- Email: [email protected]
Description of draping behaviour of woven fabrics over single curvatures by image processing and simulation techniques
Composites: Part B 45 (2013) 792–799
Contents lists available at SciVerse ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Description of draping behaviour of woven fabrics over single curvatures by 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, Egypt Ain Shams University, Faculty of Engineering, Cairo, Egypt c Clausthal University of Technology, Institute for Polymer Materials and Plastics Processing, Clausthal-Zellerfeld, Germany b
a r t i c l e
i n f o
Article history: Received 14 March 2012 Accepted 2 June 2012 Available online 15 June 2012 Keywords: A. Fabrics/textiles A. Preform C. Finite element analysis (FEA) Draping behaviour
a b s t r a c t The use of natural fibres in polymer composite applications has gained great attention over the last decade, due to weight, economic and environmental aspects. Processing textile reinforced composites in various lay-up, resin infusion or compression moulding techniques requires good reproduction of mould shape. Thus, this study is concerned with the analysis of deformation and draping behaviour of woven fabrics over single curvatures. Experimental investigations of draping several jute and glass fibre woven fabrics of varying densities over a standard circular disc have been performed. Draping behaviour was analysed using image processing techniques and MATLAB application. Further simulation of the draping patterns has been achieved using PamForm software. Good prediction of draping behaviour of woven textiles is accessible, but requires a set of preliminary experiments to well characterise the fabric in question. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The use of woven fabrics in various orientation patterns plays a vital role, especially in the field of polymer composite applications. Within this scope, the deformation (draping) behaviour of textiles over open or within closed moulds is vital for the guarantee of end product performance and aesthetics. Thus, the draping behaviour of textiles is considered as an important mechanical property that affects the functionality of fabrics [1,2]. Drape has been recently defined as ‘‘the extent to which a fabric will deform when it is allowed to hang under its own weight’’ (BS 5058:1973; British Standard Institute, 1974b) [1,2]. It is suggested that Fabric drape depends on fibre content and different physical, structural and mechanical properties, in addition to the geometry over which it drapes. In early literature, Peirce [6] regarded the bending behaviour of fabrics as an indicator for its draping qualities. The bending length – defined as ‘‘the length of fabric which will bend under its own weight to a definite extent’’ – is considered as the main parameter characterising cloth drape behaviour. Thus, stiffer fabrics would tend to bend at a greater length, indicating their poor draping behaviour in 2D [7]. Chu et al. [4] distinguished draping from paperiness (paper bending behaviour) by accounting for 3D deformation behaviour
using a drapemeter that is capable of distorting fabric samples in all three dimensions over a circular disc. Providing an accurate vertical projection of the draped sample by optical means allowed the determination of the Drape Coefficient (DC), which they defined as ‘‘the fraction of the area of the annular ring covered by the projection of the draped sample’’. Hence, a high drape coefficient reflects poor or little deformation. The Cusick drapemeter [3,8] uses a similar principle, but presented a much simpler apparatus and operating mechanism. Sample dimensions were found to influence the draping behaviour, where Cusick [9] reported that a standard 30 cm diameter sample was convenient and that a suitable diameter for the disc was then 18 cm. Over several years it was the main concern of drape researchers to accurately record the draped contour. From complex projection techniques [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 accuracies. most measuring methods produced similar results. However, image analysis techniques greatly reduced result dispersion as well as measuring time [5]. 2. Materials and methods 2.1. Materials
⇑ Corresponding author. Address: 1 El-Sarayat Str., Abdou Pasha Square, Abbasia, Cairo, Egypt. Tel.: +20 18 9369100; fax: +20 2 24152991. E-mail address: [email protected] (I. Taha). 1359-8368/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2012.06.004
Five commercially available jute woven fabrics were supplied by El-Manasra, Egypt. Two glass fibre woven fabrics were further
Y. Abdin et al. / Composites: Part B 45 (2013) 792–799 Table 1 Woven fabric properties. Material type
Fibre diameter (lm)
Yarn count (tex)
Areal density (g/m2)
Cover factor
Tensile modulus (MPa)
NF_192 NF_241 NF_250 NF_272 NF_616 GF_267 GF_611
1311 1368 1129 1333 2553 1250 2900
341 372 289 311 770 123 1188
192 241 250 272 616 267 611
10.7 11.5 13.3 17.0 8.1 13.0 20.4
13.4 20.9 25.5 27.5 2.5 240 260
supplied by HP Textiles, Germany. The fabrics are all of the plain weave type and show measured variations in density and weave dimensions as listed in Table 1. The cover factor is a textile property that indicates the extent to which the area of the fabric is covered by one set of threads [11]. The cover factor allows for comparison among textiles taking into consideration not only their areal densities but also their thickness and p mesh ffiffiffiffiffiffiffi tightness. The cover factor is calculated as CF ¼ threads=cm tex where the tex is the linear mass density of 10 the fabric yarns in g/km. 2.2. Drape circular disc test Circular samples of 30 cm diameter are placed over an 18 cm circular disc. Samples are properly fixed by means of a protruding pin in the centre of the disc. To further investigate the effect of sample size on the draping behaviour, a second set of experiments using 36 cm diameter fabrics is performed. Tests are performed on three different samples of each investigated woven fabric. Images of resolution 3264 2448 pixels are captured using a high definition CCD (Charge Coupled Device) camera as soon as the samples are clamped. The camera is fixed on a wooden frame at a distance of 450 mm from the sample surface. A background sheet is placed under the drapemeter to create a colour contrast for further image analysis and processing with an appropriate math processor (Matlab). 2.3. Image processing and analysis Image processing operations performed using the MATLAB Algorithm, are described as follows: (1) reading and displaying
793
the acquired Red Green Black (RGB) image (imread); (2) subtracting the background from the original image; (3) image binarisation: converting the RGB (real colour) image into a binary image (im2bw) by using thresholding. A graythresholding function (graythresh) automatically computes an appropriate threshold to use in the conversion; (4) morphology: erosion followed by dilation (imclose) morphological closing done on the binary image using addition of structure square elements (SE) resulting in homogeneous and continuous white area within the drape outline; (5) edge detection: detection of the edge of the drape outline silhouette using a gradient edge detection function (edge canny). This code is used for each sample tested, as well as for the reference disc image. Following edge detection, the outline of the draped sample is analysed into a number (n) of discrete points with definite position coordinates (xi, yi). The same is done for the detected edge of the reference disc. Results are applied for the determination of the undraped area as well as the area of the annular ring draped over the disc. 2.4. Determination of drape outline parameters A1 The Drape Coefficient (DC) is calculated as DC ¼ AA20 A , where A0, 1 A1, A2 denote undraped, circular disc, and draped sample areas, respectively. In contrast, the Drape Distance Ratio (DDR) denotes the reduction in the annular portion of the specimen due to draping and is R R determined by DDR ¼ R00 Rav1g , where R0, R1, Ravg denote detected undraped sample, circular disc, and average drape outline radius, respectively. The number of nodes (n) in the draped fabric is determined by counting the number of folded apexes formed when hanged over the disc. The Fold Depth Index (FDI) shows how sharp these nodes Rmin are. It is calculated according to the relation FDR ¼ Rmax , where R0 R1 Rmax and Rmin represent the maximum and minimum radii of the drape outline.
2.5. Numerical techniques Making use of the PamForm software, PamForm2G is a calculation code that uses the Finite Element (FE) method [12]. Material type 140 is applied being generally used for composite materials simulation comprising the extensible reinforcing fibre component,
Fig. 1. Simulation using PamForm2G of (a) draping setup over a circular disc and (b) drape circular disc attributes.
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Table 2 Summary 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 NF_241 NF_250 NF_272 NF_616 GF_267 GF_611
0.8507 0.72917 0.7021 0.74611 1.8 0.382 0.81
2.26E07 3.43E07 3.44E07 3.65E07 3.4E07 6.67E07 7.63E07
0.0162 0.0184 0.0248 0.0198 0.0022 0.2509 0.2502
0.0134 0.0288 0.0255 0.028 0.0249 0.227 0.265
0.4 0.04 0.065 0.067 0.03 0.032 0.09
0.4 0.04 0.065 0.067 0.025 0.032 0.09
0.04 0.04 0.065 0.067 0.03 0.032 0.09
Parent sheet variable parameters Fabric type
alock(deg)
G(GPa)
Glock(GPa)
NF_192 NF_241 NF_250 NF_272 NF_616 GF_267 GF_611
54 51.5 47 42.5 41 53.5 52
2.57E05 5.52E05 5.72E05 0.000102 7.45E05 7.42E05 9.2E05
3.71E05 6.33E05 9.6E05 0.000161 0.000125 8.52E05 0.000141
Fig. 2. Image processing operations. (a) Reading of experimental images, (b) background elimination, (c) binarisation and (d) morphology.
the matrix component, and the parent sheet component. The latter component is merely a numerical fitting component used to overcome strong numerical instabilities that occur due to the high anisotropic behaviour of the materials. Fig. 1a shows the simulation of the fabric draping over a circular disc lying under the implicit gravity simulation mode within the software. The circular disc (solid part) is drawn using SolidWorks CAD software and further imported in PamForm and further converted into meshes. The woven fabric is simulated as a meshed ‘‘surface blank’’, for which the fabric properties are further defined in terms of tensile modulus, bending factor Fb, the out-of-plane shear factor Fs, the shear modulus G, and Poisson’s ratio m. The bending factor represents the fabric bending resistance. Following Vanclooster et al. [12] in assuming a negligible bending
resistance resulted into excessively large number of wrinkles, contradicting experimental observations. Instead, Fb was obtained using multiple trial-and-error runs to model the experimental observations. 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 achieved bending lengths c. In contrast, for all fabrics under investigation, a ‘‘knock down’’ value for Fs = 0.0001 is found applicable, based on the fact that the deformation mechanism of fabrics is only in-plane shear where fabric out-of-plane shearing is negligible. A Poisson’s ratio of m = 0.2 is adapted. The shear modulus is supplied in accordance with the advanced shear model approach, where the shear characteristics of the fabric are entered into the
Y. Abdin et al. / Composites: Part B 45 (2013) 792–799
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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.
model in form of a continuous curve describing the shear modulus with respect to various shear angles, providing a smooth and continuous description of the shear behaviour over the complete course of deformation. A drawback, however, remains the complication of solution and the increase of computation time. Generally, the material input parameters can be summarised in Table 2, describing the fixed, fibre component variable, and parent sheet variable parameters. Fbm and Fsm denote the out-of-plane bending and shear factors of the matrix, respectively. l is the friction coefficient characterizing friction behaviour between the tool and the blank [12]. Fig. 1b summarises the drape circular disc simulation attributes in PamForm2G, where contact 36 describes a user defined card,
allowing the simulation of large folds of fabric under deformation as observed during experimental investigation. This lies in contrast to insignificant amounts of deformation expected for reinforced polymer materials. The use of the contact 36 card prevents nodes to self-lock (crash), hence allowing the formation of folds. 3. Results and discussion Fig. 2 shows the Image Processing operations performed using the MATLAB Algorithm, for the samples. The same procedure is also applied on the naked circular disc. Fig. 3i shows the obtained draping outlines for the natural and glass fibre fabrics under investigation. The radius of the disc R1, the
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Fig. 4. Detected edges of (a) circular disc and (b) draped sample.
radius of undraped sample Ro and the radius of the draped sample outline at a point i, R2(i) are calculated in pixel values from the detected outlines in Fig. 4. Here, a circle is fitted to both the disc and draped fabric outlines, from which the position (xc, yc) of the outline centres can be obtained. The radius of the circle fitted on the detected edge of the disc is approximated as Ravg. The radius R2(i) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi at a point (xi, yi) is calculated as R2 ðiÞ ¼ ðxi xc Þ2 þ ðyi yc Þ2 . Ravg is then further calculated from the R2(i) matrix variable, where the P average drape outline radius is Rav g ¼ ð1=nÞ ðRi Þ .
3.1. Drape coefficient DC
Both, the 30 and 36 cm samples show identical trends. However, 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 larger specimen size. The results can be well validated by the drape outlines shown in Fig. 3, where the area inside the draped outline clearly increases from NF_192 to NF_272. Moreover, it can be well observed that the high density NF_616 exhibited a smaller draping outline which is only out-smalled by the GF_267. Finally, the high density GF_611 exhibited a much larger area. Similar observations are made for the 36 cm samples.
DC calculation results as presented in Fig. 5, show an increase in DC with increased woven cover factor. Since high DC values reflect lower drapability, it can be concluded that deformation behaviour decreases with increased cover factor as also observed by Joeng [13,14]. The only exception to the trend was found for the low density glass fibre woven (GF_267) due to its very low thickness compared to the other fabric types.
3.2. Drape distance ratio DDR
Fig. 5. Draping coefficient against cover factor for 30 and 36 cm woven fabrics draped over an 18 cm circular disc.
Fig. 6. Drape distance ratio against cover factor for 30 and 36 cm woven fabrics draped over an 18 cm circular disc.
The Drape Distance Ratio (DDR) is an alternative for the DC [5,14–16]. The main advantage of this parameter is that, contrary to the DC, the DDR increases with increased fabric draping, thus being consistent with intuition. Fig. 6 presents the DDR
Y. Abdin et al. / Composites: Part B 45 (2013) 792–799
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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.
values against the cover factor of the woven fabrics under investigation. General trends indicate a decrease of the DDR with increasing CF. This reflects decreased draping at higher DC, as above discussed. The same deviation of the GF_267 woven is also observed in DDR calculations, where the GF_267 show large DDR despite its high CF. It could also be noted that the 36 cm samples have higher DDR values (and consequently) have improved drapability than the 30 cm samples, as also proven by DC results.
3.3. Number of nodes A nodal graph, as illustrated in Fig. 7a is developed from the detected edge in Fig. 4. Here, the radius R2(i) at each point i of the out i yc Þ . line is plotted against its corresponding angle h h ¼ tan1 ðy ðxi xc Þ The value of Ravg is plotted as a line in the nodal graph and the number of nodes is determined as the number of peaks of the outline above Ravg. Fig. 7b shows the number of nodes in relation to the cover factor. The figure indicates no apparent trends between the number of nodes and the cover factor. In general, as can also be depicted from Fig. 3, most profile outlines exhibited on average between four and five folds. The high density GF_611 undergoes a much lower number of folds due to its higher stiffness. Thus, it can be concluded that the number of nodes cannot be used alone as a draping parameter and must be combined with other parameters such as the fold depth index (FDI) or deviation from circularity.
3.4. Fold depth index (FDI) FDI results plotted against the cover factor are presented in Fig. 8. Trendlines indicate the decrease of FDI with increasing cover factor, as also reported by literature [15,16]. This observation indicates increased node sharpness at higher cover factors. This is in complete agreement with visual observation of the draping outlines (Fig. 3). By comparison, for example, the NF_192 undergoes much sharper nodes compared to the GF_611 with a very regular draping outline. The exception of the GF_267 is again observed in FDI results, where this woven shows very high values, supported by its very irregular sharp nodal outline in Fig. 3. Generally, the 36 cm samples show higher FDI values compared to the 30 cm samples. This can be clearly seen in Fig. 3, where the 36 cm samples result in very sharp outlines.
Fig. 8. Fold depth index against cover factor for 30 and 36 cm woven fabrics draped over an 18 cm circular disc.
3.5. Numerical simulation Fig. 9 shows a typical output of the simulation, where the blank has been draped by gravity forces. The nodes forming the drape outline in Fig. 9a have been extracted into a separate object in Fig. 9b.Exporting this outline in form of an ASCII file further allows the definition of position coordinates. The circular disc itself is similarly handled. The resulting position matrices are then used for the calculations of the DC. Fig. 3 presents a comparison of the experimental and simulated drape outlines of both the 30 and 36 cm samples. It can be observed that simulation results generally predict larger areas within the draping outline than experimental results, thus resulting in slightly higher estimates for the draping coefficient as illustrated in Fig. 10a on the example of the 36 cm blank size. Moreover, in contrast to experimental investigation, a much larger number of folds is predicted, where each major fold included 2–3 smaller folds. In comparison with the 30 cm samples, the simulated 36 cm drape outlines are found less accurate. This leads to the conclusion that accuracy tends to decrease with increasing blank size. This is conceivable based on the increase of the number of mesh elements and hence the complexity of the model. Observing the difference between the outlines of the easily drapable NF_611 and GF_267 on the one hand and the stiffer
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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.
GF_611 on the other hand, it can be concluded that the stiffer the material, the more accurate the predictions. This is also a reasonable conclusion that reflects the nature of the model equations which are based on the scaling of models based on conventional materials (mainly metallic materials) to account for the non-linearity of composite or textile materials. The simulated drape outlines resulted in roughly 15% larger areas (and consequently higher DC values) compared to experiments. Therefore, results from the simulation could be scaled with a modification factor of 0.85, leading to satisfactory results for both the 30 cm and 36 cm samples as shown in Fig. 10b.
PamForm2G software, for example. However, good characterisation of the fabrics in question are necessary. Acknowledgements This work was supported by the German Academic Exchange Office (DAAD) in Germany and the Science and Technology Development Fund (STDF) in Egypt, within the framework of a joint cooperation project. References
4. Conclusions Draping ability of wovens is found to improve with decreased fabric cover factor. This is reflected in low DC and high DDR values. Although the current study evidences no clear relationship between the cover factor and the number of folds created when fabric is draped, the depth of each fold, in terms of the FDI, is observed to decrease with increasing cover factor. Experimental observations can be easily predicted with Fininte Element tools, as the
[1] Kenkare N, May-Plumlee T. Evaluation of drape characteristics in fabrics. IJCST 2005;17(2):109–23. [2] Kenkare N, May-Plumlee T. Fabric drape measurement: a modified method using digital image processing. JTATM 2005;4(3):1–8. [3] Cusick GE. The dependence of fabric drape on bending and shear stiffness. J Text Inst Trans 1965;56(1):596–606. [4] Chu CC, Cummings CL, Teixeira NA. Mechanics of elastic performance of textile materials: Part V: A study of the factors affecting the drape of fabrics – the development of a drapemeter. Text Res J 1965;2(8):539–48. [5] Vangheluwe L, Kiekens P. Time dependence of the drape coefficient of fabrics. IJCST 1993;5(5):5–8.
Y. Abdin et al. / Composites: Part B 45 (2013) 792–799 [6] Peirce FT. The ‘‘handle’’ of cloth as a measurable quantity. J Text Inst Trans 1930;21(9):377–416. [7] Pourboghrat F, Chung K, Kang TJ, Yu WR, Zampaloni M. Analysis of flexible bending behavior of woven preforms using non-orthogonal constitutive equation. Compos Part A – Appl Sci Manuf 2005;36(6):839–50. [8] Cusick GE. The resistance of fabrics to shearing forces. J Text I 1961;52(1):395–406. [9] Cusick GE. The measurement of fabric drape. J Text I 1968;59(1):253–60. [10] Scarberry H, Swearingen A, Collier B J, Collier J R. Development of digital drape tester. In: ACPTC Combined Proc. 1988. p. 35. [11] Horrocks AR, Anand SC. Handbook of technical textiles. Woodhead Publishing; 2004.
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[12] Vanclooster K, Lomov SV, Verpoest I. Experimental validation of forming simulations of fabric reinforced polymers using an unsymmetrical mould configuration. Compos Part A – Appl Sci Manuf 2009;40(4):530–9. [13] Jeong YJ, Phillips DG. A study of fabric-drape behaviour with image analysis part ii: The effects of fabric structure and mechanical properties on fabric drape. J Text I 1998;89(1):70–9. [14] Jeong YJ. A study of fabric-drape behaviour with image analysis, Part i: Measurement, characterisation, and instability. J Text I 1998;89(1):59–69. [15] Behera BK, Pattanayak AK. Measurement and modeling of drape using digital image processing. IJFTR 2008;33(1):230–8. [16] Robson D, Long CC. Drape analysis using imaging techniques. CTRJ 2000;18(1):1–8.
Contents lists available at SciVerse ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Description of draping behaviour of woven fabrics over single curvatures by 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, Egypt Ain Shams University, Faculty of Engineering, Cairo, Egypt c Clausthal University of Technology, Institute for Polymer Materials and Plastics Processing, Clausthal-Zellerfeld, Germany b
a r t i c l e
i n f o
Article history: Received 14 March 2012 Accepted 2 June 2012 Available online 15 June 2012 Keywords: A. Fabrics/textiles A. Preform C. Finite element analysis (FEA) Draping behaviour
a b s t r a c t The use of natural fibres in polymer composite applications has gained great attention over the last decade, due to weight, economic and environmental aspects. Processing textile reinforced composites in various lay-up, resin infusion or compression moulding techniques requires good reproduction of mould shape. Thus, this study is concerned with the analysis of deformation and draping behaviour of woven fabrics over single curvatures. Experimental investigations of draping several jute and glass fibre woven fabrics of varying densities over a standard circular disc have been performed. Draping behaviour was analysed using image processing techniques and MATLAB application. Further simulation of the draping patterns has been achieved using PamForm software. Good prediction of draping behaviour of woven textiles is accessible, but requires a set of preliminary experiments to well characterise the fabric in question. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The use of woven fabrics in various orientation patterns plays a vital role, especially in the field of polymer composite applications. Within this scope, the deformation (draping) behaviour of textiles over open or within closed moulds is vital for the guarantee of end product performance and aesthetics. Thus, the draping behaviour of textiles is considered as an important mechanical property that affects the functionality of fabrics [1,2]. Drape has been recently defined as ‘‘the extent to which a fabric will deform when it is allowed to hang under its own weight’’ (BS 5058:1973; British Standard Institute, 1974b) [1,2]. It is suggested that Fabric drape depends on fibre content and different physical, structural and mechanical properties, in addition to the geometry over which it drapes. In early literature, Peirce [6] regarded the bending behaviour of fabrics as an indicator for its draping qualities. The bending length – defined as ‘‘the length of fabric which will bend under its own weight to a definite extent’’ – is considered as the main parameter characterising cloth drape behaviour. Thus, stiffer fabrics would tend to bend at a greater length, indicating their poor draping behaviour in 2D [7]. Chu et al. [4] distinguished draping from paperiness (paper bending behaviour) by accounting for 3D deformation behaviour
using a drapemeter that is capable of distorting fabric samples in all three dimensions over a circular disc. Providing an accurate vertical projection of the draped sample by optical means allowed the determination of the Drape Coefficient (DC), which they defined as ‘‘the fraction of the area of the annular ring covered by the projection of the draped sample’’. Hence, a high drape coefficient reflects poor or little deformation. The Cusick drapemeter [3,8] uses a similar principle, but presented a much simpler apparatus and operating mechanism. Sample dimensions were found to influence the draping behaviour, where Cusick [9] reported that a standard 30 cm diameter sample was convenient and that a suitable diameter for the disc was then 18 cm. Over several years it was the main concern of drape researchers to accurately record the draped contour. From complex projection techniques [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 accuracies. most measuring methods produced similar results. However, image analysis techniques greatly reduced result dispersion as well as measuring time [5]. 2. Materials and methods 2.1. Materials
⇑ Corresponding author. Address: 1 El-Sarayat Str., Abdou Pasha Square, Abbasia, Cairo, Egypt. Tel.: +20 18 9369100; fax: +20 2 24152991. E-mail address: [email protected] (I. Taha). 1359-8368/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2012.06.004
Five commercially available jute woven fabrics were supplied by El-Manasra, Egypt. Two glass fibre woven fabrics were further
Y. Abdin et al. / Composites: Part B 45 (2013) 792–799 Table 1 Woven fabric properties. Material type
Fibre diameter (lm)
Yarn count (tex)
Areal density (g/m2)
Cover factor
Tensile modulus (MPa)
NF_192 NF_241 NF_250 NF_272 NF_616 GF_267 GF_611
1311 1368 1129 1333 2553 1250 2900
341 372 289 311 770 123 1188
192 241 250 272 616 267 611
10.7 11.5 13.3 17.0 8.1 13.0 20.4
13.4 20.9 25.5 27.5 2.5 240 260
supplied by HP Textiles, Germany. The fabrics are all of the plain weave type and show measured variations in density and weave dimensions as listed in Table 1. The cover factor is a textile property that indicates the extent to which the area of the fabric is covered by one set of threads [11]. The cover factor allows for comparison among textiles taking into consideration not only their areal densities but also their thickness and p mesh ffiffiffiffiffiffiffi tightness. The cover factor is calculated as CF ¼ threads=cm tex where the tex is the linear mass density of 10 the fabric yarns in g/km. 2.2. Drape circular disc test Circular samples of 30 cm diameter are placed over an 18 cm circular disc. Samples are properly fixed by means of a protruding pin in the centre of the disc. To further investigate the effect of sample size on the draping behaviour, a second set of experiments using 36 cm diameter fabrics is performed. Tests are performed on three different samples of each investigated woven fabric. Images of resolution 3264 2448 pixels are captured using a high definition CCD (Charge Coupled Device) camera as soon as the samples are clamped. The camera is fixed on a wooden frame at a distance of 450 mm from the sample surface. A background sheet is placed under the drapemeter to create a colour contrast for further image analysis and processing with an appropriate math processor (Matlab). 2.3. Image processing and analysis Image processing operations performed using the MATLAB Algorithm, are described as follows: (1) reading and displaying
793
the acquired Red Green Black (RGB) image (imread); (2) subtracting the background from the original image; (3) image binarisation: converting the RGB (real colour) image into a binary image (im2bw) by using thresholding. A graythresholding function (graythresh) automatically computes an appropriate threshold to use in the conversion; (4) morphology: erosion followed by dilation (imclose) morphological closing done on the binary image using addition of structure square elements (SE) resulting in homogeneous and continuous white area within the drape outline; (5) edge detection: detection of the edge of the drape outline silhouette using a gradient edge detection function (edge canny). This code is used for each sample tested, as well as for the reference disc image. Following edge detection, the outline of the draped sample is analysed into a number (n) of discrete points with definite position coordinates (xi, yi). The same is done for the detected edge of the reference disc. Results are applied for the determination of the undraped area as well as the area of the annular ring draped over the disc. 2.4. Determination of drape outline parameters A1 The Drape Coefficient (DC) is calculated as DC ¼ AA20 A , where A0, 1 A1, A2 denote undraped, circular disc, and draped sample areas, respectively. In contrast, the Drape Distance Ratio (DDR) denotes the reduction in the annular portion of the specimen due to draping and is R R determined by DDR ¼ R00 Rav1g , where R0, R1, Ravg denote detected undraped sample, circular disc, and average drape outline radius, respectively. The number of nodes (n) in the draped fabric is determined by counting the number of folded apexes formed when hanged over the disc. The Fold Depth Index (FDI) shows how sharp these nodes Rmin are. It is calculated according to the relation FDR ¼ Rmax , where R0 R1 Rmax and Rmin represent the maximum and minimum radii of the drape outline.
2.5. Numerical techniques Making use of the PamForm software, PamForm2G is a calculation code that uses the Finite Element (FE) method [12]. Material type 140 is applied being generally used for composite materials simulation comprising the extensible reinforcing fibre component,
Fig. 1. Simulation using PamForm2G of (a) draping setup over a circular disc and (b) drape circular disc attributes.
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Y. Abdin et al. / Composites: Part B 45 (2013) 792–799
Table 2 Summary 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 NF_241 NF_250 NF_272 NF_616 GF_267 GF_611
0.8507 0.72917 0.7021 0.74611 1.8 0.382 0.81
2.26E07 3.43E07 3.44E07 3.65E07 3.4E07 6.67E07 7.63E07
0.0162 0.0184 0.0248 0.0198 0.0022 0.2509 0.2502
0.0134 0.0288 0.0255 0.028 0.0249 0.227 0.265
0.4 0.04 0.065 0.067 0.03 0.032 0.09
0.4 0.04 0.065 0.067 0.025 0.032 0.09
0.04 0.04 0.065 0.067 0.03 0.032 0.09
Parent sheet variable parameters Fabric type
alock(deg)
G(GPa)
Glock(GPa)
NF_192 NF_241 NF_250 NF_272 NF_616 GF_267 GF_611
54 51.5 47 42.5 41 53.5 52
2.57E05 5.52E05 5.72E05 0.000102 7.45E05 7.42E05 9.2E05
3.71E05 6.33E05 9.6E05 0.000161 0.000125 8.52E05 0.000141
Fig. 2. Image processing operations. (a) Reading of experimental images, (b) background elimination, (c) binarisation and (d) morphology.
the matrix component, and the parent sheet component. The latter component is merely a numerical fitting component used to overcome strong numerical instabilities that occur due to the high anisotropic behaviour of the materials. Fig. 1a shows the simulation of the fabric draping over a circular disc lying under the implicit gravity simulation mode within the software. The circular disc (solid part) is drawn using SolidWorks CAD software and further imported in PamForm and further converted into meshes. The woven fabric is simulated as a meshed ‘‘surface blank’’, for which the fabric properties are further defined in terms of tensile modulus, bending factor Fb, the out-of-plane shear factor Fs, the shear modulus G, and Poisson’s ratio m. The bending factor represents the fabric bending resistance. Following Vanclooster et al. [12] in assuming a negligible bending
resistance resulted into excessively large number of wrinkles, contradicting experimental observations. Instead, Fb was obtained using multiple trial-and-error runs to model the experimental observations. 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 achieved bending lengths c. In contrast, for all fabrics under investigation, a ‘‘knock down’’ value for Fs = 0.0001 is found applicable, based on the fact that the deformation mechanism of fabrics is only in-plane shear where fabric out-of-plane shearing is negligible. A Poisson’s ratio of m = 0.2 is adapted. The shear modulus is supplied in accordance with the advanced shear model approach, where the shear characteristics of the fabric are entered into the
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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.
model in form of a continuous curve describing the shear modulus with respect to various shear angles, providing a smooth and continuous description of the shear behaviour over the complete course of deformation. A drawback, however, remains the complication of solution and the increase of computation time. Generally, the material input parameters can be summarised in Table 2, describing the fixed, fibre component variable, and parent sheet variable parameters. Fbm and Fsm denote the out-of-plane bending and shear factors of the matrix, respectively. l is the friction coefficient characterizing friction behaviour between the tool and the blank [12]. Fig. 1b summarises the drape circular disc simulation attributes in PamForm2G, where contact 36 describes a user defined card,
allowing the simulation of large folds of fabric under deformation as observed during experimental investigation. This lies in contrast to insignificant amounts of deformation expected for reinforced polymer materials. The use of the contact 36 card prevents nodes to self-lock (crash), hence allowing the formation of folds. 3. Results and discussion Fig. 2 shows the Image Processing operations performed using the MATLAB Algorithm, for the samples. The same procedure is also applied on the naked circular disc. Fig. 3i shows the obtained draping outlines for the natural and glass fibre fabrics under investigation. The radius of the disc R1, the
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Fig. 4. Detected edges of (a) circular disc and (b) draped sample.
radius of undraped sample Ro and the radius of the draped sample outline at a point i, R2(i) are calculated in pixel values from the detected outlines in Fig. 4. Here, a circle is fitted to both the disc and draped fabric outlines, from which the position (xc, yc) of the outline centres can be obtained. The radius of the circle fitted on the detected edge of the disc is approximated as Ravg. The radius R2(i) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi at a point (xi, yi) is calculated as R2 ðiÞ ¼ ðxi xc Þ2 þ ðyi yc Þ2 . Ravg is then further calculated from the R2(i) matrix variable, where the P average drape outline radius is Rav g ¼ ð1=nÞ ðRi Þ .
3.1. Drape coefficient DC
Both, the 30 and 36 cm samples show identical trends. However, 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 larger specimen size. The results can be well validated by the drape outlines shown in Fig. 3, where the area inside the draped outline clearly increases from NF_192 to NF_272. Moreover, it can be well observed that the high density NF_616 exhibited a smaller draping outline which is only out-smalled by the GF_267. Finally, the high density GF_611 exhibited a much larger area. Similar observations are made for the 36 cm samples.
DC calculation results as presented in Fig. 5, show an increase in DC with increased woven cover factor. Since high DC values reflect lower drapability, it can be concluded that deformation behaviour decreases with increased cover factor as also observed by Joeng [13,14]. The only exception to the trend was found for the low density glass fibre woven (GF_267) due to its very low thickness compared to the other fabric types.
3.2. Drape distance ratio DDR
Fig. 5. Draping coefficient against cover factor for 30 and 36 cm woven fabrics draped over an 18 cm circular disc.
Fig. 6. Drape distance ratio against cover factor for 30 and 36 cm woven fabrics draped over an 18 cm circular disc.
The Drape Distance Ratio (DDR) is an alternative for the DC [5,14–16]. The main advantage of this parameter is that, contrary to the DC, the DDR increases with increased fabric draping, thus being consistent with intuition. Fig. 6 presents the DDR
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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.
values against the cover factor of the woven fabrics under investigation. General trends indicate a decrease of the DDR with increasing CF. This reflects decreased draping at higher DC, as above discussed. The same deviation of the GF_267 woven is also observed in DDR calculations, where the GF_267 show large DDR despite its high CF. It could also be noted that the 36 cm samples have higher DDR values (and consequently) have improved drapability than the 30 cm samples, as also proven by DC results.
3.3. Number of nodes A nodal graph, as illustrated in Fig. 7a is developed from the detected edge in Fig. 4. Here, the radius R2(i) at each point i of the out i yc Þ . line is plotted against its corresponding angle h h ¼ tan1 ðy ðxi xc Þ The value of Ravg is plotted as a line in the nodal graph and the number of nodes is determined as the number of peaks of the outline above Ravg. Fig. 7b shows the number of nodes in relation to the cover factor. The figure indicates no apparent trends between the number of nodes and the cover factor. In general, as can also be depicted from Fig. 3, most profile outlines exhibited on average between four and five folds. The high density GF_611 undergoes a much lower number of folds due to its higher stiffness. Thus, it can be concluded that the number of nodes cannot be used alone as a draping parameter and must be combined with other parameters such as the fold depth index (FDI) or deviation from circularity.
3.4. Fold depth index (FDI) FDI results plotted against the cover factor are presented in Fig. 8. Trendlines indicate the decrease of FDI with increasing cover factor, as also reported by literature [15,16]. This observation indicates increased node sharpness at higher cover factors. This is in complete agreement with visual observation of the draping outlines (Fig. 3). By comparison, for example, the NF_192 undergoes much sharper nodes compared to the GF_611 with a very regular draping outline. The exception of the GF_267 is again observed in FDI results, where this woven shows very high values, supported by its very irregular sharp nodal outline in Fig. 3. Generally, the 36 cm samples show higher FDI values compared to the 30 cm samples. This can be clearly seen in Fig. 3, where the 36 cm samples result in very sharp outlines.
Fig. 8. Fold depth index against cover factor for 30 and 36 cm woven fabrics draped over an 18 cm circular disc.
3.5. Numerical simulation Fig. 9 shows a typical output of the simulation, where the blank has been draped by gravity forces. The nodes forming the drape outline in Fig. 9a have been extracted into a separate object in Fig. 9b.Exporting this outline in form of an ASCII file further allows the definition of position coordinates. The circular disc itself is similarly handled. The resulting position matrices are then used for the calculations of the DC. Fig. 3 presents a comparison of the experimental and simulated drape outlines of both the 30 and 36 cm samples. It can be observed that simulation results generally predict larger areas within the draping outline than experimental results, thus resulting in slightly higher estimates for the draping coefficient as illustrated in Fig. 10a on the example of the 36 cm blank size. Moreover, in contrast to experimental investigation, a much larger number of folds is predicted, where each major fold included 2–3 smaller folds. In comparison with the 30 cm samples, the simulated 36 cm drape outlines are found less accurate. This leads to the conclusion that accuracy tends to decrease with increasing blank size. This is conceivable based on the increase of the number of mesh elements and hence the complexity of the model. Observing the difference between the outlines of the easily drapable NF_611 and GF_267 on the one hand and the stiffer
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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.
GF_611 on the other hand, it can be concluded that the stiffer the material, the more accurate the predictions. This is also a reasonable conclusion that reflects the nature of the model equations which are based on the scaling of models based on conventional materials (mainly metallic materials) to account for the non-linearity of composite or textile materials. The simulated drape outlines resulted in roughly 15% larger areas (and consequently higher DC values) compared to experiments. Therefore, results from the simulation could be scaled with a modification factor of 0.85, leading to satisfactory results for both the 30 cm and 36 cm samples as shown in Fig. 10b.
PamForm2G software, for example. However, good characterisation of the fabrics in question are necessary. Acknowledgements This work was supported by the German Academic Exchange Office (DAAD) in Germany and the Science and Technology Development Fund (STDF) in Egypt, within the framework of a joint cooperation project. References
4. Conclusions Draping ability of wovens is found to improve with decreased fabric cover factor. This is reflected in low DC and high DDR values. Although the current study evidences no clear relationship between the cover factor and the number of folds created when fabric is draped, the depth of each fold, in terms of the FDI, is observed to decrease with increasing cover factor. Experimental observations can be easily predicted with Fininte Element tools, as the
[1] Kenkare N, May-Plumlee T. Evaluation of drape characteristics in fabrics. IJCST 2005;17(2):109–23. [2] Kenkare N, May-Plumlee T. Fabric drape measurement: a modified method using digital image processing. JTATM 2005;4(3):1–8. [3] Cusick GE. The dependence of fabric drape on bending and shear stiffness. J Text Inst Trans 1965;56(1):596–606. [4] Chu CC, Cummings CL, Teixeira NA. Mechanics of elastic performance of textile materials: Part V: A study of the factors affecting the drape of fabrics – the development of a drapemeter. Text Res J 1965;2(8):539–48. [5] Vangheluwe L, Kiekens P. Time dependence of the drape coefficient of fabrics. IJCST 1993;5(5):5–8.
Y. Abdin et al. / Composites: Part B 45 (2013) 792–799 [6] Peirce FT. The ‘‘handle’’ of cloth as a measurable quantity. J Text Inst Trans 1930;21(9):377–416. [7] Pourboghrat F, Chung K, Kang TJ, Yu WR, Zampaloni M. Analysis of flexible bending behavior of woven preforms using non-orthogonal constitutive equation. Compos Part A – Appl Sci Manuf 2005;36(6):839–50. [8] Cusick GE. The resistance of fabrics to shearing forces. J Text I 1961;52(1):395–406. [9] Cusick GE. The measurement of fabric drape. J Text I 1968;59(1):253–60. [10] Scarberry H, Swearingen A, Collier B J, Collier J R. Development of digital drape tester. In: ACPTC Combined Proc. 1988. p. 35. [11] Horrocks AR, Anand SC. Handbook of technical textiles. Woodhead Publishing; 2004.
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[12] Vanclooster K, Lomov SV, Verpoest I. Experimental validation of forming simulations of fabric reinforced polymers using an unsymmetrical mould configuration. Compos Part A – Appl Sci Manuf 2009;40(4):530–9. [13] Jeong YJ, Phillips DG. A study of fabric-drape behaviour with image analysis part ii: The effects of fabric structure and mechanical properties on fabric drape. J Text I 1998;89(1):70–9. [14] Jeong YJ. A study of fabric-drape behaviour with image analysis, Part i: Measurement, characterisation, and instability. J Text I 1998;89(1):59–69. [15] Behera BK, Pattanayak AK. Measurement and modeling of drape using digital image processing. IJFTR 2008;33(1):230–8. [16] Robson D, Long CC. Drape analysis using imaging techniques. CTRJ 2000;18(1):1–8.