1A. A. Gawandi, 1J. M. Whitney, 2G. P. Tandon, 1R. B. Brockman

1
Parametric Studies of Nanofiber - Crack
Interaction in a Nanocomposite

• 1A. A. Gawandi, 1J. M. Whitney, 2G. P. Tandon,
  1R. B. Brockman
• 1 University of Dayton
• 2 University of Dayton Research Institute

2
Nanocomposite

• Reinforcement of matrix with nanoscale material
• Possible thermo-mechanical property improvement
  due to presence of strong nanofiller material
• Improvement comes about at a very small weight
  percent of nanofiller
• Traditionally weak links in laminated composite
  materials like through the thickness and
  matrix-dominated properties can be improved
• Nanoscale Reinforcement Materials
• Equiaxed Carbon Black, Silica
• Tubular Nanotubes, Carbon Nanofibers
• Platelet Nanoclay

3
Vapor Grown Carbon Nanofiber(VGCNF)as
Composite Reinforcement

• Geometry
• 100 200 nanometers outer diameter
• 50 100 micron length as received
• Hollow
• Approximately 100 times smaller than conventional
  carbon fibers, but significantly larger than
  nanotubes (1-10 nm diameter)
• Elastic Properties
• Orthotropic
• Longitudinal Modulus may be up to 600 GPa
• Transverse properties not very well known

Nanofiber Bundle courtesy, www.ml.afrl.af.mil
Single nanofiber
courtesy, www. apsci.com
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Fracture Behavior in Presence of Nanofiber

• Most of work to date has been empirical
• Tandon et al. (2002)
• Considered carbon nanofibers in Epon862 in
  conjunction with IM7(conventional carbon fibers)
• Results from compact tension tests showed up to
  20 improvement in fracture toughness for
  nanofibersEpon862
• However, in presence of conventional IM7 fibers
  there was no significant difference in fracture
  toughness
• Analytical models that take into account
  nanofibers hollow structure and orthotropic
  elastic properties are needed
• Fracture behavior of nanocomposites can be
  studied by considering interactions between
  nanofibers and matrix cracks

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Conventional Analytical Treatment of
Crack-Fiber Interaction

• Typically two-dimensional
• Isotropic fiber and matrix properties, for
  example
• Erdogen et al. (1974)
• Helsing et al. (2002)
• Wang et al. (2003)
• Solid fiber cross-section considered
• To consider a nanofiber-crack interaction one
  must include nanofiber features like hollow
  cross-section geometry and orthotropic fiber
  properties
• The present study is an effort to include the
  above in the analytical treatment of crack
  nanofiber interaction problem

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Nanofiber-Crack Interaction

• A parametric two dimensional study is undertaken
  using finite element method
• Isolated hollow nanofiber considered interacting
  with a propagating crack in an infinite matrix
  phase, subjected to a uniaxial stress
• Mode I (GI)and mode II (GII) energy release
  rates, and interface stresses are computed
• Results compared with those of a similar fiber
  with solid section

• Assumptions
• Plane strain loading conditions
• Perfect nanofiber- matrix bond
• Self-similar crack propagation

• Results
• Energy release rates (GI and GII) normalized
  with respect to that for an identical matrix
  crack in an infinite medium (G0).
• Maximum interface stresses normalized with
  respect to the applied uniaxial stress(S)

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Schematic of Problem
Parameters studied crack length (2a) crack
orientation (?) Constituent elastic property
mismatch (Eftl / Em and ?ft /?m) Nanofiber wall
thickness (tw) Interphase thickness (ti)
Interphase
A crack of length 2a is propagated self similarly
towards nanofiber center. At any given instant
the left crack tip is at a radial distance r from
nanofiber center
Matrix
S
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Finite Element Model
Fiber
Crack
Crack tip
Finite element mesh in ANSYS Plane 8-noded
isoparametric element 45000-50000 nodes
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Results Influence of Elastic Modulus
Mismatch on Mode I Energy Release Rate
Solid Fiber
Hollow Fiber
ti 0 ?f / ?m 1

• Energy release rate increases as nanofiber to
  matrix modulus ratio decreases
• For the nanofiber wall thickness considered (35
  nm) GI values are relatively
• insensitive to crack orientation

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Results Influence of Elastic Modulus
Mismatch on Mode II Energy Release Rate
Hollow Fiber
Solid Fiber
ti 0 ?f / ?m 1

• Mode II energy release rate GII is higher for
  hollow fiber, and for the fiber wall thickness
  considered, it decreases as crack tip approaches
  fiber
• GII for hollow fiber seems more sensitive to
  fiber matrix modulus mismatch

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Results Influence of Elastic Modulus
Mismatch on Interface Stresses
Maximum Normal Stress
Maximum Shear Stress
?f / ?m 1

• Maximum normal stresses(SRmax) at the interface
  show greater gradient than maximum shear stresses
  as crack tip approaches fiber.
• SRmax is higher for hollow fiber when the crack
  is relatively farther from the fiber, but this
  trend reverses when the crack is very close to
  the fiber.
• Maximum shear stresses decay faster than maximum
  normal stresses and are higher for hollow fiber.

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ResultsInfluence of Poissons Ratio Mismatch on
GI
Hollow Fiber
Solid Fiber

• GI is higher for hollow fiber as the crack
  approaches the fiber, irrespective
• of degree of Poissons ratio mismatch between
  nanofiber and matrix.
• For hollow fiber higher GI results as ?f / ?m
  decreases.
• For solid fiber GI increases as ?f / ?m
  decreases, but unlike in the case of hollow
• fiber, for ?f / ?m gt1, GI decreases as crack
  approaches the fiber.

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ResultsInfluence of Poissons Ratio Mismatch on
SR max
Solid Fiber
Hollow Fiber

• In case of a hollow fiber there is a faster decay
  of maximum interfacial normal stress with
  increasing distance from fiber
• Higher value of ?f /?m results in higher maximum
  normal stresses for both solid and hollow fibers
• Maximum interfacial normal stress for solid fiber
  experiences a high gradient as the crack nears
  the fiber

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ResultsInfluence of Nanofiber Wall Thickness (tw)
Mode I Energy Release Rate
Interface Stresses

• GI is considerably sensitive to nanofiber wall
  thickness.
• Thinner fiber wall results in higher GI.
• SRmax values decrease as fiber wall thickness
  decreases and are lower than that for solid
  fiber.
• But trend is reversed as the crack approaches the
  fiber, as lower wall thicknesses now
• result in higher traction values.
• SRTmax values for all hollow fiber wall
  thicknesses are higher than those for solid
  fiber.

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Results Influence of Interphase Thickness
(ti) on GI
Ei / Em lt1
Ei / Em gt1
?f ?m ?i

• Opposite behavior for soft v/s stiff interphase
• A soft interphase seems to result in a higher GI
  with increasing
• interphase thickness
• Hollow fiber with Ei / Em lt 1 seems to be more
  sensitive to interphase
• thickness variation

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Conclusions
Parametric studies show that nanofiber wall
thickness and mismatch in elastic properties
with respect to the matrix have significant
influence on its interaction with a propagating
crack.

• Crack orientations considered do not seem to have
  significant influence on mode I and mode II
  energy release rates
• The modulus mismatch between the nanofiber and
  matrix influences energy release rate and
  interface stresses
• The Poissons ratio mismatch between nanofiber
  and matrix seems to have a degrading effect on
  matrix toughening by nanofiber irrespective of
  the mismatch value.
• The nanofiber wall thickness seems to have a
  considerable influence on energy release rate.
• For an interphase between the nanofiber and
  matrix, the interphase thickness seems to have
  positive or negative influence on energy release
  rate depending on whether the interphase is
  softer or stiffer as compared to the matrix.