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Computation of mechanical anisotropy in thermally bonded bicomponent fibre nonwovens
Computational Materials Science 52 (2012) 157–163
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Computation of mechanical anisotropy in thermally bonded bicomponent fibre nonwovens Emrah Demirci a,⇑, Memisß Acar a, Behnam Pourdeyhimi b, Vadim V. Silberschmidt a a b
Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, LE11 3TU Leicestershire, UK Nonwovens Cooperative Research Center, North Carolina State University, NC27695-8301 Raleigh, NC, USA
a r t i c l e
i n f o
Article history: Available online 21 February 2011 Keywords: Thermally bonded nonwoven Bicomponent fibre Orientation distribution function Mechanical anisotropy Digital image processing Hough transform
a b s t r a c t Having a unique microstructure composed of randomly-oriented polymer-based fibres, nonwovens exhibit complex deformation characteristics. The most prominent one is the mechanical anisotropy leading to their direction-dependent deformation behaviour. This paper focuses on mechanical anisotropy of thermally bonded bicomponent fibre nonwovens with polymer-based bicomponent core/sheath fibres. A relation between mechanical anisotropy of these nonwovens and random orientation of their fibres is developed in this study. Random orientation of individual fibres is quantified in terms of the orientation distribution function (ODF) in order to determine the material’s anisotropy. The ODF is obtained by analysing the data acquired with scanning electron microscopy or X-ray micro-computed tomography using digital image processing techniques based on the Hough transform. A numerical tool is developed to perform this analysis and determine the anisotropic parameters in order to define direction-dependency of the structure’s mechanical properties. Finally, anisotropic parameters of various nonwovens computed with the introduced numerical approach are compared with those obtained from tensile tests applied in machine and cross directions of nonwovens. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Nonwovens are polymer-based engineered textiles having randomly distributed fibres bonded together with mechanical, thermal or chemical techniques. This paper focuses on thermally bonded nonwoven fabrics with bicomponent fibres made of polymers. Such fibres have a core/sheath structure, with a material of the inner region – core – having a higher melting temperature than that of the outer region (sheath). During the bonding of these fibres, a hot calender with an engraved pattern presses a fibrous web causing the sheath part of the fibres to melt and providing the desired bonding between the fibres while their core part with a higher melting point remains fully intact. As a result of the bonding process, two distinct regions, namely, bond points and a fibre matrix, with different characteristics, collectively form the nonwoven fabric. The structure of the resulting thermally bonded bicomponent fibre nonwoven obtained with scanning electron microscopy (SEM) is shown in Fig. 1. Having two distinct regions with different structures, nonwovens exhibit a unique deformation behaviour which is dissimilar to that of composites and woven fabrics. Mechanical anisotropy is the most prominent deformation characteristics of nonwoven materials, and leads to their direc⇑ Corresponding author. Tel.: +44(0) 1509 227566. E-mail address: [email protected] (E. Demirci). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.01.033
tion-dependent mechanical response. This phenomenon is related to random orientation of fibres constituting complex microstructures of nonwovens, which is inherited from the web formation process in manufacturing [1]. Randomness in the microstructure defines the related direction-dependent response, observed in the tensile test results of nonwovens [2,3]. This behaviour should be considered in design and numerical modelling of nonwovens since it characterizes their mechanical properties. Several numerical models have been developed for simulating the mechanical behaviour of thermally bonded nonwovens [3–5]. These studies offer effective numerical tools for designing and optimizing nonwovens considering their mechanical properties affected by their random microstructure. A comprehensive simulation of direction-dependent mechanical behaviour of nonwovens requires the analysis of their mechanical anisotropy based on the randomness in their fibrous microstructure. To authors’ knowledge the only attempts to provide sufficient insight into the mechanisms responsible for the mechanical anisotropy of nonwovens are given in [6,7]. There, the tensile modulus is computed in various directions with regard to the machine direction of the fabric using the orientation distribution function (ODF) calculated with the fast Fourier transform (FFT) of the microstructural image. However, they claim that different load transfer mechanisms govern the mechanical anisotropy of thermally bonded nonwovens rather than random orientation of fibres. Furthermore, reproducibility of the approach introduced in
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E. Demirci et al. / Computational Materials Science 52 (2012) 157–163
2. Orientation distribution function
Fig. 1. SEM images of bicomponent fibre nonwoven fabric composed of bond points and fibre matrix.
these studies is limited to low-planar-density nonwovens. The experimental results illustrated in this paper prove that random orientation of fibres is the main source of mechanical anisotropy, and the ODF of the fibrous matrix can be used to analyse the structure’s direction-dependent behaviour. Besides, a practical tool is developed to determine a nonwoven’s ODF and anisotropic parameters based on its images obtained with scanning electron microscopy (SEM) or X-ray micro-computed tomography (CT) regardless of its planar density. This paper aims to develop a novel approach to study the relation between mechanical anisotropy of thermally bonded nonwovens and their random microstructure. The procedure to derive this relation starts with obtaining of orientation distribution function (ODF) that quantifies randomness of the microstructure. Then, anisotropic parameters representing the direction-dependent mechanical response of these materials are computed based on the ODF of fibres. Finally, the effect of deformation on the anisotropic parameters is considered based on several experimental case studies, to check the validity of these parameters for large deformations.
The character of orientation distribution of fibres can be represented by ODF [8,9]. The ODF of a nonwoven can be computed using micro-scale images of its fibre matrix employing digital image processing techniques. There are two main methods used in image processing to determine ODF: the fast Fourier transform (FFT) [10,11] and the Hough transform (HT) [12–14]. Application of the HT technique to determine ODF is more recent than that of the FFT method. Each method has various advantages depending on the noise, lighting conditions and web structure. Main advantages of the HT method are that it is tolerant to gaps at object edges, relatively unaffected by the image noise and requires less computational power when compared with the fast Fourier transform [15]. Shorter computation times and robustness with regard to image noise lead to introduction of a new code based on HT method to analyse the ODF of nonwoven fibrous materials in this study. The new code – Nonwovens Anisotropy V1 – is generated in MATLABÒ software because of its broad function library for digital image processing. The code has a user-friendly graphical user interface (GUI) and could be used as a stand-alone application in MicrosoftÒ WindowsÒ-based systems (Fig. 2). Nonwovens Anisotropy V1 can compute the ODF of a fibre matrix from its micro-scale image obtained with SEM or X-ray micro-CT techniques. The code acquires the image and transforms it into a 3D matrix containing 8 bits of red (R), green (G) and blue (B) colour channels for image processing. Initially, the acquired image in RGB (colour scale) format is converted to a 2D grey scale image and filtered for several noise conditions, such as salt & pepper [16]. Then edges of the objects (fibres) in the grey scale image are detected and value 1 is assigned to them; 0 is assigned to the rest of the image by the algorithm. As a result of this process, a 2D image matrix containing binary values is generated for
Fig. 2. GUI of Nonwovens Anisotropy V1 for computing ODF and mechanical anisotropy of fibrous materials.
E. Demirci et al. / Computational Materials Science 52 (2012) 157–163
SEM / X-ray micro CT image
3D image matrix with 8 bits of red, blue and green channels
2D image matrix with 8 bits of grey-scale values
2D image matrix with binary values
Edge detection
Noise filtering (Opening filter and contrast adjustment)
Hough transform
Detection of fibres
Orientations of fibres
159
Fig. 3. Image processing steps followed in Nonwovens Anisotropy V1 algorithm.
the Hough transform. Finally, pixel coordinates of edge points are converted into a Hough domain in order to calculate the connectivity and continuity of fibre lines. The image processing steps followed for detecting fibres and their orientations in a fibre matrix from its micro-scale image are illustrated as blocks in Fig. 3. When a line is detected in the algorithm, a red line is drawn on it to verify its detection (Fig. 4a). Once the line is detected, its orientation is calculated based on its start and end points. Curvature (physical nonlinearity) on the lines is tolerated up to a threshold value defined by Rho and Theta Resolution parameters (Fig. 2), which could be changed depending on the microstructure. This code could detect the ODF of fibres in any type of fibrous material with distinguishable fibres, e.g. fibrous metal networks, fibre-reinforced composites. An image containing 12 artificial white lines with random orientations is used to demonstrate the algorithm (Fig. 4a). In the image red lines are drawn on the white ones by the code indicating their detection. In this way, a user can calibrate the digital image processing parameters of the code regarding light and noise conditions, and a size of fibres. The ODF of lines in Fig. 4a is given in Fig. 4b in the form of frequency of fibres (in percent) vs. fibre orientation (degrees) graph. The frequency of fibres for an angle refers to the ratio of number of fibres aligned along the direction with an angle from the respective range to the total amount of fibres: hence the sum of the frequency values in an ODF graph yields 100%. In this study, the angle range [0°, 180°] is used for the axes of abscissas for ODF graphs, with 90° corresponding to the machine direction of nonwoven fabric. Nonwoven materials have three principal directions, namely, machine direction (MD), cross direction (CD) and thickness direction (TD). MD is the flow direction of the nonwoven fibres on the conveyor during manufacturing, CD is perpendicular to MD on the plane of fabric and TD is normal to the plane of fabric. Therefore, vertical and horizontal directions of the image, which will be processed by the code, should coincide with MD and CD of fabric, respectively. Nonwovens Anisotropy V1 is tested with two fibre matrix images (Figs. 5a and 6a) having distinct ODF characteristics. In the first case, a micro-scale image of a nonwoven’s matrix region – Fig. 5a – containing fibres parallel to MD is processed with the code. According to its ODF graph (Fig. 5b), the majority of fibres are oriented along angles close to 90°, as can be observed in the image of fibre matrix (Fig. 5a). In the second case, orientation of fibres in the image (Fig. 6a) is nearly random. Randomness in the microstructure is reflected in its ODF graph (Fig. 6b) determined by the code. The character of ODF is confirmed by the micro-scale image shown in Fig. 6a. Thus, Figs. 5 and 6, showing fibre matrix images and their ODF graphs, demonstrate effectiveness of the developed code.
Fig. 4. Binary image containing randomly-oriented 12 lines (a) and their ODF computed with Nonwovens Anisotropy V1 (b).
Another feature of the code is subdomain processing, which improves the results by dividing the image into a user-defined number of subdomains for processing. In this technique, the ODF of each subdomain is computed separately considering its own
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(a)
60
14
50
12
Frequency (%)
Frequency (%)
(a)
40 30 20 10 0
10 8 6 4 2 0
Fibre Orientation (Degrees)
Fibre Orientation (Degrees)
(b)
(b)
Fig. 5. SEM image of nonwoven fabric (a) and its ODF computed with Nonwovens Anisotropy V1 (b).
Fig. 6. SEM image of nonwoven fabric (a) and its ODF computed with Nonwovens Anisotropy V1 (b).
noise and light conditions. A weighted mean of subdomain ODFs is employed as the resultant ODF of the complete image. This homogenized approach yields a more adequate ODF for the nonwoven fabric, since it considers local deviations in orientation. The most important rule to use this feature is to keep aspect ratio of image subdomains approximately square. This feature is useful not only for dense materials, but also for several issues originating in imaging conditions, such as local brightness in SEM images or salt & pepper noise in X-ray micro-CT images. The subdomain processing feature of the code is tested using an X-ray micro-CT image of the PP/PE nonwoven fabric having a dense fibrous structure shown in Fig. 7. It is obvious that fibres in Fig. 7 are less distinguishable than the ones in Figs. 5a and 6a due to the image scale and high fibre density. In order to increase distinguishability of individual fibres, the image is divided into six subimages having aspect ratios closed to that of a square. The code generates these sub-images (Fig. 8) each showing a specific region of the main image (Fig. 7). Detected fibres in each subdomain are designated with lines drawn on top of them (Fig. 8). Fibredetection accuracy and efficiency could be modified with the digital image processing parameters on the GUI of the code illustrated in Fig. 2. The lines indicating orientations of fibres help a user to optimize the outcome with respect to microstructure and imaging conditions. An interesting point is that two of the sub-images in Fig. 8 are brighter than the others because each one is processed based on its own brightness and noise conditions. In other words, pixel
values change as a result of histogram equalization applied to the binary form of sub-images for making fibre boundaries more distinguishable. In this case, the light source, which increases brightness of nearby regions, is located at the right bottom corner of the image in Fig. 7. The ODF of each subdomain in Fig. 8 is computed separately by the code and given in Fig. 9. It is obvious that ODF characteristics of each region are different, due to randomness in the microstructure. At this point, it should be emphasized that position and size of the input image area of the nonwoven material play an important role in determining a representative ODF. The X-ray micro-CT image in Fig. 7 covers an area between neighbouring bond points along CD and MD that form a periodic bond pattern. Two horizontal boundary bond points along CD, which are excluded from ODF computation due to lack of fibre boundaries, could be seen partially at the right and left edges of fibre matrix in Fig. 7. Computation efficiency of the code could be improved by increasing the resolution and sharpness of input image. The fibre detection possibility increases with increased sharpness and resolution at pixels located on fibreboundary regions. Additionally, the number of image divisions could be increased together with image resolution and sharpness to obtain a more adequate ODF for nonwoven material. The resultant ODF of the PP/PE nonwoven fibre matrix shown in Fig. 7, computed based on ODFs obtained for each subdomain (Fig. 9), is given in Fig. 10. Based on the number and orientations of fibres computed in each sub-image, a resultant ODF graph is generated by the code. This ODF graph reflects randomness of
E. Demirci et al. / Computational Materials Science 52 (2012) 157–163
161
Fig. 7. X-ray micro-CT image of fibre matrix region of nonwoven (fibre: PP/PE, planar density: 50 g/m2).
Fig. 8. Subdomains of fibre matrix image (Fig. 7) processed with Nonwovens Anisotropy V1.
the overall fibrous network based on particular regions. The resultant ODF computed by the code will be used to characterize the randomness of the fabric’s microstructure. To sum up this part, a practical user-friendly code for computing the ODF of fibrous materials is introduced. Using the subdomain processing feature with a larger number of image divisions will improve ODF results. Additionally, increased image resolution and sharpness contribute to fibre detection capability of the code, which improves the computed resultant ODF. This ODF graph will be used to determine anisotropic parameters, which are necessary for assessing anisotropic mechanical properties of nonwoven materials. The derivation of these parameters from the ODF graph will be explained in the next section.
3. Anisotropic parameters Anisotropy is an unavoidable phenomenon in nonwovens; therefore it should be taken into account in computation of their mechanical properties. The level of direction-dependency of the
mechanical response is very important for results of simulations. As the number of material symmetry planes decreases, the amount of parameters defining the direction-dependant behaviour increases significantly, hence increasing the complexity of material definition as well as the computation time. Orthogonal anisotropy (orthotropy), having three symmetry planes, can adequately define the level of anisotropy for thermally bonded nonwovens. The principal directions of orthotropy in nonwovens can be assumed as coincident with their principal directions – MD, CD and TD – for definition of their viscoelastic–plastic parameters. The main source of anisotropy is the nonuniform orientational distribution of fibres causing a direction-dependent response. Deformation level of bond points is significantly less than that of fibre matrix due to differences in their microstructures [3]. Since nonwovens exhibit large-strain deformation behaviour, which is observed in fibre matrix rather than in bond points, source of anisotropy is assumed as fibre matrix in this paper. The nonuniformity can be quantified with the use of the ODF, which will be used to calculate of orthotropic parameters. Due to the nature of orthotropy, these parameters are assumed to be symmetric with respect
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Frequency (%)
Fig. 9. ODF of each subdomain in Fig. 8.
18 16 14 12 10 8 6 4 2 0
Fibre Orientation (Degrees) Fig. 10. Resultant ODF obtained from subdomain ODFs in Fig. 9.
to MD and CD on fabric plane. The parameters defining the level of orthotropy are calculated from the ODF in Nonwovens Anisotropy V1, according to the following equations; i¼1
i¼1
C CD ¼ PN i¼1
RE ¼
PN
C MD ¼ PN
jsin ai j
PN
jsin ai jþ
PN
i¼1
oretical (RT) – are introduced to define the level of direction-dependent mechanical behaviour on fabric plane. RE is defined as
i¼1
jcos ai j
jcos ai j
PN
jsin ai jþ
i¼1
jcos ai j
; ð1Þ ;
where CMD and CCD are the parameters defining the level of orthotropy in MD and CD (obviously, CMD + CCD = 1) that are used to calculate the stress–strain curves of the nonwoven material for MD and CD; ai is the angle between the axis of the ith fibre and CD; N is the total number of fibres accounted by the ODF algorithm. Orthotropy of a nonwoven material could be determined with two possible approaches: (i) using parameters obtained from the ODF (Eq. (1)) and (ii) using the stress–strain results of tensile tests performed along MD and CD. In order to compare these approaches quantitatively, two orthotropic ratios – experimental (RE) and the-
rMD ; rCD
ð2Þ
where rMD and rCD are the stresses along MD and CD obtained from the tensile test results. On the other hand, to obtain the level of orthotropy from the constants CMD and CCD, which are computed with Nonwovens Anisotropy V1 using the ODF of nonwoven fabric, RT is introduced as follows
RT ¼
C MD : C CD
ð3Þ
4. Results and discussion Values of RE and RT of the PP/PE nonwoven fabric shown in Fig. 7 are compared using the ODF of the fabric given in Fig. 10. Here, RT is found using Eq. (3), which requires CMD and CCD parameters.
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3.0 2.5
RE
2.0
1.77
0.34
1.5 RE=1 for isotropic materials
1.0 0.5
Experimental Data Mean of Experimental Data
0.0 0
0.1
0.2
0.3
0.4
0.5
True Strain Fig. 11. Experimental orthotropic ratio of nonwoven fabric (fibre: PP/PE, planar density: 50 g/m2).
Table 1 Experimental and theoretical orthotropic ratios of several nonwoven fabrics.
RE RT
PP/PE 50 g/m2
PA6/PE 100 g/m2
PA6/PE 150 g/m2
1.77 ± 0.34 1.86
2.55 ± 0.30 2.64
2.30 ± 0.16 2.59
According to Eq. (1), CMD and CCD of the PP/PE nonwoven fabric are 0.65 and 0.35, respectively, which in turn yield a RT value of 1.86. On the other hand, tensile test results of the fabric in MD and CD are used to draw the RE curve using Eq. (2). According to Fig. 11, orthotropy of the nonwoven varies with deformation due to reorientation of fibres. The mean value of RE curve – 1.77 ± 22% – is also given in Fig. 11. For an isotropic material, RE is always 1 due to an infinite number of symmetry planes causing direction-independent stress–strain curve. According to Table 1, which contains the mean value of RE curve and RT for various nonwoven fabrics, their orthotropic ratios calculated from the ODF are close to those determined in tensile tests. Apparently, RT values are well within the variability range of RE curves. So according to the results in Table 1, accuracy of Nonwovens Anisotropy V1 in predicting the level of mechanical orthotropy using microstructural images of a nonwoven fabric is promising. As a consequence of this agreement, CMD and CCD parameters computed by the code could be used to assess orthotropic mechanical properties of nonwoven fabrics in their numerical models for design and optimization. 5. Conclusions To sum up, anisotropy of nonwoven materials is analysed in this paper by means of quantification of their random fibrous microstructure. The developed code – Nonwovens Anisotropy V1 – is used to perform this analysis using micro-scale images of fibrous matrix obtained with SEM or X-ray micro-CT techniques. Randomness in the fabric microstructure is quantified with the ODF, which is computed with the developed code from the microstructural image of nonwovens. A relation between the ODF and structure’s mechanical anisotropy is suggested introducing orthotropic parameters representing a direction-dependent mechanical response of nonwovens. These parameters could be used in numeri-
cal models to define the direction-dependency of mechanical properties of thermally bonded nonwoven materials. The numerical tool described in this study is effective in predicting the anisotropic deformation characteristics of thermally bonded nonwovens; it verified with experiments and ready to use for applications. There are no complex input parameters, and the graphical user interface does not require a deep knowledge of digital image processing. The developed algorithm is fully parametric and independent of the bond pattern and shape. The code may serve industry and research as a useful tool for product development and optimization as well as numerical modelling. Acknowledgement The authors gratefully acknowledge the support of Nonwovens Cooperative Research Center, North Carolina State University, USA. References [1] S.J. Russell, Handbook of Nonwovens, Woodhead Publishing Ltd., Cambridge, 2007. [2] S. Michielsen, B. Pourdeyhimi, P. Desai, Processes, and properties, Journal of Applied Polymer Science 99 (2006) 2489–2496. [3] E. Demirci, M. Acar, B. Pourdeyhimi, V.V. Silberschmidt, Finite element modelling of thermally bonded bicomponent fibre nonwovens: tensile behaviour, Computational Materials Science 50 (4) (2011) 1286–1291. [4] X. Hou, M. Acar, V.V. Silberschmidt, Computational Materials Science 46 (3) (2009) 700–707. [5] X. Hou, M. Acar, V.V. Silberschmidt, Finite element simulation of low-density thermally bonded nonwoven materials: effects of orientation distribution function and arrangement of bond points, Computational Materials Science (2010), doi: 10.1016/j.commatsci.2010.03.009. [6] H.S. Kim, Fibers and Polymers 5 (3) (2004) 177–181. [7] H.S. Kim, Fiber and Polymers 5 (2) (2004) 139–144. [8] B. Pourdeyhimi, R. Ramanathan, R. Dent, Textile Research Journal 66 (11) (1996) 713–722. [9] B. Pourdeyhimi, R. Ramanathan, R. Dent, Textile Research Journal 66 (12) (1996) 747–753. [10] B. Pourdeyhimi, R. Dent, H. Davis, Textile Research Journal 67 (2) (1997) 143– 151. [11] H.S. Kim, B. Pourdeyhimi, Technology and Management 1 (4) (2001) 1–7. [12] B. Xu, L. Yu, Textile Research Journal 67 (8) (1997) 563–571. [13] B. Pourdeyhimi, H.S. Kim, Textile Research Journal 72 (9) (2002) 803–809. [14] E. Ghassemieh, H. Versteeg, M. Acar, International Nonwovens Journal 10 (2) (2001) 26–31. [15] E. Ghassemieh, M. Acar, H. Versteeg, Proceedings of the Institution of Mechanical Engineers Part L: Journal of Materials: Design and Applications 216 (3) (2002) 199–207. [16] R.C. Gonzalez, R.E. Woods, Digital Image Processing, second ed., Prentice Hall, New Jersey, 2002.
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Computation of mechanical anisotropy in thermally bonded bicomponent fibre nonwovens Emrah Demirci a,⇑, Memisß Acar a, Behnam Pourdeyhimi b, Vadim V. Silberschmidt a a b
Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, LE11 3TU Leicestershire, UK Nonwovens Cooperative Research Center, North Carolina State University, NC27695-8301 Raleigh, NC, USA
a r t i c l e
i n f o
Article history: Available online 21 February 2011 Keywords: Thermally bonded nonwoven Bicomponent fibre Orientation distribution function Mechanical anisotropy Digital image processing Hough transform
a b s t r a c t Having a unique microstructure composed of randomly-oriented polymer-based fibres, nonwovens exhibit complex deformation characteristics. The most prominent one is the mechanical anisotropy leading to their direction-dependent deformation behaviour. This paper focuses on mechanical anisotropy of thermally bonded bicomponent fibre nonwovens with polymer-based bicomponent core/sheath fibres. A relation between mechanical anisotropy of these nonwovens and random orientation of their fibres is developed in this study. Random orientation of individual fibres is quantified in terms of the orientation distribution function (ODF) in order to determine the material’s anisotropy. The ODF is obtained by analysing the data acquired with scanning electron microscopy or X-ray micro-computed tomography using digital image processing techniques based on the Hough transform. A numerical tool is developed to perform this analysis and determine the anisotropic parameters in order to define direction-dependency of the structure’s mechanical properties. Finally, anisotropic parameters of various nonwovens computed with the introduced numerical approach are compared with those obtained from tensile tests applied in machine and cross directions of nonwovens. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Nonwovens are polymer-based engineered textiles having randomly distributed fibres bonded together with mechanical, thermal or chemical techniques. This paper focuses on thermally bonded nonwoven fabrics with bicomponent fibres made of polymers. Such fibres have a core/sheath structure, with a material of the inner region – core – having a higher melting temperature than that of the outer region (sheath). During the bonding of these fibres, a hot calender with an engraved pattern presses a fibrous web causing the sheath part of the fibres to melt and providing the desired bonding between the fibres while their core part with a higher melting point remains fully intact. As a result of the bonding process, two distinct regions, namely, bond points and a fibre matrix, with different characteristics, collectively form the nonwoven fabric. The structure of the resulting thermally bonded bicomponent fibre nonwoven obtained with scanning electron microscopy (SEM) is shown in Fig. 1. Having two distinct regions with different structures, nonwovens exhibit a unique deformation behaviour which is dissimilar to that of composites and woven fabrics. Mechanical anisotropy is the most prominent deformation characteristics of nonwoven materials, and leads to their direc⇑ Corresponding author. Tel.: +44(0) 1509 227566. E-mail address: [email protected] (E. Demirci). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.01.033
tion-dependent mechanical response. This phenomenon is related to random orientation of fibres constituting complex microstructures of nonwovens, which is inherited from the web formation process in manufacturing [1]. Randomness in the microstructure defines the related direction-dependent response, observed in the tensile test results of nonwovens [2,3]. This behaviour should be considered in design and numerical modelling of nonwovens since it characterizes their mechanical properties. Several numerical models have been developed for simulating the mechanical behaviour of thermally bonded nonwovens [3–5]. These studies offer effective numerical tools for designing and optimizing nonwovens considering their mechanical properties affected by their random microstructure. A comprehensive simulation of direction-dependent mechanical behaviour of nonwovens requires the analysis of their mechanical anisotropy based on the randomness in their fibrous microstructure. To authors’ knowledge the only attempts to provide sufficient insight into the mechanisms responsible for the mechanical anisotropy of nonwovens are given in [6,7]. There, the tensile modulus is computed in various directions with regard to the machine direction of the fabric using the orientation distribution function (ODF) calculated with the fast Fourier transform (FFT) of the microstructural image. However, they claim that different load transfer mechanisms govern the mechanical anisotropy of thermally bonded nonwovens rather than random orientation of fibres. Furthermore, reproducibility of the approach introduced in
158
E. Demirci et al. / Computational Materials Science 52 (2012) 157–163
2. Orientation distribution function
Fig. 1. SEM images of bicomponent fibre nonwoven fabric composed of bond points and fibre matrix.
these studies is limited to low-planar-density nonwovens. The experimental results illustrated in this paper prove that random orientation of fibres is the main source of mechanical anisotropy, and the ODF of the fibrous matrix can be used to analyse the structure’s direction-dependent behaviour. Besides, a practical tool is developed to determine a nonwoven’s ODF and anisotropic parameters based on its images obtained with scanning electron microscopy (SEM) or X-ray micro-computed tomography (CT) regardless of its planar density. This paper aims to develop a novel approach to study the relation between mechanical anisotropy of thermally bonded nonwovens and their random microstructure. The procedure to derive this relation starts with obtaining of orientation distribution function (ODF) that quantifies randomness of the microstructure. Then, anisotropic parameters representing the direction-dependent mechanical response of these materials are computed based on the ODF of fibres. Finally, the effect of deformation on the anisotropic parameters is considered based on several experimental case studies, to check the validity of these parameters for large deformations.
The character of orientation distribution of fibres can be represented by ODF [8,9]. The ODF of a nonwoven can be computed using micro-scale images of its fibre matrix employing digital image processing techniques. There are two main methods used in image processing to determine ODF: the fast Fourier transform (FFT) [10,11] and the Hough transform (HT) [12–14]. Application of the HT technique to determine ODF is more recent than that of the FFT method. Each method has various advantages depending on the noise, lighting conditions and web structure. Main advantages of the HT method are that it is tolerant to gaps at object edges, relatively unaffected by the image noise and requires less computational power when compared with the fast Fourier transform [15]. Shorter computation times and robustness with regard to image noise lead to introduction of a new code based on HT method to analyse the ODF of nonwoven fibrous materials in this study. The new code – Nonwovens Anisotropy V1 – is generated in MATLABÒ software because of its broad function library for digital image processing. The code has a user-friendly graphical user interface (GUI) and could be used as a stand-alone application in MicrosoftÒ WindowsÒ-based systems (Fig. 2). Nonwovens Anisotropy V1 can compute the ODF of a fibre matrix from its micro-scale image obtained with SEM or X-ray micro-CT techniques. The code acquires the image and transforms it into a 3D matrix containing 8 bits of red (R), green (G) and blue (B) colour channels for image processing. Initially, the acquired image in RGB (colour scale) format is converted to a 2D grey scale image and filtered for several noise conditions, such as salt & pepper [16]. Then edges of the objects (fibres) in the grey scale image are detected and value 1 is assigned to them; 0 is assigned to the rest of the image by the algorithm. As a result of this process, a 2D image matrix containing binary values is generated for
Fig. 2. GUI of Nonwovens Anisotropy V1 for computing ODF and mechanical anisotropy of fibrous materials.
E. Demirci et al. / Computational Materials Science 52 (2012) 157–163
SEM / X-ray micro CT image
3D image matrix with 8 bits of red, blue and green channels
2D image matrix with 8 bits of grey-scale values
2D image matrix with binary values
Edge detection
Noise filtering (Opening filter and contrast adjustment)
Hough transform
Detection of fibres
Orientations of fibres
159
Fig. 3. Image processing steps followed in Nonwovens Anisotropy V1 algorithm.
the Hough transform. Finally, pixel coordinates of edge points are converted into a Hough domain in order to calculate the connectivity and continuity of fibre lines. The image processing steps followed for detecting fibres and their orientations in a fibre matrix from its micro-scale image are illustrated as blocks in Fig. 3. When a line is detected in the algorithm, a red line is drawn on it to verify its detection (Fig. 4a). Once the line is detected, its orientation is calculated based on its start and end points. Curvature (physical nonlinearity) on the lines is tolerated up to a threshold value defined by Rho and Theta Resolution parameters (Fig. 2), which could be changed depending on the microstructure. This code could detect the ODF of fibres in any type of fibrous material with distinguishable fibres, e.g. fibrous metal networks, fibre-reinforced composites. An image containing 12 artificial white lines with random orientations is used to demonstrate the algorithm (Fig. 4a). In the image red lines are drawn on the white ones by the code indicating their detection. In this way, a user can calibrate the digital image processing parameters of the code regarding light and noise conditions, and a size of fibres. The ODF of lines in Fig. 4a is given in Fig. 4b in the form of frequency of fibres (in percent) vs. fibre orientation (degrees) graph. The frequency of fibres for an angle refers to the ratio of number of fibres aligned along the direction with an angle from the respective range to the total amount of fibres: hence the sum of the frequency values in an ODF graph yields 100%. In this study, the angle range [0°, 180°] is used for the axes of abscissas for ODF graphs, with 90° corresponding to the machine direction of nonwoven fabric. Nonwoven materials have three principal directions, namely, machine direction (MD), cross direction (CD) and thickness direction (TD). MD is the flow direction of the nonwoven fibres on the conveyor during manufacturing, CD is perpendicular to MD on the plane of fabric and TD is normal to the plane of fabric. Therefore, vertical and horizontal directions of the image, which will be processed by the code, should coincide with MD and CD of fabric, respectively. Nonwovens Anisotropy V1 is tested with two fibre matrix images (Figs. 5a and 6a) having distinct ODF characteristics. In the first case, a micro-scale image of a nonwoven’s matrix region – Fig. 5a – containing fibres parallel to MD is processed with the code. According to its ODF graph (Fig. 5b), the majority of fibres are oriented along angles close to 90°, as can be observed in the image of fibre matrix (Fig. 5a). In the second case, orientation of fibres in the image (Fig. 6a) is nearly random. Randomness in the microstructure is reflected in its ODF graph (Fig. 6b) determined by the code. The character of ODF is confirmed by the micro-scale image shown in Fig. 6a. Thus, Figs. 5 and 6, showing fibre matrix images and their ODF graphs, demonstrate effectiveness of the developed code.
Fig. 4. Binary image containing randomly-oriented 12 lines (a) and their ODF computed with Nonwovens Anisotropy V1 (b).
Another feature of the code is subdomain processing, which improves the results by dividing the image into a user-defined number of subdomains for processing. In this technique, the ODF of each subdomain is computed separately considering its own
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(a)
60
14
50
12
Frequency (%)
Frequency (%)
(a)
40 30 20 10 0
10 8 6 4 2 0
Fibre Orientation (Degrees)
Fibre Orientation (Degrees)
(b)
(b)
Fig. 5. SEM image of nonwoven fabric (a) and its ODF computed with Nonwovens Anisotropy V1 (b).
Fig. 6. SEM image of nonwoven fabric (a) and its ODF computed with Nonwovens Anisotropy V1 (b).
noise and light conditions. A weighted mean of subdomain ODFs is employed as the resultant ODF of the complete image. This homogenized approach yields a more adequate ODF for the nonwoven fabric, since it considers local deviations in orientation. The most important rule to use this feature is to keep aspect ratio of image subdomains approximately square. This feature is useful not only for dense materials, but also for several issues originating in imaging conditions, such as local brightness in SEM images or salt & pepper noise in X-ray micro-CT images. The subdomain processing feature of the code is tested using an X-ray micro-CT image of the PP/PE nonwoven fabric having a dense fibrous structure shown in Fig. 7. It is obvious that fibres in Fig. 7 are less distinguishable than the ones in Figs. 5a and 6a due to the image scale and high fibre density. In order to increase distinguishability of individual fibres, the image is divided into six subimages having aspect ratios closed to that of a square. The code generates these sub-images (Fig. 8) each showing a specific region of the main image (Fig. 7). Detected fibres in each subdomain are designated with lines drawn on top of them (Fig. 8). Fibredetection accuracy and efficiency could be modified with the digital image processing parameters on the GUI of the code illustrated in Fig. 2. The lines indicating orientations of fibres help a user to optimize the outcome with respect to microstructure and imaging conditions. An interesting point is that two of the sub-images in Fig. 8 are brighter than the others because each one is processed based on its own brightness and noise conditions. In other words, pixel
values change as a result of histogram equalization applied to the binary form of sub-images for making fibre boundaries more distinguishable. In this case, the light source, which increases brightness of nearby regions, is located at the right bottom corner of the image in Fig. 7. The ODF of each subdomain in Fig. 8 is computed separately by the code and given in Fig. 9. It is obvious that ODF characteristics of each region are different, due to randomness in the microstructure. At this point, it should be emphasized that position and size of the input image area of the nonwoven material play an important role in determining a representative ODF. The X-ray micro-CT image in Fig. 7 covers an area between neighbouring bond points along CD and MD that form a periodic bond pattern. Two horizontal boundary bond points along CD, which are excluded from ODF computation due to lack of fibre boundaries, could be seen partially at the right and left edges of fibre matrix in Fig. 7. Computation efficiency of the code could be improved by increasing the resolution and sharpness of input image. The fibre detection possibility increases with increased sharpness and resolution at pixels located on fibreboundary regions. Additionally, the number of image divisions could be increased together with image resolution and sharpness to obtain a more adequate ODF for nonwoven material. The resultant ODF of the PP/PE nonwoven fibre matrix shown in Fig. 7, computed based on ODFs obtained for each subdomain (Fig. 9), is given in Fig. 10. Based on the number and orientations of fibres computed in each sub-image, a resultant ODF graph is generated by the code. This ODF graph reflects randomness of
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Fig. 7. X-ray micro-CT image of fibre matrix region of nonwoven (fibre: PP/PE, planar density: 50 g/m2).
Fig. 8. Subdomains of fibre matrix image (Fig. 7) processed with Nonwovens Anisotropy V1.
the overall fibrous network based on particular regions. The resultant ODF computed by the code will be used to characterize the randomness of the fabric’s microstructure. To sum up this part, a practical user-friendly code for computing the ODF of fibrous materials is introduced. Using the subdomain processing feature with a larger number of image divisions will improve ODF results. Additionally, increased image resolution and sharpness contribute to fibre detection capability of the code, which improves the computed resultant ODF. This ODF graph will be used to determine anisotropic parameters, which are necessary for assessing anisotropic mechanical properties of nonwoven materials. The derivation of these parameters from the ODF graph will be explained in the next section.
3. Anisotropic parameters Anisotropy is an unavoidable phenomenon in nonwovens; therefore it should be taken into account in computation of their mechanical properties. The level of direction-dependency of the
mechanical response is very important for results of simulations. As the number of material symmetry planes decreases, the amount of parameters defining the direction-dependant behaviour increases significantly, hence increasing the complexity of material definition as well as the computation time. Orthogonal anisotropy (orthotropy), having three symmetry planes, can adequately define the level of anisotropy for thermally bonded nonwovens. The principal directions of orthotropy in nonwovens can be assumed as coincident with their principal directions – MD, CD and TD – for definition of their viscoelastic–plastic parameters. The main source of anisotropy is the nonuniform orientational distribution of fibres causing a direction-dependent response. Deformation level of bond points is significantly less than that of fibre matrix due to differences in their microstructures [3]. Since nonwovens exhibit large-strain deformation behaviour, which is observed in fibre matrix rather than in bond points, source of anisotropy is assumed as fibre matrix in this paper. The nonuniformity can be quantified with the use of the ODF, which will be used to calculate of orthotropic parameters. Due to the nature of orthotropy, these parameters are assumed to be symmetric with respect
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Frequency (%)
Fig. 9. ODF of each subdomain in Fig. 8.
18 16 14 12 10 8 6 4 2 0
Fibre Orientation (Degrees) Fig. 10. Resultant ODF obtained from subdomain ODFs in Fig. 9.
to MD and CD on fabric plane. The parameters defining the level of orthotropy are calculated from the ODF in Nonwovens Anisotropy V1, according to the following equations; i¼1
i¼1
C CD ¼ PN i¼1
RE ¼
PN
C MD ¼ PN
jsin ai j
PN
jsin ai jþ
PN
i¼1
oretical (RT) – are introduced to define the level of direction-dependent mechanical behaviour on fabric plane. RE is defined as
i¼1
jcos ai j
jcos ai j
PN
jsin ai jþ
i¼1
jcos ai j
; ð1Þ ;
where CMD and CCD are the parameters defining the level of orthotropy in MD and CD (obviously, CMD + CCD = 1) that are used to calculate the stress–strain curves of the nonwoven material for MD and CD; ai is the angle between the axis of the ith fibre and CD; N is the total number of fibres accounted by the ODF algorithm. Orthotropy of a nonwoven material could be determined with two possible approaches: (i) using parameters obtained from the ODF (Eq. (1)) and (ii) using the stress–strain results of tensile tests performed along MD and CD. In order to compare these approaches quantitatively, two orthotropic ratios – experimental (RE) and the-
rMD ; rCD
ð2Þ
where rMD and rCD are the stresses along MD and CD obtained from the tensile test results. On the other hand, to obtain the level of orthotropy from the constants CMD and CCD, which are computed with Nonwovens Anisotropy V1 using the ODF of nonwoven fabric, RT is introduced as follows
RT ¼
C MD : C CD
ð3Þ
4. Results and discussion Values of RE and RT of the PP/PE nonwoven fabric shown in Fig. 7 are compared using the ODF of the fabric given in Fig. 10. Here, RT is found using Eq. (3), which requires CMD and CCD parameters.
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3.0 2.5
RE
2.0
1.77
0.34
1.5 RE=1 for isotropic materials
1.0 0.5
Experimental Data Mean of Experimental Data
0.0 0
0.1
0.2
0.3
0.4
0.5
True Strain Fig. 11. Experimental orthotropic ratio of nonwoven fabric (fibre: PP/PE, planar density: 50 g/m2).
Table 1 Experimental and theoretical orthotropic ratios of several nonwoven fabrics.
RE RT
PP/PE 50 g/m2
PA6/PE 100 g/m2
PA6/PE 150 g/m2
1.77 ± 0.34 1.86
2.55 ± 0.30 2.64
2.30 ± 0.16 2.59
According to Eq. (1), CMD and CCD of the PP/PE nonwoven fabric are 0.65 and 0.35, respectively, which in turn yield a RT value of 1.86. On the other hand, tensile test results of the fabric in MD and CD are used to draw the RE curve using Eq. (2). According to Fig. 11, orthotropy of the nonwoven varies with deformation due to reorientation of fibres. The mean value of RE curve – 1.77 ± 22% – is also given in Fig. 11. For an isotropic material, RE is always 1 due to an infinite number of symmetry planes causing direction-independent stress–strain curve. According to Table 1, which contains the mean value of RE curve and RT for various nonwoven fabrics, their orthotropic ratios calculated from the ODF are close to those determined in tensile tests. Apparently, RT values are well within the variability range of RE curves. So according to the results in Table 1, accuracy of Nonwovens Anisotropy V1 in predicting the level of mechanical orthotropy using microstructural images of a nonwoven fabric is promising. As a consequence of this agreement, CMD and CCD parameters computed by the code could be used to assess orthotropic mechanical properties of nonwoven fabrics in their numerical models for design and optimization. 5. Conclusions To sum up, anisotropy of nonwoven materials is analysed in this paper by means of quantification of their random fibrous microstructure. The developed code – Nonwovens Anisotropy V1 – is used to perform this analysis using micro-scale images of fibrous matrix obtained with SEM or X-ray micro-CT techniques. Randomness in the fabric microstructure is quantified with the ODF, which is computed with the developed code from the microstructural image of nonwovens. A relation between the ODF and structure’s mechanical anisotropy is suggested introducing orthotropic parameters representing a direction-dependent mechanical response of nonwovens. These parameters could be used in numeri-
cal models to define the direction-dependency of mechanical properties of thermally bonded nonwoven materials. The numerical tool described in this study is effective in predicting the anisotropic deformation characteristics of thermally bonded nonwovens; it verified with experiments and ready to use for applications. There are no complex input parameters, and the graphical user interface does not require a deep knowledge of digital image processing. The developed algorithm is fully parametric and independent of the bond pattern and shape. The code may serve industry and research as a useful tool for product development and optimization as well as numerical modelling. Acknowledgement The authors gratefully acknowledge the support of Nonwovens Cooperative Research Center, North Carolina State University, USA. References [1] S.J. Russell, Handbook of Nonwovens, Woodhead Publishing Ltd., Cambridge, 2007. [2] S. Michielsen, B. Pourdeyhimi, P. Desai, Processes, and properties, Journal of Applied Polymer Science 99 (2006) 2489–2496. [3] E. Demirci, M. Acar, B. Pourdeyhimi, V.V. Silberschmidt, Finite element modelling of thermally bonded bicomponent fibre nonwovens: tensile behaviour, Computational Materials Science 50 (4) (2011) 1286–1291. [4] X. Hou, M. Acar, V.V. Silberschmidt, Computational Materials Science 46 (3) (2009) 700–707. [5] X. Hou, M. Acar, V.V. Silberschmidt, Finite element simulation of low-density thermally bonded nonwoven materials: effects of orientation distribution function and arrangement of bond points, Computational Materials Science (2010), doi: 10.1016/j.commatsci.2010.03.009. [6] H.S. Kim, Fibers and Polymers 5 (3) (2004) 177–181. [7] H.S. Kim, Fiber and Polymers 5 (2) (2004) 139–144. [8] B. Pourdeyhimi, R. Ramanathan, R. Dent, Textile Research Journal 66 (11) (1996) 713–722. [9] B. Pourdeyhimi, R. Ramanathan, R. Dent, Textile Research Journal 66 (12) (1996) 747–753. [10] B. Pourdeyhimi, R. Dent, H. Davis, Textile Research Journal 67 (2) (1997) 143– 151. [11] H.S. Kim, B. Pourdeyhimi, Technology and Management 1 (4) (2001) 1–7. [12] B. Xu, L. Yu, Textile Research Journal 67 (8) (1997) 563–571. [13] B. Pourdeyhimi, H.S. Kim, Textile Research Journal 72 (9) (2002) 803–809. [14] E. Ghassemieh, H. Versteeg, M. Acar, International Nonwovens Journal 10 (2) (2001) 26–31. [15] E. Ghassemieh, M. Acar, H. Versteeg, Proceedings of the Institution of Mechanical Engineers Part L: Journal of Materials: Design and Applications 216 (3) (2002) 199–207. [16] R.C. Gonzalez, R.E. Woods, Digital Image Processing, second ed., Prentice Hall, New Jersey, 2002.