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MECHANICS
COMPOSITE MATERIALS
COMPOSITE MATERIALS MECHANICSFIBER FRACTION
Fibre Content x Manufacturing Process
40%
60% 60% 65% 70%
60%
40% 40% 35% 30%
0%
20%
40%
60%
80%
100%
Fibre Resin
Hand Layup Vacuum Bag Infusion Pre Preg Autoclave
COMPOSITE MATERIALS MECHANICSEXAMPLE
COMPOSITE MATERIALS MECHANICSEXAMPLE
b
h e
d
COMPOSITE MATERIALS MECHANICSEXAMPLE
FibreResin
BASIC PRINCIPLES
COMPOSITE MATERIALS MECHANICS
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 35 wt%.
Volume Fraction Used in design to calculate composite properties. Almost always refers to fibre content.
COMPOSITE MATERIALS MECHANICS
CONVERSION
Weight Fraction - Volume Fraction For the Special Case of a Two-Component Composite
(eg Fibre and Matrix)
VW
W Wff f
f f f m=
+ −/
/ ( ) /ρ
ρ ρ1
WV
V Vff f
f f m f=
+ −ρ
ρ ρ ( )1
COMPOSITE MATERIALS MECHANICS
CONVERSION
Weight Fraction - Volume Fraction (Epoxy Resin Matrix)
00,10,20,30,40,50,60,70,80,9
1
0 0,2 0,4 0,6 0,8 1
FIBR
E V
OLU
ME
FRA
CTIO
N
FIBRE WEIGHT FRACTION
VOLUME FRACTION - WEIGHT FRACTION CONVERSION(EPOXY RESIN MATRIX)
GLASS
HS CARBON
ARAMID
GlassHS Carbon
Fibre Weigth Fraction
Aramid
Fibr
e Vo
lum
e Fr
actio
nCOMPOSITE MATERIALS MECHANICS
MAXIMUM FRACTION
Maximum Fibre Volume FractionA composite cannot contain 100% fibre. Maximum volume fraction could be achieved only if unidirectional fibres are hexagonally ‘close packed’ - ie all fibres are touching.
The triangular unit cell has area √3R².The unit cell contains an area of fibre (three 60 segments) equal to πR²/2
2R
COMPOSITE MATERIALS MECHANICS
Maximum Fibre Volume FractionIn a unidirectional fibre composite, the fibre area fraction is the same as the fibre volume fraction, so:
%91908.0323
22
2max ≈===
ππR
RVf
MAXIMUM FRACTION
COMPOSITE MATERIALS MECHANICS
Maximum Fibre Volume FractionTheoretically, a unidirectional fibre composite could have Vf ≈ 91%. 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 ≈ 70-72%.
MAXIMUM FRACTION
COMPOSITE MATERIALS MECHANICS
MAXIMUM FRACTION
Maximum Fibre Volume FractionFor other forms of reinforcement, maximum volume fraction also depends on the detailed arrangement of the fibres.
The following values are typical:
Unidirectional 0.70 – 0.72stitched ‘non-crimp’ 0.60 – 0.65woven fabric random 0.40 - 0.55chopped strand mat 0.15 - 0.25
COMPOSITE MATERIALS MECHANICS
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 de-pends 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.
COMPOSITE MATERIALS MECHANICS
LAMINATE THICKNESS
The thickness of a composite laminate depends on the amount of reinforce-ment and the relative amount of resin which has been included.
For a given quantity of reinforcement, a laminate with a high fibre volume fraction will be thinner than one with a lower fibre volume fraction, since it will contain less resin.
COMPOSITE MATERIALS MECHANICS
LAMINATE THICKNESS
Two Laminates, Both Containing 5 Plies of Reinforcement
Matrix
Fibre
high matrix content = low fibre content = thick laminate
low matrix content = high fibre content = thin laminate
COMPOSITE MATERIALS MECHANICS
LAMINATE THICKNESS
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
Fibre Volume Fraction is Thus Inversely Proportional to Laminate Thickness.
dnAV
f
wf ρ=
ff
w
VnAdρ
=
COMPOSITE MATERIALS MECHANICS
dnAV
f
wf ρ=
ff
w
VnAdρ
=
LAMINATE THICKNESS
Fibre Volume Fraction
0
0,5
1
1,5
2
2,5
3
0,1 0,2 0,3 0,4 0,5 0,6 0,7
PLY
THIC
KNES
S (M
M)
FIBRE VOLUME FRACTION
PLY THICKNESS VS FIBRE VOLUME FRACTION (GLASS)
200 g/m2
300 g/m2
450 g/m2
600 g/m2
AREA WEIGHT
Ply
Thic
knes
s (m
m)
Ply Thickness x Fibre Volume Fraction(Glass)
COMPOSITE MATERIALS MECHANICS
LAMINATE THICKNESS
Fibre Volume Fraction
Ply
Thic
knes
s (m
m)
Ply Thickness x 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
PLY
THIC
KNES
S (M
M)
FIBRE VOLUME FRACTION
PLY THICKNESS VS FIBRE VOLUME FRACTION (HS CARBON)
100 g/m2
150 g/m2
200 g/m2
300 g/m2
500 g/m2
AREA WEIGHT
COMPOSITE MATERIALS MECHANICS
MIXTURE RULES
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!
COMPOSITE MATERIALS MECHANICS
DENSITY
For the Special Case of a Fibre-Reinforced Matrix
mmff VV ρ+ρ=ρ
mfff )V1(V ρ−+ρ=ρ
mmff )(V ρ+ρ−ρ=ρ
Since Vf + Vm = 1
COMPOSITE MATERIALS MECHANICS
Fibre Volume Fraction
Kg/m
³
Rule of Mixtures Density for Glass/Epoxy Composites
DENSITY
0
500
1000
1500
2000
2500
3000
0 0,2 0,4 0,6 0,8 1
KG/M
3
FIBRE VOLUME FRACTION
ρf
ρm
COMPOSITE MATERIALS MECHANICS
Generalised Rule of Mixtures for Tensile Modulus
TENSILE MODULUS
E = hLho Ef Vf + Em (1-Vf )
hL is a length correction factor. Typically, hL = 1 for fibres longer than about 10 mm.
h0 corrects for non-unidirectional reinforcement:
COMPOSITE MATERIALS MECHANICS
Rule of Mixtures Tensile Modulus(Glass Fibre / Polyester)
TENSILE MODULUS
COMPOSITE MATERIALS MECHANICS
Fibre Volume Fraction
Tens
ile M
odul
us (G
Pa)
0
10
20
30
40
50
60
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
TEN
SILE
MO
DU
LUS
(GPA
)
FIBRE VOLUME FRACTION
UD
BIAXIAL
CSM
Rule of Mixtures Tensile Modulus(Carbon Fibre)
TENSILE MODULUS
COMPOSITE MATERIALS MECHANICS
Fibre Volume Fraction
Tens
ile M
odul
us (G
Pa)
020406080
100120140160180200
0 0,2 0,4 0,6 0,8TEN
SILE
MO
DU
LUS
(GPA
)
FIBRE VOLUME FRACTION
UD
BIAXIAL
QUASI-ISOTROPIC
Rule of Mixtures Tensile Modulus(Carbon Fibre)
TENSILE MODULUS
COMPOSITE MATERIALS MECHANICS
Fibre Volume Fraction
Tens
ile M
odul
us (G
Pa)
020406080
100120140160180200
0 0,2 0,4 0,6 0,8TEN
SILE
MO
DU
LUS
(GPA
)
FIBRE VOLUME FRACTION
UD
BIAXIAL
QUASI-ISOTROPIC
Obrigado!
COMPOSITE MATERIALS MECHANICS
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