fibre volume fraction and laminate thickness. how much fibre…?
TRANSCRIPT
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Fibre Volume Fraction and Laminate Thickness
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How much fibre…?
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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.
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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
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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
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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%.
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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
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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.
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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:
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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
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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
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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
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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?
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Rules of Mixturefor Elastic Properties
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'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!
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Density
For the special case of a fibre-reinforced matrix:
mmff VV
since Vf + Vm = 1
mfff )V1(V
mmff )(V
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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
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Micromechanical models for stiffness
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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
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This rule of mixtures is a good fit to experimental data
(source: Hull, Introduction to Composite Materials, CUP)
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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
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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
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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
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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