Thermal Stress Analysis of a Composite Cylinder Reinforced with FG SWCNTs

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Faculty of Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan

2 Department of Mechanical Engineering, Faculty of Engineering, University of Kashan

Abstract

Thermal stress analysis of a thick-walled cylinder reinforced with functionally graded (FG) single-walled carbon nanotubes (SWCNTs) is considered in radial direction. Thick-walled cylinder is subjected to a thermal field. Two layouts of variations in the volume fraction of SWCNTs were considered in the composite cylinder along the radius from inner to outer surface, where their names are incrementally decreasing (Inc Dec) and incrementally increasing (Inc Inc). Micromechanical models based on the Mori-Tanaka is used to define effective macroscopic properties of the nano composite shell. Using equations of motion, stress-strain and their corresponding constitutive correlations of a polystyrene vessel, a second order ordinary differential equation was proposed based on the radial displacement. The higher order governing equation was solved in order to obtain the distribution of displacement and thermal stresses in radial, circumferential and axial directions. The results indicate that FG distributions of SWCNTs have significant effect on thermal stresses and displacements in axial, radial and circumferential directions, so that in Inc Inc layout, the radial and circumferential stresses are lower than of other FG structures.

Keywords

[1] Saito R., Dresselhaus G., Dresselhaus M.S., 1998, Physical Properties of Carbon Nanotubes, Imperial College Press, London.

[2] Qian D., Wagner G.J., Liu W.K., Yu M.F., Ruoff R.S., 2002, Mechanics of Carbon Nanotubes, Applied Mechanics Reviews 55(6): 495-533.

[3] Ajayan P.M., Stephan O., Colliex C., Trauth D., 1994, Aligned carbon nanotube arrays formed by cutting a polymer resin—nanotube composite, Science 256: 1212-1214.

[4] Lourie O., Cox D.M., Wagner H.D., 1998, Buckling and Collapse of Embedded Carbon Nanotube, Physical Review Letters 81(8): 1638-1641.

[5] Haggenmueller R., Gommans H.H., Rinzler A.G., Fischer J.E., Winey K.I., 2000, Aligned Single-Wall Carbon Nanotubes In Composites by Melt Processing Methods, Chemical Physics Letters 330: 219-225.

[6] Fidelus J.D., Wiesel E., Gojny F.H., Schulte K.,Wagner H.D., 2005, Thermo-mechanical properties of randomly oriented Carbon/epoxy nanocomposites, Composites Part A: Applied Science and Manufacturing 36: 1555-1361.

[7] Bonnet P., Sireude D., Garnier B., Chauvet O., 2007, Thermal properties and percolation in carbon nanotube–polymer composites, Journal of Applied Physics 91: 201910.

[8] Qian D., Dickey E.C., Andrews R., Rantell T., 2000, Load Transferand and Deformation Mechanisms in Carbon Nanotube-Polystyrene Composites, Applied Physics Letters 76: 2868-2870.

[9] Odegard G.M., Gates T.S., Wise K.E., Park C., Siochi E.J., 2002, Constitutive Modeling of Nanotube-Reinforced Polymer Composites, Composites Science and Technology 63(11): 1671-1687.

[10] Wuite J., Adali S., 2005, Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis, Composite Structures 71: 388-396.

[11] Vodenitcharova T., Zhang L.C., 2006, Bending and local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube, International Journal of Solids and Structures 43: 3006-3024.

[12] Han Y., Elliott J., 2007, Molecular dynamics simulations of the elastic properties of polymer/ carbon nanotube composites, Computation Materials Science 39: 315-323.

[13] Zhu R., Pan E., Roy A.K., 2007, Molecular dynamics study of the stress-strain behavior of carbon-nanotube reinforced Epon 862 composites, Materials Science and Engineering A 447: 51-57.

[14] Shen H.S., 2009, Nonlinear bending of functionally graded carbon nanotubereinforced composite plates in thermal environments, Composite Structures 91: 9-19.

[15] Ke L.L., Yang J., Kitipornchai S., 2010, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Composite Structures 92(3): 676-683.

[16] Wang X., 1995, Thermal shock in a hollow cylinder caused by rapid arbitrary heating, Journal of Sound and Vibration 183: 899-906.

[17] Cho H., Kardomateas G.A., Valle C.S.,1998, Elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell, Journal of Applied Mechanics 65: 184-192.

[18] Ding H.J., Wang H.M., Chen W.Q., 2001, A theoretical solution of cylindrically isotropic cylindrical tube for axisymmetric plane strain dynamic thermoelastic problem, Acta Mechanica Solida Sinica 14: 357-363.

[19] Pelletier J.L., Vel S.S., 2006, An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells, International Journal of Solidsand Structures 43: 1131-1158.

[20] Horgan C.O., Chan A.M., 1999, the pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials,Journal of Elasticity55: 43-59.

[21] Tarn J.Q., 2001, Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads. International Journal of Solids and Structures 38: 8189-8206.

[22] Abd-Alla A.M., Farhan A.M., 2008, Effect of the non-homogenity on the composite infinite cylinder of orthotropic material, Physics Letters A 372: 756-260.

[23] Shi D.L., Feng X.Q., Huang Y.Y., Hwang K.C., Gao H., 2004, The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites, JournalofEngineeringMaterials andTechnology 126: 250-257.

[24] Hill R., 1965, A Self- Consistent Mechanics of Composite Materials, Journalof the Mechanics andPhysicsofSolids13: 213-222.

[25] Popov V.N., Van Doren V.E., Balkanski M., 2000, Elastic Properties of Crystals of Single-Walled Carbon Nanotubes, Solid State Communications 114: 395–399.

[26] Mark J.E., 1999, Polymer Data Handbook, Oxford University Press, New York. Oxford.

[27] Hetnarski R.B., Eslami M.R., 2008, Thermal Stresses Advanced Theory and Application, Springer.