by Wu et al. [17].

In the picture frame test, corner cut-off is typicallyneeded to allow rotation of the hinges and prevent immedi-ate wrinkling [18]. In order to eliminate the contributionfrom the marginal parts, yarns, which are not clamped intothe fixture in each part between all the crossovers, areremoved. However, when shear deformation becomes sig-nificantly large, the fabric composite may still interfere withthe fixture, as seen in Fig. 2. The two joints of the fixturepress the middle portion of the test sample, imposing anundesired lateral compressive load to the specimen andaccelerating the onset of wrinkling.

In this paper, a modified fixture was designed, so thatthe lateral pressure to specimen can be avoided, leadingto a more reliable and accurate characterization of mate-rial. To investigate the size effect, different samples weretested and the relevant influence is analysed.

It has been shown that the pin-joint model does nottruly represent the shear behavior of woven fabrics, andlateral compression to yarns, which is relevant to theboundary clamping condition in the picture frame test,affects the onset and evolution of wrinkles. These factorsshould be considered so as to establish a more precise wrin-kling criterion.

Fig. 2. Compression between fixture and fabric in a picture frame test.

254 B. Zhu et al. / Composites Science and Technology 67 (2007) 252–261

3. Modified picture frame test

3.1. Composite test sample

Plain-weave textile fabrics comprise continuous E-glassfilaments as the reinforcement and thermoplastic polypro-pylene filaments as the matrix. The volume fraction ofthe glass fiber is about 0.35. The fabric is made of twogroups of yarns initially orthogonal to each other. Theglass and polypropylene filaments are commingled togetherin the yarns at room temperature; therefore, the fabric itselfis a composite material. The material properties of glass fil-aments and polypropylene are given in Table 1. The aver-age geometric parameters of the specimen are shown inTable 2. Fig. 3 represents its structure and appearance.To minimize the marginal restriction and facilitate theclamping of fabric, moderate corner cut-off on the square

Table 1Properties of glass fibers and polypropylene

Property Polypropylene Glass type

E C S

Diameter (lm) 8–14 10Density (kg/m3) 900 2540 2490 2490Tensile modulus (GPa) 1–1.4 72.4 68.9 85.5Tensile strength (MPa) 25–38 3450 3160 4590Elongation (%) 300 1.8–3.2 4.8 5.7Coefficients of thermal

expansion (·10�6/�C)110 5.0 7.2 5.6

Thermal conductivity (W/m/�C) 0.2 1.3Specific heat (J/kg/K) 840 780 940Glass transition

temperature (�C)�20 to �5

Table 2Geometry of fabric and specimen

Property Fabric Specimen size

Large Small

Width of yarn (mm) 4.34 ± 0.39Gap between yarns (mm) 0.65 ± 0.38Maximum fabric thickness (mm) 1.34Off-angle 0� 0�Yarn number 27 · 27 17 · 17Side length (mm) 140 · 140 88 · 88

Fig. 3. Balanced pla

sample was still made, and yarns not clamped into the fix-ture were removed.

3.2. Loading fixture

A modified fixture was designed to implement in-planeshear test as shown in Fig. 4. Most features remain thesame as before except the two middle joints, deviated fromthe plane where the fabric is clamped, so that there will beno contact or no pressure imposed on to the fabric sampleduring its large shear deformation. As mentioned before,the middle joints of the old fixture are in the same planeof the fabric; while in the modified one, there is a gapbetween the joints and the arms which avoids the contactof screws and sample, thus the fixture can be sheared upto a collinear state. The improvement in the result of themodified fixture will be discussed in Section 4.2. A problemcaused is the moment to the fixture under non-collinearforces and the increase of friction within the fixture. How-ever, these effects may be neglected if the deviation of jointsis relatively small compared with the whole fixture whilstthe internal friction can be reduced by lubrication. Anothereffective way is to subtract empty fixture loading from thatwith clamped sample, excluding the influence on the mea-sured material’s behaviour due to the fixture itself.

The tensile machine used was Universal TestingMachine. The specification follows MTS SINTECH 10/DFrame. During the operation, displacement was controlledand the adopted crosshead speed varied from 10 mm/minto 500 mm/min. The load cell was 1 kN, and the toleranceis 0.005%. Force values were instantaneously recorded byTESTWORKS 4.

3.3. Test conditions

Different loading speeds were adopted as 10, 100, 200and 500 mm/min.

3.4. Test results

Based on the deformed configuration of the fixture, shearangle of the arms is calculated by the following formulae:

in woven fabric.

Fig. 4. Modified fixture of picture frame test: (a) the front view and (b) the side view.

Fig. 6. Photos taken during picture frame test.


c ¼ p2� h

cos h2¼

ffiffi2p

Lframeþd2�Lframe

(ð3Þ

where Lframe is the side length of the picture frame(Lframe = 180 mm for the frame used in our tests); d is thedisplacement of the crosshead; h and c are the current angleand shear angle of the arms, respectively.

Fig. 5 represents the results of the picture frame tests atroom temperature (20 �C) under different loading speeds.The overall deformation stiffness increases with the loadingspeed. In addition, photos were taken during the test, asshown in Fig. 6. It is obvious that during the large sheardeformation, the yarn width decreases under lateral com-pression, which offers more space for the material to besheared before wrinkling.

To correlate the shear angle with the occurrence of wrin-kling, the values of shear angle calculated from Eq. (3) arecompared with the measured ones from the large and smallfabrics, as shown in Fig. 7. The shear angle of the fabricdoes not follow Eq. (3) at large deformation. Instead, itgradually levels and will no longer increase after wrinkling.Further shear of the fixture only increases the wrinkling.

During small deformation, the shear angle of the fabricalmost remains the same as that of the fixture. The maxi-mum deviation in this stage is about 9.3%, which is causedby the errors in clamping and measurement. When the fix-ture’s displacement reaches about 90 mm, the increasing

-100

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90 100 110

Displacement (mm)

Load

(N

)

10mm/min 100mm/min200mm/min 500mm/min

Fig. 5. Picture frame test results at 20 �C under different loading speeds.

rate of the measured shear angle decreases compared withthe calculated one. Therefore, it may be estimated thatwrinkling occurs between a fixture’s displacement of80 mm and 100 mm.

In order to observe the wrinkling more distinctly, a nor-malized load vs. measured fabric shear angle curve is plot-ted in Fig. 8 according to Eq. (1). Initially, the shearstiffness remains small. Later, it increases rapidly after a

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80 90 100 110Displacement (mm)

She

ar a

ngle

(de

g.) calculated

measured (large)

measured (small)

Fig. 7. Comparison between calculated and measured shear angles.

0

100

200

300

400

500

600

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Measured shear angle (deg.)

Nor

mal

ized

load

(N

)

large sample

small sample

Fig. 8. Normalized picture frame test results at 20 �C under 10 mm/min.

Fig. 10. Photo taken at c = 32�.

Fig. 11. Photo taken at c = 50�.


certain shear angle, and such a turning point can beregarded as the locking shear angle as well as the onsetof wrinkling. Another conclusion can be drawn from Figs.7 and 8; that is, the test samples of different sizes havealmost identical normalized load before wrinkling, whichverifies Eq. (1), and the locking shear angles of two samplesare very close to each other.

4. Analysis of large shear deformation

4.1. Three stages during large shear deformation

At room temperature, measurement was taken to findthe relationship between the yarn width and shear angle.In Fig. 9, the calculated curve pertains to the rotation ofyarns without change of the clamping side length in the fix-ture, i.e.

w ¼ w0 cos c0 ð4Þ

where w0 is the initial yarn width and c 0 is the measuredshear angle of the fabric.

Fig. 9 shows that in the first stage when c 0 < 50�, the var-iation in the yarn width may be slightly different from theprediction of the simple theory. In this stage, the lateralpressure to the yarns is small and there are still gapsbetween them (Fig. 10). When the shear angle reachesabout 50�, the yarn width decreases more quickly, whichstands for the vanishing of gaps and a much larger lateralpressure to the yarn (Fig. 11). Further shear results in localwrinkling on the fabric whilst the yarn width keeps as aconstant.

Therefore, three typical stages can be identified duringthe large shear deformation of the woven composite sheets.

0

1

2

3

4

5

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Shear angle (deg.)

Yar

n w

idth

(m

m)

calculated measured

Fig. 9. Variation of yarn width during shear deformation.

For the current initial weave density of fabric, the stagescan be distinguished as follows:

1. Stage I (0 < c 0 < 50�): Two groups of yarns rotate withgaps between yarns;

2. Stage II (50� < c 0 < 60�): Yarns rotate without gapsunder larger lateral pressure;

3. Stage III (c 0 � 60�): Wrinkling due to the exhaustion ofyarns’ compressibility.

4.2. Onset of wrinkling

Based on the physical mechanism illustrated above, thepreviously calculated and measured shear angle curves onlyprovide an approximate range for the onset of wrinkling.In order to directly observe the wrinkling, the surface pro-file of the sample during the picture frame test was mea-sured using Reversa Laser Scanner (Fig. 12). At a certainshear angle, the joints of fixture were tightened by screws,so that the shear deformation on the fabric could be ‘‘fro-zen’’. After the scanner went through a 2-D horizontalregion, the height values on the surface points of the sam-ple were measured and recorded, thus a 3-D view of thesample surface could be displayed. The scanning regionwas 50 · 50 mm2; the step length was 0.1 mm; and theaccuracy of measured height was ±0.02 mm.

Fig. 12. Laser scanning technique: (a) equipment and (b) scanning.

Fig. 13. Surface profile of sample (a) c 0 = 0�; (b) c 0 � 20�; (c) c 0 � 40�; (d) c 0 � 55�; (e) c 0 � 58� and (f) c 0 � 59�.


Fig. 13 depicts the scanning results at discrete shearangles in the test in a 3-D view. The onset and aggravationof local wrinkling was observed. Fig. 14 shows the variationof the surface profile from the horizontal direction. It is seenmore distinctly that wrinkling occurs when the shear angleof fabric reaches about 58�, which agrees with the result

Fig. 14. View of surface profile from horizontal direction (a) c 0 � 55�; (b)c 0 � 58� and (c) c 0 � 59�.

observed from shear angle curves. This scanning methodcan not only detect wrinkling, but also measure the shapeof yarn surface before wrinkling, as well as the yarn widthand gaps between them. Those data are valuable for estab-lishing a theoretical model under large shear deformation.

An alternative method to determine the exact onset ofwrinkling is to find a densification point from the experi-mental load–displacement curve. Similar to the densifica-tion phenomenon of cellular materials under compression,wrinkling of a woven fabric can be regarded as the resultof an in-plane densification (i.e., a generalized densifica-tion), while both processes involve a sudden increase ofthe material stiffness. Based on this analogy, the onset ofwrinkling could be determined from the point of view ofthe efficiency in the external energy consumption by usingthe following formula [19]:

df ðsÞds¼

d

R s

0F ds

F

� �ds

¼ 0) sc ð5Þ

where F and s are the diagonal tensile force and the corre-

sponding displacement, respectively; and f ðsÞ ¼R s

0F ds

F is theconsumed external energy efficiency with respect to currentforce. Determined by Eq. (5), sc is the critical displacement,at which wrinkling occurs. The integration can be done

Fig. 16. Boundary bending effect in picture frame test.


numerically based on the experimental data of F vs. s. As amatter of fact, two extremums for the function f(s) wouldexist for the whole F–s curve. However, the first extremumis relevant to the gap-vanishing phenomenon, which alsoresults in a sudden increase of the shear stiffness; whilethe second one appears at the locking angle when wrinklingof the sample takes place. To determine the second one,when the displacement reached the first extremum, the cor-responding force and displacement are purposely re-set aszero. This will eliminate the gap-vanishing effect and re-fo-cus on the wrinkling behaviour in the later stage. Thus,based on the concept of in-plane densification, the onsetof wrinkling is shown in Fig. 15. Results indicate that wrin-kling occurs at a critical displacement of 93 mm for a largetest sample under a loading speed of 10 mm/min; at 95 mmfor a large sample under 500 mm/min; and at 92 mm for asmall sample under 10 mm/min. This again concludes thatloading speed and size effect do not significantly affect theonset of wrinkling.

From the critical displacement obtained, it is found thatthe locking shear angle of the fabric at the onset of wrin-kling is about 58�. In the old fixture test, wrinkling occursat about 50� of the shear angle. Considering 16% larger ofthe shear deformation, the modified fixture provides amuch better result. On the other hand, compared with36� for the current sample based on Eq. (2), the actualonset of wrinkling is much later in the picture frame test.This discrepancy is attributed to the fact that yarn widthreduces during shear deformation, and the onset of wrin-kling is greatly delayed as a result of the lateral compress-ibility of yarn. To establish a more precise critical conditionfor wrinkling, the reduction in the yarn width, togetherwith the variation of the gap width, will be analysed in Sec-tion 4.3.

4.3. Yarn width and gap width

It is noted that the variation of yarn width is closelyrelated to the boundary condition in the picture frame test.When the fabric sample is fixed on the fixture, the clampedpart cannot deform, while the central overlapped part, aswell as the free yarns, will experience shear deformation.Therefore, there is an angular discontinuity of fibers alongthe boundary of fixture, especially when the shear is large.

Fig. 15. Determination of onset of wrinkling by densification method.

Another boundary effect is that during the shear deforma-tion, fibers in a single yarn will slip among each other; how-ever, such slip is restricted by the friction between the twogroups of yarns in the overlapped region, then such a slipdelay will bend the relevant fibers in the free yarns. Thesetwo factors not only cause the phenomenon as seen inFig. 16, but also affect the yarn width.

Fig. 17 sketches how the yarn width is related to theboundary bending effect, where w0 is the initial yarn widththat remains constant inside the clamping arms. If the mar-ginal fibers kept straight during the test, the marginal freeyarn section would possess a shape of parallelogramABCD. The relative slip distance between fibers AD andBC would be D, while the yarn width would be w = w0 sinh.In fact, however, point C can only take a new position at C 0

with a smaller slip distance D 0, hence the actual yarn width

Fig. 17. Configuration of boundary bending and yarn width.

0

1

2

3

4

5

0 10 20 30 40 50 60 70

Shear angle (deg.)

Yar

n w

idth

(m

m)

theoretical measured_1

measured_2 measured_3

Fig. 18. Prediction of yarn width during picture frame test.

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60

Shear angle (deg.)

Gap

wid

th (

mm

)

theoretical measured

Fig. 19. Prediction of gap width during picture frame test.


is w 0 and BC must be bent. Consequently, there will also bea little inconsistency between the shear angles of fixture andfabric.

Since the shear deformation of fabric is delayed in com-parison with the situation of straight marginal fibers, froman energy point of view, the delayed energy transfers to thebending of the free fibers. Therefore, it is possible to inves-tigate the delay by equating the bending energy of the fiberswith the delaying shear energy.

To estimate the bending energy, the following assump-tions are made: (i) the fibers are regarded as elastic materialwith constant Young’s modulus, E, and cross-sectional sec-ond moment, I [20]; (ii) the shape of bent fiber BC is sinu-soidal as described by y ¼ a � l sin px

2l, where 2l is theprojection length of fiber on x axis; a is a non-dimensionalparameter; and OXY is the local coordinate; and (iii)CD and C0D are of the same length. Hence, the bendingenergy of a single fiber is

Eb ¼ 2

Z n=2

0

M2ðtÞ2EI

dt ð6Þ

where n is the total fiber length, and M(t) is the bendingmoment along the fiber:

MðxÞ ¼EI � ap2

4l sin px2l

1þ a2p2

4cos2 px

2l

� �32

ð7Þ

Therefore, the bending energy can be expressed as a func-tion of a:

EbðaÞ ¼ 2

Z l

0

M2ðxÞ2EI

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ a2p2

4cos2

px2l

r� dx

¼Z l

0

EI � a2p4

16l2 sin2 px2l

1þ a2p2

4cos2 px

2l

� �5=2� dx ð8Þ

Eq. (8) can be rewritten as a non-dimensional relationas:

Eb ¼p4

16�Z 1

0

a2 sin2 pt2

� �� dt

1þ a2p2

4cos2 pt

2

� �� 5=2ð9Þ

where non-dimensional parameter Eb ¼ EblEI . Eq. (9) may be

rewritten in a polynomial expression after curve fitting:

EbðaÞ � 0:086a4 � 0:212a3 þ 0:178a2 þ 0:014a ð10ÞOn the other hand, at a certain deformed state, follow-

ing relations hold:

2a ¼ w0 � wDh2¼ arcsin w0

w0� h

Dc2¼ arccos s�Dsþ180�

ffiffi2p

360� arccos sþ180�

ffiffi2p

360

Dh2¼ Dc

2

8>>>><>>>>:

ð11Þ

where s is the crosshead displacement in the situation ofstraight marginal fibers; Dc is the delayed shear angle;and Ds is the delayed crosshead displacement related toDc. Ds(s,a) can be numerically derived based on the rela-tionship above.

Finally, according to energy conservation, consideringF = dE/ds, we have

EdsðsÞ ¼ Edsðs� DsÞ þ EbðaÞ ) F ðsÞ

¼ f ðs; aÞ þ dEbðaÞda

� dads

ð12Þ

where F(s), f(s,a) are known and dEbðaÞda ¼

dEb

da � EIl . By solving

the differential Eq. (12), a(s) as well as w 0(c) can beobtained.

It is quite hard to accurately determine the materialproperty of yarn, EI, and the projection length of bent fiber,l; however, if it is assumed that the gaps between yarns van-ish at c = 50�, i.e., s � 80 mm, which can be obtained fromthe experimental measurement, the value of EI

l can be calcu-lated from Ebðs ¼ 80 mmÞ=Ebðs ¼ 80 mmÞ. Therefore, thedelayed crosshead displacement in the picture frame testcan be determined by the current crosshead displacement,and the result is expressed approximately as a piecewise fit-ted function:

DsðsÞ �0 ðs < 31Þ3:08 lnðs� 30Þ þ 0:37 ðs P 31Þ

ð13Þ

It indicates that before displacement reaches 30 mm, thedelay in shear angle is indistinct, even negligible, whichagrees with our observation.

From the delayed displacement function obtainedabove, the dependences of the yarn width and gap widthon the shear angle of the fabric are presented in Figs. 18and 19, respectively. Good agreement is achieved betweenthe predicted and measured results.

1

1.5

2

2.5

3

3.5

0 10 20 30 40 50 60 70Shear angle (deg.)

Nor

mal

ized

val

ue

yarn thinkness

cross-sectional area

Fig. 21. Normalized variation of yarn thickness and yarn cross-sectionalarea.


4.4. Yarn cross-section during large shear deformation

Shear stiffness and wrinkling of the sample are closelyrelated to the interaction between the two groups of yarns,such as the lateral compression to yarns and rotary frictionat the joint regions. Hence, in order to build up a detailedmodel for large shear and to understand the mechanism ofwrinkling, a key issue is to know the variation of yarncross-section during the test.

To observe the cross-section of yarns, first, before theshear test, one group of yarns in the fabric was dyed blackto distinguish from the other group. Then, the whole fabricwas solidified, using epoxy curing agent, at different shearstages in a picture frame test. Later, the sample was cutperpendicularly to the yarn direction. Finally, the cross-section of yarn was captured by a digital camera.

As shown in Fig. 20, the profile of yarn cross-sectionremains an olive-shape during the whole shear deformation.The width reduces gradually under the lateral compression,as mentioned before, with a little increase in the thickness.The nominal yarn thickness and cross-sectional area mea-sured from the photos are plotted in Fig. 21. When sheardeformation is small, a notable increase in the yarn thick-ness occurs accompanied by a minor decrease in thecross-sectional area, which indicates a relatively small com-pression; at a large shear deformation, the yarn thicknessremains constant whilst the cross-sectional area is muchreduced, resulted from a large compression. Through theshear process, not only the gaps between yarns reduce,but the gaps inside a yarn, so-called inter-fibre spacing, alsoshrink. The interesting thing is that in the first stage, it is theouter gaps that mostly reduce; while in the second stageafter the elimination of the outer gaps, the inter-fibre gapsbegin to shrink greatly. In this sense, the two kinds of gapsdominate the two shear stages, respectively.

Moreover, Fig. 20 exhibits the change of the contactregion between the upper and lower yarns, which affectsthe rotary friction at the joints of yarns and hence the shearstiffness of the sample. As revealed in Fig. 20e, there is anangle between the lower boundaries of neighbouring yarns.In other words, the yarn width reduction is restricted bywrinkling, i.e., after the width has been reduced to a certainlimit, the fabric cannot be further deformed within the ori-ginal plane, but buckles out of the plane. Analysis of thesetwo different deformation modes will lay a basis for a the-oretical model of woven composite sheets under large sheardeformation up to wrinkling.

Fig. 20. Cross-section of yarn at different shear angles (a) c =

5. Concluding remarks

Wrinkling acts as a predominate factor in the stampingoperation of woven textile composites. The present studyfocuses on the experiment and characterization of in-planelarge shear deformation on the composite fabric, and mainlyanalyse the large shear deformation close to the lockingangle as well as its contribution to wrinkling. Experimentalset-up, named ‘‘picture frame test’’, was again employed butwith a new modification, obtaining more accurate and reli-able results. Geometrical parameters of the fabric during thelarge shear deformation, as well as the onset of wrinkling,were determined. Differences between a simple model usedin previous papers and our observations are identified, withthe causes being analysed quantitatively. Through a semi-theoretical simulation, the variation of the yarn width ismodelled, which agrees well with the measured value. Basedon the observation of yarn cross-section, the mechanism ofwrinkling behaviour was further investigated.

As for the further studies on the topic, a more precise the-oretical model is now under construction based on the wrin-kling mechanism described in the present paper. Meanwhile,the material behaviour under higher temperatures will beinvestigated. Besides, other factors related to wrinkling inthe real stamping operations, such as composite-tool/mouldfriction, compression along yarns, normal pressure to thematerial, and so on, are under research to provide a moregeneral understanding of the wrinkling phenomenon.

Acknowledgements

The work reported in this paper is a part of a HongKong RGC project HKUST6012/02E. The financial

0�; (b) c = 20�; (c) c = 40�; (d) c = 60� and (e) winkling.


support from Hong Kong Research Grant Council (RGC)is gratefully acknowledged. The authors would also like toacknowledge the Benchmark group led by Prof. J. Cao ofNorthwestern University, USA, for supplying compositefabric.

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an experimental study of in-plane large shear deformation of woven fabric composite

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