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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 - !"# manufacturers will

s$ecify a glass content of %e.&.' () wt*+ a $re$re&su$$lier mi&ht &i,e a resin content of wt*.

Volume fraction 

Used in desi&n to calculate com$osite $ro$erties. /lmost always refers to fibre content.

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0ei&ht fraction ↔ ,olume fraction

con,ersion

V   W 

W W f 

f f 

f f f m

=+ −

1

1 % ' 1

 ρ 

 ρ ρ 2

For the s$ecial case of a two-com$onent

com$osite %e& fibre and matri3'4

W   V 

V V f 

f f 

f f m f  

=+ −

 ρ 

 ρ ρ   % '2

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Volume fraction - weight fraction conversion(epoxy resin matrix)

5

5.(

5.

5.6

5.7

2

5 5.( 5. 5.6 5.7 2

fibre weight fraction

   f   i   b

  r  e  v  o   l  u  m  e   f  r  a  c   t

   i  o  n

&lass

H8 carbon

aramid

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Ma3imum fibre ,olume fraction

Theoretically9 a unidirectional fibre com$osite could ha,e Vf  :;5*.

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Ma3imum fibre ,olume fraction

For other forms of reinforcement9 ma3imum ,olume fraction also de$ends

on the detailed arran&ement of the fibres.

The followin& ,alues are ty$ical4

  stitched >non-crim$ 5.6  wo,en fabric 5. - 5.))

  random

%cho$$ed strand mat' 5.2) - 5.()

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How much fibre?

@ommercial reinforcements are characterised by

their areal weight (Aw  ).  This is sim$ly the wei&ht

%usually &i,en in &' of 2 m( of the reinforcement. /w 

de$ends on many factors - fibre density9 tow orbundle siAe9 wea,e style9 etc.

 /w may ran&e from )5 &1m( or less %for li&htwei&ht

surfacin& tissues'9 u$ to more than (555 &1m( for

some hea,ywei&ht non-crim$ fabrics.

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Laminate thickness

fibre

matri3

hi&h matri3 content

low fibre content

B thick laminate

low matri3 content

hi&h fibre content

B thin laminate

Two laminates9 both containin& ) $lies of reinforcement4

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Laminate thickness

Fibre ,olume fraction is thus in,ersely $ro$ortionalto laminate thickness.

d 

nAV 

f 

w 

f  ρ 

=

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Ply thickness vs fibre volume fraction (glass)

5

5.)

2

2.)

(

(.)

5.2 5.( 5. 5. 5.) 5.6 5.=

fibre volume fraction

  p   l  y   t   h   i  c   k  n  e  s  s   (  m  m   )

(55 &1m(

55 &1m(

)5 &1m(

655 &1m(

 Area weight 

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Ply thickness vs fibre volume fraction (HS carbon)

5

5.(

5.

5.6

5.7

2

2.(

2.

2.6

5.( 5. 5. 5.) 5.6 5.= 5.7

fibre volume fraction

  p   l  y   t   h   i  c   k  n  e  s  s   (  m  m   )

255 &1m(

2)5 &1m(

(55 &1m(

55 &1m(

)55 &1m(

 Area weight 

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Example calculationsExample calculations

!! 0hat will be the thickness of a laminate

consistin& of ( layers of )5 &1m( cho$$ed

strand mat if a resin to &lass ratio %by wei&ht'of (42 is used?

"!"!  0hat fibre ,olume fraction is achie,ed if(

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"ules of Mi3ture

for Clastic #ro$erties

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"ules of Mi3tures are mathematical

e3$ressions which &i,e some $ro$erty ofthe com$osite in terms of the $ro$erties9

Duantity and arran&ement of its

constituents.

They may be based on a number of

sim$lifyin& assum$tions9 and their use indesi&n should tem$ered with e3treme

cautionE

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ensity

For the s$ecial case of a fibre-reinforced matri34

mmf f    VV   ρ+ρ=ρ

since V f  + V m = 2

mf f f    'V2%V   ρ−+ρ=ρ

mmf f    '%V   ρ+ρ−ρ=ρ

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"ule of mi3tures density for

&lass1e$o3y com$osites

5

)55

2555

2)55

(555

()55

555

5 5.( 5. 5.6 5.7 2

fibre volume fraction

     k    g     #    m     $

ρf 

ρm

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Micromechanical models for stiffness

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Unidirectional $ly - lon&itudinal

tensile modulus

E 1 = E f  V f  + E m ( 1-V f )

Gote the similarity to the rules of mi3ture

e3$ression for density.

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This rule of

mi3tures is a&ood fit to

e3$erimental

data

%source4 Hull9

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!eneralised rule of mi3tures for

tensile modulus

E = L o E f  V f  + E m (1-V f )

η L is a len&th correction factor. Ty$ically9 η L ≈ 2

for fibres lon&er than about 25 mm.

η o corrects for non-unidirectional reinforcement4

η o

unidirectional 2.5bia3ial 5.)bia3ial at ±)o 5.()random %in-$lane' 5.=)random %F' 5.(

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%ule of mixtures tensile mo&ulus

(glass fibre#polyester)

5

25

(5

55

)5

65

5 5.( 5. 5.6 5.7

fibre volume fraction

   t  e  n  s   i   l  e  m  o   &  u   l  u  s

   (   '   P  a   )

UF

bia3ial

@8M

%ule of mixtures tensile mo&ulus

($ carbon fibre)

5

)5

255

2)5

(55

5 5.( 5. 5.6 5.7

fibre volume fraction

   t  e  n  s   i   l  e  m  o   &  u   l  u  s   (   '   P  a   )

UF

bia3ial

Duasi-isotro$ic

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