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Research Papers

Shear Lag Model for Regularly Staggered Short Fuzzy Fiber Reinforced Composite

[+] Author and Article Information
S. I. Kundalwal

Mechanics and Aerospace Design Laboratory,
Department of Mechanical
and Industrial Engineering,
University of Toronto,
Toronto, ON M5S 3G8, Canada

M. C. Ray

Department of Mechanical Engineering,
Indian Institute of Technology,
Kharagpur 721302, India

S. A. Meguid

Fellow ASME
Mechanics and Aerospace Design Laboratory,
Department of Mechanical
and Industrial Engineering,
University of Toronto,
Toronto, ON M5S 3G8, Canada
e-mail: meguid@mie.utoronto.ca

1Corresponding author.

Manuscript received February 26, 2014; final manuscript received June 1, 2014; accepted manuscript posted June 4, 2014; published online June 19, 2014. Assoc. Editor: Xue Feng.

J. Appl. Mech 81(9), 091001 (Jun 19, 2014) (14 pages) Paper No: JAM-14-1083; doi: 10.1115/1.4027801 History: Received February 26, 2014; Revised June 01, 2014; Accepted June 04, 2014

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.

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Figures

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Fig. 1

(a) Conceptual illustration of the FFRC (from Ref. [23]) and (b) SEM image of aligned CNTs grown on the alumina fiber (from Ref. [24])

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Fig. 2

(a) A schematic diagram of a lamina made of the SFFRC (from Ref. [30]) and (b) in-plane cross section of the SFFRC lamina (from Ref. [27])

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Fig. 3

(a) Fuzzy fiber with CNTs radially grown on its circumferential surface (from Ref. [27]) and (b) load carrying structure of the RVE-A of the SFFRC in which the SCFF embedded in the polymer material (from Ref. [27])

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Fig. 4

Transverse cross sections of the SCFF with unwound and wound PMNC (from Ref. [27])

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Fig. 5

(a) Transverse and longitudinal cross sections of the three-phase RVE-A of the SFFRC (from Ref. [27]) and (b) interfacial shear stresses along the lengths of the carbon fiber and the SCFF

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Fig. 6

Transverse cross section of the hexagonal packing array comprising SCFFs and the polymer matrix (from Ref. [27])

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Fig. 7

Transverse and longitudinal cross sections of the NRLC (from Ref. [14])

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Fig. 8

(a) A schematic arrangement of the SCFFs in the RVE–B and (b) three-dimensional FE mesh of the three-phase RVE–B

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Fig. 9

Comparison of the axial stress in the carbon fiber along its length predicted by the analytical shear lag model and by the FE shear lag model (R/b = L/Lf = 1.1, q = 0)

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Fig. 10

Comparison of the interfacial shear stress between the PMNC and the carbon fiber predicted by the analytical shear lag model and by the FE shear lag model (R/b = L/Lf = 1.1, q = 0)

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Fig. 11

Variation of the axial stress in the carbon fiber along its length for different values of q (R/b = L/Lf = 1.1)

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Fig. 12

Variation of the interfacial shear stress between the PMNC and the carbon fiber for different values of q (R/b = L/Lf = 1.1)

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Fig. 13

Variation of the axial stress in the carbon fiber along its length for different values of R/b and L/Lf (q = 0)

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Fig. 14

Variation of the interfacial shear stress between the PMNC and the carbon fiber for different values of R/b and L/Lf (q = 0)

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Fig. 15

Variation of the axial stress in the carbon fiber at a point (x/Lf = 0.5) for different values of q, R/b, and L/Lf

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Fig. 16

Variation of the interfacial shear stress between the PMNC and the carbon fiber at a point (x/Lf = 0.98) for different values of q, R/b, and L/Lf

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