Finite Element Evaluation of Effective Thermal Conductivity of Short Carbon Nano Tubes: A Comparative Study

Abstract:

In the current study, two extreme cases are considered for the dispersion of carbon nanotubes(CNTs) in a polymeric matrix: randomly-oriented and randomly-aligned. The representative volume element (RVE) is used to represent the composite material consisting of epoxy resin matrix and CNT-reinforcement. The finite element method acts as the computational tool to conduct the simulations and investigate the effective parameters, i.e., the influence of the aspect ratio and the orientation, on the thermal conductivity of the matrix. A Fortran subroutine was used for both generation and analysis of the models by means of the MSC Marc finite element package and a Python script was used for the sensitivity analysis. The results indicate that optimum performance of the CNTs in terms of thermal conductivity can be reached by orienting them along the temperature gradient whereas a random distribution improves the conductivity by a smaller magnitude.

• Periodical: Defect and Diffusion Forum (Volume 372)
• Pages: 208-214
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.372.208
• Online since: March 2017
• Authors: Zia Javanbakht*, Wayne Hall, Andreas Öchsner
• Keywords: Computational Analysis, Finite Element Method, Reinforced Composites, Thermal Analysis

References

[1] V. V. Vasiliev and E. V. Morozov. Advanced mechanics of composite materials. 2nd edn. Amsterdam and London: Elsevier, (2007).

[2] J. R. Vinson and R. L. Sierakowski. The behavior of structures composed of composite materials. 2nd ed. Vol. 105. Solid mechanics and its applications. Dordrecht and London: Kluwer Academic Publishers, (2002).

DOI: 10.1007/0-306-48414-5

[3] R. M. Jones. Mechanics of composite materials. 2nd ed. Philadelphia, Pa. and London: Taylor & Francis, (1999).

[4] J. N. Coleman et al. Small but strong: A review of the mechanical properties of carbon nanotube- polymer composites. Carbon 44 (2006), pp.1624-1652.

DOI: 10.1016/j.carbon.2006.02.038

[5] S. Iijima. Helical microtubules of graphitic carbon. Nature 354 (1991), pp.56-58.

DOI: 10.1038/354056a0

[6] E. T. Thostenson, Z. Ren, and T. -W. Chou. Advances in the science and technology of carbon nanotubes and their composites: A review. Compos. Sci. Technol. 61 (2001), p.1899-(1912).

DOI: 10.1016/s0266-3538(01)00094-x

[7] E. T. Thostenson, C. Li, and T. -W. Chou. Nanocomposites in context. Compos. Sci. Technol. 65 (2005), pp.491-516.

[8] S. Berber, Y. -K. Kwon, and D. Tománek. Unusually High Thermal Conductivity of Carbon Nanotubes. Phys. Rev. Lett. 84 (2000). May, pp.4613-4616.

DOI: 10.1103/physrevlett.84.4613

[9] Z. Han and A. Fina. Thermal conductivity of carbon nanotubes and their polymer nanocomposites: A review. Prog. Polym. Sci. 36 (2011), pp.914-944.

DOI: 10.1016/j.progpolymsci.2010.11.004

[10] N. Behabtu et al. Strong, light, multifunctional fibers of carbon nanotubes with ultrahigh conductivity. Science 339 (2013), pp.182-186.

[11] R. H. Baughman, A. A. Zakhidov, and W. A. de Heer. Carbon nanotubes-the route toward applications. Science 297 (2002), pp.787-792.

DOI: 10.1126/science.1060928

[12] R. S. Ruoff and D. C. Lorents. Mechanical and thermal properties of carbon nanotubes. Carbon 33 (1995), pp.925-930.

DOI: 10.1016/0008-6223(95)00021-5

[13] H. Chen et al. Thermal conductivity of polymer-based composites: Fundamentals and applications. Prog. Polym. Sci. 59 (2016), pp.41-85.

[14] M. Mahdavi et al. Effective thermal and mechanical properties of short carbon fiber/natural rubber composites as a function of mechanical loading. Appl. Therm. Eng. 117 (2017), pp.8-16.

DOI: 10.1016/j.applthermaleng.2017.02.004

[15] H. R. Lusti and A. A. Gusev. Finite element predictions for the thermoelastic properties of nanotube reinforced polymers. Modelling Simul. Mater. Sci. Eng. 12 (2004), S107-S119.

DOI: 10.1088/0965-0393/12/3/s05

[16] I. E. Afrooz and A. Öchsner. Effect of the Carbon Nanotube Distribution on the Thermal Conductivity of Composite Materials. J. Heat Transfer 137 (2015), p.034501.

DOI: 10.1115/1.4029034

[17] N. Khani, M. Yildiz, and B. Koc. Elastic properties of coiled carbon nanotube reinforced nanocomposite: A finite element study. Mater. Des. 109 (2016), pp.123-132.

DOI: 10.1016/j.matdes.2016.06.126

[18] R. Makvandi and A. Öchsner. On a Finite Element Approach to Predict the Thermal Conductivity of Carbon Fiber Reinforced Composite Materials. Defect. Diffus. Forum 354 (2014), pp.215-225.

DOI: 10.4028/www.scientific.net/ddf.354.215

[19] S. R. Bakshi, R. R. Patel, and A. Agarwal. Thermal conductivity of carbon nanotube reinforced aluminum composites: A multi-scale study using object oriented finite element method. Comput. Mater. Sci. 50 (2010), pp.419-428.

DOI: 10.1016/j.commatsci.2010.08.034

[20] H. S. Hedia et al. Effect of agglomeration and dispersion on the elastic properties of polymer nanocomposites: A Monte Carlo finite element analysis. MP 58 (2016), pp.269-279.

DOI: 10.3139/120.110843

[21] K. Alasvand Zarasvand and H. Golestanian. Determination of nonlinear behavior of multiwalled carbon nanotube reinforced polymer: Experimental, numerical, and micromechanical. Mater. Des. 109 (2016), pp.314-323.

DOI: 10.1016/j.matdes.2016.07.071

[22] X. L. Chen and Y. J. Liu. Square representative volume elements for evaluating the effective material properties of carbon nanotube-based composites. Comput. Mater. Sci. 29 (2004), pp.1-11.

DOI: 10.1016/s0927-0256(03)00090-9

[23] I. V. Belova et al. The Lattice Monte Carlo Method for Solving Phenomenological Mass and Thermal Diffusion Problems. Defect. Diffus. Forum 279 (2008), pp.13-22.

DOI: 10.4028/www.scientific.net/ddf.279.13

[24] I. V. Belova et al. The lattice Monte Carlo method for solving phenomenological mass and heat transport problems. DDC 4 (2007), pp.15-1.

[25] A. Öchsner and M. Merkel. One-Dimensional Finite Elements: An Introduction to the FE Method. Berlin and Heidelberg: Springer, (2013).

[26] A. Öchsner. Computational statics and dynamics: An introduction based on the finite element method. Singapore: Springer, (2016).

[27] Z. Javanbakht and A. Öchsner. Advanced finite element simulation with MSC Marc: Application of user subroutines. Cham: Springer, (2017).

DOI: 10.1007/978-3-319-47668-1

[28] T. Fiedler, E. Solórzano, and A. Öchsner. Numerical and experimental analysis of the thermal conductivity of metallic hollow sphere structures. Mater. Lett. 62 (2008), pp.1204-1207.

DOI: 10.1016/j.matlet.2007.08.050

[29] T. Fiedler et al. A refined finite element analysis on the thermal conductivity of perforated hollow sphere structures. Comput. Mater. Sci. 47 (2009), pp.314-319.

DOI: 10.1016/j.commatsci.2009.08.007

[30] Z. Javanbakht, W. Hall, and A. Öchsner. Automatized Estimation of the Effective Thermal Conductivity of Carbon Fiber Reinforced Composite Materials. Defect. Diffus. Forum 370 (2016), pp.177-183.

DOI: 10.4028/www.scientific.net/ddf.370.177

[31] MSC Software Corporation. Marc 2015: Theory and User Information. Vol. A. Newport Beach, California: MSC Software Corporation, (2015).