Research Papers

Failure of Carbon Fibers at a Crease in a Fiber-Reinforced Silicone Sheet

[+] Author and Article Information
Francisco López Jiménez

Postdoctoral Researcher
Laboratoire de Mécanique des Solides
École Polytechnique
91128 Palaiseau, France
e-mail: lopez@lms.polytechnique.fr

Sergio Pellegrino

Joyce and Kent Kresa Professor of Aeronautics
and Professor of Civil Engineering
California Institute of Technology
1200 E. California Blvd
MC 301-46, Pasadena, CA91125
e-mail: sergiop@caltech.edu

Contributed by Applied Mechanics of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 5, 2011; final manuscript received April 9, 2012; accepted manuscript posted July 6, 2012; published online November 19, 2012. Editor: Robert M. McMeeking.

J. Appl. Mech 80(1), 011020 (Nov 19, 2012) (8 pages) Paper No: JAM-11-1417; doi: 10.1115/1.4007082 History: Received November 05, 2011; Revised April 09, 2012; Accepted July 06, 2012

Thin sheets of unidirectional carbon fibers embedded in a silicone matrix can be folded to very high curvatures, as elastic microbuckles with a half-wavelength on the order of 1 mm decrease the maximum strain in the fibers near the compression surface. This paper shows that probabilistic failure models derived from tension tests on individual fibers can be used to predict accurately the value of the outer surface curvature of the sheet, at which a small percentage of fibers break when a crease is formed in the sheet. The most accurate results are obtained by using a strain-based Weibull distribution of the failure probability in tension.

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Fig. 1

Position of neutral axis in the fiber cross section for Et>Ec

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Fig. 2

Weibull fit to probability of tensile failure for AS4 fibers versus (a) applied stress and (b) strain

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Fig. 3

Example of image used to measure rf

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Fig. 4

Weibull fit of probability of failure in bending versus applied curvature for AS4 fibers; κ0=12.349 mm-1

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Fig. 6

Curvature κ and value of I1 for different values of m as a function of the arc length s

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Fig. 7

Failure probability versus maximum curvature for loop test; the two sets of predictions are based on the stress- and strain-based Weibull moduli for tensile failure

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Fig. 8

Fiber microbuckling on compression side of 0.54-mm-thick sheet

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Fig. 9

Examples of curvature measurement: (a) κ=0.83 mm-1; (b) κ=1.25 mm-1 showing also edge waviness

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Fig. 10

Measurement of broken fibers after creasing

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Fig. 11

Kinematics of bending deformation for a segment of composite sheet of initial length λ0, subject to a curvature κ. The neutral surface is assumed to coincide with the tension surface.

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Fig. 12

Probability of failure for fibers on compression side of 0.54-mm-thick sheet with a fold of π radians with curvature κ

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Fig. 13

Values of κt and ɛf for creases with a single buckle and a failure probability of 1%




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