Short Fibre Composites

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Short Fibre Composites
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Short fibres dont reinforce as effectively as
long or continuous fibres

• The load transfer mechanism results in end
  effects which may reduce the fibre stress.
• Difficult to control the alignment of short
  fibres.
• Randomly-oriented short fibres cannot be packed
  at such high volume fractions as continuous
  fibres.

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• Short fibres are more often used with
  thermoplastic resins. Processes like injection
  moulding lead to considerable fibre damage and
  reduction in length

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Load transfer between matrix and fibre

• Under applied tension, load is transferred by
  shear at the matrix/fibre interface.

At fibre ends, the strain in the matrix is higher
than in the fibre (Matthews Rawlings,
Composite Materials, Woodhead)
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Stress variation in a short fibre
(Matthews Rawlings, Composite Materials,
Woodhead)
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Stress variation in a short fibre - experimental
evidence
(Matthews Rawlings, Composite Materials,
Woodhead)
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When a stiff fibre is embedded in a relatively
flexible matrix, shear stress and strain are a
maximum at the fibre ends. The tensile
stress in the fibre, on the other hand, is zero
at the fibre end and increases towards the
centre.Note low stress at fibre end, increasing
to maximum value about 7 radii towards the centre.
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• The tensile stress in the fibre thus increases
  from zero at the ends to a maximum value of sfmax
  Ef e, where e is the strain applied to the
  composite.
• A fibre is said to be of the critical length if
  it is just long enough for the tensile stress to
  reach its maximum value.

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sfmax Ef e
fibre tensile stress
L lt Lc
L Lc
sfmax Ef e
fibre tensile stress
Lc / 2
L gt Lc
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Simple model for critical length
Consider a half fibre. The maximum tensile force
in the fibre, diameter D, is balanced by the
shear force at the fibre/matrix interface, so
centre line
t
sfmax
Lc / 2
l is fibre aspect ratio
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Critical fibre length

• Critical fibre length thus depends on t, the
  interfacial or matrix shear strength, and varies
  according to both fibre and matrix

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Fibre end effects

• Because of the low stress at fibre ends, the
  average stress in the fibre will be lower than
  that in a continuous fibre, even if it is longer
  than the critical length.
• For fibre length L 5 Lc, the average fibre
  stress (sfav) is about 90 of the maximum stress
  (sfmax) .
• It can be shown that (for L gt Lc)

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Stiffness of short fibre composites

• For aligned short fibre composites (difficult to
  achieve in polymers!), the rule of mixtures for
  modulus in the fibre direction is

The length correction factor (hL) can be derived
theoretically. Provided L gt 1 mm, hL gt 0.9
For composites in which fibres are not perfectly
aligned the full rule of mixtures expression is
used, incorporating both hL and ho.
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Theoretical length correction factor
Theoretical length correction factor for glass
fibre/epoxy, assuming inter-fibre separation of
20 D.
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Strength of short fibre composites

• The micromechanics of strength are more
  complicated than for stiffness. Strength depends
  on the relative failure strains of fibre and
  matrix (amongst other things).

Essentially, there is little difference between
short and continuous fibre composite strengths
once L ? 10 Lc.
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The fibre-matrix interface

• The interface between fibre and matrix is crucial
  to the performance of the composite - in
  particular fracture toughness corrosion
  moisture resistance.
• Weak interfaces provide a good energy absorption
  mechanism - composites have low strength and
  stiffness, but high fracture toughness.
• Strong interface results in a strong and stiff,
  but brittle composite.

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The fibre-matrix interface

• Adhesion between fibre and matrix is due to one
  (or more) of 5 main mechanisms

1. Adsorption and wetting - depending on the
surface energies or surface tensions of the two
surfaces. Glass and carbon are readily wetted by
epoxy and polyester resins, which have lower
surface energies.
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The fibre-matrix interface - adhesion mechanisms

• 2. Interdiffusion (autohesion) - diffusion and
  entanglement of molecules

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The fibre-matrix interface - adhesion mechanisms

• 3. Electrostatic attraction - important in the
  application of coupling agents. Glass fibre
  surface may be ionic due to oxide composition

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The fibre-matrix interface - adhesion mechanisms

• 4. Chemical bonding - between chemical group in
  the matrix and a compatible chemical on the fibre
  surface

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The fibre-matrix interface - adhesion mechanisms

• 5. Mechanical adhesion - depending on degree of
  roughness of fibre surface.

Larger surface area may also increase strength of
chemical bond.