PERILAKU MEKANIK PADA KOMPOSIT

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& %

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V E V E

Ec= f f+ m m

V Vf m m f

c=σ +σ

σ

Ec

σc

!

"

#

%

+,

% %

V Vf m m f

c=σ′ +σ′

σ

V d d V d d E

Modulus c f m

m m f

f

     

ε σ +      

ε σ =

ε ε

V Vf m m fu

cu=σ +σ′

σ σfu

σ′m

Effect of Fiber Volume Fraction on Tensile Strength (Kelly and Davies, 1965)

Assumption : Ductile matrix ( ) work hardens. All fibers are identical and uniform. → same UTS

Jika serat retak, sebuah matriks menjadi mengeras mengimbangi kehilangan beban/daya dukung.

Agar memiliki penguatan komposit dari serat,

UTS of composite UTS of matrix after fiber fracture

fraksi volum fiber minimum:

As ↓, ↑.

As ↑, ↑.

degree of work hardening

_f,matrix

fiber ,

f

<

ε

ε

σ′ − σ + σ

σ′ − σ = ≥

m mu fu

m mu min

V Vf

fu

σ _Vmin

(

σmu−σ′m

)

Vmin

)

V

1

(

)

V

1

(

V

f m f mu f

fu

cu

=

σ

+

σ′

−

≥

σ

−

σ ≥ − σ′ + σ =

σcu fuVf m(1 Vf) mu

σfu Vcrit

In order to be the strength of composite higher than that of monolithic matrix,

UTS of pure matrix Critical Fiber Volume Fraction

As ↓, ↑.

As ↑, ↑.

degree of work hardening

Note that Vcrit>Vminalways! (∵ )

σ′ − σ

σ′ − σ = ≥

m fu

m mu crit

V Vf

(

σmu−σ′m

)

0

mu>

σ

-(. / , ! / % !

2 Types of Compressive Deformation

1) In/phase Buckling : melibatkan deformasi geser pada matrix

→ terutama pada fraksi volum fiber yang besar.

2) Out/of/phase Buckling : melibatkan kompresi transversal dan tegangan pada matrix dan fiber

→ terutama pada fraksi volum fiber rendah. Faktor/faktor yang mempengaruhi kekuatan kompresi:

Interfacial Bond Strength : poor bonding → easy buckling ) matrix, isostropic for

-(1

(%

$

'

/ %

2

3

/ ! ! %

$

'

! %

!

%

!

! ! %

$

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4 ! ! %

!

%

→

4 ! ! %

%

%

→

matrix , f fiber , f

≠

ε

ε

2'

(

%

! &

%

( %

%

%

( !

!

%

%

%

.'

(

%

&

%

(

%

(

%

V V

Vf mu m m m

fu >σ −σ′

σ

σ′m

V

V

V

f mu m m m fu

<

σ

−

σ′

. 5 * 5 %

* !

5 ) %

$ '

→5 *

→3

→

→3

2 l end fiber to plane crack from distance

If _< c

2 l end fiber to plane crack from distance

If _> c

l

Fracture of Continuous Fiber Reinforced Composite

Patahan fiber pada bidang retak atau posisi lain yang tergantung pada posisi cacat. ↓

Pullout of fibers

For max. fiber strengthening → fiber fracture is desired. For max. fiber toughening → fiber pullout is desired.

Analysis of Fiber Pullout

Assumption : Single fiber in matrix : fiber radius

l : fiber length in matrix : tensile stress on fiber : interfacial shear strength

f

r

f

σ

i

τ

f

σ

i

Force Equilibrium

( lc: critical length of fiber )

1) Condition for fiber fracture,

2) Condition for fiber pullout, l

Load

Displacement WP

Energy Required for Fracture & Debonding

elastic strain E. volume

Energy Required for Pullout

Let k : distance (lekat) of a broken fiber from crack plane : pullout distance at a certain moment

: interfacial shear strength

Force to resist the pullout =

fiber contact area

Total energy(work) to pullout a fiber for distance k

Average energy to pullout per fiber(considering all fibers with different k, ) distance a

pullout to ave ,

length debond

Fracture of Discontinuous Fiber Reinforced Composite

→ pullout

Average energy to pullout per fiber with length, l

probability for pullout energy required for pullout Energy for Fiber Pullout vs Fiber Length(l)

plane, crack from , 2 l distance, a

within located is fiber a length, with fiber a of pullout for y

Probabilit _≈ c

24 ave , length increasing

with increases

distance pullout fiber length increasing

with increases tendency

fracture fiber , l l If > c

constant l length increasing with

decreases,

Wp p  c= maximum, becomes

6 " 77 "

6 & %

% %

, % ) %

2' * % % ( % % %

.'

1' ! $ 5 % ' ( % % %

! 3 !

diameter fiber

: d V V d fracture of Energy

f m

2

      ∝

τ ∝

i

d fracture of

Energy

p p d

fracture W W W

W = + ≈

σ

σ

σyy

σ

xx

8 → %

→ !

5 % 9 % %

→

→ !

-(: 6

) % →

; $ % ' ( %

5 $ % ' ( & %

;

→

→ < = > ?

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% 9

( )

_{σ = αβσ}β−

(

_{− ασ}β

)

L exp L

f 1

( )

σ

f

β α ,

σ σ+dσ

-(@ %

A %

→ !

) 9 % %

* ( % ( % ! B%

! %

→ ! $ ; '

→)

6 & % % % %

( ( % ,

5 % 6 % &

! % % (

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( & + * & 3 B* B*

% &

→

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% % & %

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( %

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%

* & ! ,

& & & % =

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→ n

0 2

0 2 max

0 E (1 E/E )

A dN dE E

1

   

 

− σ =

−

max

σ

time max

σ

m

σ

min

σ σ

plot ) E / E 1 ( E log vs dN dE E

1 log

0 2

0 2 max 0

   

 

− σ 

  

  −

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