ENGINEERING MATERIALS
MODULUS OF
ELASTICITY
MPA
PSI
FIBERGLASS 7.000 1 E
06
FIBERGLASS INFUSION 35.000 5 E
06
CARBON FIBER 150.000 22 E
06
ALUMINIUM 70.000 10 E 06
STEEL 200.000 30 E 06
40%
60% 60% 65%
70%
60%
40% 40% 35%
30%
0%
20%
40%
60%
80%
100%
HAND LAYUP VACUUM BAG INFUSÃO PRÉ PREG AUTOCLAVE
Fibra Resina RESIN FIBRE
FIBRE WEIGHT CONTENT X MANUFACTURING PROCESS
HOW MUCH REINFORCEMENT?
WEIGHT FRACTION
Used in manufacture and refer to fibre or resin weight
percentages.
Manufacturers will specify a glass content of (e.g.) 25 wt%
a prepreg supplier might give a resin content (e.g) of 34
wt%.
VOLUME FRACTION
Used in structural design to calculate composite properties
and almost always refers to fibre volume content.
WEIGHT FRACTION
X
VOLUME FRACTION CONVERSION
For the special case of a two-component composite (fibre and
matrix)
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00
FIBRE VOLUME FRACTION
FIBRE WEIGHT FRACTION
GLASS HS CARBON ARAMID
VOLUME FRACTION X WEIGHT FRACTION CONVERSION
(EPOXY RESIN MATRIX)
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00
FIBRE VOLUME FRACTION
FIBRE WEIGHT FRACTION
GLASS HS CARBON ARAMID
VOLUME FRACTION X WEIGHT FRACTION CONVERSION
(EPOXY RESIN MATRIX)
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00
FIBRE VOLUME FRACTION
FIBRE WEIGHT FRACTION
GLASS HS CARBON ARAMID
VOLUME FRACTION X WEIGHT FRACTION CONVERSION
(EPOXY RESIN MATRIX)
A composite cannot contain 100% fibre. Maximum volume fraction could be
achieved only if unidirectional fibres are hexagonally ‘close packed’. The
triangular unit cell has area R2 3 The unit cell contains an area of fibre (three 60o segments) equal to πR2 / 2
2R
3R
MAXIMUM FIBRE VOLUME FRACTION
R 3
In a unidirectional fibre composite the fibre area fraction is
the same as the fibre volume fraction:
MAXIMUM FIBRE VOLUME FRACTION
For other forms of reinforcement, maximum volume fraction also depends on the detailed arrangement of the fibres. Unidirectional 0.70 – 0.72 Stitched ‘non-crimp’ 0.60 – 0.65 Woven Fabric 0.40 - 0.55 Chopped Strand Mat 0.15 - 0.25
MAXIMUM FIBRE VOLUME FRACTION
Commercial reinforcements are characterised by their areal weight (Aw). This is simply the weight (usually given in grams of 1 m2 of the reinforcement (gr/m2).
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.
MAXIMUM FIBRE VOLUME FRACTION
The thickness of a composite laminate depends on the amount of
reinforcement 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.
LAMINATE THICKNESS
The thickness of a composite laminate depends on the amount of
reinforcement 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.
LAMINATE THICKNESS
FIBRE
MATRIX
HIGH MATRIX CONTENT=LOW FIBRE CONTENT =THICK
LAMINATE
The thickness of a composite laminate depends on the amount of
reinforcement 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.
LAMINATE THICKNESS
FIBRE
MATRIX
HIGH MATRIX CONTENT=LOW FIBRE CONTENT =THICK
LAMINATE
LOW MATRIX CONTENT = HIGH FIBRE CONTENT = THIN
LAMINATE
0
20
40
60
80
100
0 0,5 1 1,5 2
FRAÇÃO EM VOLUME (%)
PRESSÃO DE MOLDAGEM (ATM)1/2
Mat Vidro
WR Vidro
Biax Vidro
WR Carbono
Uni Carbono
COMPRESSIBILIDADE DAS FIBRAS FRAÇÃO EM VOLUME
Fibre volume fraction is inversely proportional to
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:
LAMINATE THICKNESS
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8
PLY THICKNESS (MM)
FIBRE VOLUME FRACTION
100 g/m2 150 g/m2 200 g/m2 300 g/m2 500 g/m2
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 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8
PLY THICKNESS (MM)
FIBRE VOLUME FRACTION
100 g/m2 150 g/m2 200 g/m2 300 g/m2 500 g/m2
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 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8
PLY THICKNESS (MM)
FIBRE VOLUME FRACTION
100 g/m2 150 g/m2 200 g/m2 300 g/m2 500 g/m2
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 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8
PLY THICKNESS (MM)
FIBRE VOLUME FRACTION
100 g/m2 150 g/m2 200 g/m2 300 g/m2 500 g/m2
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 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8
PLY THICKNESS (MM)
FIBRE VOLUME FRACTION
100 g/m2 150 g/m2 200 g/m2 300 g/m2 500 g/m2
PLY THICKNESS X FIBRE VOLUME FRACTION (HS CARBON)
'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!
RULES OF MIXTURE AND ELASTIC PROPERTIES
0
50 0
100 0
150 0
20 00
2500
300 0
0 0 ,2 0 ,4 0 ,6 0 ,8 1
KG
/M
3
FIBRE VOLUME FRA CTION
RULE OF MIXTURES DENSITY FOR GLASS/EPOXY COMPOSITES
rf
rm
GENERALISED RULE OF MIXTURES FOR TENSILE MODULUS
is a length correction factor ( 1 for fibres longer than about 10 mm)
corrects for non-unidirectional reinforcement:
UNIDIRECIONAL 1.000
BIAXIAL 0/90 0.500
BIAXIAL 45/-45 0.250
RANDOM 0.375
0
10
20
30
40
50
60
0 ,0 00 00 1 0 ,0 5 0 ,1 0 ,15 0 ,2 0 ,25 0 ,3 0 ,35 0 ,4 0 ,45 0 ,5 0 ,55 0 ,6 0 ,65 0 ,7 0 ,75
TE
NS
ILE
MO
DU
LU
S (
GP
A)
FIBRE VOLUME FRACTION
UD BIAXIAL CSM
RULE OF MIXTURES TENSILE MODULUS
(GLASS FIBRE/POLYESTER)
0
10
20
30
40
50
60
0 ,0 00 00 1 0 ,0 5 0 ,1 0 ,15 0 ,2 0 ,25 0 ,3 0 ,35 0 ,4 0 ,45 0 ,5 0 ,55 0 ,6 0 ,65 0 ,7 0 ,75
TE
NS
ILE
MO
DU
LU
S (
GP
A)
FIBRE VOLUME FRACTION
UD BIAXIAL CSM
RULE OF MIXTURES TENSILE MODULUS
(GLASS FIBRE/POLYESTER)
0
10
20
30
40
50
60
0 ,0 00 00 1 0 ,0 5 0 ,1 0 ,15 0 ,2 0 ,25 0 ,3 0 ,35 0 ,4 0 ,45 0 ,5 0 ,55 0 ,6 0 ,65 0 ,7 0 ,75
TE
NS
ILE
MO
DU
LU
S (
GP
A)
FIBRE VOLUME FRACTION
UD BIAXIAL CSM
RULE OF MIXTURES TENSILE MODULUS
(GLASS FIBRE/POLYESTER)
0
20
40
60
80
100
120
140
160
180
20 0
0 ,0 00 00 1 0 ,1 0 ,2 0 ,3 0 ,4 0 ,5 0 ,6 0 ,7
TE
NS
ILE
MO
DU
LU
S (
GP
A)
FIBRE VOLUME FRA CTION
UD BIA XIA L QUA SI-ISOTROPIC
RULE OF MIXTURES TENSILE MODULUS
(T300 CARBON FIBRE)
0
20
40
60
80
100
120
140
160
180
20 0
0 ,0 00 00 1 0 ,1 0 ,2 0 ,3 0 ,4 0 ,5 0 ,6 0 ,7
TE
NS
ILE
MO
DU
LU
S (
GP
A)
FIBRE VOLUME FRA CTION
UD BIA XIA L QUA SI-ISOTROPIC
RULE OF MIXTURES TENSILE MODULUS
(T300 CARBON FIBRE)
0
20
40
60
80
100
120
140
160
180
20 0
0 ,0 00 00 1 0 ,1 0 ,2 0 ,3 0 ,4 0 ,5 0 ,6 0 ,7
TE
NS
ILE
MO
DU
LU
S (
GP
A)
FIBRE VOLUME FRA CTION
UD BIA XIA L QUA SI-ISOTROPIC
RULE OF MIXTURES TENSILE MODULUS
(T300 CARBON FIBRE)
0
20
40
60
80
100
120
140
160
180
0 ,15 0 ,2 0 ,25 0 ,3 0 ,35 0 ,4 0 ,45 0 ,5 0 ,55 0 ,6 0 ,65 0 ,7
GP
a
FIBRE VOLUME FRA CTION
UD BIA XIA L UD QUA SI-ISOTROPIC UD PLA IN W OVEN
RULE OF MIXTURES ELASTIC MODULUS
HS CARBON / EPOXY RESIN
0
20
40
60
80
100
120
140
160
180
0 ,15 0 ,2 0 ,25 0 ,3 0 ,35 0 ,4 0 ,45 0 ,5 0 ,55 0 ,6 0 ,65 0 ,7
GP
a
FIBRE VOLUME FRA CTION
UD BIA XIA L UD QUA SI-ISOTROPIC UD PLA IN W OVEN
RULE OF MIXTURES ELASTIC MODULUS
HS CARBON / EPOXY RESIN
0
20
40
60
80
100
120
140
160
180
0 ,15 0 ,2 0 ,25 0 ,3 0 ,35 0 ,4 0 ,45 0 ,5 0 ,55 0 ,6 0 ,65 0 ,7
GP
a
FIBRE VOLUME FRA CTION
UD BIA XIA L UD QUA SI-ISOTROPIC UD PLA IN W OVEN
RULE OF MIXTURES ELASTIC MODULUS
HS CARBON / EPOXY RESIN