COMPOSITE MATERIALS MECHANICS - TM - · PDF file · 2015-08-27COMPOSITE MATERIALS...

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


b

h e

d


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.


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


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


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


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


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


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.


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.


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


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

=


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)


LAMINATE THICKNESS


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)


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


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!


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



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


ρf

ρm


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:


Rule of Mixtures Tensile Modulus(Glass Fibre / Polyester)

TENSILE MODULUS



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

)


UD

BIAXIAL

CSM

Rule of Mixtures Tensile Modulus(Carbon Fibre)

TENSILE MODULUS



Tens

ile M

odul

us (G

Pa)

020406080

100120140160180200

0 0,2 0,4 0,6 0,8TEN

SILE

MO

DU

LUS

(GPA

)


UD

BIAXIAL

QUASI-ISOTROPIC

Obrigado!


COMPOSITE MATERIALS MECHANICS - TM - · PDF file · 2015-08-27COMPOSITE MATERIALS...

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