In this article, we investigate the stress transfer characteristics of a novel hybrid hierarchical nanocomposite in which the regularly staggered short fuzzy fibers are interlaced in the polymer matrix. The advanced fiber augmented with carbon nanotubes (CNTs) on its circumferential surface is known as “fuzzy fiber.” A three-phase shear lag model is developed to analyze the stress transfer characteristics of the short fuzzy fiber reinforced composite (SFFRC) incorporating the staggering effect of the adjacent representative volume elements (RVEs). The effect of the variation of the axial and lateral spacing between the adjacent staggered RVEs in the polymer matrix on the load transfer characteristics of the SFFRC is investigated. The present shear lag model also accounts for the application of the radial loads on the RVE and the radial as well as the axial deformations of the different orthotropic constituent phases of the SFFRC. Our study reveals that the existence of the non-negligible shear tractions along the length of the RVE of the SFFRC plays a significant role in the stress transfer characteristics and cannot be neglected. Reductions in the maximum values of the axial stress in the carbon fiber and the interfacial shear stress along its length become more pronounced in the presence of the externally applied radial loads on the RVE. The results from the newly developed analytical shear lag model are validated with the finite element (FE) shear lag simulations and found to be in good agreement.
Issue Section:
Research Papers
Keywords:
shear lag model,
stress transfer,
staggered,
fuzzy fibers,
hybrid,
hierarchical,
nanocomposite
References
1.
Iijima
, S.
, 1991
, “Helical Microtubules of Graphitic Carbon
,” Nature
, 354
(6348), pp. 56
–58
.10.1038/354056a02.
Treacy
, M. M. J.
, Ebbesen
, T. W.
, and Gibson
, J. M.
, 1996
, “Exceptionally High Young's Modulus Observed for Individual Carbon Nanotubes
,” Nature
, 381
(6584), pp. 678
–680
.10.1038/381678a03.
Krishnan
, A.
, Dujardin
, E.
, Ebbesen
, E. W.
, Yianilos
, P. N.
, and Treacy
, M. M. J.
, 1998
, “Young's Modulus of Single-Walled Nanotubes
,” Phys. Rev. B
, 58
(20
), pp. 14013
–14019
.10.1103/PhysRevB.58.140134.
Lourie
, O.
, and Wagner
, H. D.
, 1998
, “Evaluation of Young's Modulus of Carbon Nanotubes by Micro-Raman Spectroscopy
,” J. Mater. Res.
, 13
(9
), pp. 2418
–2422
.10.1557/JMR.1998.03365.
Popov
, V. N.
, Van Doren
, V. E.
, and Balkanski
, M.
, 2000
, “Elastic Properties of Single-Walled Carbon Nanotubes
,” Phys. Rev. B
, 61
(4
), pp. 3078
–3084
.10.1103/PhysRevB.61.30786.
Li
, C.
, and Chou
, T. W.
, 2003
, “Multiscale Modeling of Carbon Nanotube Reinforced Polymer Composites
,” J. Nanosci. Nanotechnol.
, 3
(5), pp. 423
–430
.10.1166/jnn.2003.2337.
Shen
, L.
, and Li
, J.
, 2004
, “Transversely Isotropic Elastic Properties of Single-Walled Carbon Nanotubes
,” Phys. Rev. B
, 69
(4), p. 045414
.10.1103/PhysRevB.69.0454148.
Tsai
, J. L.
, Tzeng
, S. H.
, and Chiu
, Y. T.
, 2010
, “Characterizing Elastic Properties of Carbon Nanotube/Polyimide Nanocomposites Using Multi-Scale Simulation
,” Composites, Part B
, 41
(1
), pp. 106
–115
.10.1016/j.compositesb.2009.06.0039.
Liu
, Y. J.
, and Chen
, X. L.
, 2003
, “Evaluations of the Effective Material Properties of Carbon Nanotube-Based Composites Using a Nanoscale Representative Volume Element
,” Mech. Mater.
, 35
(1–2), pp. 69
–81
.10.1016/S0167-6636(02)00200-410.
Thostenson
, E. T.
, and Chou
, T. W.
, 2003
, “On the Elastic Properties of Carbon Nanotube-Based Composites: Modeling and Characterization
,” J. Phys. D: Appl. Phys.
, 36
(5
), pp. 573
–582
.10.1088/0022-3727/36/5/32311.
Odegard
, G. M.
, Gates
, T. S.
, Wise
, K. E.
, Park
, C.
, and Siochi
, E. J.
, 2003
, “Constitutive Modeling of Nanotube-Reinforced Polymer Composites
,” Compos. Sci. Technol.
, 63
(11
), pp. 1671
–1687
.10.1016/S0266-3538(03)00063-012.
Seidel
, G. D.
, and Lagoudas
, D, C.
, 2006
, “Micromechanical Analysis of the Effective Elastic Properties of Carbon Nanotube Reinforced Composites
,” Mech. Mater.
, 38
(8–10), pp. 884
–907
.10.1016/j.mechmat.2005.06.02913.
Ray
, M. C.
, and Batra
, R. C.
, 2009
, “Effective Properties of Carbon Nanotube and Piezoelectric Fiber Reinforced Hybrid Smart Composites
,” ASME J. Appl. Mech.
, 76(3)
, p. 034503
.10.1115/1.306363314.
Kulkarni
, M.
, Carnahan
, M. D.
, Kulkarni
, K.
, Qian
, D.
, and Abot
, J. L.
, 2010
, “Elastic Response of a Carbon Nanotube Fiber Reinforced Polymeric Composite: A Numerical and Experimental Study
,” Composites, Part B
, 41
(5
), pp. 414
–421
.10.1016/j.compositesb.2009.09.00315.
Meguid
, S. A.
, Wernik
, J. M.
, and Cheng
, Z. Q.
, 2010
, “Atomistic-Based Continuum Representation of the Effective Properties of Nano-Reinforced Epoxies
,” Int. J. Solids Struct.
, 47
(13
), pp. 1723
–1736
.10.1016/j.ijsolstr.2010.03.00916.
Thostenson
, E. T.
, Ren
, Z.
, and Chou
, T. W.
, 2001
, “Advances in the Science and Technology of Carbon Nanotubes and Their Composites: A Review
,” Compos. Sci. Technol.
, 61
(13
), pp. 1899
–1912
.10.1016/S0266-3538(01)00094-X17.
Wernik
, J. M.
, and Meguid
, S. A.
, 2010
, “Recent Developments in Multifunctional Nanocomposites Using Carbon Nanotubes
,” ASME Appl. Mech. Rev.
, 63
(5), p. 050801
.10.1115/1.400350318.
Thostenson
, E. T.
, Li
, W. Z.
, Wang
, D. Z.
, Ren
, Z. F.
, and Chou
, T. W.
, 2002
, “Carbon Nanotube/Carbon Fiber Hybrid Multiscale Composites
,” Appl. Phys. Lett.
, 91
(9
), pp. 6034
–6037
.10.1063/1.146688019.
Chen
, L. H.
, AuBuchon
, J. F.
, Chen
, I. C.
, Daraio
, C.
, Ye
, X. R.
, Gapin
, A.
, and Jin
, S.
, 2006
, “Growth of Aligned Carbon Nanotubes on Carbon Microfibers by DC Plasma-Enhanced Chemical Vapor Deposition
,” Appl. Phys. Lett.
, 88
(3), p. 033103
.10.1063/1.216647220.
Veedu
, V. P.
, Cao
, A.
, Li
, X.
, Ma
, K.
, Soldano
, C.
, Kar
, S.
, Ajayan
, P. M.
, and Ghasemi-Nejhad
, M. N.
, 2006
, “Multifunctional Composites Using Reinforced Laminae With Carbon-Nanotube Forests
,” Nature Mater.
, 5
(6), pp. 457
–462
.10.1038/nmat165021.
Kepple
, K. L.
, Sanborn
, G. P.
, Lacasse
, P. A.
, Gruenberg
, K. M.
, and Ready
, W. J.
, 2008
, “Improved Fracture Toughness of Carbon Fiber Composite Functionalized With Multi Walled Nanotubes
,” Carbon
, 46
(15), pp. 2026
–2033
.10.1016/j.carbon.2008.08.01022.
Sager
, R. J.
, Klein
, P. J.
, Lagoudas
, D. C.
, Zhang
, Q.
, Liu
, J.
, Dai
, L.
, and Baur
, J. W.
, 2009
, “Effect of Carbon Nanotubes on the Interfacial Shear Strength of T650 Carbon Fiber in an Epoxy Matrix
,” Compos. Sci. Technol.
, 69
(7–8), pp. 898
–904
.10.1016/j.compscitech.2008.12.02123.
Garcia
, E. J.
, Wardle
, B. L.
, Hart
, A. J.
, and Yamamoto
, N.
, 2008
, “Fabrication and Multifunctional Properties of a Hybrid Laminate With Aligned Carbon Nanotubes Grown In Situ
,” Compos. Sci. Technol.
, 68
(9
), pp. 2034
–2041
.10.1016/j.compscitech.2008.02.02824.
Yamamoto
, N.
, Hart
, A. J.
, Garcia
, E. J.
, Wicks
, S. S.
, Duong
, H. M.
, Slocum
, A. H.
, and Wardle
, B. L.
, 2009
, “High-Yield Growth and Morphology Control of Aligned Carbon Nanotubes on Ceramic Fibers for Multifunctional Enhancement of Structural Composites
,” Carbon
, 47
(3
), pp. 551
–560
.10.1016/j.carbon.2008.10.03025.
Kundalwal
, S. I.
, and Ray
, M. C.
, 2011
, “Micromechanical Analysis of Fuzzy Fiber Reinforced Composites
,” Int. J. Mech. Mater. Des.
, 7
(2
), pp. 149
–166
.10.1007/s10999-011-9156-426.
Chatzigeorgiou
, G.
, Efendiev
, Y.
, and Lagoudas
, D. C.
, 2011
, “Homogenization of Aligned “Fuzzy Fiber” Composites
,” Int. J. Solids Struct.
, 48
(19
), pp. 2668
–2680
.10.1016/j.ijsolstr.2011.05.01127.
Kundalwal
, S. I.
, and Ray
, M. C.
, 2012
, “Effective Properties of a Novel Composite Reinforced With Short Carbon Fibers and Radially Aligned Carbon Nanotubes
,” Mech. Mater.
, 53
, pp. 47
–60
.10.1016/j.mechmat.2012.05.00828.
Kundalwal
, S. I.
, and Ray
, M. C.
, 2013
, “Effect of Carbon Nanotube Waviness on the Elastic Properties of the Fuzzy Fiber Reinforced Composites
,” ASME J. Appl. Mech.
, 80
(2), p. 021010
.10.1115/1.400772229.
Kundalwal
, S. I.
, and Ray
, M. C.
, 2013
, “Thermoelastic Properties of a Novel Fuzzy Fiber-Reinforced Composite
,” ASME J. Appl. Mech.
, 80
(6), p. 061011
.10.1115/1.402369130.
Kundalwal
, S. I.
, and Ray
, M. C.
, 2014
, “Improved Thermoelastic Coefficients of a Novel Short Fuzzy Fiber-Reinforced Composite With Wavy Carbon Nanotubes
,” J. Mech. Mater. Struct.
, 9
(1
), pp. 1
–25
.10.2140/jomms.2014.9.131.
He
, J.
, Beyerlein
, I. J.
, and Clarke
, D. R.
, 1999
, “Load Transfer From Broken Fibers in Continuous Fiber Al2O3-Al Composites and Dependence on Local Volume Fraction
,” J. Mech. Phys. Solids
, 47
(3), pp. 465
–502
.10.1016/S0022-5096(98)00053-232.
Gao
, X. L.
, and Li
, K.
, 2005
, “A Shear-Lag Model for Carbon Nanotube-Reinforced Polymer Composites
,” Int. J. Solids Struct.
, 42
(5–6), pp. 1649
–1667
.10.1016/j.ijsolstr.2004.08.02033.
Zhang
, Y. C.
, and Wang
, X.
, 2005
, “Thermal Effects on Interfacial Stress Transfer Characteristics of Carbon Nanotubes/Polymer Composites
,” Int. J. Solids Struct.
, 42
(20
), pp. 5399
–5412
.10.1016/j.ijsolstr.2005.02.03834.
Jiang
, L. Y.
, Huang
, Y.
, Jiang
, H.
, Ravichandran
, G.
, Gao
, H.
, Hwang
, K. C.
, and Liu
, B.
, 2006
, “A Cohesive Law for Carbon Nanotube/Polymer Interfaces Based on the van der Waals Force
,” J. Mech. Phys. Solids
, 54
(11), pp. 2436
–2452
.10.1016/j.jmps.2006.04.00935.
Li
, K.
, and Saigal
, S.
, 2007
, “Micromechanical Modeling of Stress Transfer in Carbon Nanotube Reinforced Polymer Composites
,” Mater. Sci. Eng., A
, 457
(1–2), pp. 44
–57
.10.1016/j.msea.2006.12.01836.
Zhang
, J.
, and He
, C.
, 2008
, “A Three-Phase Cylindrical Shear-Lag Model for Carbon Nanotube Composites
,” Acta Mech.
, 196
(1–2), pp. 33
–54
.10.1007/s00707-007-0489-x37.
Ang
, K. K.
, and Ahmed
, K. S.
, 2013
, “An Improved Shear-Lag Model for Carbon Nanotube Reinforced Polymer Composites
,” Composites, Part B
, 50
, pp. 7
–14
.10.1016/j.compositesb.2013.01.01638.
Ray
, M. C.
, Guzman de Villoria
, R.
, and Wardle
, B. L.
, 2009
, “Load Transfer Analysis in Short Carbon Fibers With Radially-Aligned Carbon Nanotubes Embedded in a Polymer Matrix
,” J. Adv. Mater.
, 41
(4
), pp. 82
–94
, available at: http://hdl.handle.net/1721.1/7185239.
Pavia
, F.
, and Curtin
, W. A.
, 2012
, “Optimizing Strength and Toughness of Nano Fiber-Reinforced CMCs
,” J. Mech. Phys. Solids
, 60
(9), pp. 1688
–1702
.10.1016/j.jmps.2012.04.00540.
Kotha
, S. P.
, Li
, Y.
, and Guzelsu
, N.
, 2001
, “Micromechanical Model of Nacre Tested in Tension
,” J. Mater. Sci.
, 36
(8), pp. 2001
–2007
.10.1023/A:101752683087441.
Gao
, H.
, Ji
, B.
, Buehler
, M. J.
, and Yao
, H.
, 2004
, “Flaw Tolerant Bulk and Surface Nanostructures of Biological Systems
,” Mech. Chem. Biosyst.
, 1
(1), pp. 37
–52
.42.
Ji
, B.
, and Gao
, H.
, 2004
, “How Do Slender Mineral Crystals Resist Buckling in Biological Materials?
,” Philos. Mag. Lett.
, 84
(10
), pp. 631
–641
.10.1080/0950083051233132914143.
Ji
, B.
, and Gao
, H.
, 2004
, “Mechanical Properties of Nanostructure of Biological Materials
,” J. Mech. Phys. Solids
, 52
(9), pp. 1963
–1990
.10.1016/j.jmps.2004.03.00644.
Ji
, B.
, and Gao
, H.
, 2006
, “Elastic Properties of Nanocomposite Structure of Bone
,” Compos. Sci. Technol.
, 66
(9), pp. 1212
–1218
.10.1016/j.compscitech.2005.10.01745.
Zhang
, Z. Q.
, Liu
, B.
, Huang
, Y.
, Hwang
, K. C.
, and Gao
, H.
, 2010
, “Mechanical Properties of Unidirectional Nanocomposites With Non-Uniformly or Randomly Staggered Platelet Distribution
,” J. Mech. Phys. Solids
, 58
(10), pp. 1646
–1660
.10.1016/j.jmps.2010.07.00446.
Zhang
, Z.
, Zhang
, Y. W.
, and Gao
, H.
, 2010
, “On Optimal Hierarchy of Load-Bearing Biological Materials
,” Proc. R. Soc. B.
, 278
(1705), pp. 519
–525
.10.1098/rspb.2010.109347.
Bar-On
, B.
, and Wagner
, H. D.
, 2011
, “Mechanical Model for Staggered Bio-Structures
,” J. Mech. Phys. Solids
, 59
(9), pp. 1685
–1701
.10.1016/j.jmps.2011.06.00548.
Lei
, H. F.
, Zhang
, Z. Q.
, and Liu
, B.
, 2012
, “Effect of Fiber Arrangement on Mechanical Properties of Short Fiber Reinforced Composites
,” Compos. Sci. Technol.
, 72
(4), pp. 506
–514
.10.1016/j.compscitech.2011.12.01149.
Ray
, M. C.
, and Kundalwal
, S. I.
, 2013
, “Effect of Carbon Nanotube Waviness on the Load Transfer Characteristics of Short Fuzzy Fiber-Reinforced Composite
,” ASCE J. Nanomech. Micromech.
, 4
(2), p. A4013010
.10.1061/(ASCE)NM.2153-5477.000008250.
Ray
, M. C.
, and Kundalwal
, S. I.
, 2014
, “A Thermomechanical Shear Lag Analysis of Short Fuzzy Fiber Reinforced Composite Containing Wavy Carbon Nanotubes
,” Eur. J. Mech. Solids
, 44
, pp. 41
–60
.10.1016/j.euromechsol.2013.10.00151.
Kundalwal
, S. I.
, and Ray
, M. C.
, 2014
, “Shear Lag Analysis of a Novel Short Fuzzy Fiber-Reinforced Composite
,” Acta Mech.
(in press).10.1007/s00707-014-1095-352.
Mori
, T.
, and Tanaka
, K.
, 1973
, “Average Stress in Matrix and Average Elastic Energy of Materials With Misfitting Inclusions
,” Acta Metall.
, 21
(5
), pp. 571
–574
.10.1016/0001-6160(73)90064-353.
Li
, Y.
, Waas
, A. M.
, and Arruda
, E. M.
, 2011
, “A Closed-Form, Hierarchical, Multi-Interphase Model for Composites—Derivation, Verification and Application to Nanocomposites
,” J. Mech. Phys. Solids
, 59
(1), pp. 43
–63
.10.1016/j.jmps.2010.09.01554.
Li
, Y.
, Waas
, A. M.
, and Arruda
, E. M.
, 2011
, “The Effects of the Interphase and Strain Gradients on the Elasticity of Layer by Layer (LBL) Polymer/Clay Nanocomposites
,” Int. J. Solids Struct.
, 48
(6), pp. 1044
–1053
.10.1016/j.ijsolstr.2010.12.00855.
Wernik
, J. M.
, Cornwell-Mott
, B. J.
, and Meguid
, S. A.
, 2012
, “Determination of the Interfacial Properties of Carbon Nanotube Reinforced Polymer Composites Using Atomistic-Based Continuum Model
,” Int. J. Solids Struct.
, 49
(13), pp. 1852
–1863
.10.1016/j.ijsolstr.2012.03.02456.
Dunn
, M. L.
, and Ledbetter
, H.
, 1995
, “Elastic Moduli of Composites Reinforced by Multiphase Particles
,” ASME J. Appl. Mech.
, 62
(4
), pp. 1023
–1028
.10.1115/1.289603857.
Qui
, Y. P.
, and Weng
, G. J.
, 1990
, “On the Application of Mori-Tanaka's Theory Involving Transversely Isotropic Spheroidal Inclusions
,” Int. J. Eng. Sci.
, 28
(11
), pp. 1121
–1137
.10.1016/0020-7225(90)90112-V58.
Cowin
, S. C.
, and Fraldi
, M.
, 2005
, “On Singularities Associated With the Curvilinear Anisotropic Elastic Symmetries
,” Int. J. Nonlinear Mech.
, 40
(2–3), pp. 361
–371
.10.1016/j.ijnonlinmec.2004.07.00559.
Nairn
, J. A.
, 1997
, “On the Use of Shear-Lag Methods for Analysis of Stress Transfer in Unidirectional Composites
,” Mech. Mater.
, 26
(2
), pp. 63
–80
.10.1016/S0167-6636(97)00023-960.
Timoshenko
, S. P.
, and Goodier
, J. N.
, 1970
, Theory of Elasticity
, 3rd ed., McGraw-Hill
, New York
.61.
Hashin
, Z.
, and Rosen
, B. W.
, 1964
, “The Elastic Moduli of Fiber-Reinforced Materials
,” ASME J. Appl. Mech.
, 31
(2), pp. 223
–232
.10.1115/1.362959062.
Honjo
, K.
, 2007
, “Thermal Stresses and Effective Properties Calculated for Fiber Composites Using Actual Cylindrically-Anisotropic Properties of Interfacial Carbon Coating
,” Carbon
, 45
(4
), pp. 865
–872
.10.1016/j.carbon.2006.11.00763.
Odegard
, G. M.
, Clancy
, T. C.
, and Gates
, T. S.
, 2005
, “Modeling of the Mechanical Properties of Nanoparticle/Polymer Composites
,” Polymer
, 46
(2
), pp. 553
–562
.10.1016/j.polymer.2004.11.02264.
Karami
, G.
, and Garnich
, M.
, 2005
, “Micromechanical Study of Thermoelastic Behavior of Composites With Periodic Fiber Waviness
,” Composites, Part B
, 36
(3), pp. 241
–248
.10.1016/j.compositesb.2004.09.005Copyright © 2014 by ASME
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