Thermal Conductivities of 2.5 Dimensional Woven Composites. analogy has been successfully applied for solving problems of thermal conductivity 8-15.

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1 Thermal Conductivities of 2.5 Dimensional Woven Composites Thermal Conductivities of 2.5 Dimensional Woven Composites Leilei Song, Wei Geng, Yufen Zhao, Xiaoming Chen, and Jialu Li * Composites Research Institute of Tianjin Polytechnic University & Tianjin and Education Ministry Key Laboratory of Advanced Textile Composite Materials, Tianjin , China Received: 3 September 2014, Accepted: 2 June 2015 SUMMARY The thermal conductivities of 2.5 dimensional (2.5D) woven composites were measured by using transient hot-wire method (THWM) in this study. The results showed that the THWM could also be used to measure the thermal conductivity of 2.5D woven composites, which were considered to be homogeneous materials. Heat diffusion models of the samples were simulated. The thermal conductivities of 2.5 dimensional woven composites increased with the warp fibre volume fraction when the hot wire was perpendicular to the warp direction. It was important that the thermal conductivity of 2.5 dimensional woven composites was found to be affected by the yarn size. Thermal conductivities also increased with the effective yarn size. Finally, thermal conductivities of 2.5 dimensional woven composites increased with the temperature from K to K, although the enhancement was not great. These conclusions indicated that the thermal conductivity of 2.5 dimensional woven composites was affected by the internal structure and the external environment. Keywords: Carbon fibre; Thermal conductivity; 2.5 Dimensional woven composites; Transient hot-wire method 1. Introduction Fibre-reinforced composites have been widely used quite successfully for decades within industry sectors such as aerospace, maritime, transportation, infrastructure and consumer goods 1-5. The thermal conductivity of composites is an important parameter to many applications. The research on heat transfer processes of composites date from the 19th century. In 1965, Thornburgh and Pears studied the longitudinal and transverse thermal conduction of unidirectional reinforced plastics. They predicted the transverse thermal conductivity with simple approaches, but ignored interface conditions 6,7. During the past five decades, numerous studies have been made concerning this subject, and a variety of solution methods have been attempted. Among these methods, it is interesting to note that the method of * Corresponding author: lijialu@tjpu.edu.cn Smithers Information Ltd., 2016 analogy has been successfully applied for solving problems of thermal conductivity More recently, many researchers focused on the prediction models to estimate the thermal conductivities of fibre reinforced composites. Because of the heterogeneous nature of composites, the thermal conductivity appears to be the most tricky to determine experimentally and also to model 16. Many researchers used finite element methods to calculate the thermal conductivity On the other hand, heat diffusion is influenced by the thermal characteristics of the composites, which in turn depend on the orientation of the fibres 23. Therefore, the effects of fibre orientation on thermal conductivity also attracted the attention of many researchers. The thermal conductivities of laminated composite 24-28, 2.5D composites 29, three-dimensional (3D) braided composites 18,19,29, 3D woven composites 30 etc. 31,32 were investigated. However, there are very few reports for the measurement of thermal conductivity of 2.5D woven composites and even fewer using the THWM. More importantly, the effects of carbon yarn size on the thermal conductivities of 2.5D woven composites have not been considered yet. In this study, we measured the thermal conductivities of 2.5D woven composites by using THWM. At first, an investigation on the effects of fibre orientation on thermal conductivity was carried out. Then the thermal conductivities of composites with different yarn sizes were compared. Finally, we explored the effects of temperature on thermal conductivity. In fact, the term thermal conductivity is referred only for homogeneous materials. Therefore, the term effective thermal conductivity should be strictly employed for fibre Polymers & Polymer Composites, Vol. 24, No. 4,

2 Leilei Song, Wei Geng, Yufen Zhao, Xiaoming Chen, and Jialu Li reinforced composites 33. In this article, we use the term thermal conductivity throughout the text for simplicity. 2. ExperimentAL 2.1 Materials The 2.5D woven composites were reinforced by 2.5D woven fabrics, which are a unique kind of multilayer fabrics. The unit cell contains warp yarns and weft yarns interlaced at 90 Figure 1. Structure of 2.5D woven fabrics in the plane (Figure 1). The first set of tows that run in the weaving direction is called warp yarns, while the second set of tows that run transverse to the weaving direction is called weft yarns. The 2.5D woven fabric is composed of layers of straight weft yarns and a set of sinusoidal warp yarns, with the adjacent layers of weft yarns interlaced together by warp yarns In this paper the reinforcements were made of T-800 carbon fibre and the fibre volume fraction was 50%. The parameters of the reinforcements are listed in Table 1. The composites were prepared by RTM and the matrix was epoxy resin. The thickness of the composites was 4 mm, and each sample was cut into two pieces (40 mm*40 mm) for testing. A schematic of the sample is shown in Figure Thermal Conductivity Measurement The thermal conductivities of 2.5D woven composites were measured by using the transient hot-wire method. The testing equipment was TC3000 XIATECH made in China. Hotwire 3.0 software was used for recording and calculation. Figure 2. Schematic of the sample The THWM, considered as a simple, fast and accurate technique, was originally applied by van der Held and van Drunen in the determination of thermal conductivity of liquids. The THWM is a transient dynamic technique based on a linear heat source of infinite length and infinitesimal diameter and on the measurement of the temperature rise at a defined distance from the linear heat source embedded in the test material The geometry of THWM proposed here for the measurement of the thermal conductivity of solids is shown in Figure Results and discussion Table 1. Parameters of the reinforcements Sample Warp yarn Weft yarn Fibre volume fraction Size Fibre volume fraction Size A1 20% 6K 30% 18K A2 25% 6K 25% 12K A3 33.3% 6K 16.7% 6K B1 20% 12K 30% 24K B2 25% 12K 25% 24K B3 33.3% 12K 16.7% 12K 3.1 Effects of Fibre Orientation on the Thermal Conductivity of 2.5D Woven Composites Generally, fibre-reinforced composites are anisotropic materials. The anisotropic reinforcement, which is caused by the structure of 2.5D woven fabric, leads to anisotropy of the composites. Therefore, the thermal conductivities of 2.5D woven composites varied with the change of fibre orientation. For the purpose of 242 Polymers & Polymer Composites, Vol. 24, No. 4, 2016

3 Thermal Conductivities of 2.5 Dimensional Woven Composites comparison, the thermal conductivities of six samples were measured when the hot wire was perpendicular to the warp direction. The measurements were carried out at the temperatures of K and K. Group A included A1, A2 and A3, and their warp yarn size was 6K. Group B included B1, B2 and B3, and their warp yarn size was 12K. For the same-numbered samples in group A and group B, the warp fibre volume fraction was the same. The resulting thermal conductivities of samples when the hot wire was perpendicular to the warp direction are listed in Table 2. of carbon fibres. They created a better conductive pathway. With an increase of the warp fibre volume fraction, more and more fast-flowing channels were provided for heat flow. Meanwhile, the weft yarn was parallel to the hot wire. Epoxy resin between the fibres Figure 3. The sensor of THWM hindered the spread of heat flow from warp to weft, or from weft to warp. Compared with the warp yarn, the effects of the weft yarn on the thermal conductivity were not obvious in this case. Therefore, thermal conductivities of 2.5D woven composites measured The effects of warp fibre volume fraction on thermal conductivity are depicted in Figure 5. In Figure 4A, thermal conductivities increased with the warp fibre volume fraction at K, and the highest thermal conductivity (1.45 W/m K) was obtained for the highest warp fibre volume fraction (33.3%). Compared with A1, the thermal conductivity of A3 increased by 16%. The same tendency appeared at K, and the thermal conductivity increased by 21.8% from A1 to A3. In Figure 4B, the highest thermal conductivity (1.55 W/m K) was obtained for the highest warp fibre volume fraction (33.3%) at K. Compared with B1, the thermal conductivity of B3 increased by 22%. The tendency was verified again at K, and thermal conductivity increased by 24.4% from B1 to B3. It was considered that, when the hot wire was perpendicular to warp direction, the warp yarn played a major role in the heat transfer process. The hot wire produced a thermal pulse for a finite time with constant heating power and generated cylindrical coaxial isotherms in the samples. Heat spread radially in the cross section of the samples (Figure 5). Carbon fibre had good conducting nature compared to epoxy-resin matrix. In the cross section, there were continuous warp yarns, which consisted of filaments Figure 4. Effects of warp fibre volume fraction on thermal conductivity when hot wire was perpendicular to warp direction Table 2. Thermal conductivities of samples when hot wire was perpendicular to warp direction Sample Warp fibre volume Thermal conductivity [W/(m K)] fraction (%) Measured at K Measured at K Group A A A A Group B B B B Polymers & Polymer Composites, Vol. 24, No. 4,

4 Leilei Song, Wei Geng, Yufen Zhao, Xiaoming Chen, and Jialu Li Figure 5. Heat diffusion model of samples when hot wire was perpendicular to warp direction Figure 6. Effects of warp fibre volume fraction on thermal conductivity when hot wire was perpendicular to weft direction Table 3. Thermal conductivities of samples when hot wire was perpendicular to weft direction Sample Warp fibre volume Thermal conductivity [W/(m K)] fraction (%) Measured at K Measured at K Group A A A A Group B B B B by using THWM increased with the increase of warp fibre volume fraction. Validation of the analysis was performed by placing the hot wire perpendicular to the weft direction, and Table 3 shows the test results. When the weft yarn played a major role in the heat transfer process, it could be seen that the effects of the warp fibre volume fraction on thermal conductivity were different. Figure 6A shows that the thermal conductivities decreased with an increase of the warp fibre volume fraction, and the highest thermal conductivity was obtained for the lowest warp fibre volume fraction (20%) at K and K. Compared with A1, the thermal conductivity of A3 decreased by 13.9% at K, and by 17% at K. In Figure 6B, the highest thermal conductivity was obtained for the lowest warp fibre volume fraction (20%) at K and K, too. Compared with B1, the thermal conductivity of B3 decreased by 7.5% at K, and by 13.5% at K. Obviously, the thermal conductivities decreased with increasing warp fibre volume fraction. In contrast, when the hot wire was perpendicular to the weft direction, the weft yarn played a major role in the heat transfer process. A heat diffusion model of the samples is shown in Figure 7. In the cross section of the sample, the continuous weft yarns, which consisted of filaments of carbon fibres, created a better conductive pathway for heat flow. With an increase of weft fibre volume fraction, more fast flowing channels were provided. Therefore, the thermal conductivities of 2.5D woven composites decreased with increasing warp fibre volume fraction. However, the absence of continuous warp yarns weakened the influence of warp yarn on thermal conductivity. Epoxy resin between the fibres hindered the heat flow in the cross section. Compared with the weft yarn, the effects of the warp yarn on thermal conductivity were not obvious in this case. 244 Polymers & Polymer Composites, Vol. 24, No. 4, 2016

5 Thermal Conductivities of 2.5 Dimensional Woven Composites 3.2 Effects of Yarn Size on Thermal Conductivity of 2.5D Woven Composites The warp fibre volume fraction of A1 and B1 was 20%, and that of A2 and B2 was 25%, and that of A3 and B3 was 33%. In group A, which included A1, A2 and A3, the warp yarn size was 6K. The warp yarn size of samples in group B, which includes B1, B2 and B3, was 12K. For the case when the hot wire is perpendicular to the warp direction, a comparison of thermal conductivities of samples with different warp yarn size is shown in Figure 8. In Figure 8, thermal conductivities increased with the warp yarn size from 6K to 12K. At K, the enhancement of thermal conductivity from A1 to B1 was 1.6%, from A2 to B2 was 2.3%, and from A3 to B3 was 6.9% (Figure 8A). At K, the enhancement of thermal conductivity from A1 to B1 was 2.4%, and from A3 to B3 it was 4.6% (Figure 8B). Although the thermal conductivity of A2 was equal to B2, it was considered that the results obtained at K verified the tendency obtained at K. When hot wire was perpendicular to weft direction, a similar conclusion was obtained by comparing the thermal conductivities of samples with different weft yarn size (Figure 9). From A1 to B1, thermal conductivity increased by 10.5% at K, by 6% from A2 to B2, and by 2.8% from A3 to B3 (Figure 9A). At K, the thermal conductivity increased by 6.3% from A1 to B1, by 8.1% from A2 to B2 and by 3% from A3 to B3 (Figure 9B). Figure 7. Heat diffusion model of samples when hot wire was perpendicular to weft direction Figure 8. Comparison of the thermal conductivities of samples with different warp yarn size when hot wire was perpendicular to warp direction Figure 9. Comparison of the thermal conductivities of samples with different weft yarn size when hot wire was perpendicular to weft direction 3.3 Effects of Temperature on the Thermal Conductivity of 2.5D Woven Composites In order to explore the effects of temperature on thermal conductivity of 2.5D woven composites, the thermal conductivities of samples were measured at K and K, Polymers & Polymer Composites, Vol. 24, No. 4,

6 Leilei Song, Wei Geng, Yufen Zhao, Xiaoming Chen, and Jialu Li respectively. The results are shown in Tables 2 and 3. Comparisons of the thermal conductivities of samples measured at different temperature are shown in Figure 10. The results in Figure 10A were obtained when the hot wire was perpendicular to the warp direction, and the average enhancement of thermal conductivities from K to K was 1.8%. The results in Figure 10B were obtained when the hot wire was perpendicular to the weft direction, and the average enhancement of thermal conductivities from K to K was 2.9%. A full discussion of these results would be very complicated and a detailed discussion was given by some earlier research 10,33. However, with increasing temperature, the thermal conductivities of A1 in Figure 10A and B3 in Figure 10B decreased. This was probably because 10K was a small change of temperature. Overall, the thermal conductivities of 2.5D woven composites increased with the temperature from K to K, although the enhancement was not much. 4. ConclusionS In this study, the thermal conductivities of 2.5D woven composites were measured by using THWM. The 2.5D woven composites were considered to be homogeneous materials. Heat diffusion models of samples were simulated. More importantly, the thermal conductivity of 2.5 dimensional woven composites was affected by the yarn size. From the above comparisons, it could be concluded that: 1. The thermal conductivities increased with the warp fibre Figure 10. Effects of temperature on thermal conductivity of 2.5D woven composites volume fraction when the hot wire was perpendicular to the warp direction. By contrast, the thermal conductivities decreased with the warp fibre volume fraction when the hot wire was perpendicular to weft direction. 2. When the hot wire was perpendicular to the warp direction, thermal conductivities were increased by changing the warp yarn size from 6K to 12K. When the hot wire was perpendicular to the weft direction, a similar conclusion was obtained by comparing the thermal conductivities of samples with different weft yarn sizes. 3. Thermal conductivities of 2.5D woven composites increased with the temperature from K to K, although the enhancement was not great. These conclusions indicated that the thermal conductivity of 2.5D woven composites would be affected by internal structure and external environments. Therefore, we need to do more research to exploit the thermal conductivity of fibre-reinforced composites, which helps us to guide the design of new composites with optimized thermal properties. Acknowledgements The authors wish to express their thanks to the Tianjin Municipal Science and Technology Commission for the financial supports (Grants No: 11ZCKFSF00500) that made the present study possible. References 1. J. Hearle, G. Du, Forming rigid fibre assemblies: the interaction of textile technology and composites engineering, Journal of the Textile Institute, 81 (1990) A. Mouritz, M. Bannister, P. Falzon, K. Leong, Review of applications for advanced three-dimensional fibre textile composites, Composites Part A: Applied Science and 246 Polymers & Polymer Composites, Vol. 24, No. 4, 2016

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