Stretchability of integrated conductive yarns in woven electronic textile Master s thesis

Transcription

1 Stretchability of integrated conductive yarns in woven electronic textile Master s thesis E.S.C. de Boer Report number: MT Eindhoven University of Technology Department of Mechanical Engineering Mechanics of Materials Philips Research Laboratories Human Interaction & Experiences Coaches: dr. ir. R.H.J. Peerlings ir. J.P.J. van Os dr. ir. S.B. Luitjens Graduation professor: prof. dr. ir. M.G.D. Geers Eindhoven, May 7, 2012

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3 Abstract Electronic textiles are textile fabrics, that have electronic components embedded in or attached to them. A basis for electronic textile has been developed at Philips Research by integrating conductive yarns (made from silver plated copper) in woven textile. Textile is an interesting base for electronics because of its unique mechanical properties, such as flexibility and stretchability. It is therefore essential, that a conductive yarn that is integrated into textile, can withstand the deformation that comes with the everyday use of a textile product. The electronic textile samples have been experimentally characterized in order to study the deformation of the conductive yarns during the stretching of woven electronic textile. Woven electronic textile samples have been experimentally characterized in order to determine which effects govern the extensibility of integrated conductive yarns. Failure of the conductive yarns was observed for extensions in the range of 9 14%, which is relatively small in comparison with the maximum extension of the textile. Furthermore, it was observed that the conductive yarn deforms mostly plastically. A conductive yarn, that is integrated in woven textile, has a wave-like shape due to the yarns that alternatingly pass below and above it. From experiments it was concluded that the extensibility of integrated conductive yarns are determined by two effects: 1. Over-length effect: Due to the initial wave-like shape, the actual length of the yarn is greater than the length of the fabric it is removed from. 2. Pre-deformation effect: The interlacing of conductive yarns introduces plastic deformation, thereby reducing the yarn s ductility. A simple analytical model has been developed to quantitatively predict how the weaving parameters influence these effects. The model can be used to create a more reliable electronic textile product by increasing the extensibility of conductive yarn in woven electronic textile or even preventing plastic deformation. In the current woven electronic textile samples, the extensibility of the integrated conductive yarn is slightly smaller than that of the virgin conductive yarn. Several measures can be taken to prevent this reduction in extensibility, such as decreasing the weaving density and using a different conductive yarn with low twist and a smaller filament diameter. However, in order to gain extensibility relative to that of virgin conductive yarn, the amplitude of the wave-geometry has to be increased significantly. This may not be feasible in the current weaving structure. Therefore, alternative weaving structures will have to be considered. Unlike the current conductive yarns, woven textile exhibits a significant amount of elasticity when it is loaded and subsequently loaded. This mismatch in material properties may lead to problems in the daily use of textiles such as clothing. In order to be able to elastically stretch the current conductive yarn, a wave-like geometry can be used. However, the required amplitude and wavelength of such a conductive yarn are in the order of millimeters. Such dimensions are not feasible for conductive yarns that are interlaced in woven textile. Unless conductive yarns with a larger elastic regime can be used, alternative methods of attaching a conductive yarn to a textile will have to be investigated.

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5 Contents 1 Introduction Weaving Previous work on the mechanics of electronic textiles Problem description Strategy Outline Experimental characterization Introduction Material Experimental setup Sample preparation Plain woven electronic textile Woven electronic textile with simulated components Conductive yarn Conductive yarn segments Results Plain woven electronic textile Woven electronic textile with simulated components Conductive yarn Conductive yarn segments Discussion Modelling Introduction Material characterization Over-length effect Pre-deformation effect Combined prediction Segment of conductive yarn without float Segment of conductive yarn with float Discussion Increasing the stretchability of woven electronic textile Introduction Improving the extensibility of integrated conductive yarn Preventing plastic deformation during straightening Discussion Conclusion 51 References 53 3

6 A Experimental characterization of the anisotropy of woven textile 55 A.1 Sample preparation A.2 Results A.3 Discussion B Comparison of the mechanical response of the woven electronic textile samples with earlier research 59 C Arc length of a sine wave 61 D Average value on a circular cross section 63 E Integrating the arcsine function 67 4

7 Chapter 1 Introduction Most present day electronics are rigid. In order to create new application fields, much attention is given to the development of flexible electronic devices. Small rigid electronic devices are already being incorporated into flexible substrates. Even more potential applications would emerge if such devices could also be incorporated into stretchable substrates [1]. Textiles are a flexible and stretchable substrate, that has been used for centuries. Textiles have several unique properties, such as being soft, drapeable, lightweight and in many cases stretchable. Electronic textiles are textile fabrics that have electronic components embedded in or attached to them. (a) Fashion (b) Decoration (c) Photo therapy Figure 1.1: Various applications of electronic textiles developed by Philips Research. The flexibility and stretchability of textiles combined with integrated electrical components can have various applications. LEDs can be fixed on a textile substrate that is integrated into clothing for fashion purposes (like in figure 1.1(a)) or a matrix of LEDs on fabric can be used to create a decorative, low resolution flexible display (see figure 1.1(b)). In healthcare, textile integration for medical applications could allow for the unobtrusive monitoring of viral parameters. For example, conductive yarns can be attached to garments to create textile electrodes for ECG monitoring. Furthermore, arrays of coloured LEDs can be mounted on electronic textile (e.g. inside a flexible pad, see figure 1.1(c)) for light treatment applications. The use of electronic textile for these applications allows for comfortable daily use. A basis for electronic textile has been developed at Philips Research by integrating electrically conductive yarn into woven textile. Integrating electrical components into fabrics creates challenges in reliability, because of the mismatch in material properties. Conductive yarns with sufficient conductivity are generally stiffer than common textile yarns. Furthermore, textile yarns can in general be extended further. As a result, conductive yarns in a textile under tension will carry a large part of the load and will fail before the textile yarns do. Failure of 5

8 conductive yarns may lead to loss of functionality of an electronic textile device, and is therefore undesired. Textiles, in for example clothing, will have to be able to withstand significant deformation during everyday use. In order to understand issues such as reliability and failure, research is done on the mechanics of electronic textiles. 1.1 Weaving Woven fabrics generally consist of two sets of yarns, that are interlaced at perpendicular angles with respect to each other. To create a woven fabric, one set of yarns is stretched on the weaving machine while the other set is interlaced. The yarns that run along the length of the fabric are known as warp ends, while the yarns that are woven into the warp yarns are known as weft ends. Yarns in a woven fabric do not follow a straight line, because the warp and weft yarns are forced to bend around each other when they are interlaced. As a result of this waviness, the actual length of the yarn is larger than the fabric length. By lifting or lowering the warp yarns during the insertion of the weft yarns, various weave structures can be created. Multi-layered fabrics can be constructed by using multiple layers of warp yarns and connecting these by the weft yarns. In some weave structures, one yarn may pass over multiple perpendicular yarns before interlacing again. A length of warp or weft yarn on the surface of a fabric without being interlaced is called a float. Further information on the manufacturing techniques of textiles can be found e.g. in the publications of the Textile Institute [2, 3]. 1.2 Previous work on the mechanics of electronic textiles Several numerical models have been developed at Philips Research to account for the anisotropic, inelastic non-linear behaviour of plain woven electronic textile (i.e. without any components but with integrated conductive yarns). Feron [4] modelled the electronic textile as a sheet of uniform material. Based on experimental results, he assumed orthotropic material behaviour in the elastic regime and an anisotropic yielding criterion to account for orthotropic plasticity. However, since the harding law could only be fitted on one direction, the model was not accurate in describing the material behaviour in diagonal direction. To overcome this problem, Fonteyn [5] modelled the textile as a combination of a discrete lattice structure and a compliant continuum material. Elastic trusses represent the tensile response of the yarns in the textile, and elastic continuum elements model other effects such as friction between the yarns. This resulted in a nonlinearity and evolving anisotropy in the global response, that is similar to that of the actual electronic textile. Based on this model, Verberne [6] chose to model woven electronic textile as an elasto-plastic lattice structure (later published by Beex [7]). Similar to the model by Fonteyn [5], the tensile response of the textile yarns is represented by truss elements in warp and weft direction. However, effects such as friction are now modelled by diagonal truss elements instead of a continuum elements. The resulting model was validated using a three dimensional punch test. The experimental results were in good agreement with the numerical model. The model includes several mechanisms, that occur during mechanical loading of electronic textile, such as rotation of yarns and negligible stiffness in compression and bending. During the experimental characterization of the fabric samples, Verberne [6] observed that the conductive yarns in the textile fail at strains, which are significantly smaller than those at which the textile fails. The damage to the conductive yarns was visualized by taking X-ray 6

9 images of the deformed samples. Damage was consistently observed in the area where the conductive yarn stands out of the textile for component attachment (floats). Furthermore, it was observed that the conductive yarns still contribute to the stiffness of the fabric after they have failed. 1.3 Problem description Previous work has led to the development of a numerical model, that quite accurately describes the material behaviour of plain woven electronic textile. However, it has also been pointed out, that failure of the conductive yarns may occur at strains which are significantly smaller than those at which the textile fails. Failure of conductive yarns may lead to loss of conductivity in an electronic textile product and is therefore undesired. Textile is an interesting base for electronics because of its flexibility and stretchability. It is therefore essential, that a conductive yarn, that is integrated into textile, can withstand the deformation, that comes with the everyday use of a textile product. The goal of this research is to investigate the deformation of the conductive yarns during the stretching of woven electronic textile. More precisely, the research performed by Verberne [6] raises questions about the failure mechanism of conductive yarns in woven textile. From the observations reported, it can be concluded that failure is consistently localized at the floats and that the textile exerts friction on the conductive yarn during deformation. Particularly the failure at the floats is remarkable, since the conductive yarns appear to have some clearance at the floats and one would therefore expect them to be stretched less than where they are woven into the textile. Furthermore, the literature review [8], that was performed for this study, has revealed, that a heat treatment during the weaving process severely deforms the conductive yarns by shrinking the surrounding textile. These effects should be further investigated in order to derive design rules, which can be applied to design a more reliable electronic textile product. During weaving, yarns are deformed as they are bent around each other. Since conductive yarns are usually made from metal, they are expected to loose some of their ductility due to this pre-deformation. On the other hand, the waviness of a yarn in a woven textile (and the clearance at the floats) allows it to be extended further than a yarn that is placed in a straight line, because the over-length stored in the waviness, contributes to the extensibility of the yarn. The loss of ductility and the waviness of the yarn are two opposing effects, whose interplay governs the extensibility of a conductive yarn. When a conductive yarn is integrated in woven textile, the friction exerted by the surrounding textile may further influence its extensibility by enforcing a more uniform deformation than a freestanding yarn would exhibit. The magnitudes of these effects are investigated, in order to be able to predict the influence of weaving parameters and the choice of conductive yarns on the extensibility of conductive yarns in woven electronic textile. 1.4 Strategy The focus of this research lies on the interaction between conductive yarn and textile as it is stretched. For this purpose a literature study has been performed on the manufacturing and mechanical properties of yarns and textiles [8]. Since it is unknown what effects cause the failure of integrated conductive yarns, an experimental approach is required. Woven electronic textile samples, similar to the samples that were tested by Verberne [6], have been manufactured at Philips Research. The samples are subjected to an experimental characterization using a setup 7

10 consisting of a tensile tester with imaging equipment. As a first step, the findings by Verberne [6] are verified by performing tensile tests on plain woven electronic textile (i.e. without any components) in the three characteristic directions (warp, weft and diagonal direction). The deformed samples are optically characterized in order to determine if failure of the conductive yarns has occurred. Subsequently, stretching of the textile in directions where failure occurs is studied in more detail by recording the deformation with an optical microscope. This will reveal how far the textile can be extended before failure occurs. It was determined by Verberne [6] that failure of the conductive yarns in plain woven electronic textile exclusively occurs at the floats. In practice, stiff electronic components (such as LEDs) are fixed (e.g. glued or soldered) on these floats. Adding components restricts the movement of the conductive yarn through the textile and strengthens the float region. In order to simulate the presence of components, glue spots are placed on the floats. The woven electronic textile samples with simulated components are stretched in the tensile tester, while an optical microscope records the deformation. Attention is now given to failure of conductive yarn in between floats. The failure of conductive yarns in textile at small strains may be a result of pre-existing damage (i.e. loss of ductility during weaving), interaction between textile and conductive yarn or a combination of these effects. In order to find out which effect is dominant, conductive yarns are extracted from electronic textile samples and extended in the tensile tester. By comparing the response of the extracted yarn with that of virgin (i.e. unused) conductive yarn, the influence of the weaving process (loss of ductility) can be quantified. Consequently, by comparing the extensibility of extracted conductive yarn and conductive yarn in textile samples, the influence of the surrounding textile can be quantified. Extracted conductive yarns have two distinctly deformed regions as a result of the local weaving structures at the floats and in-between floats. By testing short segments of conductive yarn, the influence of these weaving structures on the extensibility can be analyzed. The experimental results are analyzed in order to determine which effects govern the extensibility of the conductive yarns in woven electronic textile. These effects are then modelled to determine which parameters influence the extensibility of the integrated conductive yarns. This model can finally be used to improve the design of the textile by changing weaving parameters or using different conductive yarns. 1.5 Outline The experimental characterization of electronic textile and conductive yarn samples is discussed in chapter 2. In chapter 3, a model is presented that captures the observed effects and predicts the mechanical behaviour of the integrated conductive yarns. The model is compared with experimental results in order to asses its usefulness. Finally, in chapter 4 the model is used to create a more reliable electronic textile product. 8

11 Chapter 2 Experimental characterization 2.1 Introduction In this chapter, various experiments are performed, in order to characterize the stretchability of woven electronic textile. Tensile tests are performed on: Plain woven electronic textile (i.e. without any components) Electronic textile samples with simulated components Virgin and extracted conductive yarn Extracted conductive yarn segments The material and experimental setup are discussed in detail in the sections 2.2 and 2.3 respectively. The four types of experiments each require a different method of sample preparation, as discussed in section 2.4. The experimental results for the various experiments are presented in section Material Woven electronic textile samples have been developed at Philips Research. Conductive yarn is integrated into a woven textile structure, to connect electronic components (see figure 2.1(a)). The electronic textile was designed as a substrate for LEDs, to act as a light source or even as a textile display. The samples, that are investigated in this study, are similar to the samples tested by Verberne [6]. Compared to this earlier study, the textile was woven into the same weaving structure, although different textile yarns were used. The samples, that are investigated in this study, are made out of polyester yarns. In warp direction, a filament yarn with a linear density of dtex 76 is used. In order to give the textile a more natural feel, a spun fiber yarn of dtex 145 is used in the weft direction. Spun fiber yarns are made from staple (i.e. short) lengths of man-made fibers instead of continuous-length filaments. In order to imitate natural fibers, long filament fibers are chopped up into staple lengths and spun. The density of the yarns in warp direction is 220 ends/cm and 85 picks/cm in weft. Three layers of warp yarns are interlaced by weft yarns, to create a densely woven three layered structure. Conductive yarns are integrated into the textile by using conductive warp yarn in the central warp layer at regular intervals. As a result, the conductive yarn is insulated from the wearer s skin. Sets of two conductive yarns are woven in warp direction with a spacing of mm. The Elektrisola Litzwire CuAg conductive yarns (see figure 2.2) consist of 20 silver plated 9

12 (a) (b) Figure 2.1: (a) Woven electronic textile developed by Philips Research. magnification of the floats meant for component attachment. Image (b) shows a 10

13 Figure 2.2: The Elektrisola Litzwire CuAg electrically conductive yarn, that is used in the woven electronic textile samples. (a) (b) Figure 2.3: (a) Cross section along the warp direction of the woven electronic textile. Image (b) schematically shows how the conductive yarn (yellow) passes around the (grey) weft yarns. copper filaments with a diameter of 0.04 mm each that are wrapped with a twist of approximately 240 m 1. The yarn was chosen, because it has a relatively low electrical resistance (R < 1 Ω/m) and high flexibility. During weaving, very little tension (i.e. less than 1 N) is applied on the conductive warp yarns. In order to be able to attach components by means of soldering or gluing, 3.3 mm of conductive (warp) yarn is brought to the surface of the textile (as floats) at regular intervals (see figure 2.1(b)). In order to keep the float close to the textile, a single weft yarn (binder yarn) is placed over the float at its center. A heat treatment is applied after weaving, to make the fabric more stable (i.e. to prevent shrinkage in a later stage). The heat treatment shrinks the polyester yarns by several percent, but does not influence the length of the conductive yarns. Consequently, the conductive yarn is bent around the shrunk weft yarns and pushed out of the textile at the floats, as can be seen in figure 2.1(b). Figure 2.3 shows how the conductive yarn is placed in the woven structure. In between floats, the conductive yarn alternatingly passes below and above weft yarns. At the floats, the yarn is brought to the surface and passes above four weft yarns, below a single weft yarn and again above four weft yarns, before going back into the textile. Conductive yarns have been carefully removed from textile samples and have been optically characterized. The extracted yarns have significant plastic deformation, as can be seen in figure 2.4(a). The shape of the float is clearly visible in the extracted yarn. The largest deformation can be observed at the float in figure 2.4(b). In between the float regions, the yarn has a regular 11

14 wave-like shape (see figure 2.4(c)) as a result of the weft yarns, that are alternatingly passing below and above the conductive yarn. (a) (b) (c) Figure 2.4: Conductive yarn that has been extracted from woven electronic textile samples. Image (a) shows an overview of the deformed yarn, image (b) shows a magnification of the float region and image (c) shows the wave-like shape in between floats. 2.3 Experimental setup Tensile tests are performed on an an Instron 5566 universal testing machine. An AVT F201B Stingray black and white camera is used to take images of the sample during deformation. These images can be used to calculate local strains or to investigate damage. The camera is attached to a linear guide, that moves with half the displacement of the moving clamp of the tensile tester. As a result, the camera moves with the center of the sample and a larger part of the recorded area is useful for the optical analysis. Both the tensile tester and the camera are connected to a computer using the Labview software, that stores the force, displacement and time for every recorded image In order to capture more detail during deformation, a Leica MZ6 binocular microscope can be placed in front of the tensile tester (see figure 2.5). Because of the microscope s size and weight, it must be fixed to the testing machine and cannot move with half the displacement of the moving clamp. Therefore, in order to prevent movement of the area of interest out of the field of view, only parts of the sample close to the immobile clamp can be investigated. The AVT Stingray camera can be attached to the microscope to record images at high magnifications. For the optical characterization of deformed samples, a Leica MZ12 binocular microscope is used. Due to the use of two lenses (0.4 and 1.0 ) and the 12-fold zoom, magnifications up to 12

15 200 can be realized. The microscope is equipped with a Leica DFC320 digital camera to take pictures. Figure 2.5: A Lieca MZ6 microscope is placed in front of an Instron 5566 testing machine, in order to capture images at high magnification during deformation. In previous research on the mechanical properties of woven textile by Feron [4], Fonteyn [5] and Verberne [6], an optical method was used to determine local strains in tensile and lateral directions. It was found by Fonteyn [5] that the global strain, determined from the clamp displacement, does not differ from the locally (optically) measured strain, when the textile is loaded in warp or weft direction. The lateral contraction is relatively small in these directions and as a result the deformation is quite uniform. However, lateral contraction cannot be neglected when the textile is loaded in diagonal direction. As a result, global strain is expected to differ from the actual local strains in the center of a sample that is extended in diagonal direction. Since the focus of this research lies on the extensibility of conductive yarns, which lie in the warp direction, it is decided to use the clamp displacement to determine (global) strain. When slipping of material out of the clamps is prevented, global strains do not differ from locally measured strains in a uniformly deforming sample. 2.4 Sample preparation Plain woven electronic textile In order for a textile sample to be representative for the mechanical behaviour of the textile, heterogeneities in the sample have to be taken into account. In the case of the woven electronic textile, the heterogeneities that may effect the mechanical behaviour of the textile are the conductive yarns. Sets of two conductive yarns lie in warp direction with a spacing of mm (see figure 2.6). So in order for a test on a warp sample to be representative for the textile, warp samples need to have a width of a multiple of mm. In weft and diagonal direction, the presence of floats may influence the global material behaviour as the textile locally has a different weaving structure. However, for sufficiently large samples (i.e. larger than the spacing of the floats) this influence is assumed to be negligible. 13

16 Figure 2.6: Spacing of the conductive yarns in the woven electronic textile. The woven electronic textile samples were provided on a roll of width of 94 mm, with the warp yarns oriented in the longitudinal direction. Clamping of samples in the Instron tester requires 20 mm on both sides. Therefore the length of a weft sample is limited to 54 mm and it was chosen to cut warp and weft samples with dimensions of mm. The influence of sample size for the warp direction was tested in order to develop a reproducible testing method. Table 2.1 shows the dimensions and extension rates that were used for testing the textile samples. The extension rate is the same as that used by Verberne [6], in order to be able to compare results. Table 2.1: Dimensions and extension rates for the textile samples that were cut. Direction Width Length Deformation rate [mm] [mm] [s 1 ] Warp Weft Diagonal Textile samples are susceptible to slipping out of the tester s clamps during experiments. The amount of slip can be optically measured by placing markers. Various clamping methods have been compared. The most effective way to reduce the amount of slip was found to be by fixing sandpaper on the surface of the clamps. The sandpaper was fixed using duct tape at the outer edges of the clamps. The tape works as a wedge, that focuses the pressure of the clamps on the edge of the sample Woven electronic textile with simulated components Components on woven electronic textile restrict the movement of the conductive yarn through the textile and strengthen the float region. In order to simulate the presence of components, glue is positioned on the textile where the conductive yarn comes out of the textile (see the dashed area in figure 2.7). The glue locally fixates the conductive yarn to the surrounding textile, thereby restricting movement of the conductive yarn through the textile. Dymax

17 UV Curing Plastic Bonding Adhesive was used to simulate components. The samples were cut to the same size and loaded at the same deformation rate as the plain electronic textile samples. Figure 2.7: Woven electronic textile sample with glue spots (dashed area), that fix the conductive yarn to the surrounding textile at the floats Conductive yarn A spool of (virgin) Elektrisola Litzwire CuAg conductive yarn was provided by Philips Research and could be used to cut samples of any desired length. In order to study the influence of weaving, conductive yarn was carefully extracted from the electronic textile samples. The integrated conductive yarn was removed by cutting away the surrounding textile yarns and carefully unraveling the textile. Both the length of a sample and the method of clamping may influence the measured response of tensile tests on metal yarns. Long samples may contain more imperfections, that could result in failure, whereas clamping could damage the yarn and cause failure to localize at the clamps. To prevent damage to the yarn, a layer of soft material (such as paper or rubber) can be placed between the clamps or the yarn can be wound on cylindrical clamps. The effects of sample length, deformation rate and clamping method was compared in order to determine a reproducible testing method. It was chosen to use mechanical clamps with a layer of rubber to fixate the yarns in the tensile tester. The used yarn samples have a length of 100 mm. A longer sample length is desired to reduce the effect of slip from the clamps, but the lengths of yarn that can be extracted from textile samples are limited. The deformation rate was chosen to be s Conductive yarn segments Extracted conductive yarn (see figure 2.4) has two distinctly deformed segments. The float segment is most heavily deformed, whereas the segment in between floats has a regularly deformed shape. In order to analyze the mechanical behaviour of these separate segments, the mechanical response of the individual segments is also measured. The spacing between floats on the conductive yarn is approximately 10.5 mm, and the float region itself has a length of approximately 3.3 mm (see figure 2.6). The measuring of very short samples introduces inaccuracies, as it is difficult to accurately determine the length of samples, and the relative influence of slipping of yarns out of the tester s clamps is increased. It is therefore not feasible to test samples with a length of several millimeters (such as the float segment) in the current experimental setup. Instead, it was chosen to test samples with a length of 10 mm and take measures to minimize slip at the clamps. By testing samples with and without a float segment, the mechanical response of the float segment can later be calculated. In order to serve as a benchmark and to verify the accuracy of the results, samples with virgin conductive yarn were tested as well. 15

18 (a) (b) Figure 2.8: Short yarn sections are glued onto pieces of cardboard. Image (a) shows a prepared sample with virgin conductive yarn and image (b) shows an extracted conductive yarn section that contains a float. In order to minimize slipping of the sample out of the tensile tester s clamps, the yarn segments are glued to pieces of cardboard (see figure 2.8). The cardboard is cut to the same dimensions as the tensile tester s clamps such that they can be clamped effectively. Preferably, the yarn segments should be tested at the same strain rate as the longer yarn samples. However, extending a 10 mm long sample with an extension rate of s 1 would require the tester s moving clamp to move with a velocity of 4 mm/min. It was observed that the force measurement showed oscillations with an amplitude of 0.02 N during an experiment with this velocity. This resulted in a large scatter of the maximum extension of a yarn segment, as the maximum was often exceeded at smaller extensions. In order to avoid this problem, samples were extended with a rate of 13.3 ms Results Plain woven electronic textile Plain woven electronic textile (i.e. without components) was loaded in warp, weft and diagonal direction, in order to find out if failure of the conductive yarns occurs. Failure of the conductive yarns was only observed for tensile tests in warp direction, i.e. the direction in which the conductive yarns are oriented. Figure 2.9 shows the load-elongation curve of a plain woven electronic textile sample that has been extended by 14 % in warp direction and was subsequently unloaded. The mechanical response of woven electronic textile in weft and diagonal direction is further discussed in appendix A, where the anisotropy of woven textile is characterized. 15 F/w [N/mm] u/l [ ] Figure 2.9: Load-elongation curves of woven electronic textile in warp direction. 16

19 For textile and yarn samples, stress is an ill-defined concept, because of the empty space between yarns and even fibers. However, in order to be able to compare textile samples of different width, it is useful to express load in terms of force divided by sample width (F/w). The elongation of the textile samples is expressed as displacement divided by initial length (u/l). The bumps, that are visible in the curve near the peak load, are a result of edge effects. Failure of conductive yarns is not visible in the load-elongation curve. In order to determine how much the textile can be extended in warp direction before failure of the conductive yarns occurs, tensile tests are performed on different textile samples, that are loaded to extensions of u/l = 0.05, 0.06,..., 0.14, The deformed samples are unloaded and optically inspected for damage of the conductive yarns. Up to 8% extension no damage is observed in the conductive yarns. After 9% extension some failed filaments can be observed at the floats. The situation is dramatically worse after 10% extension, although no conductive yarn has failed completely. When the textile has been extended for more than 11%, complete failure of the conductive yarn is visible at some of the floats. Further elongation of the textile gives similar results. Figure 2.10: Part of a deformed textile sample after 14% elongation in warp direction. The circled areas show failure of the conductive yarns. A magnification of the float that is marked with a (*) is shown in figure Failure of the conductive yarns at the floats is visible in the deformed sample, after 14% elongation, in figure One yarn may fail at multiple locations and typically one in every two or three floats shows failure. This indicates, that movement of the conductive yarn with respect to the textile is limited and the textile exerts friction on the conductive yarn. However, this friction is limited as the failure of one float appears to relieve nearby floats. It was observed, that floats close to the tensile tester s clamps always fail. It is unclear how much the conductive yarns are able to slip with respect to the clamps, but the clamps are likely to further restrict the movement of the yarns through the textile. Ideally, the textile would be clamped such that the edge of the clamp is half-way in between floats. However, this is not possible since the floats are placed alternatingly (as can be seen in figure 2.10). Despite the effect of the clamps, the floats near the clamps are not always the first to fail. 17

20 Figure 2.11: Magnification of the failed conductive yarn that is marked (*) in figure Most filaments in the conductive yarn fail at the same location, as can be seen in figure The failure is localized at the center of the float, where one weft yarn passes over the conductive yarn (see also figure 2.3(b)). Microscopic imaging of deformation By placing a microscope over a float near the stationary clamp, the failure of conductive yarns during deformation of the textile can be studied in more detail. Four warp samples were extended by 20% and subsequently unloaded and the failure of a total of six floats was recorded. Figure 2.12 shows images that illustrate the failure of conductive yarns in woven textile. These images were recorded at increments of (u/l) = Initially, the conductive yarn stands out of the textile at the floats (as can be seen in figures 2.12(a) and 2.1(b)). As the textile is deformed, the yarn becomes stretched (see figure 2.12(b)) at approximately 2% global extension. From this moment onwards, the yarn deforms with the textile. Failure of filaments in the conductive yarns can be observed for elongations in the range of 5 9 % (see figure 2.12(c)). No movement of the yarn with respect to the surrounding textile is observed until the yarn fails at 9 14 % global extension (figure 2.12(d)). After failure, the yarn ends are pulled into the textile as it is further deformed, thereby relieving the tension in nearby floats. As a result, only one in every two or three floats fails (see figure 2.10). As the broken ends of the conductive yarn are pulled from below the overpassing weft yarn in figure 2.12(e), it can be observed, that most filaments have failed at approximately the same place. Complete failure of the conductive yarn is localized below the binder weft yarn at the center of the float. In order to accurately determine the strain that the conductive yarn has experienced at the floats, local strains can be measured from the recorded images. Since no movement of the yarn with respect to the textile is observed before failure, the length of conductive yarn in between weft yarns (as in figures 2.12(a) and 2.12(d)) can be used to determine local (linear) strains, that occur at failure of the conductive yarn. Table 2.2 shows the difference between the global extension (u/l) and local (ε local ) strains at conductive yarn failure. The relative difference between the two varies with a maximum of 15% and is a result of slipping of the sample out of the clamps. Based on these local strain measurements, it can be concluded, that the conductive yarn in the electronic textile samples fails at strains in the range of

21 (a) Undeformed sample. (b) The float has become stretched at 2.1% extension. (c) Some filaments in the conductive yarn (see the marked area) fail, 9.1% extension. (d) The conductive yarn completely fails at the center of the float at 12.4% extension. (e) The yarn is pulled from underneath the overpassing weft yarn, 16.1% extension. (f) As the textile is extended to 20.0%, the conductive yarn moves into the textile Figure 2.12: Images captured during elongation of woven textile in warp direction. The mentioned extensions are global displacements measured at the clamps divided by initial length. 19

22 Table 2.2: Comparison of the global strain measured at the clamps and the local strains measured from optical recordings at conductive yarn failure in several plain woven electronic textile samples. Sample u/l [-] ε local [-] Woven electronic textile with simulated components Woven electronic textile samples with simulated components are loaded in warp direction in order to analyze how the presence of components would influence the failure of conductive yarns. Figure 2.13 shows the load-elongation curves of a plain woven electronic textile sample and a sample with simulated components, that have both been extended by 20%. The response of the textile with simulated components is somewhat stiffer. The difference between the curves is approximately constant ( 1 N/mm) during loading. 15 F/w [N/mm] 10 5 Plain electronic textile Electronic textile with components u/l [ ] Figure 2.13: Load-elongation curves of textile in warp direction with and without glue spots that simulate components. Microscopic imaging of the deformation The failure of conductive yarns in between glued floats was studied in detail by placing a microscope over the samples during deformation. Three samples were extended until failure of the textile occurred, and the failure of six segments of conductive yarn in between floats was recorded. Figure 2.14 shows images that illustrate the failure of the conductive yarns. Images were recorded at increments of (u/l) = Unlike the samples that were tested in section 2.5.1, the floats in the glued samples do not become stretched after 3.0% extension (see figures 2.12(b) and 2.14(b)). Because the glue locally fixates the conductive yarn to the surround textile, tension in the conductive yarn segments in-between floats does not cause the float to be stretched. Instead, the floats deform with the textile and eventually fail at respectively 11.2% and 13.6% extension (figures 2.14(c) and 2.14(d)). Float failure occurs at the center of the float, where a weft yarn passes over the 20

23 Table 2.3: Comparison of the global strain measured at the clamps and the local strains measured from optical recordings at conductive yarn failure in woven electronic textile samples with simulated components. Sample u/l [-] ε local [-] conductive yarn. Since the glue restricts the movement of the conductive yarn through textile, the region in between floats can be further extended before failure occurs. Failure of the conductive yarn is observed at 19.1% extension (figure 2.14(e)). After failure, the yarn ends are pulled through the textile as it deforms. Just before the conductive yarn in between floats fails, the textile around the glue spots locally deforms. Figure 2.15 illustrates how the weft yarns are pulled together where the glue is attached to the stiff conductive yarns. As a result, the textile no longer deforms uniformly. In order to determine the strain experienced by a conductive yarn when it fails, local (linear) strains are determined from optical recordings. Since the glue forces the conductive yarn to deform with the surrounding textile, the lengths in between weft yarns (see figures 2.14(a) and 2.14(e)) can be used to calculate local strains. Table 2.3 shows the difference between global extension (u/l) and local (ε local ) strains at yarn failure. The relative difference varies in the range 35 50% and can be attributed to a combination of inhomogeneous deformation and slip at the clamps. Since the glued sample was deformed much further than the plain electronic textile sample, the influence of slip at the clamps is larger than before. It can be concluded that the region of conductive yarn in between floats fails at strains in the range of Conductive yarn Both virgin and extracted conductive yarns were loaded until failure occurred. Figure 2.16(a) shows the load vs elongation curves for three samples of each type. The scatter between the measurements is small, although the behaviour of extracted yarn varies significantly after failure. Failure of conductive yarn occurs in steps, because the yarn is made of 20 copper filaments and not all filaments fail simultaneously. This is especially the case for the extracted conductive yarn, as it already has undergone significant plastic deformation before it is loaded (see figure 2.4). 21

24 (a) Undeformed sample. (b) 3.0% extension. (c) Conductive yarn at the float on the right fails at 11.2% extension (see marked area). (d) At 13.6% extension, the conductive yarn at the float on the left fails (see marked area). (e) The region of yarn in between fails at 19.1% extension (see marked area). Figure 2.14: Images captured during elongation of woven textile with simulated components in warp direction. The mentioned extensions are global displacements measured at the clamps divided by initial length. Figure 2.15: Image of a woven electronic textile sample with simulated components, just before failure of the regions of conductive yarn in between floats. The dashed curves highlight the deformation of the weft yarns. 22

25 F [N] Virgin conductive yarn Extracted conductive yarn u/l [ ] (a) Loading to failure F [N] Virgin conductive yarn Extracted conductive yarn u/l [ ] (b) Cyclic loading Figure 2.16: Load-elongation curves of both virgin (unused) conductive yarn and conductive yarn that has been extracted from woven electronic textile samples. Since the scatter in extension at maximum load is small for all samples, failure is defined as the moment where the yarn carries its maximum load. In optical recordings however, failure can only be observed when the yarn loses its ability to carry any load. For tensile tests on extracted yarns this method is ill-defined, as there is a large scatter in the results. Virgin conductive yarns fail at a maximum extension of on average 20.8% (for 10 measurements). The initial response of the extracted yarn is non-linear and more compliant than virgin conductive yarn. The extracted yarn already fails at an average extension of 5.7% (for 10 measurements). Cyclic loading In order to be able to analyze the difference in elastic modulus between virgin and extracted yarns as they deform, cyclic loading experiments are performed. Yarns are loaded to a certain force at a constant extension rate, subsequently unloaded to a very small load and again loaded to a larger force. This procedure is repeated until failure of the yarn occurs. The virgin conductive yarn is loaded to 4.5 N, 5 N, 5.5 N and 5.75 N, and the extracted conductive yarn is loaded to 1 N, 2 N, 3 N and 4 N. Figure 2.16(b) shows the load elongation curves for the cyclic loading experiments. For the virgin conductive yarn, the unloading slope gradually decreases from K = F u/l 1.55 kn to K 1.33 kn as the sample is extended. The slope of the extracted conductive yarn initially is much smaller (K 0.35 kn), but gradually increases to K 1.31 kn, which is very similar to the final unloading slope of the virgin conductive yarn Conductive yarn segments Segments of virgin conductive yarn as well as extracted conductive yarn with and without float were loaded until failure occurred. Figure 2.17(a) shows the load-elongation curve for three virgin conductive yarn samples with a length of 10 mm and three with a length of 100 mm. The difference between the curves is small, although the short yarn segments have a larger scatter in the maximum elongation before failure. On average for three samples, the virgin conductive yarn segments fail at an extension of 21.2%. After failure, the load-carrying ability of the yarn segments decreases more gradually than for the long samples. 23

26 F [N] L = 10 mm L = 100 mm u/l [ ] (a) Comparison between segments of virgin conductive yarn and the longer samples, that were tested in section F [N] Virgin conductive yarn Segment in between floats Segment with float u/l [ ] (b) Comparison between the conductive yarn segments. Figure 2.17: Load elongation curves of conductive yarn segments. Similar to the extracted conductive yarn samples, that were tested in section 2.5.3, the initial slope of the extracted conductive yarn segments is lower than that of the virgin conductive yarn (see figure 2.17(b)). The response of segments with float is similar to the segments without float, although segments with float fail at smaller extensions. The samples without float have a maximum extension of 16.1% on average for three experiments, and the scatter between the extension at failure is similar to that of virgin conductive yarn segments. The samples with float have a large scatter in the maximum extension before failure. Furthermore, the float samples show drops in force before the maximum load is reached. On average the extension at maximum load is 12.6% for the conductive yarn segments with float. 2.6 Discussion In agreement with the observations of Verberne [6], failure of the conductive yarns was only observed for tensile tests in warp direction. The conductive yarns are oriented in warp direction and the warp yarns are not loaded during extension in weft direction, as discussed in appendix A. In diagonal direction, the warp yarns only become loaded at large extensions. Although failure of the conductive yarns was not observed for loading in diagonal direction, it may eventually occur when the textile is extended beyond 45%. For plain woven electronic textile (i.e. without any components), failure was only observed at the floats. More specifically, optical recordings of tensile tests with a microscope placed over float regions have revealed, that failure is consistently localized at the binder weft yarn (the single weft yarn that passes over the float). Failure was observed at local strains in the range of After failure, the yarn ends are pulled into the textile, to relieve the tension in nearby floats. Despite this movement of the conductive yarns through the textile, one yarn fails at multiple locations: typically one in every two or three floats fail. This means that the textile exerts a frictional force on the conductive yarn that is large enough to cause a yarn to fail (approximately 6 N). The presence of stiff components on the electronic textile was simulated by placing droplets of glue over the floats. As a result, movement of the conductive yarns through the textile was restricted at the floats. Failure was then also observed in the regions of conductive yarn inbetween floats for local strains in the range of Therefore it can be concluded that 24

27 plain woven electronic textile without floats could potentially be extended much further than the current samples. From the optical analysis of extracted conductive yarns (see figure 2.4) it may be concluded, that integrated conductive yarns have undergone a significant amount of plastic deformation. The largest amount of deformation was observed at the floats. During tensile tests on extracted conductive yarn segments with floats, failure was always localized at the center of the float (where the binder yarn would pass over the float). It can therefore be concluded, that the conductive yarn has lost a large part of its ductility at the floats. Since the amount of plastic deformation varies over the extracted conductive yarn s length, the yarn may not deform uniformly due to variations in the amount of hardening, that has occurred. Therefore, the effect, which the surrounding weft yarns (especially the binder yarn) have on the failure at the floats, cannot be determined directly by comparing experiments on textile with tensile tests on extracted yarns. However, segments of extracted conductive yarn without floats have a regular wave-like shape. It may therefore be assumed, that these samples deform more or less uniformly. From the tensile tests on textile with simulated components (section 2.5.2) it was determined, that the segments in-between floats fail at local strains in the range of Tensile tests on extracted segments without float fail at an average extension of 16.1%. Therefore, we can conclude that the frictional force exerted by the textile does not significantly influence the extensibility of integrated conductive yarn with a regular wave-like shape. The influence of integrating conductive yarn in woven textile (without floats) can therefore be analyzed by comparing the mechanical properties of virgin and extracted conductive yarn. Since the friction effect has no influence, the extensibility of conductive yarn with a wave-like shape must be governed by loss of ductility due to the pre-deformation during weaving and the over-length effect. It was observed, that extracted conductive yarns initially have a more compliant response than virgin conductive yarns. This may be attributed to the wave-like shape of extracted yarn, since the actual length of the yarn is longer than the dimensions of the fabric it is removed from. The yarn initially straightens out when a load is applied, thereby increasing its length. This results in an initially more compliant response. The over-length effect therefore increases the extensibility of conductive yarn in woven textile. Segments of extracted conductive yarn without float have experienced more hardening than a virgin conductive yarn. As a result, extending the extracted yarn beyond 6% requires more force than for a virgin conductive yarn (see figure 2.17(b)). Experiments also show that virgin conductive yarns and segments of conductive yarn fail at approximately the same load. Therefore it may be concluded that the pre-deformation effect reduces the extensibility of an integrated conductive yarn. Both opposing effects are modelled in chapter 3 in order to determine their magnitude. 25

28 26

29 Chapter 3 Modelling 3.1 Introduction In electronic textile products, stiff components are placed on the floats that locally strengthen the conductive yarn. As a result, the extensibility of the integrated conductive yarns will be determined by the mechanical properties of the segments without floats. In the remainder of this study, the focus will therefore lie on the extensibility of integrated conductive yarns without floats. During the experimental characterization of woven electronic textile it was observed, that the extensibility of conductive yarn without floats is governed by two opposing effects: 1. Pre-deformation effect: The interlacing of conductive yarns introduces plastic deformation, thereby reducing the yarn s ductility. 2. Over-length effect: The actual length of an interlaced yarn is greater than the dimensions of the fabric it was removed from. The over-length effect increases a yarn s extensibility while the pre-deformation consumes part of the ductility of the yarn, so that the maximum extension is reached sooner (see figure 3.2). The net result of these effects determines if a woven conductive yarn s extensibility is increased or decreased with respect to the straight virgin yarns. In this chapter, the two effects are modelled separately for a length of conductive yarn without floats in order to quantitatively determine which parameters influence their magnitude. Figure 3.1: Schematic representation of the influence of the over-length and pre-deformation effects on the mechanical properties of conductive yarns. 27

30 R -R Figure 3.2: Representation of the yarn geometry as a concatenation of yarn segments with a constant radius of curvature. During the weaving of electronic textile, the maximum tension, that is applied on the warp yarns, is approximately 0.70 N per yarn [8]. This amount of tension is well below the yarn s initial yield strength (see figure 2.16(a)) and therefore does not result in plastic deformation. During weaving, the conductive yarns are forced bent around the weft yarns, that alternatingly pass above them. Furthermore, a heat treatment is applied after weaving, in order to make the fabric more stable (i.e. to prevent shrinkage at a later stage). The heat treatment shrinks the polyester yarns by several percent, but does not influence the conductive yarns. Consequently the conductive yarns are further bent around the weft yarns. As a result, the conductive yarns in electronic textile have a wave-like shape (see figure 2.4(c)). When a load is applied on a yarn with a wave-like shape, it straightens out whilst it is extended. Therefore the yarn s length increases due to straightening (because of its over-length) as well as extension. Since the straightening of an element requires a moment and no axial force, it is difficult to determine how much axial force is required for the straightening of a yarn. For simplicity, it is therefore assumed, that the yarn is first straightened before it is extended. The geometric non-linearity can then be captured by the over-length effect and geometric linearity is assumed for the analysis of the pre-deformation effect. The contributions of both effects are simply added in order to predict the extensibility of an integrated conductive yarn. Strictly speaking, this is not correct. However, considering the inaccuracies that are involved, this is acceptable. In order to determine the amount of plastic deformation that has occurred during production, the mechanical treatment of the conductive yarns should be taken into account. The bending of the conductive yarns around radii as small as the radius of the weft yarns (R 0.1 mm) introduces a significant amount of plastic deformation. The longitudinal strain (ε), that is introduced by a state of pure bending, depends on the radius of curvature (R) and varies over the distance (y) with respect to the neutral axis of the yarn s cross-section [9]: ε(x, y) = y R(x) where R(x) is defined to be positive for sagging and negative for hogging. Since the yarn has a wave-like shape, the radius of curvature varies along the longitudinal coordinate x. As a result, the longitudinal strain varies with both x and y. Figure 3.2 shows a schematic representation of the deformation due to bending when the yarn geometry is described by a concatenation of segments with a constant radius of curvature. In the segment on the left, the material above the neutral axis is extended, while the material (3.1) 28

31 below the neutral axis is compressed. The opposite happens in the segment on the right, where the material above the neutral axis is compressed. In reality, the transition from tension to compression does not occur as sharply as in figure 3.2. Instead, we describe the geometry of the conductive yarn as a sine wave. The curvature can then easily be determined by evaluating the inverse of the second derivative and it is a continuous function. The geometric description can be used to quantify the over-length effect and determine the amount of pre-deformation due to production. The mechanical behaviour of the conductive yarn is first characterized in section 3.2, and a simple material model is fitted to the experimental results. The over-length effect is discussed in section 3.3. How the pre-deformation affects the mechanical behaviour of extracted conductive yarn is modelled in section Material characterization The mechanical behaviour of the virgin silver plated copper yarns was measured in section Figure 3.3(a) shows the relation between true stress and strain for a virgin conductive yarn in both a simple extension and a cyclic loading experiment. Although engineering measures of stress and strain are used in the model below, true stress vs true strain is shown in figure 3.3(a) to eliminate the effect of cross-section changes on the elastic unloading response. The material exhibits elastoplastic behaviour with nonlinear hardening. σtrue [M P a] ε true [-] (a) True stress-strain curves for a cyclic loading experiment (red) and an extension to failure experiment (blue). σe[m P a] Experiments Model ε[-] (b) Engineering stress-strain curves of the measured and modelled response. Figure 3.3: Load elongation curves of virgin conductive yarn. The material s Young s modulus E can be determined from the (elastic) unloading curves and was found to be 66.1 GP a on average. The total strain consists of an elastic and a plastic component. The amount of elastic strain can be calculated at any point using the Young s modulus. At the moment of failure, approximately 2% of the applied deformation is elastic. Since the amount of elastic deformation is small with respect to the amount of plastic deformation, it is chosen to model the material as rigid plastic. We furthermore, for simplicity, assume linear hardening until the maximum extension ε failure is reached. Since geometric linearity is assumed, 29

32 the material model becomes: ε = ε p = l l 0 (3.2) l 0 σ = F { σy0 + H ε = p if ε p ε failure (3.3) S 0 0 if ε p > ε failure where S 0 is the yarn s initial cross-sectional area, σ y0 is the material s initial yield stress, H is the hardening modulus and ε p is the effective plastic strain. The effective plastic strain is used because it is assumed, that all plastic deformation results in hardening and therefore the entire deformation history should be taken into account. For rigid plastic behaviour, the effective plastic strain rate is given by ε p = ε p = ε (3.4) The initial cross-sectional area of the virgin conductive yarn can easily be determined, since the yarn consists of 20 filaments with a circular cross-section of diameter d = 40 µm, so that we have S 0 = πd µm 2. The parameters σ y0 and H are fitted to the monotonic tensile response of figure 3.3(b), using a least squares approximation on the the part of the curve where ε > 0.01 and extrapolating this fit to 0 ε Figure 3.3(b) shows a comparison between the measured and modelled material behaviour of the virgin conductive yarn. The model parameters are shown in table 3.1. The value for the maximum extension ε failure is based on the average of 10 measurements (see section 2.5.3). Table 3.1: Material model parameters Parameter Value σ y0 176 MP a H 381 MP a ε failure Over-length effect In this section, the increase in length, due to the straightening of a conductive yarn with a regular wave-like shape is considered. We consider one period of conductive yarn of length λ with infinite stiffness in the longitudinal direction and negligible bending stiffness. When a small load is applied to this yarn, it immediately straightens out to length l o, i.e. to the actual length of the yarn. The increase in length (see figure 3.4) depends on the actual length l o of the yarn relative to the apparent length λ in the interlaced configuration: a more curved initial configuration has a greater potential for extension. λ lo Figure 3.4: Schematic representation of the initial interlaced configuration (top) and straightened out configuration (bottom). 30

33 The over-length of the conductive yarn in woven electronic textile can be estimated by calculating the arc length of a sine wave with the same amplitude and wavelength as the yarn. The yarn s wavelength can be determined from the textile s yarn density in weft direction (85 cm 1 ), by considering the textile s weaving structure: λ = 3 85cm 350 µm. Figure 3.5 shows a segment of conductive yarn in-between floats, where one period of a sine wave is fitted on the geometry. This procedure was repeated several times, and it was determined, that the wavelength of the conductive yarn is indeed approximately λ = 350 µm. The amplitude of the wave shows more scatter, but was found to be A = 15 µm on average. Figure 3.5: Wave-like geometry of of conductive yarn in-between floats, that has been extracted from woven textile. The geometry of the yarn is assumed to have a sinusoidal shape with amplitude A and wavelength λ. Therefore the out-of-plane position over the length of the yarn can be expressed as ( ) 2πx w(x) = A sin λ (3.5) where w(x) is the amplitude and x is the coordinate in the longitudinal direction. Using the derivation that is presented in appendix C, the actual length of one period of the yarn can be approximated as: l o = λ [1 + π2 A 2 ] λ 2 (3.6) The global extension E o, due to the over-length effect, can now be defined as E o = l o λ λ = π2 A 2 λ % (3.7) Figure 3.6 illustrates the resulting model for the over-length effect. When an arbitrary stress Σ is applied to the yarn, it straightens out and extends by π2 A 2. This extension is independent of λ 2 the applied stress. 31

34 Σ π A 2 λ Eo Figure 3.6: Relation between load and extension due to the over-length effect, when a load Σ is applied on a yarn. 3.4 Pre-deformation effect In this section we consider the influence of the plastic deformation, that is introduced during production and straightening of an integrated conductive yarn, on its mechanical response. Since we analyze the over-length and pre-deformation effects separately, we now disregard the elongation due to straightening and assume λ l o. We first consider the plastic deformation, that is present in an integrated conductive yarn with initial length λ (initial configuration in figure 3.7). This yarn immediately straightens out when a load is applied (straightened configuration in figure 3.7), which again introduces plastic deformation. When the load is further increased, the yarn will extend to length l (extended configuration in figure 3.7). The goal is to determine how the pre-deformation determines the mechanical behaviour during extension. λ λ l Figure 3.7: Schematic representation of the initial (top), straightened (center) and extended (bottom) configurations. Due to the initial bent geometry of the yarn, the amount of initial plastic deformation, and consequently the amount of harding that has occurred, varies along the length of the yarn. As a result, when a gradually increasing load is applied to the straightened yarn, it deforms nonuniformly until the yield stress has increased to the same value along the length of the yarn. 32

35 Beyond that point, the yarn will deform uniformly according to the material model of equation (3.3). In order to determine the amount of plastic deformation that is present after production, the initial state of the yarn is first analyzed. The bending of a conductive yarn introduces deformation of which the magnitude depends on the radius of curvature and the thickness (diameter) of the conductive yarn. Using the assumption that the geometry of the yarn can be described by a sine wave and that all deformation is plastic, the amount of plastic deformation, that is present after weaving, can be derived from equations (3.1) and (3.5) as ε p (x, y) = y ( ) R(x) = y δ2 w 2πx δx 2 = ya4π2 λ 2 sin λ where ε p (x, y) is the local plastic strain. From inspection of extracted conductive yarn segments in-between floats (see figures 2.2 and 2.4) it can be observed, that the conductive yarn has flattened to a thickness of approximately W = 150 µm during the production process. If we assume the flattened yarn to be a solid continuum, the maximum strain due to bending, can be calculated by evaluating equation (3.8) for x = 1 4 λ and y = 1 2 W as ε p max = (3.8) 2W Aπ2 λ (3.9) From the tensile tests on conductive yarns, that are discussed in chapter 2, we know that virgin conductive yarns can only be extended by approximately 20%. Furthermore, extracted conductive yarn segments in-between floats can still be extended by approximately 16% before they fail. Strains in the order of 0.36 would cause immediate failure of the conductive yarn and are therefore not expected to occur during production of the textile. It can be concluded that the assumption that the conductive yarn can be regarded as a solid continuum, does not hold. Figure 3.8: Bending of a solid rod (left) and a bundle of filaments without twist (right). When a yarn is bent, the amount of twist will determine if it will act as a solid rod or if the filaments are free to bend independently [11] (see figure 3.8). In the case of a loosely twisted yarn, filaments may slide with respect to each other, thereby reducing the bending stiffness of the yarn. As discussed in section 2.2, the conductive yarn consists of 20 filaments wrapped with a twist of T = 240 m 1. This means, that a filament makes one complete turn every 1 T 4.2 mm. Since this distance is one order of magnitude larger than the yarn s wavelength, it can be assumed, that the filaments in the conductive yarn are free to bend independently. To determine the pre-deformation due to weaving, the bending of individual filaments should therefore be considered. A continuum approach is used to analyze the bending of individual filaments with diameter d = 40 µm. For simplicity, it is assumed that filament s cross-section does not deform (e.g. flatten) during bending. The maximum strain due to bending of a filament can be calculated by evaluating equation (3.8) for x = 1 4 λ and y = 1 2 d. ε p max = 2dAπ2 λ (3.10) 33

36 This is a more reasonable value, since it is of the order of magnitude of the observed loss of ductility of the yarn. For a more precise quantitative analysis of the effect of pre-deformation, we now consider the distribution of plastic strain throughout one period of the filament. Since the yarn was assumed to have no plastic deformation prior to weaving, the effective plastic strain, that is present after weaving, can be expressed using equations (3.4) and (3.8) as ( ) ε p (x, y) = 2πx ya4π2 λ 2 sin (3.11) λ where the coordinate y varies from 1 2 d y 1 2d. As a result of this effective plastic strain distribution, the yield stress σ y varies over the filament: σ y (x, y) = σ y0 + H ε p (x, y) (3.12) It is assumed that by straightening out the yarn, the displacements due to bending are reduced, until finally the plastic strain becomes zero at all material points: ε p (x, y) = 0 (3.13) The deformation, that comes with straightening of the yarn, doubles the effective plastic strain, since an opposite amount of deformation needs to be applied to undo the bent shape, so that after straightening we have ( ) ε p (x, y) = 2 2πx ya4π2 λ 2 sin (3.14) λ The resulting strain-profiles at x = 1 4 λ (where together with x = 3 4λ the largest deformation occurs) are shown in figure y[µm] Initially Straightened y[µm] Initially Straightened ε p [-] (a) Plastic strain ε p [-] (b) Effective plastic strain Figure 3.9: Strain profiles at x = 1 4λ over the cross-section of a conductive yarn filament in the initial and straightened configuration. Combining equation (3.12) and (3.14) the yield stress now becomes ( ) σ y (x, y) = σ y0 + 2H 2πx ya4π2 λ 2 sin (3.15) λ The yield stress thus varies over the length and thickness of the filament. When the filament is loaded, the axial force F must be equal along the length of the yarn. Therefore the average 34

37 stress over the cross-section of the filament σ must also be equal along the length of the yarn: σ (x) = F 1 = d 1 4 πd2 πd 2 σ(x, y) d 4 d2 y 2 dy (3.16) Yielding can only occur when the average stress exceeds the average yield stress on a crosssection. Combining equations (3.15) and (3.16) gives an expression for the average yield stress in terms of the initial waviness parameters: σ y (x) = σ y0 + 64πHA d 2 λ 2 ( 2πx sin λ ) 1 2 d 1 2 d y 1 4 d2 y 2 dy (3.17) Evaluating the integral via the derivation that is presented in appendix D, the average yield stress over the cross-section of a straightened out filament can be expressed as ( ) 2πx σ y (x) = σ y0 + σ y sin (3.18) λ with σ y = 16πHAd. In a similar fashion, the average effective plastic strain can be expressed 3λ 2 as ε p (x) = σ ( ) y 2πx H sin (3.19) λ The variation of the average yield stress and average effective plastic strain in the straightened configuration is shown in figure σy [M P a] εp [-] σ y0 σ y (x) 150 σ y max E p /(Hλ) x[µm] (a) Yield stress 0.02 ε p (x) ε p max E p x/λ[ ] (b) Effective plastic strain Figure 3.10: Variation of the amount of pre-deformation over the length of the filament. When a load is applied to the straightened yarn, the applied stress Σ will have to exceed the average yield stress σ y (x), before yielding can occur at an arbitrary point x. Since σ y fluctuates with x, this condition is met at different load levels for different cross sections. As a result, the sample deforms non-uniformly, until the applied stress exceeds the maximum initial yield stress σ y max = σ y0 + σ y. The amount of global extension, E p, at Σ = σ y max can be determined by averaging the necessary additional plastic strain ε p (x) = ε p max ε p (x) over the dimensionless longitudinal coordinate x/λ (see also figure 3.10(b)): E p = 1 λ λ 0 ( ε p max ε p (x)) dx (3.20) 35

38 where ε p max = σy H is the maximum average effective plastic strain after straightening of the filament and ε p (x) the average effective plastic strain distribution after straightening Alternatively, E p can be expressed in terms of the average yield stresses as (see also figure 3.10(a)) E p = 1 λ λ = 4 Hλ 1 H ( σ y max σ y (x)) dx (3.21) λ 0 ( σ y max σ y (x)) dx (3.22) Using equations (3.18) and (3.22), E p can also be found by integrating over the average yield stress σ y : E p = 2 σ max sin 1 πh σ y0 ( σy σ y0 σ y ) d σ y (3.23) The solution to this integral is presented in appendix E and reads E p = 2 [ ( ) ] ( σ y σ y0 ) sin 1 σy σ σ max y0 + σy πh σ 2 ( σ y σ y0 ) 2 (3.24) y σ y0 ( π )] [ σ y 2 1 = 2 πh = σ y H ( 1 2 ) π (3.25) (3.26) (3.27) Therefore, the model predicts, that a filament of conductive yarn that is extracted from textile and straightened, deforms non-uniformly up to 2.98% extension. Beyond this point, each material point will have the same average effective plastic strain and the filament deforms uniformly as described by equation (3.3). In order to find an expression for the global extension as a function of the applied stress Σ = σ in the range σ y0 < Σ < σ y max, the integration limits of equation (3.23) are changed: E p (Σ) = 2 Σ πh = 2 πh ( sin 1 σy σ y0 σ y0 σ y [ ( Σ (Σ σ y0 ) sin 1 σy0 σ y ) d σ y (3.28) ) ] + σy 2 (Σ σ y0 ) 2 σ y (3.29) Figure 3.11 shows the resulting average stress vs extension, taking into account the influence of pre-deformation during weaving and straightening. As expected, the response is non-linear. Initially, only a small part of the material deforms and the hardening slope is high. As the applied stress is increased, a larger portion of material deforms and this slope drops. Ultimately, at Σ = σ y max, the hardening slope is H. 36

39 Σ [M P a] E p (Σ) Σ = σ y0 150 Σ = σ y σ y Σ = σ y max E p [ ] (a) Global extension due to pre-deformtation effect σy [M P a] Σ = σ y0 150 Σ = σ y σ y Σ = σ y max x[µm] (b) Change in yield stress due to the applied load Figure 3.11: Material behaviour due to the applied pre-deformation during weaving and straightening. Figure 3.12 schematically illustrates, how the mechanical response of the conductive yarn is influenced by the plastic deformation that is introduced during weaving and straightening. If the applied stress is below the material s initial yield stress, no deformation occurs. Beyond the initial yield stress, E p is a non-linear function of Σ (given by equation (3.29)) until each material point has the same average effective plastic strain at Σ = σ y0 + σ y. When the applied stress is further increased, linear hardening occurs. From this point onwards, the hardening response of the bent and straightened yarn is obtained from that of the virgin yarn by a horizontal shift of 2 σy 2 σy πh. Accordingly, the maximum extension of the yarn is reduced by πh note that this reduction does not depend on the hardening modulus H. = 32Ad 3λ 2. Please Σ σmax 2 σy πh H σy0 + σy σy0 Virgin yarn Extracted yarn 0 σy H (1- π 2 ) σy H Ep Figure 3.12: Comparison between the modelled response of virgin conductive yarn and conductive yarn, that has been pre-deformed due to weaving and straightening (pre-deformation effect). 3.5 Combined prediction The following assumptions have been made in the derivation of the presented model: 37

40 1. The conductive yarn is first straightened before it is extended 2. Geometric linearity is assumed for the analysis of the pre-deformation effect. 3. The geometry of the sine wave is described as a sine wave. 4. The material is modeled as rigid plastic with linear hardening until the maximum extension is reached. 5. The conductive yarn is regarded as a bundle of filaments with not twist. Under these conditions, the global extension E of a modelled conductive yarn filament with an initial wave like shape is comprised of an extension component due to the initial wave-like geometry of the yarn (E o ) and an extension component due to plastic deformation of the yarn (E p ): E(Σ) = E o + E p (Σ) (3.30) The global extension is a function of the applied stress Σ. As discussed in section 3.1, it is assumed that the yarn is first straightened, before it is extended. Since straightening locally requires a moment and no axial force, the extension component due to the geometry change, is assumed to not depend on the applied stress and to be available immediately. This implies, that it is visible in the global response as an offset strain. The plastic extension E p, after an initial nonlinear increase with Σ, has a linear dependence on Σ which is influenced shifted with respect to the hardening response of the virgin yarn. Beyond this point, the combined hardening response is thus obtained from that of the virgin yarn by the combined effect of a shift of π2 A 2 λ 2 to the right (due to the over-length) and 2 σy πh to the left (due to the pre-deformation). Figure 3.13 schematically shows the modelled global response of a conductive yarn that has been integrated in woven electronic textile. The change of the maximum extension, with respect to a virgin conductive yarn, is determined by π2 A 2 2 σy λ 2 πh. The influence of the model parameters on the extensibility of integrated conductive yarn are discussed in section 4.2. Σ π A 2 λ + 2 σy πh σmax H σy0 + σy σy0 Virgin yarn Extracted yarn Virgin yarn (shifted) 0 π A λ 2 2 σy 2 + π 2 A 2 2 H (1- π 2 ) λ E Figure 3.13: Comparison between the modelled response of virgin conductive yarn and conductive yarn in woven electronic textile. In the material model, that was discussed in section 3.2, it was assumed that a conductive yarn loses its ability to carry load, when the effective plastic strain exceeds a certain measured 38

41 value (ε failure ). In the pre-deformation model, that was presented in section 3.4, the effective plastic strains varies over the yarn cross-sections, due to the initial bent shape. Therefore, the average effective plastic strain was calculated for the circular cross-sections. As far as failure is concerned, it is reasonable to assume, that a filament with a straindistribution as sketched in figure 3.9 will not immediately loose its ability to carry load, when the effective plastic strain exceeds the maximum value in a single point of the cross-section. On the other hand, the filament will fail completely, well before the effective plastic strain has exceeded the maximum value in all material points. In order to predict the failure of the conductive yarn, that has been extracted from textile, the following failure criteria are examined: 1. ε p (x, y) > ε failure for any material point (x, y) 2. ε p (x) > ε failure for any cross-section x 3. ε p (x, y) > ε failure for all material points (x, y) The first of these criteria is expected to be extremely conservative, whereas the third criterion gives an upper bound. It will be shown below, that the second, which requires that the average effective plastic strains in a cross section exceeds the failure strain, predicts failure reasonably well. 3.6 Segment of conductive yarn without float The presented model can be used to predict the mechanical behaviour of the segments of conductive yarn without floats, that were tested in section The yarn segment is assumed to have a sinusoidal shape with amplitude A = 15 µm and wavelength λ = 350 µm (see figure 3.5) σ e [MPa] Experiments without float Model without float Model of virgin yarn Failure criterion 1 Failure criterion 2 Failure criterion u/l [ ] Figure 3.14: Comparison of the measured and modelled mechanical response of segments of conductive yarn without floats, as well as the modelled response of virgin conductive yarn. A comparison between model and experiments is made in figure The fitted response of the virgin yarn is also shown as a reference. Initially, the difference between model and experiment is large. In the presented model, elasticity is neglected and it is assumed, that the yarn immediately straightens when a load is applied. In reality, the initial response is a combination 39

42 of elasticity and gradual straightening of the yarn. Furthermore, the material model, that is used, over-predicts the stress in the initial, non-linear yielding regime of the simple tensile test (figure 3.3(b)). When the load is increased beyond 200 MP a, the difference between model and experiments becomes smaller. At this point, the yarn is completely straightened in experiments and the model successfully predicts the amount of hardening that has occurred. The markers in figure 3.14 indicate when the filament is predicted to fail according to the three failure criteria. Assuming that the yarn fails when the effective plastic strain first exceeds the critical value in a single material point underestimates the yarn s strength and ductility. On the other hand, failure criterion 3 overestimates the yarns extensibility. Considering the average effective plastic strain (failure criterion 2) gives a good approximation. Furthermore, during experiments on extracted conductive yarns, it was observed that failure occurred at approximately the same loads as for the virgin conductive yarn. Since this observation agrees with the modelled response for failure criterion 2, the average effective plastic strain is used to determine failure from now on. 3.7 Segment of conductive yarn with float The mechanical behaviour of the segments of conductive yarn with float, that were tested in section 2.5.4, can be modelled by assuming that the geometry is a concatenation of sine waves with different wavelength and amplitude (see figure 3.15). Figure 3.15: modelling of the geometry of a segment of conductive yarn as a concatenation of sine waves with different amplitude. A length of conductive yarn with a float region is regarded as several periods of wavelength λ 1 and amplitude A 1 (with the regular geometry as in figure 3.5), two periods of wavelength λ 2 with the larger amplitude A 2 and two lengths l 3 of straight conductive yarn. If we assume, that the yarn density does not vary in the float region, the various lengths can easily be determined using figure 3.16: L 2 = 2λ 2 = 4λ 1 and L 3 = 2l 3 = 6λ 1. Figure 3.16: Schematic representation of the weave structure at the float region. 40

43 Table 3.2: Yarn geometry dimensions for a L = 10 mm long conductive yarn segment with float Section Parameter Value 1 λ µm A 1 15 µm L mm 2 λ µm A 2 50 µm L mm 3 l µm L mm Figure 3.17: Dimensions of the geometry of conductive yarn at the float region. The dimensions of yarn geometry at the float are determined from figure From the dimensions it can be concluded, that the yarn density indeed remains constant. The dimensions of the yarn geometry are shown in table 3.2. The global predicted response of the yarn with length L = 10 mm is a combination of individual responses (E o i and E p i (Σ)) of the three sections and can be determined by taking into account the length (L i ) of each section: E o = 1 L [E o 1L 1 + E o 2 L 2 + E o 3 L 3 ] (3.31) E p (Σ) = 1 L [E p 1(Σ)L 1 + E p 2 (Σ)L 2 + E p 3 (Σ)L 3 ] (3.32) The resulting prediction is shown in figure Compared with the prediction for a segment of yarn without float, the over-length effect is slightly larger for the modelled yarn with float. In reality, the difference appears to be even larger. The assumption, that the float consists of a straight section of yarn may not be justified, since there appears to be some over length at the floats (see figure 2.1(b)). However, the magnitude of this effect is difficult to determine. After the initial yielding point, the response of the float model is more compliant than the model without float. This is a result of the relatively large section of straight yarn without pre-deformation that is assumed to be present. Contrary to what was observed in the experiments, the modelled conductive yarn with float is more extensible than a modelled yarn without float. This is because section 2 of the yarn geometry (see figure 3.15) has less plastic deformation, due to bending and straightening than section 1: Section 2 has a minimum radius of R min 2 = λ2 2 4π 2 A µm, whereas for section 1 a smaller radius is assumed, R min µm. Judging from figure 3.17, this does not appear to be valid. Therefore, assuming a sinusoidal geometry at the transition between the float and the woven yarn, as well as at the center of the float, is inaccurate in predicting the magnitude of the pre-deformation effect. 41

44 In addition to the inaccurate geometrical description of the float region, other effects that are not included in the presented model, such as friction, may influence the extensibility of integrated conductive yarns with float. It can be concluded, that the model does not describe the trend, that conductive yarn with float has a lower extensibility than that without float σ e [MPa] Experiments without float Experiments with float Model without float Model with float Failure u/l [ ] Figure 3.18: Comparison of the measured and modelled mechanical response of segments of conductive yarn with and without float. 3.8 Discussion Based on observations during experiments on woven electronic textile and a few assumptions, a simple analytical model has been developed, that quantitatively describes, which parameters influence an integrated conductive yarn s extensibility. In this section, each of the assumptions is discussed, in order to asses what their consequences are and how the model could be improved to more accurately describe the effect of interlacing a conductive yarn. In the presented model, it was assumed, that integrated conductive yarns are first straightened before they are stretched. In reality, the yarns straighten out whilst they are extended. This means, that the straightening does not result in an equal (but opposite) amount of plastic deformation as was introduced during production. Therefore, the model gives an overestimation of the loss of ductility in extension. This effect, and the geometric non-linearities could be taken into account in a finite element method analysis of the extension of a bent yarn. This could provide more insight in the consequences of this assumption. It was assumed, that the conductive yarns can be regarded as bundles of filaments without twist. For practical reasons some twist is applied on the yarns. As a result the yarns have some coherence and do not completely flatten, when they are interlaced. During the bending of a twisted yarn, filaments are not completely free to move with respect to each other. By considering the bending of individual filaments, we have therefore underestimated the amount of plastic deformation, that is introduced during bending. In reality some filaments may experience more deformation than others. From images of extracted segments of conductive yarn without float it was observed, that the amplitude of the conductive yarn shows a significant scatter. An average value was used to 42

45 account for the average amount of damage, that is present. However, since the expression that determines the change in extensibility of integrated conductive yarn depends quadratically on the amplitude (see figure 3.13), the final result is not very accurate. In order to verify the model, experiments could be performed on single filaments with a geometry that can be measured more accurately. For simplicity, it was assumed, that the circular cross-sections of the filaments do not change during bending. In reality the filaments will flatten, thereby reducing in thickness. The bending of a thinner filament introduces less plastic deformation. We have therefore overestimated the amount of damage, that is introduced by weaving and straightening. The material model, that is used, assumes rigid plastic behaviour, since the relative amount of elastic deformation in experiments is very small. This results in a slight overestimation of the amount of damage, that is introduced by weaving and straightening. Taking elasticity into account renders the analysis more complex, since we would have to take into account residual stresses during bending and straightening. However, the result will not differ much since the amount of elastic deformation is negligible. A linear hardening law was fitted on experimental results. The hardening law over-predicts the stress in the initial non-linear yielding regime. A power-law model could be used for a more accurate material description of the initial response. However, this would not influence the predicted maximum extension since rigid plasticity is assumed. 43

46 44

47 Chapter 4 Increasing the stretchability of woven electronic textile 4.1 Introduction During the experimental characterization of woven electronic textile in chapter 2, it was determined that plain woven electronic textile can only be extended by 9 14% before failure of the conductive yarns occurs at the floats. By simulating components on these floats, it was determined that the segments of conductive yarn in-between floats can be extended by 14 19%. Integrated conductive yarn without floats has a regular wave-like shape, and its extensibility is not influenced by the surrounding textile in the samples that were investigated. In chapter 3, a model is presented that predicts the mechanical properties, and in particular the extensibility, of conductive yarns with such a wave-like shape. Since the model is analytical, it can easily be used to determine how weaving parameters and the choice of conductive yarns influence the textile s stretchability. In section 4.2, it is discussed how the extensibility of integrated conductive yarn in the current electronic textile samples can be improved by changing the parameters of the systems. In the current electronic textile samples, the conductive yarns deform mostly plastically when they are stretched. The textile however, exhibits a significant amount of elasticity when it is loaded and subsequently unloaded (see figure 2.9). This mismatch in material properties may lead to problems in the daily use of textile products such as clothing. In section 4.3, the model of chapter 3 is used to predict what kind of yarn-geometry would be required to prevent plastic deformation during the straightening of wave-like conductive yarns. 4.2 Improving the extensibility of integrated conductive yarn The total change in extensibility E of a conductive yarn with a wave-like geometry relative to the virgin conductive yarn, consists of a component due to the over-length effect, E o, and a component due to the pre-deformation effect, E p : E = E o + E p (4.1) Where the over-length effect has a positive effect on the extensiblity of the integrated yarns ( E o 0) and the pre-deformation has a negative effect ( E o 0). The model of chapter 3 45

48 predicts these contributions to be: E = π2 A 2 λ 2 = π2 A 2 λ 2 2 σ y ( πh 1 32 ) d 3π 2 A This model assumes that the conductive yarn does not fail during straightening of the yarn. Equation (4.3) is only valid if the average effective plastic strain in the straightened configuration does not exceed ε failure. Since the largest amount of plastic deformation occurs at x = 1 4 λ, equation (3.19) can be used to find ε p (x = 1 4 λ) = σ y H (4.2) (4.3) (4.4) = 16Ad 3λ 2 (4.5) Therefore, equation (4.3) can be used to analyze the change in extensibility if 16Ad 3λ 2 ε failure (4.6) In order to gain extensibility by integrating a conductive yarn in woven textile, A d will have to be large (at least A d > 32 ) according to equation (4.3). Furthermore, A2 should be large although 3π 2 λ 2 must be small in order to prevent failure during straightening (according to equation da λ 2 = A d A 2 λ 2 (4.6)). Therefore the system parameters should be as such that A d A2 λ 2. In general it can be concluded that reducing the filament diameter is desirable, as it reduces the pre-deformation effect and would make it possible to apply more extreme curvatures to the yarn. Increasing the amplitude A is also desirable since the over-length effect depends quadratically on A. However, in order to prevent failure during straightening, the wavelength λ will have to be increased as well for large values of A. In order to further analyze the influence of the model parameters, the contour lines of E are shown in figure 4.1 as a function of the normalized amplitude A d and wavelength λ d. The gray area in figure 4.1 denotes combinations of the system parameters where the yarn fails during ( straightening and which should thus be avoided. There is a critical nonzero value for A ) d c = where there is no change in extensibility ( E = 0) because the over-length 3π 2 and pre-deformation effects cancel each other ( E o = E p ). If the normalized amplitude exceeds ( ) A d, the over-length effect is larger than the pre-deformation effect and the extensibility c of the yarn is increased ( E > 0). For amplitudes below A c, the pre-deformation effect exceeds the over-length effect and the extensibility of the yarn is reduced ( E < 0). For a straight yarn (A = 0) both the over-length effect and the pre-deformation effect vanishes. Since E depends quadratically on A, the change in extensibility will have a minimum value at A λ = 1 ( A ) 2 d c The marker in figure 4.1, at λ d = = 8.75 and A d = = 0.375, denotes the yarn geometry in the current woven electronic textile samples ( E 0.034). The system parameters can be changed in various ways to increase the extensibility of integrated conductive yarn, depending on what is feasible. For example, using a conductive yarn with filaments of a diameter that is three times smaller than of the current yarn, could improve the situation ( E 0). However, by reducing the filament diameter, no extensibility can be gained relative to the virgin conductive yarn, as the over-length effect only depends on A and λ. In a similar fashion, the wavelength can be increased, by decreasing the weaving density in weft direction, to achieve the same extensibility as that of virgin conductive yarn. 46

49 A/d [ ] E Failure during straightening Current textile samples λ/d [ ] Figure 4.1: Contour plot of the change in extensibility E of integrated conductive yarn with respect to virgin conductive yarn as a function of the normalized wave amplitude A/d and wavelength λ/d. In order to significantly increase E, the amplitude A will have to be increased. For example, in order to achieve the same extensibility as that of the textile (35%), the required increase in extensibility relative to virgin yarn is E In the current electronic textile samples, the normalized amplitude will have to be increased to A d 1.75 and therefore A = 70µm. However, changing the amplitude of integrated conductive yarns may be limited in woven textile. In the current weaving structure (left image in figure 4.2), the yarn amplitude appears to be related to the diameter of the weft yarns D 100 µm. Using weft yarns with a larger diameter may, to some extent, lead to a larger yarn amplitude. Although it may also require a smaller weaving density of the weft yarns, thereby increasing λ and consequently not changing the factor A d. λ λ λ Α Α Α Figure 4.2: Schematic representation of possible ways to interlace a conductive yarn (yellow) around the weft yarns (grey). The image on the left shows the current weaving structure. The amplitude A can be further increased by changing the weaving structure of the textile. Figure 4.2 shows two examples of alternative weaving structures that significantly increase A and λ. However, the weft yarns may restrict the straightening of the conductive yarn in such weaving structures. In the current textile samples, the weft yarns are pushed away as the conductive yarn straightens out. This may not be possible for the alternative weaving structures in figure 4.2 (especially the rightmost example). However, alternative weaving structures could be beneficial to increase the ratio A λ. 47

50 Measures can be taken to minimize the reduction in extension of integrated conductive yarn. However, unless the amplitude A is significantly increased, no gain in extension can be achieved. In order to improve the extension of integrated conductive yarn, a different weaving structure should be considered. 4.3 Preventing plastic deformation during straightening In order to allow the cyclic loading of the current conductive yarn, a wave-like yarn geometry could be used to prevent plastic deformation during stretching. In this section, the model of chapter 3 is used to prevent plastic deformation during the straightening of such a yarn. To completely prevent plastic deformation during stretching, it is assumed that the strains during production and straightening may not exceed the strain at the onset of yielding. Using figure 3.3 and the Young s modulus that was determined in section 3.2, this maximum allowable strain for the current conductive yarn can be expressed as ε y0 = σ y0 E (4.7) Using equation (3.10), the maximum strain due to bending may not exceed ε y0 : ε max = 2dAπ2 λ (4.8) Since we are looking for yarn-geometries where no plastic deformation occurs during production and straightening, there will be no pre-deformation effect and the extensibility will only change due to the over-length effect: E = E o = π2 A 2 λ 2 (4.9) Equations (4.9) and (4.8) can be used to determine which yarn geometry is required to be able to stretch the current conductive yarn without introducing plastic deformation. Figure 4.3 shows the contour lines of E o as a function of the yarn s amplitude and wavelength. Since the over-length effect does not depend on the filament diameter d, the amplitude and wavelength are not normalized. The gray area in figure 4.3 denotes combinations of A and λ where the plastic deformation occurs during straightening. For example: a sample of conductive yarn with an amplitude of 5 mm and a wavelength of 50 mm can be elastically extended by approximately 10%. For the current system parameters (A = 15 µm and λ = 350 µm), plastic deformation does occur during stretching. Therefore, the amplitude and wavelength will have to be significantly increased to allow for elastic stretching. 48

51 A[mm] E o Plastic deformation λ[mm] Figure 4.3: Contour plot of the increase in extensibility due to the over-length effect E o of conductive yarn with a wave-like shape for various values of A and λ. Since the over-length of a yarn depends quadratically on the amplitude of the yarn (see equation (4.9)), a large amplitude is desirable. However, increasing the amplitude also increases the curvature of the yarn and could result in plastic deformation. Therefore, in order to be able to elastically stretch the current conductive yarn, the amplitude and wavelength of the yarn geometry need to be in the order of millimeters 4.4 Discussion The model of chapter 3 was used to investigate if the extensibility of integrated conductive yarn can be increased by changing the weaving parameters. It was found that the reduction in mechanical properties due to production and straightening can be reduced by changing the weaving density and increasing the diameter of the weft yarns. However, the extensibility of the conductive yarn in the current weaving structure cannot be made greater than that of virgin conductive yarn unless a significantly larger amplitude is used. In order to achieve this, alternative weaving structures will have to be considered. Alternatively, the extensibility of integrated conductive yarn can be increased by using a different type of conductive yarn. Desirable mechanical properties for conductive yarns are a small filament diameter d with low twist T, to reduce the pre-deformation effect and allow for more extreme curvature to be applied, and a large maximum extension ε failure. In order to straighten a wave-like conductive yarn without introducing plastic deformation, the amplitude and wavelength for the current conductive yarn need to be in the order of millimeters. For practical reasons, such dimensions cannot be achieved by integrating the conductive yarn in woven textile. Therefore, alternative methods of attaching the conductive yarn such as in figure 4.4 should be considered. 49

52 Figure 4.4: Embroidered stretchable circuit connecting to LEDs, developed at Philips Research. In order to integrate conductive yarn in woven textile and still be able to elastically straighten it, a different conductive yarn will have to be considered. Similar to what was mentioned above, a small filament diameter d and low twist T are desirable. Furthermore, a larger elastic regime allows for more extreme curvature to be applied. In practice, completely preventing plastic deformation may not be required in order to create a product that can withstand cyclic loading. Some degree of plastic deformation during the straightening of conductive yarns may be tolerable. The developed model can be used to investigate this further. 50