Coupled systems mechanics

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Thermo-mechanical analysis of carbon nanotube-reinforced composite sandwich beams

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Farazamandnia, Navid (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • Received : 2016.10.27
  • Accepted : 2017.05.11
  • Published : 2017.06.25
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Abstract

In this paper Timoshenko beam theory is employed to investigate the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) Beams with a stiff core in thermal environment. The material characteristic of carbon nanotubes (CNT) are supposed to change in the thickness direction in a functionally graded form. They can also be calculated through a micromechanical model where the CNT efficiency parameter is determined by matching the elastic modulus of CNTRCs calculated from the rule of mixture with those gained from the molecular dynamics simulations. The differential transform method (DTM) which is established upon the Taylor series expansion is one of the effective mathematical techniques employed to the differential governing equations of sandwich beams. Effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, different thermal environment and various boundary conditions on the free vibration characteristics of FG-CNTRC sandwich beams are studied. It is observed that vibration response of FG-CNTRC sandwich beams is prominently influenced by these parameters.

Keywords

References

  1. Ajayan, P.O., Stephan, C.C. and Trauth, D. (1994), "Aligned carbon nanotube arrays formed by cutting a polymer resin-nanotube composite", Sci. 265(5176), 1212-1214. https://doi.org/10.1126/science.265.5176.1212
  2. Anandrao, K.S., Gupta, R., Ramchandran, P. and Rao, G.V. (2010), "Thermal post-buckling analysis of uniform slender functionally graded material beams", Struct. Eng. Mech., 36(5), 545-560. https://doi.org/10.12989/sem.2010.36.5.545
  3. Ashrafi, B. and Hubert, P. (2006), "Modeling the elastic properties of carbon nanotube array/polymer composites", Compos. Sci. Technol., 66(3), 387-396. https://doi.org/10.1016/j.compscitech.2005.07.020
  4. Barzoki, A.A.M., Loghman, A. and Arani, A.G. (2015), "Temperature-dependent nonlocal nonlinear buckling analysis of functionally graded SWCNT-reinforced microplates embedded in an orthotropic elastomeric medium", Struct. Eng. Mech., 53(3), 497-517. https://doi.org/10.12989/sem.2015.53.3.497
  5. Bhangale, R.K. and Ganesan, N. (2006), "Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core", J. Sound Vibr., 295(1-2), 294-316. https://doi.org/10.1016/j.jsv.2006.01.026
  6. Bidgoli, M.R., Karimi, M.S. and Arani, A.G. (2015), "Viscous fluid induced vibration and instability of FGCNT-reinforced cylindrical shells integrated with piezoelectric layers", Steel Compos. Struct., 19(3), 713-733. https://doi.org/10.12989/scs.2015.19.3.713
  7. Bonnet, P., Sireude, D., Garnier, B. and Chauvet, O. (2007), "Thermal properties and percolation in carbon nanotube-polymer composites", Appl. Phys. Lett., 91(20), 201910-201910-201913.
  8. Ebrahimi, F. and Rastgoo, A. (2008a) "Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers", Smart Mater. Struct. 17(1), 015044. https://doi.org/10.1088/0964-1726/17/1/015044
  9. Ebrahimi, F. and Rastgoo, A. (2008b), "An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory", Thin-Wall. Struct., 46(12), 1402-1408. https://doi.org/10.1016/j.tws.2008.03.008
  10. Ebrahimi, F. and Rastgoo, A. (2008c), "Free vibration analysis of smart FGM plates", J. Mech. Syst. Sci. Eng., 2(2), 94-99.
  11. Ebrahimi, F., Rastgoo, A. and Kargarnovin, M.H. (2008), "Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers", J. Mech. Sci. Technol., 22(6), 1058-1072. https://doi.org/10.1007/s12206-008-0303-2
  12. Ebrahimi F., Rastgoo, A. and Atai, A.A. (2009a), "Theoretical analysis of smart moderately thick shear deformable annular functionally graded plate", Eur. J. Mech.-A/Sol., 28(5), 962-997. https://doi.org/10.1016/j.euromechsol.2008.12.008
  13. Ebrahimi, F., Naei, M.H. and Rastgoo, A. (2009b), "Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation", J. Mech. Sci. Technol., 23(8), 2107-2124. https://doi.org/10.1007/s12206-009-0358-8
  14. Ebrahimi, F. (2013), "Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment", Mech. Adv. Mater. Struct., 20(10), 854-870. https://doi.org/10.1080/15376494.2012.677098
  15. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016a), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded euler beams with porosities", Meccan., 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  16. Ebrahimi, F. and Zia, M. (2015), "Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities", Acta Astronaut., 116, 117-125. https://doi.org/10.1016/j.actaastro.2015.06.014
  17. Ebrahimi, F. and Mokhtari, M. (2015), "Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method", J. Brazil. Soc. Mech. Sci. Eng., 37(4), 1435-1444. https://doi.org/10.1007/s40430-014-0255-7
  18. Ebrahimi, F. and Salari, E (2015a), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007. https://doi.org/10.1088/0964-1726/24/12/125007
  19. Ebrahimi, F. and Salari, E. (2015b), "Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment", Acta Astronaut., 113, 29-50. https://doi.org/10.1016/j.actaastro.2015.03.031
  20. Ebrahimi, F. and Salari, E. (2015c), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Compos. B, 79, 156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  21. Ebrahimi, F. and Salari, E. (2015d), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", CMES: Comput. Model. Eng. Sci., 105(2), 151-181.
  22. Ebrahimi, F. and Salari, E. (2015e), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. https://doi.org/10.1016/j.compstruct.2015.03.023
  23. Ebrahimi, F. and Salari, E. (2015f), "Thermo-mechanical vibration analysis of nonlocal temperaturedependent FG nanobeams with various boundary conditions", Compos. B, 78, 272-290. https://doi.org/10.1016/j.compositesb.2015.03.068
  24. Ebrahimi, F. and Salari, E. (2016), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams", Mech. Adv. Mater. Struct., 23(12), 1379-1397. https://doi.org/10.1080/15376494.2015.1091524
  25. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions", J. Therm. Stress., 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  26. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2016c), "In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams", Meccan., 51(4), 951-977. https://doi.org/10.1007/s11012-015-0248-3
  27. Ebrahimi, F. and Barati, M.R. (2016a), "Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams", Eur. Phys. J. Plus, 131(9), 346. https://doi.org/10.1140/epjp/i2016-16346-5
  28. Ebrahimi, F. and Barati, M.R. (2016b), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  29. Ebrahimi, F. and Barati, M.R. (2016c), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", J. Smart Nano Mater., 1-25.
  30. Ebrahimi, F. and Barati, M.R. (2016d), "An exact solution for buckling analysis of embedded piezoelectromagnetically actuated nanoscale beams", Adv. Nano Res., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  31. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of smart size-dependent higher order magnetoelectro-thermo-elastic functionally graded nanosize beams", J. Mech., 1-11.
  32. Ebrahimi, F. and Barati, M.R. (2016f), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  33. Ebrahimi, F. and Hosseini, S.H.S. (2016a), "Double nanoplate-based NEMS under hydrostatic and electrostatic actuations", Eur. Phys. J. Plus, 131(5), 1-19. https://doi.org/10.1140/epjp/i2016-16001-3
  34. Ebrahimi, F. and Hosseini, S.H.S. (2016b), "Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates", Appl. Phys. A, 122(10), 922. https://doi.org/10.1007/s00339-016-0452-6
  35. Ebrahimi, F. and Hosseini, S.H.S. (2016c), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Stress., 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  36. Ebrahimi, F. and Nasirzadeh, P. (2015), "A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method", J. Theoret. Appl. Mech., 53(4), 1041-1052.
  37. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017), "Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams", J. Therm. Stress., 40(5), 535-547. https://doi.org/10.1080/01495739.2016.1230483
  38. Ebrahimi, F. and Barati, M.R. (2016g), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vibr. Contr., 1077546316646239.
  39. Ebrahimi, F. and Barati, M.R. (2016h), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 1-16.
  40. Ebrahimi, F. and Barati, M.R. (2016i), "Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., In press.
  41. Ebrahimi, F. and Barati, M.R. (2016j), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  42. Ebrahimi, F. and Barati, M.R. (2016k), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  43. Ebrahimi, F. and Barati, M.R. (2016l), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y
  44. Ebrahimi, F. and Barati, M.R. (2016m), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001
  45. Ebrahimi, F. and Barati, M.R. (2016n), "Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 1-13.
  46. Ebrahimi, F. and Barati, M.R. (2016o), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122(9), 792. https://doi.org/10.1007/s00339-016-0322-2
  47. Ebrahimi, F. and Barati, M.R. (2016p), "Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment", J. Smart Nano Mater., 7(2), 69-90. https://doi.org/10.1080/19475411.2016.1191556
  48. Ebrahimi, F. and Barati, M.R. (2016q), "Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory", Appl. Phys. A, 122(9), 843. https://doi.org/10.1007/s00339-016-0368-1
  49. Ebrahimi, F. and Barati, M.R. (2016r), "Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 1-12.
  50. Ebrahimi, F. and Barati, M.R. (2016s), "On nonlocal characteristics of curved inhomogeneous Euler-Bernoulli nanobeams under different temperature distributions", Appl. Phys. A, 122(10), 880. https://doi.org/10.1007/s00339-016-0399-7
  51. Ebrahimi, F. and Barati, M.R. (2016t), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intell. Mater. Syst. Struct., 1045389X16672569.
  52. Ebrahimi, F. and Barati, M.R. (2016u), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys. A, 122(10), 910. https://doi.org/10.1007/s00339-016-0441-9
  53. Ebrahimi, F. and Barati, M.R. (2016v), "Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates", J. Brazil. Soc. Mech. Sci. Eng., 1-21.
  54. Ebrahimi, F. and Barati, M.R. (2017a), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092
  55. Ebrahimi, F. and Barati, M.R. (2017b), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. https://doi.org/10.1016/j.compstruct.2016.09.058
  56. Ebrahimi, F., Ehyaei, J. and Babaei, R. (2016), "Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation", Adv. Mater. Res., 5(4), 245-261. https://doi.org/10.12989/amr.2016.5.4.245
  57. Ebrahimi, F. and Jafari, A. (2016), "Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory", Adv. Mater. Res., 5(4), 261-276.
  58. Ebrahimi, F. and Barati, M.R. (2016), "An exact solution for buckling analysis of embedded piezoelectromagnetically actuated nanoscale beams", Adv. Nano Res., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  59. Ebrahimi, F. and Mohsen, D. (2007), "Dynamic modeling of embedded curved nanobeams incorporating surface effects", Coupled Syst. Mech., 5(3), 255-267. https://doi.org/10.12989/CSM.2016.5.3.255
  60. Esawi, A.M. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: potential and current challenges", Mater. Des., 28(9), 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022
  61. Fidelus, J., Wiesel, E., Gojny, F., Schulte, K. and Wagner, H. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Compos. Part A: Appl. Sci. Manufact., 36(11), 1555-1561. https://doi.org/10.1016/j.compositesa.2005.02.006
  62. Griebel, M. and Hamaekers, J. (2004), "Molecular dynamics simulations of the elastic moduli of polymercarbon nanotube composites", Comput. Meth. Appl. Mech. Eng., 193(17), 1773-1788. https://doi.org/10.1016/j.cma.2003.12.025
  63. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011
  64. Hassan, I.A.H. (2002), "On solving some eigenvalue problems by using a differential transformation", Appl. Math. Comput., 127(1), 1-22. https://doi.org/10.1016/S0096-3003(00)00123-5
  65. Hu, N., Fukunaga, H., Lu, C., Kameyama, M. and Yan, B. (2005), "Prediction of elastic properties of carbon nanotube reinforced composites", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 461(2058), 1685-1710. https://doi.org/10.1098/rspa.2004.1422
  66. Ju, S.P. (2004), "Application of differential transformation to transient advective-dispersive transport equation", Appl. Math. Comput., 155(1), 25-38. https://doi.org/10.1016/S0096-3003(03)00755-0
  67. Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Compos. Struct., 92(3), 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024
  68. Ke, L.L., Yang, J. and Kitipornchai, S. (2013), "Dynamic stability of functionally graded carbon nanotubereinforced composite beams", Mech. Adv. Mater. Struct., 20(1), 28-37. https://doi.org/10.1080/15376494.2011.581412
  69. Lau, A.K.T. and Hui, D. (2002), "The revolutionary creation of new advanced materials-carbon nanotube composites", Compos. Part B: Eng., 33(4), 263-277. https://doi.org/10.1016/S1359-8368(02)00012-4
  70. Lau, K.T., Gu, C., Gao, G.H., Ling, H.Y. and Reid, S.R. (2004), "Stretching process of single-and multiwalled carbon nanotubes for nanocomposite applications", Carb., 42(2), 426-428. https://doi.org/10.1016/j.carbon.2003.10.040
  71. Odegard, G., Gates, T., Wise, K., Park, C. and Siochi, E. (2003), "Constitutive modeling of nanotube-reinforced polymer composites", Compos. Sci. Technol., 63(11), 1671-1687. https://doi.org/10.1016/S0266-3538(03)00063-0
  72. Pradhan, S. and Murmu, T. (2009), "Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method", J. Sound Vibr., 321(1), 342-362. https://doi.org/10.1016/j.jsv.2008.09.018
  73. Qian, D., Dickey, E.C., Andrews, R. and Rantell, T. (2000), "Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites", Appl. Phys. Lett., 76(20), 2868-2870. https://doi.org/10.1063/1.126500
  74. Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
  75. Seidel, G.D. and Lagoudas, D.C. (2006), "Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites", Mech. Mater., 38(8), 884-907. https://doi.org/10.1016/j.mechmat.2005.06.029
  76. Shen, H.S. (2004), "Thermal postbuckling behavior of functionally graded cylindrical shells with temperature-dependent properties", J. Sol. Struct., 41(7), 1961-1974. https://doi.org/10.1016/j.ijsolstr.2003.10.023
  77. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026
  78. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Des., 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048
  79. Thostenson, E.T. and Chou, T.W. (2003), "On the elastic properties of carbon nanotube-based composites: modelling and characterization", J. Phys. D: Appl. Phys. 36(5), 573. https://doi.org/10.1088/0022-3727/36/5/323
  80. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerospace Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  81. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50(8), 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005
  82. Wang, Z.X. and Shen, H.S. (2012), "Nonlinear vibration and bending of sandwich plates with nanotubereinforced composite face sheets", Compos. Part B: Eng., 43(2), 411-421. https://doi.org/10.1016/j.compositesb.2011.04.040
  83. Wu, H., Kitipornchai, S. and Yang, J. (2015), "Free vibration and buckling analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets", J. Struct. Stabil. Dyn., 1540011.
  84. Xu, Y., Ray, G. and Abdel-Magid, B. (2006), "Thermal behavior of single-walled carbon nanotube polymermatrix composites", Compos. Part A: Appl. Sci. Manufact., 37(1), 114-121. https://doi.org/10.1016/j.compositesa.2005.04.009
  85. Yang, J., Ke, L.L. and Feng, C. (2015), "Dynamic buckling of thermo-electro-mechanically loaded FGCNTRC beams", J. Struct. Stabil. Dyn., 1540017.
  86. Zenkour, A. and Sobhy, M. (2010), "Thermal buckling of various types of FGM sandwich plates", Compos. Struct., 93(1), 93-102. https://doi.org/10.1016/j.compstruct.2010.06.012
  87. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2-buckling and free vibration", J. Sol. Struct., 42(18-19), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016
  88. Zhang, C.L. and Shen, H.S. (2006), "Temperature-dependent elastic properties of single-walled carbon nanotubes: Prediction from molecular dynamics simulation", Appl. Phys. Lett., 89(8), 081904. https://doi.org/10.1063/1.2336622
  89. Zhu, R., Pan, E. and Roy, A. (2007), "Molecular dynamics study of the stress-strain behavior of carbonnanotube reinforced Epon 862 composites", Mater. Sci. Eng.: A., 447(1), 51-57. https://doi.org/10.1016/j.msea.2006.10.054