Composites: Part B 45 (2013) 792–799

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Composites: Part B

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Description of draping behaviour of woven fabrics over single curvaturesby image processing and simulation techniques

Y. Abdin a, I. Taha b,⇑, A. El-Sabbagh c, S. Ebeid b

a The British University in Egypt, Mechanical Engineering Department, Cairo, Egyptb Ain Shams University, Faculty of Engineering, Cairo, Egyptc Clausthal University of Technology, Institute for Polymer Materials and Plastics Processing, Clausthal-Zellerfeld, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 14 March 2012Accepted 2 June 2012Available online 15 June 2012

Keywords:A. Fabrics/textilesA. PreformC. Finite element analysis (FEA)Draping behaviour

1359-8368/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.compositesb.2012.06.004

⇑ Corresponding author. Address: 1 El-Sarayat Str., ACairo, Egypt. Tel.: +20 18 9369100; fax: +20 2 24152

E-mail address: iman_taha@eng.asu.edu.eg (I. Tah

The use of natural fibres in polymer composite applications has gained great attention over the last dec-ade, due to weight, economic and environmental aspects. Processing textile reinforced composites in var-ious lay-up, resin infusion or compression moulding techniques requires good reproduction of mouldshape. Thus, this study is concerned with the analysis of deformation and draping behaviour of wovenfabrics over single curvatures. Experimental investigations of draping several jute and glass fibre wovenfabrics of varying densities over a standard circular disc have been performed. Draping behaviour wasanalysed using image processing techniques and MATLAB application. Further simulation of the drapingpatterns has been achieved using PamForm software. Good prediction of draping behaviour of woven tex-tiles is accessible, but requires a set of preliminary experiments to well characterise the fabric inquestion.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The use of woven fabrics in various orientation patterns plays avital role, especially in the field of polymer composite applications.Within this scope, the deformation (draping) behaviour of textilesover open or within closed moulds is vital for the guarantee of endproduct performance and aesthetics. Thus, the draping behaviourof textiles is considered as an important mechanical property thataffects the functionality of fabrics [1,2]. Drape has been recently de-fined as ‘‘the extent to which a fabric will deform when it is allowedto hang under its own weight’’ (BS 5058:1973; British StandardInstitute, 1974b) [1,2]. It is suggested that Fabric drape depends onfibre content and different physical, structural and mechanical prop-erties, in addition to the geometry over which it drapes.

In early literature, Peirce [6] regarded the bending behaviour offabrics as an indicator for its draping qualities. The bending length– defined as ‘‘the length of fabric which will bend under its ownweight to a definite extent’’ – is considered as the main parametercharacterising cloth drape behaviour. Thus, stiffer fabrics wouldtend to bend at a greater length, indicating their poor drapingbehaviour in 2D [7].

Chu et al. [4] distinguished draping from paperiness (paperbending behaviour) by accounting for 3D deformation behaviour

ll rights reserved.

bdou Pasha Square, Abbasia,991.a).

using a drapemeter that is capable of distorting fabric samples inall three dimensions over a circular disc. Providing an accurate ver-tical projection of the draped sample by optical means allowed thedetermination of the Drape Coefficient (DC), which they defined as‘‘the fraction of the area of the annular ring covered by the projec-tion of the draped sample’’. Hence, a high drape coefficient reflectspoor or little deformation.

The Cusick drapemeter [3,8] uses a similar principle, but pre-sented a much simpler apparatus and operating mechanism. Sampledimensions were found to influence the draping behaviour, whereCusick [9] reported that a standard 30 cm diameter sample was con-venient and that a suitable diameter for the disc was then 18 cm.

Over several years it was the main concern of drape researchersto accurately record the draped contour. From complex projectiontechniques [3,4,8] over to the use of photovoltaic cells [10] and‘‘cut-and-weigh’’ techniques, image analysis techniques [1,2,5]have definitely simplified investigations, providing higher accura-cies. most measuring methods produced similar results. However,image analysis techniques greatly reduced result dispersion as wellas measuring time [5].

2. Materials and methods

2.1. Materials

Five commercially available jute woven fabrics were suppliedby El-Manasra, Egypt. Two glass fibre woven fabrics were further

Table 1Woven fabric properties.

Materialtype

Fibrediameter(lm)

Yarncount(tex)

Arealdensity(g/m2)

Coverfactor

Tensilemodulus(MPa)

NF_192 1311 341 192 10.7 13.4NF_241 1368 372 241 11.5 20.9NF_250 1129 289 250 13.3 25.5NF_272 1333 311 272 17.0 27.5NF_616 2553 770 616 8.1 2.5GF_267 1250 123 267 13.0 240GF_611 2900 1188 611 20.4 260

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supplied by HP Textiles, Germany. The fabrics are all of the plainweave type and show measured variations in density and weavedimensions as listed in Table 1.

The cover factor is a textile property that indicates the extent towhich the area of the fabric is covered by one set of threads [11].The cover factor allows for comparison among textiles takinginto consideration not only their areal densities but also theirthickness and mesh tightness. The cover factor is calculated asCF ¼ threads=cm

10 �ffiffiffiffiffiffiffitexp

where the tex is the linear mass density ofthe fabric yarns in g/km.

2.2. Drape circular disc test

Circular samples of 30 cm diameter are placed over an 18 cmcircular disc. Samples are properly fixed by means of a protrudingpin in the centre of the disc. To further investigate the effect ofsample size on the draping behaviour, a second set of experimentsusing 36 cm diameter fabrics is performed.

Tests are performed on three different samples of each investi-gated woven fabric. Images of resolution 3264 � 2448 pixels arecaptured using a high definition CCD (Charge Coupled Device)camera as soon as the samples are clamped. The camera is fixedon a wooden frame at a distance of 450 mm from the sample sur-face. A background sheet is placed under the drapemeter to createa colour contrast for further image analysis and processing with anappropriate math processor (Matlab).

2.3. Image processing and analysis

Image processing operations performed using the MATLABAlgorithm, are described as follows: (1) reading and displaying

Fig. 1. Simulation using PamForm2G of (a) draping setup ov

the acquired Red Green Black (RGB) image (imread); (2) subtract-ing the background from the original image; (3) image binarisa-tion: converting the RGB (real colour) image into a binary image(im2bw) by using thresholding. A graythresholding function(graythresh) automatically computes an appropriate threshold touse in the conversion; (4) morphology: erosion followed by dila-tion (imclose) morphological closing done on the binary imageusing addition of structure square elements (SE) resulting inhomogeneous and continuous white area within the drape outline;(5) edge detection: detection of the edge of the drape outlinesilhouette using a gradient edge detection function (edge canny).This code is used for each sample tested, as well as for thereference disc image.

Following edge detection, the outline of the draped sample isanalysed into a number (n) of discrete points with definite positioncoordinates (xi, yi). The same is done for the detected edge of thereference disc. Results are applied for the determination of theundraped area as well as the area of the annular ring draped overthe disc.

2.4. Determination of drape outline parameters

The Drape Coefficient (DC) is calculated as DC ¼ A2�A1A0�A1

, where A0,A1, A2 denote undraped, circular disc, and draped sample areas,respectively.

In contrast, the Drape Distance Ratio (DDR) denotes the reduc-tion in the annular portion of the specimen due to draping and isdetermined by DDR ¼ R0�Ravg

R0�R1, where R0, R1, Ravg denote detected un-

draped sample, circular disc, and average drape outline radius,respectively.

The number of nodes (n) in the draped fabric is determined bycounting the number of folded apexes formed when hanged overthe disc. The Fold Depth Index (FDI) shows how sharp these nodesare. It is calculated according to the relation FDR ¼ Rmax�Rmin

R0�R1, where

Rmax and Rmin represent the maximum and minimum radii of thedrape outline.

2.5. Numerical techniques

Making use of the PamForm software, PamForm2G is a calcula-tion code that uses the Finite Element (FE) method [12]. Materialtype 140 is applied being generally used for composite materialssimulation comprising the extensible reinforcing fibre component,

er a circular disc and (b) drape circular disc attributes.

Table 2Summary of material input parameters.

Fixed parameters

Fs1 Fs2 l Fsm

0.0001 0.0001 0.1 0.0001

Fibre component variable parameters

Fabric type Thickness(mm) q E1(GPa) E2(GPa) Fb1 Fb2 Fbm

NF_192 0.8507 2.26E�07 0.0162 0.0134 0.4 0.4 0.04NF_241 0.72917 3.43E�07 0.0184 0.0288 0.04 0.04 0.04NF_250 0.7021 3.44E�07 0.0248 0.0255 0.065 0.065 0.065NF_272 0.74611 3.65E�07 0.0198 0.028 0.067 0.067 0.067NF_616 1.8 3.4E�07 0.0022 0.0249 0.03 0.025 0.03GF_267 0.382 6.67E�07 0.2509 0.227 0.032 0.032 0.032GF_611 0.81 7.63E�07 0.2502 0.265 0.09 0.09 0.09

Parent sheet variable parameters

Fabric type alock(deg) G(GPa) Glock(GPa)

NF_192 54 2.57E�05 3.71E�05NF_241 51.5 5.52E�05 6.33E�05NF_250 47 5.72E�05 9.6E�05NF_272 42.5 0.000102 0.000161NF_616 41 7.45E�05 0.000125GF_267 53.5 7.42E�05 8.52E�05GF_611 52 9.2E�05 0.000141

Fig. 2. Image processing operations. (a) Reading of experimental images, (b) background elimination, (c) binarisation and (d) morphology.

794 Y. Abdin et al. / Composites: Part B 45 (2013) 792–799

the matrix component, and the parent sheet component. The lattercomponent is merely a numerical fitting component used to over-come strong numerical instabilities that occur due to the highanisotropic behaviour of the materials.

Fig. 1a shows the simulation of the fabric draping over a circulardisc lying under the implicit gravity simulation mode within thesoftware. The circular disc (solid part) is drawn using SolidWorksCAD software and further imported in PamForm and further con-verted into meshes. The woven fabric is simulated as a meshed‘‘surface blank’’, for which the fabric properties are further definedin terms of tensile modulus, bending factor Fb, the out-of-planeshear factor Fs, the shear modulus G, and Poisson’s ratio m.

The bending factor represents the fabric bending resistance. Fol-lowing Vanclooster et al. [12] in assuming a negligible bending

resistance resulted into excessively large number of wrinkles, con-tradicting experimental observations. Instead, Fb was obtainedusing multiple trial-and-error runs to model the experimentalobservations. Investigating a diverse number of fabrics, however,resulted in the fact that there is a strong correlation (R2 = 0.9327)between the fitting Fb values and the experimentally achievedbending lengths c.

In contrast, for all fabrics under investigation, a ‘‘knock down’’value for Fs = 0.0001 is found applicable, based on the fact thatthe deformation mechanism of fabrics is only in-plane shear wherefabric out-of-plane shearing is negligible.

A Poisson’s ratio of m = 0.2 is adapted. The shear modulus is sup-plied in accordance with the advanced shear model approach,where the shear characteristics of the fabric are entered into the

Fig. 3. (a) Experimental and (b) simulated drape outline for (i) 30 cm and (ii) 36 cm sample size over an 18 cm drape disc.

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model in form of a continuous curve describing the shear moduluswith respect to various shear angles, providing a smooth and con-tinuous description of the shear behaviour over the completecourse of deformation. A drawback, however, remains the compli-cation of solution and the increase of computation time.

Generally, the material input parameters can be summarised inTable 2, describing the fixed, fibre component variable, and parentsheet variable parameters. Fbm and Fsm denote the out-of-planebending and shear factors of the matrix, respectively. l is the fric-tion coefficient characterizing friction behaviour between the tooland the blank [12].

Fig. 1b summarises the drape circular disc simulation attributesin PamForm2G, where contact 36 describes a user defined card,

allowing the simulation of large folds of fabric under deformationas observed during experimental investigation. This lies in contrastto insignificant amounts of deformation expected for reinforcedpolymer materials. The use of the contact 36 card prevents nodesto self-lock (crash), hence allowing the formation of folds.

3. Results and discussion

Fig. 2 shows the Image Processing operations performed usingthe MATLAB Algorithm, for the samples. The same procedure isalso applied on the naked circular disc.

Fig. 3i shows the obtained draping outlines for the natural andglass fibre fabrics under investigation. The radius of the disc R1, the

Fig. 4. Detected edges of (a) circular disc and (b) draped sample.

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radius of undraped sample Ro and the radius of the draped sampleoutline at a point i, R2(i) are calculated in pixel values from the de-tected outlines in Fig. 4. Here, a circle is fitted to both the disc anddraped fabric outlines, from which the position (xc, yc) of the out-line centres can be obtained. The radius of the circle fitted on thedetected edge of the disc is approximated as Ravg. The radius R2(i)

at a point (xi, yi) is calculated as R2ðiÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxi � xcÞ2þ

qðyi � ycÞ

2. Ravg

is then further calculated from the R2(i) matrix variable, where theaverage drape outline radius is Ravg ¼ ð1=nÞ

PðRiÞ .

3.1. Drape coefficient DC

DC calculation results as presented in Fig. 5, show an increase inDC with increased woven cover factor. Since high DC values reflectlower drapability, it can be concluded that deformation behaviourdecreases with increased cover factor as also observed by Joeng[13,14]. The only exception to the trend was found for the low den-sity glass fibre woven (GF_267) due to its very low thickness com-pared to the other fabric types.

Fig. 5. Draping coefficient against cover factor for 30 and 36 cm woven fabricsdraped over an 18 cm circular disc.

Both, the 30 and 36 cm samples show identical trends. How-ever, the 36 cm samples provide a lower DC value for all fabrics,which lies in agreement with observations published by Cusick[9] who reported that lower DC values are obtained with largerspecimen size.

The results can be well validated by the drape outlines shown inFig. 3, where the area inside the draped outline clearly increasesfrom NF_192 to NF_272. Moreover, it can be well observed thatthe high density NF_616 exhibited a smaller draping outline whichis only out-smalled by the GF_267. Finally, the high density GF_611exhibited a much larger area. Similar observations are made for the36 cm samples.

3.2. Drape distance ratio DDR

The Drape Distance Ratio (DDR) is an alternative for the DC[5,14–16]. The main advantage of this parameter is that, con-trary to the DC, the DDR increases with increased fabric draping,thus being consistent with intuition. Fig. 6 presents the DDR

Fig. 6. Drape distance ratio against cover factor for 30 and 36 cm woven fabricsdraped over an 18 cm circular disc.

Fig. 7. Number of nodes (a) in drape profile of 30 cm NF_241 sample and (b) plotted against cover factor for 30 and 36 cm woven fabrics draped over an 18 cm circular disc.

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values against the cover factor of the woven fabrics underinvestigation.

General trends indicate a decrease of the DDR with increas-ing CF. This reflects decreased draping at higher DC, as abovediscussed. The same deviation of the GF_267 woven is also ob-served in DDR calculations, where the GF_267 show large DDRdespite its high CF. It could also be noted that the 36 cm sam-ples have higher DDR values (and consequently) have im-proved drapability than the 30 cm samples, as also proven byDC results.

Fig. 8. Fold depth index against cover factor for 30 and 36 cm woven fabrics drapedover an 18 cm circular disc.

3.3. Number of nodes

A nodal graph, as illustrated in Fig. 7a is developed from the de-tected edge in Fig. 4. Here, the radius R2(i) at each point i of the out-

line is plotted against its corresponding angle h h ¼ tan�1 ðyi�ycÞðxi�xcÞ

� �� �.

The value of Ravg is plotted as a line in the nodal graph and the num-ber of nodes is determined as the number of peaks of the outlineabove Ravg.

Fig. 7b shows the number of nodes in relation to the cover fac-tor. The figure indicates no apparent trends between the number ofnodes and the cover factor. In general, as can also be depicted fromFig. 3, most profile outlines exhibited on average between four andfive folds. The high density GF_611 undergoes a much lower num-ber of folds due to its higher stiffness. Thus, it can be concludedthat the number of nodes cannot be used alone as a draping param-eter and must be combined with other parameters such as the folddepth index (FDI) or deviation from circularity.

3.4. Fold depth index (FDI)

FDI results plotted against the cover factor are presented inFig. 8. Trendlines indicate the decrease of FDI with increasing coverfactor, as also reported by literature [15,16]. This observation indi-cates increased node sharpness at higher cover factors. This is incomplete agreement with visual observation of the draping out-lines (Fig. 3). By comparison, for example, the NF_192 undergoesmuch sharper nodes compared to the GF_611 with a very regulardraping outline. The exception of the GF_267 is again observed inFDI results, where this woven shows very high values, supportedby its very irregular sharp nodal outline in Fig. 3. Generally, the36 cm samples show higher FDI values compared to the 30 cmsamples. This can be clearly seen in Fig. 3, where the 36 cmsamples result in very sharp outlines.

3.5. Numerical simulation

Fig. 9 shows a typical output of the simulation, where the blankhas been draped by gravity forces. The nodes forming the drapeoutline in Fig. 9a have been extracted into a separate object inFig. 9b.Exporting this outline in form of an ASCII file further allowsthe definition of position coordinates. The circular disc itself is sim-ilarly handled. The resulting position matrices are then used for thecalculations of the DC.

Fig. 3 presents a comparison of the experimental and simulateddrape outlines of both the 30 and 36 cm samples. It can be ob-served that simulation results generally predict larger areas withinthe draping outline than experimental results, thus resulting inslightly higher estimates for the draping coefficient as illustratedin Fig. 10a on the example of the 36 cm blank size.

Moreover, in contrast to experimental investigation, a much lar-ger number of folds is predicted, where each major fold included2–3 smaller folds. In comparison with the 30 cm samples, the sim-ulated 36 cm drape outlines are found less accurate. This leads tothe conclusion that accuracy tends to decrease with increasingblank size. This is conceivable based on the increase of the numberof mesh elements and hence the complexity of the model.

Observing the difference between the outlines of the easilydrapable NF_611 and GF_267 on the one hand and the stiffer

Fig. 9. Circular disc drape simulation output. (a) Blank after draping and (b) extracted drape outline.

Fig. 10. Comparison of DC values resulting from experimental and simulated data, for 36 cm sized samples (a) without and (b) with a correction factor of 0.85.

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GF_611 on the other hand, it can be concluded that the stiffer thematerial, the more accurate the predictions. This is also a reason-able conclusion that reflects the nature of the model equationswhich are based on the scaling of models based on conventionalmaterials (mainly metallic materials) to account for the non-line-arity of composite or textile materials.

The simulated drape outlines resulted in roughly 15% largerareas (and consequently higher DC values) compared to experi-ments. Therefore, results from the simulation could be scaled witha modification factor of 0.85, leading to satisfactory results for boththe 30 cm and 36 cm samples as shown in Fig. 10b.

4. Conclusions

Draping ability of wovens is found to improve with decreasedfabric cover factor. This is reflected in low DC and high DDR values.Although the current study evidences no clear relationship be-tween the cover factor and the number of folds created when fabricis draped, the depth of each fold, in terms of the FDI, is observed todecrease with increasing cover factor. Experimental observationscan be easily predicted with Fininte Element tools, as the

PamForm2G software, for example. However, good characterisa-tion of the fabrics in question are necessary.

Acknowledgements

This work was supported by the German Academic ExchangeOffice (DAAD) in Germany and the Science and TechnologyDevelopment Fund (STDF) in Egypt, within the framework of ajoint cooperation project.

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