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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
VW
W Wff f
f f f m
/
/ ( ) /
1
For the special case of a two-component composite (eg fibre and matrix):
WV
V Vff f
f f m f
( )1
Volume fraction - weight fraction conversion(epoxy resin matrix)
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
fibre weight fraction
fib
re v
olu
me
frac
tio
n
glass
HS carbon
aramid
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’ 0.6
woven fabric 0.4 - 0.55 random (chopped strand mat) 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
fibre
matrix
high matrix content
low fibre content
= thick laminate
low matrix content
high fibre content
= thin laminate
Two laminates, both containing 5 plies of reinforcement:
Laminate thickness
Fibre volume fraction is thus inversely proportional to laminate thickness.
d
nAV
f
wf
If the fibre content and laminate thickness are defined, we can calculate the fibre volume fraction:
If the fibre content and volume fraction are defined, we can calculate the laminate thickness:
ff
w
V
nAd
Ply thickness vs fibre volume fraction (glass)
0
0.5
1
1.5
2
2.5
3
0.1 0.2 0.3 0.4 0.5 0.6 0.7
fibre volume fraction
ply
th
ickn
ess
(mm
)
200 g/m2
300 g/m2
450 g/m2
600 g/m2
Area weight
Ply thickness vs fibre volume fraction (HS carbon)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.2 0.3 0.4 0.5 0.6 0.7 0.8
fibre volume fraction
ply
th
ickn
ess
(mm
)
100 g/m2
150 g/m2
200 g/m2
300 g/m2
500 g/m2
Area weight
Example calculationsExample calculations
1. 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?
2.2. 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 Mixturefor 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:
mmff VV
since Vf + Vm = 1
mfff )V1(V
mmff )(V
Rule of mixtures density for glass/epoxy composites
0
500
1000
1500
2000
2500
3000
0 0.2 0.4 0.6 0.8 1
fibre volume fraction
kg/m
3
f
m
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 >> 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 = L o Ef Vf + Em (1-Vf )
L is a length correction factor. Typically, L 1 for fibres longer than about 10 mm.
o corrects for non-unidirectional reinforcement:
o
unidirectional 1.0biaxial 0.5biaxial at 45o 0.25random (in-plane) 0.375random (3D) 0.2
Rule of mixtures tensile modulus (glass fibre/polyester)
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8
fibre volume fraction
ten
sile
mo
du
lus
(GP
a)
UD
biaxial
CSM
Rule of mixtures tensile modulus (T300 carbon fibre)
0
50
100
150
200
0 0.2 0.4 0.6 0.8
fibre volume fraction
ten
sile
mo
du
lus
(GP
a)
UD
biaxial
quasi-isotropic
Rule of mixtures elastic modulusglass fibre / epoxy resin
0
10
20
30
40
50
60
0.1 0.3 0.5 0.7
fibre volume fraction
GP
a
UD
biaxial
random
Rule of mixtures elastic modulusHS carbon / epoxy resin
020406080
100120140160180
0.4 0.5 0.6 0.7
fibre volume fraction
GP
a
UD
biaxial UD
quasi-isotropic UD
plain woven