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Research Papers

Fiber Diameter-Dependent Elastic Deformation in Polymer Composites—A Numerical Study

[+] Author and Article Information
Nitin Garg

Department of Mechanical Engineering,
University of Wyoming,
Laramie, WY 82071
e-mail: enitingarg@gmail.com

Gurudutt Chandrashekar

Department of Mechanical Engineering,
University of Wyoming,
Laramie, WY 82071
e-mail: chandrashekarg@trine.edu

Farid Alisafaei

Department of Mechanical Engineering,
University of Wyoming,
Laramie, WY 82071
e-mail: alisafae@seas.upenn.edu

Chung-Souk Han

Lawrence Livermore National Laboratory,
7000 East Avenue,
Livermore, CA 94550
e-mail: chungsouk.han@gmail.com

1Present address: Trine University, One University Avenue, Angola, IN 46703.

2Present address: Department of Material Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104.

3Present address: 9824 Peters Ranch Way, Elk Grove, CA 94550.

4Corresponding author.

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received March 8, 2018; final manuscript received April 22, 2019; published online June 4, 2019. Assoc. Editor: Erdogan Madenci.

J. Eng. Mater. Technol 142(1), 011002 (Jun 04, 2019) (7 pages) Paper No: MATS-18-1065; doi: 10.1115/1.4043766 History: Received March 08, 2018; Accepted April 24, 2019

Microbeam bending and nano-indentation experiments illustrate that length scale-dependent elastic deformation can be significant in polymers at micron and submicron length scales. Such length scale effects in polymers should also affect the mechanical behavior of reinforced polymer composites, as particle sizes or diameters of fibers are typically in the micron range. Corresponding experiments on particle-reinforced polymer composites have shown increased stiffening with decreasing particle size at the same volume fraction. To examine a possible linkage between the size effects in neat polymers and polymer composites, a numerical study is pursued here. Based on a couple stress elasticity theory, a finite element approach for plane strain problems is applied to predict the mechanical behavior of fiber-reinforced epoxy composite materials at micrometer length scale. Numerical results show significant changes in the stress fields and illustrate that with a constant fiber volume fraction, the effective elastic modulus increases with decreasing fiber diameter. These results exhibit similar tendencies as in mechanical experiments of particle-reinforced polymer composites.

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Figures

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Fig. 1

Indentation hardness HI versus indentation depth h redrawn from Refs. [1315,23,24]

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Fig. 2

Degrees-of-freedom for a four-node element with full and reduced integration points

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Fig. 3

Epoxy beam loading–unloading data illustrating elastic behavior (adapted from Ref. [9])

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Fig. 4

Bending rigidity versus beam thickness h (adapted from Ref. [31] with experimental data of Ref. [9])

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Fig. 5

Hexagonal configuration subjected to prescribed displacement

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Fig. 6

σp with (a) and without (b) rotation gradients for d = 8 μm, r = 5 μm, and Vf = 32.65%

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Fig. 7

σpmax versus r for Vf = 32.65% (hexagonal configuration)

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Fig. 8

Eeff over r for Vf = 32.65%

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Fig. 9

Eeff versus Vf and r with and without rotation gradients χ

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Fig. 10

ϕ3 for Vf = 60.13%

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Fig. 11

σVMmax versus r for Vf = 32.65% in the hexagonal configuration

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Fig. 12

Average shear stress τave versus r with and without rotation gradients χ

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Fig. 13

Square configuration with prescribed displacement

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Fig. 14

Eeff for Vf = 30.68%

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Fig. 15

Eeff versus Vf and r in the square configuration with and without rotation gradients χ

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Fig. 16

Effect of rotation gradients on σpmax (left) and Eeff (right) where Eeff* and Eeffo are effective elastic moduli with and without rotation gradients (Vf = 44.1%, r = 6 μm, E = 3.8 GPa, v = 0.355)

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Fig. 17

Eeff of glass–epoxy (left) and graphite–epoxy (right) composites in the square configuration over r for varying Vf

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