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Figure 1.1 Phases of a composite system:

acontinue phase (matrix); bdisperse phase (reinforcement);

c-interface

a

b

c

1. Composites are materials consisting of to or more chemically

distinct constituents on a macro-scale! ha"ing a distinct interface

separating them! and ith properties hich cannot be obtained by any

constituent or#ing indi"idually.

$he polymeric matrix is re%uired to ful&ll the folloing main

functions: to bind together the &bres and protect their surfaces from

damage during handling! fabrication and ser"ice life of the composite; to

disperse the &bres and separate them and to transfer stresses to the

&bres. $he matrix should be chemically and thermally compatible ith the

reinforcing &bres.

$he interface region is small but it has an important role in

controlling the o"erall stress-strain beha"ior of the composites. 't exhibits

a gradation of properties and it is a dominant factor in the resistance ofthe composite to corrosi"e en"ironments. 't also has a decisi"e role in the

failure mechanisms and fracture toughness of the polymeric composites.

2.Types of composites

omposites are commonly classi&ed at to distinct le"els.The frst

level of classi&cation is made with respect to the matrix constituentand

the maor composite classes include:

polymer matrix composites (PMCs);

metal-matrix composites (MMCs);

ceramic-matrix composites (CMCs).

'n each of these systems the matrix is typically a continuous phase

throughout the component. $he second le"el of classi&cation! is deri"ed

rom their orm:

Particulate reinforced compositesare generally made up of

randomly dispersed hard particle constituent in a softer matrix. *xamples

of particulate composites are metal particles in metallic! polymeric or

ceramic matrices


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Flake composites are formed by adding thin +a#es to the matrix

material

Fire reinforced composites (!rous composites) are the most

commonly used form of the constituent combinations. $he &bres of such

composites are generally strong and sti, and therefore ser"e as primary

load-carrying constituent. $he matrix holds the &bres together and ser"es

as an agent to redistribute the loads from a bro#en &bre to the adacent

&bres .

Figure 1. omposite materials ith di,erent forms of constituents

"aminated compositesare formed from thin elementary layers

(laminae! plies) fully bonded together.

#. $e!ne t%e &olume and mass fractions of !rous

composites

Fiber volume ratio! or &ber "olume fraction! is the percentage of &ber

"olume in the entire "olume of a &ber-reinforced compositematerial.

c

f

fv

vV =

andc

mm

v

vV =

;mfc vvv +=

vc- the "olume of the composite

v- the "olume of &bres

vm- the "olume of the matrix
https://en.wikipedia.org/wiki/Fiber-reinforced_compositehttps://en.wikipedia.org/wiki/Fiber-reinforced_composite


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onsidering the de&nition of mass fractions and replacing the mass by the

product of density and "olume! the con"ersion beteen the mass fractions

and "olume fractions can be obtained:

mm

c

mff

c

f

MVMV

==

; f / m 0 1

The mass ractions! similar to "olume fractions! are de&ned as the ratio

of mass of respecti"e phase to the mass of composite.

mfc mmm +=

;c

f

fm

mM =

andc

mm

m

mM =

mc, m and mmthe corresponding masses of the composite! &bres and

the matrix material respecti"ely. onsidering the de&nition of mass fractions and replacing the mass by the

product of density and "olume! the con"ersion beteen the mass fractions and

"olume fractions can be obtained:

m

c

mmf

c

f

f VMVM

==

; f / m 0 1

'. $eterminet%e density of !rous composites in terms of

!re and mass fractions

$he density cof the composite can be obtained in terms of the

densities of the constituents (and m) and their "olume fractions or

mass fractions. $he mass of a composite can be ritten as:

mmffcc vvv +=

2i"iding both sides of *%uation by vcand using the de&nition for the

"olume fractions! the folloing e%uation can be deri"ed for the

composite material density:

mmffc VV +=

$he density of composite materials in terms of mass fractions can be obtained

as:


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mmff

cMM

+

=1

1. Trans&erse modulus

$he trans"erse modulus is a matrix-dominated propertybeing sensiti"e

to the local state of stress. $he transverse modulusof a unidirectional

composite is much smallerthan its longitudinal modulus.

$he composite trans"erse elongation (cT

) is the sum of the &bre (f)

and matrix (m

) elongation respecti"ely. $he elongation of each

constituent can be ritten as the product of the strain and its

cumulati"e thic#ness:

mmffccT

mmmTfffTccTcT

mTfTcT

lll

lll

+=

===

+=

;;


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the length fractions must be e%ual to the "olume fractions:

tl

tlV

c

f

f =

tl

tlV

c

mm =

3ssuming the &bres and matrix to deform elastically and the stress is

the same in the &bre! matrix and composite! in the trans"erse direction!

e can rite:

( )m

m

mf

f

f

T

Tc VE

VEE

+=

and:

=

TE

1

m

m

f

f

E

V

E

V+

hich is the in&erse rule of mixturesfor the trans"erse modulushich can be also ritten as :


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mffm

mf

TVEVE

EEE

+=

here Eis the trans"erse modulus of the &bres.

4raphical 5epresentation

1. *%ear modulus of a unidirectional composites


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t

lf

lm

mf

6f

6m

6c

78$7$8

7$8

78$

a. b.

8

lcf

c

m

$he beha"iour of unidirectional composites under in-plane shear loading is

dominated by the matrix properties and the local stress distributions.

$he total shear deformation of the composite! c! is the sum of the shear

deformations of the &bre! ! and the matrix! m; each shear deformation

can be then expressed as the product of the corresponding shear strain

(c, , m) and the cumulati"e idths of the material(lc, l, lm):

mfc +=

mmffcc lll +=

3ssuming linear shear stress-shear strain beha"iour of &bres and matrix!

the shear strains can be replaced by the ratios of shear stress and the

corresponding shear modulus:

m

m

mf

f

f

c

LT

LT lG

lG

lG

+=

here GLTis the in-plane shear modulus of the composite! Gis the shear

modulus of &bres and Gmthe shear modulus of matrix. 9ut the shear

stresses are e%ual on composite! &bres and matrix and e obtain:

m

m

fLT G

V

G

V

G

f+=

1

ormffm

mf

LT VGVG

GG

G +=

4raphical 5epresentation


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Figure . a) odel of unidirectional composite for predicti

. .< .= .>

$he ?alpin-$sai e%uations can be used to gi"e better predictions:

f

f

mLTV

VGG

2

22

1

1

+=

here:

(( ) 2

2

1

+

=

mf

mf

GG

GG

and is the reinforcing e@ciency factor for in-plane shear. $he best

agreement ith experimental results has been found for !"

1+. Poisson,s ratios of unidirectional composite lamina

$o Poisson ratios are considered for in-plane loading of a unidirectional

&bre reinforced unidirectional composite.$he &rst Poisson ratio! LT!

relates the longitudinal stress! L! to the trans"erse strain! T! and is

normally referred to as the ma#or $oisson ratio:

L

TLT

=

here Lis the longitudinal strain and the loading scheme is:

L%, T!% andLT!%&$he second one called the minor $oisson ratio! TL!

relates the trans"erse stress! T! to the longitudinal strain! L:

T

L

TL

=

hen T%, L!%and LT!%.


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Figure .< odel of unidirprediction of Poi

lf

lm

B8

2eformed composite

Cndeformed composite

f

$he total trans"erse deformation of the composite!c! is the sum of the

constituent trans"erse deformations! andm.3ssuming that no slippage occurs at the interface and the strains experienced

by the composite!!and that the idths are proportional to the "olume fractions

the folloing formula is obtained for the maor Poisson ratio:

mmffLT VvVvv +=

*%uation is the rule of mixturesfor the maor Poisson ratio of a

unidirectional composite.


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f

f

8$

m

. .< .= .>

$he folloing functional relationship (presented in macromechanics of

composites) exists beteen engineering constants:

LTLTLT EE =

$hus the minor Poisson ratio can be obtained from the already #non

engineering constants EL! ETand LT:

L

TLTTLE

E =

or in the extended form:

( )[ ]( )

fmff

fmffmf

fmffTLVEVE

VEVEEEVV

+

+

+=

1

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1. %ic% sti/ness c%aracteristics of !rous composites

re0uire corrections and %o are t%ey performed

Figure .D Poisson ratio vLTas a function of

&bre "olume fraction (m>f)


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13.%ic% composites c%aracteristics may e determinedusin4 t%e 5rule of mixtures5


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1#. %ic% composites c%aracteristics may e determined

usin4 t%e 5in&erse rule of mixtures5

1'. $etermine t%e lon4itudinal tensile stren4t% of

unidirectional composites

Ehen a &bre reinforced composite is subected to longitudinal

tension theconstituent with the lower ultimate strain will ail frst. Ehen

the ultimate tensile strain of the &bre is loer than that of the matrix

'(u)(mu) the composite ill fail hen its longitudinal strain reaches the

ultimate strain in the &bre.

$hen! the longitudinal tensile strength of the composite can be

calculated ith:

)1( ffftLt VVff m +=

here:

f8t 0 longitudinal composite tensile strength

fft 0longitudinal &bre tensile strength

m

0 a"erage matrix stress at the &bre fracture strain (Fig. .>a)

f0 &bre "olume fraction


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*xpressing Bmby the product of the matrix elastic modulus times the

corresponding strain the folloing formula can be utilied to determine

the composite longitudinal tensile strength:

)]1([ ffL

mfftLt V

E

EVff +=

'f the &bre "olume fraction is belo the so called *minthe matrix is able to

support the entire composite load hen all the &bres brea#. $he composite

e"entually fails hen the matrix reaches its ultimate tensile strength 'mt+.

$hus the ultimate strength of a composite ith the &bre "olume fraction

less than *minis gi"en by:

)1( fmtLt Vff =

mmtft

mmtf

ff

fVV

+

== min

3 critical fbre volume raction! *crit,hich must be exceeded for strengthening

can be de&ned as follos:

mft

mmtcritf

f

fVV

==

Ehen the ultimate matrix tensile strain is loer than that of the &bre ((mu)(u)

the composite fails hen its longitudinal strain reaches the fracture strain of

the matrix.

$hen! the longitudinal tensile strength of the composite can be calculated ith:

)1( fmtffLt VfVf +=

2.$he o,shore platforms ha"e become a ne important sector of

use for ad"anced polymer composites. F5P composites are utilised not

only in underater piping but also in structural parts of the platform. 3s

the drilling in depths of ater increases the eight of pipes and

underater structural components becomes a maor issue. $he hole

assembly must be supported by the +oating platform. arbon &bre

composites ith a density D.D times loer than that of steel pro"ide


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signi&cant increased buoyancy compared to steel. 'n addition F5P

composites pro"ide greater resistance to corrosion and better thermal

insulation to the pumped oil. 9y selecting the type of carbon &bre and

suitable constituent "olume fractions F5P can match the sti,ness and

strength of steel members. Gn the o,shore platform the initial fears of &rehaard decreased after the research or# shoed that composite

laminates thic#er than >mm perform better than steel in a maor &re. $he

stairays and al#ays are also made of composites for eight sa"ing

and corrosion resistance. *"en the cables and ropes made of steel are

no being replaced by similar items made of aramid or high modulus

polyethylene &bres.

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