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