Загрузил Aleksandrs Arnautovs

# Объемная доля волокна в композитном материале

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```Fibre Volume Fraction and
Laminate Thickness
How much fibre…?
How much reinforcement?
Weight fraction
Used in manufacture.
May refer to fibre or resin - 'GRP' manufacturers will
specify a glass content of (e.g.) 25 wt%; a prepreg
supplier might give a resin content of 34 wt%.
Volume fraction
Used in design to calculate composite properties.
Almost always refers to fibre content.
Weight fraction  volume fraction
conversion
For the special case of a two-component
composite (eg fibre and matrix):
Wf / f
Vf 
Wf / f  (1  Wf ) / m
fVf
Wf 
fVf  m (1  Vf )
fibre volume fraction
Volume fraction - weight fraction conversion
(epoxy resin matrix)
1
0.8
glass
0.6
HS carbon
0.4
aramid
0.2
0
0
0.2
0.4
0.6
fibre weight fraction
0.8
1
Maximum fibre volume fraction
Theoretically, a unidirectional fibre
composite could have Vf ≈ 90%.
In practice, fibres cannot be perfectly
aligned.
Maximum volume fraction depends both on
the fibre form and method of manufacture for a unidirectional fibre composite:
Vf ≈ 60-70%.
Maximum fibre volume fraction
For other forms of reinforcement,
maximum volume fraction also depends
on the detailed arrangement of the fibres.
The following values are typical:
stitched ‘non-crimp’
woven fabric
random
(chopped strand mat)
0.6
0.4 - 0.55
0.15 - 0.25
How much fibre?
Commercial reinforcements are characterised
by their areal weight (Aw). This is simply the
weight (usually given in g) of 1 m2 of the
reinforcement. Aw depends on many factors fibre density, tow or bundle size, weave style,
etc.
Aw may range from 50 g/m2 or less (for
lightweight surfacing tissues), up to more than
2000 g/m2 for some heavyweight non-crimp
fabrics.
Laminate thickness
Two laminates, both containing 5 plies of reinforcement:
fibre
matrix
high matrix content
low matrix content
low fibre content
high fibre content
= thick laminate
= thin laminate
Laminate thickness
Fibre volume fraction is thus inversely proportional
to laminate thickness.
If the fibre content and
laminate thickness are
defined, we can calculate
the fibre volume fraction:
nAw
Vf 
f d
If the fibre content and
volume fraction are
defined, we can calculate
the laminate thickness:
nAw
d
fVf
Ply thickness vs fibre volume fraction (glass)
ply thickness (mm)
3
Area weight
2.5
200 g/m2
2
300 g/m2
1.5
450 g/m2
1
600 g/m2
0.5
0
0.1
0.2
0.3
0.4
0.5
fibre volume fraction
0.6
0.7
Ply thickness vs fibre volume fraction (HS carbon)
ply thickness (mm)
1.6
Area weight
1.4
1.2
100 g/m2
1
150 g/m2
0.8
0.6
200 g/m2
0.4
0.2
500 g/m2
300 g/m2
0
0.2
0.3
0.4
0.5
0.6
fibre volume fraction
0.7
0.8
Example calculations
1. What will be the thickness of a laminate
consisting of 2 layers of 450 g/m2 chopped
strand mat if a resin to glass ratio (by weight)
of 2:1 is used?
2. What fibre volume fraction is achieved if
3 layers of 800 g/m2 glass woven roving are
compression-moulded to a thickness of
2 mm?
Rules of Mixture
for Elastic Properties
'Rules of Mixtures' are mathematical
expressions which give some property of
the composite in terms of the properties,
quantity and arrangement of its
constituents.
They may be based on a number of
simplifying assumptions, and their use in
design should tempered with extreme
caution!
Density
For the special case of a fibre-reinforced matrix:
  Vf f  Vmm
  Vf f  (1  Vf )m
  Vf (f  m )  m
since Vf + Vm = 1
Rule of mixtures density for
glass/epoxy composites
3000
f
2500
kg/m 3
2000
1500
m
1000
500
0
0
0.2
0.4
0.6
fibre volume fraction
0.8
1
Micromechanical models for stiffness
Unidirectional ply - longitudinal
tensile modulus
E1 = Ef Vf + Em ( 1-Vf )
Note the similarity to the rules of mixture
expression for density.
In polymer composites, Ef &gt;&gt; Em, so
E1  Ef Vf
This rule of
mixtures is a
good fit to
experimental
data
(source: Hull, Introduction
to Composite Materials,
CUP)
Generalised rule of mixtures for
tensile modulus
E = hL ho Ef Vf + Em (1-Vf )
hL is a length correction factor. Typically, hL  1
for fibres longer than about 10 mm.
ho corrects for non-unidirectional reinforcement:
ho
unidirectional
biaxial
biaxial at 45o
random (in-plane)
random (3D)
1.0
0.5
0.25
0.375
0.2
60
50
40
UD
30
biaxial
20
CSM
10
0
0
0.2
0.4
0.6
0.8
fibre volume fraction
Rule of mixtures tensile modulus
(T300 carbon fibre)
tensile modulus (GPa)
tensile modulus (GPa)
Rule of mixtures tensile modulus
(glass fibre/polyester)
200
150
UD
100
biaxial
quasi-isotropic
50
0
0
0.2
0.4
fibre volume fraction
0.6
0.8
Rule of mixtures elastic modulus
glass fibre / epoxy resin
60
50
GPa
40
UD
biaxial
random
30
20
10
0
0.1
0.3
0.5
fibre volume fraction
0.7
GPa
Rule of mixtures elastic modulus
HS carbon / epoxy resin
180
160
140
120
100
80
60
40
20
0
UD
biaxial UD
quasi-isotropic UD
plain woven
0.4
0.5
0.6
fibre volume fraction
0.7
```