Abstract
The numerical evaluation of stress intensity factors (SIFs) is presented for functionally graded CNT-reinforced composite (FG-CNTRC) plate. The 3-D linear elasticity of cracked orthotropic plate is formulated in terms of 2-D FEM and the (1,1,0) hierarchic model which is sort of the first-order shear deformation theory. Meanwhile, a 2-D thickness-wise plane within FG-CNTRC plate is taken for the numerical evaluation of SIFs. The thickness-wise mixed-mode SIFs are evaluated from the interaction integral by introducing the 2-D complex-valued orthotropic crack-tip singular fields. The numerical evaluation method is validated by comparing with the other reference methods, with the maximum relative difference equal to 31.43%. Moreover, the SIF characteristics of FG-CNTRC are numerically investigated. It is revealed that the thickness-wise volume fraction distribution of CNTs significantly influences the magnitude and variation of SIFs. However, the volume fraction magnitude of CNTs does not show an apparent consistent effect on the both items of SIFs.
Similar content being viewed by others
References
Ajayan PM, Stephane O, Collix C, Trauth D (1994) Aligned carbon nanotube arrays formed by cutting a polymer resin-nanotube composite. Science 256:1212–1214, DOI: https://doi.org/10.1126/science.265.5176.1212
Arani A, Maghamikia S, Mohammadimehr M, Arefmanesh A (2011) Buckling analysis of laminated composite rectangular plates reinforced by SWCNTS using analytical and finite element methods. Journal of Mechanical Science and Technology 25:809–820, DOI: https://doi.org/10.1007/s12206-011-0127-3
Cho JR (2020a) 2-D reliable crack analysis by enriched Petrov-Galerkin natural element method. KSCE Journal of Civil Engineering 24(2): 561–568, DOI: https://doi.org/10.1007/s12205-019-0978-1
Cho JR (2020b) Natural element approximation of hierarchical models of plate-like elastic structures. Finite Elements in Analysis and Design 180(103439), DOI: https://doi.org/10.1016/j.finel.2020.103439
Cho JR, Lee HW (2014) Calculation of stress intensity factors in 2-D linear fracture mechanics by Petrov-Galerkin natural element method. International Journal for Numerical Methods in Engineering 98(11): 819–839, DOI: https://doi.org/10.1002/nme.4666
Cho JR, Oden JT (2000) Functionally graded material: A parametric study on thermal-stress characteristics using the Crank-Nicolson-Galerkin scheme. Computer Methods in Applied Mechanics Engineering 188:17–38, DOI: https://doi.org/10.1016/S0045-7825(99)00289-3
Corten HT (1968) Fracture mechanics of composites. In: Leibowitz H, editor. Fracture —An Advanced Treatise, VII. New York: Academic Press
De Saxce G, Kang CH (1992) Application of the hybrid mongrel displacement finite method to the computation of stress intensity factors in anisotropic material. Engineering Fracture Mechanics 41(1):71–83, DOI: https://doi.org/10.1016/0013-7944(92)90096-W
Di Sciuva M, Sorrenti M (2019) Bending, free vibration and buckling of functionally graded carbon nanotube-reinforced sandwich plates using the extended Refined Zigzag Theory. Composite Structures 227(111324), DOI: https://doi.org/10.1016/j.compstruct.2019.111324
Esawi AMK, Farag MM (2007) Carbon nanotube reinforced composites: Potential and current challenges. Materials Design 28:2394–2401, DOI: https://doi.org/10.1016/j.matdes.2006.09.022
Formica Q Lacarbonara W, Alessi R (2010) Vibrations of carbon nanotube-reinforced composites. Journal of Sound and Vibration 329:1875–1889, DOI: https://doi.org/10.1016/j.jsv.2009.11.020
Han Y, Elliott J (2007) Molecular dynamics simulations of the elastic properties of polymer/carbon nanobute composites. Computational Material Science 39:315–323, DOI: https://doi.org/10.1016/j.commatsci.2006.06.011
Harris PJF (2001) Carbon nanotubes and related structures: New materials for the twenty-first century. Cambridge University Press, United Kingdom
Hu N, Fugunaga H, Lu C, Kameyama M, Yan B (2005) Prediction of elastic properties of carbon nanotube reinforced composites. Proceedings of The Royal Society A 461:1685–1670, DOI: https://doi.org/10.1098/rspa.2004.1422
Ke LL, Yang J, Kitipornchai S (2010) Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Composite Structures 92:676–683, DOI: https://doi.org/10.1016/j.compstruct.2009.09.024
Kim JW (1985) A contour integral computation of stress intensity factors in the cracked orthotropic elastic plates. Engineering Fracture Mechanics 21(2):353–364, DOI: https://doi.org/10.1016/0013-7944(85)90023-2
Liew KM, Lei ZX, Zhang LW (2015) Mechanical analysis of functionally graded carbon nanotube reinforced composite: A review. Composite Structures 120:90–97, DOI: https://doi.org/10.1016/j.compstruct.2014.09.041
Mandell JF, McGarry FJ, Wang SS, Im J (1974) Stress intensity factors for anisotropic fracture test specimens of several geometries. Journal of Composite Materials 8:106–116, DOI: 10.1177%2F002199837400800201
Mirzaei M, Kiani Y (2017) Nonlinear free vibration of FG-CNT reinforced composite plates. Structural Engineering and Mechanics 64(3):381–390, DOI: https://doi.org/10.12989/sem.2017.64.3.381
Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 46:131–150, DOI: https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
Qian S, Dickey EC, Andrews R, Rantell T (2000) Load transfer and deformation mechanism in carbon nanotube-polystyrene composites. Applied Physics Letters 76:2868, DOI: https://doi.org/10.1063/1.126500
Saouma VE, Sikiotis ES (1986) Stress intensity factors in anisotropic bodies using singular isoparametric elements. Engineering Fracture Mechanics 25:115–121, DOI: https://doi.org/10.1016/0013-7944(86)90209-2
Seidel GD, Lagoudas DC (2006) Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites. Mechanics of Materials 38(8–10):884–907, DOI: https://doi.org/10.1016/j.mechmat.2005.06.029
Shen SH (2009) Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Composite Structures 19:9–19, DOI: https://doi.org/10.1016/j.compstruct.2009.04.026
Sih GC, Chen EP (1981) Cracks in composite materials. Martinus Nijhoff, The Netherlands
Van Do VN, Lee CH (2017) Bending analyses of FG-CNTRC plates using the modified mesh-free radial point interpolation method based on the higher-order shear deformation theory. Composite Structures 168:485–497, DOI: https://doi.org/10.1016/j.compstruct.2017.02.055
Wang ZX, Shen HS (2011) Nonlinear vibration of nanotube-reinforced composite plates in thermal environments. Computational Material Science 50:2319–2330, DOI: https://doi.org/10.1016/j.commatsci.2011.03.005
Wuite J, Adali S (2005) Deflection and stress behavior of nanocomposite reinforced beams using a multiscale amalysis. Composite Structures 71:388–396, DOI: https://doi.org/10.1016/j.compstruct.2005.09.011
Xiao QZ, Karihaloo BL, Williams FW (1999) Application of penalty-equilibrium hybrid stress element method to crack problems. Engineering Fracture Mechanics 63:1–22, DOI: https://doi.org/10.1016/S0013-7944(99)00015-6
Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1100924).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cho, JR. Numerical Evaluation of Stress Intensity Factors in Functionally Graded CNTRC Plates. KSCE J Civ Eng 26, 4563–4572 (2022). https://doi.org/10.1007/s12205-022-1237-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-022-1237-4