PERILAKU MEKANIK PADA KOMPOSIT

  ! " # $ % " & ' # (

• c = f f m m E E

  V E

  V

• c = f f m m σ σ

  V σ

  V _c ! E !

  σ c

  " # $% & ' $% & ' & %

  ( % % % ( ) ( " ! % ( * %

• σ′
•     
• σ = σ
• ,

  V V f _fu

  fraksi volum fiber minimum: As ↓, ↑.

  As ↑, ↑.

  degree of work hardening , matrix f fiber , f

  ε < ε σ′ −

  σ

  m mu fu m mu min

  σ

  Agar memiliki penguatan komposit dari serat,

  V ^min ( ) σ′

  − σ m mu

  V min )

  V ) 1 ( V 1 (

  V f mu f m f fu cu

  

−

σ ≥ − σ′ + σ

  UTS of composite UTS of matrix after fiber fracture

  All fibers are identical and uniform. → same UTS Jika serat retak, sebuah matriks menjadi mengeras mengimbangi kehilangan beban/daya dukung.

  = σ

  Modulus _{m f c} m m f f

  %

  % %

  V V m m f f c σ′

  = σ

  V d d

  V d d E

     

  Effect of Fiber Volume Fraction on Tensile Strength (Kelly and Davies, 1965) Assumption : Ductile matrix ( ) work hardens.

    ε σ

   ε σ =

  ε ε

  V V m m f fu cu σ′

  σ

  fu σ′ m

• σ σ′ − σ = ≥

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

  (

  1 V ) V f m − ≥ mu

• _{cu = fu}

  σ σ σ′ f σ

  UTS of pure matrix

  Critical Fiber Volume Fraction −

  σ mu σ′ m

  V V ≥ = _crit

  f _{fu − m}

  σ σ′ As ↓, ↑. σ fu

  V crit As − ↑, crit ↑.

  ( σ mu σ′ m )

  V

  degree of work hardening

>

  Note that > mu )

  V V σ

  crit min always! (∵

• (. / , ! / % ! / % / % ! % ! % % ! / ! % % ! ! , ! ! ! ! ! % % ! % 0 ! ! , ! ! ! !

  2

  2

  π E  d  σ =

   

  c

  16 l  

  % %

  2 Types of Compressive Deformation 1) In/phase Buckling : melibatkan deformasi geser pada matrix

  G E

  m m

  ( or )

  = = ∝ σ G E m c m

  1 )

• 2 (

  ν

  V m m V m _m E for isostropic matrix, =

  G ^m

  1 ν ) _m → terutama pada fraksi volum fiber yang besar. 2) Out/of/phase Buckling : melibatkan kompresi transversal dan tegangan pada matrix dan fiber

• 2 (

  1 /

  2 

  V E E 

  1 /

  2 f m f = ∝ ⋅ σ

  2 V   ( E E )

  c f m f

  3 V

  m   → terutama pada fraksi volum fiber rendah.

  Faktor/faktor yang mempengaruhi kekuatan kompresi: _{m m} , G E _f

  E V f

  Interfacial Bond Strength : poor bonding → easy buckling

• (1 (% $ ' / %

  2

  3 / ! ! % $ ' ! % ! % ! ! ! % $ '

  

4 ! ! % ! %

→

4 ! ! % % %

→

  , matrix f fiber , f ε ≠ ε

  2' ( % ! & % ( % % % ( ! !

  %

  % % .' ( % & % ( % ( %

  V V V m m m mu f fu σ′

  − σ > σ

  σ′ m

  V V

  V m m m mu f fu

  σ′ − σ <

  σ

  . 5 * 5 % ! * l

  5 ) % l

  c $ '

  If distance from crack plane to fiber end <

  2

• → 5 → 3

  l c

  If distance from crack plane to fiber end >

  2

  → → 3

  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

  r

  : fiber radius

  f

  l : fiber length in matrix

  σ : tensile stress on fiber f

  τ

  : interfacial shear strength

  i τ _i σ _f

  W

  2 d

  1 d l

  4 If l l

  l r 2 r i f f

  2 f τ π > σ π 

     = ≥

  τ → < f i fu c r

  1 2' ! .' 5 1' *

  r

  W d

  W

  p W W W p d fracture

  W

  p Load Displacement

  W

  P

  2

  f i fu c

  Force Equilibrium ( l

  c i f fu

  c

  : critical length of fiber ) 1) Condition for fiber fracture, 2) Condition for fiber pullout, l r

  2 r

  i f f

  2 f

  τ π = σ π

  2 f = 2 r τ π σ π l r d l r

  σ → >

  2 l 4 ^{c f c i fu} = =

  τ σ r l

  2 f ^{c i fu} = τ σ l r 2 r i f f

  2 f τ π < σ π

    

    

  = < τ

• ) % ) ( ( %
• =
Energy Required for Fracture & Debonding

  2

  2    π  σ fu d

  =   ⋅   ⋅ x x : debond length W d 24  E f    elastic strain E. volume

  Energy Required for Pullout  l c  k

  Let k : distance (lekat) of a broken fiber from crack plane < <  

  2  

  x : pullout distance at a certain moment

  : interfacial shear strength

  τ i

  τ π d ( k − x )

  Force to resist the pullout =

  i fiber contact area

  Energy to pullout a distance dx = τ π d ( k − x ) dx i

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

  2 k

  τ π dk

  i

  = τ π d ( k − x ) dx = W

  p i ∫

  2

  l c

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

  < < _{l 2 c}

  2

  2 τ π dl 1 τ i π dk i c

  ∴ = dk = W p , ave

  ∫

  2

  24 l

  2 c

  Fracture of Discontinuous Fiber Reinforced Composite l

  

c

  If a fiber is located within a distance, ± , from crack plane, → pullout

  2

  l c

  Probabilit y for pullout of a fiber with length, l ≈ l

  Average energy to pullout per fiber with length, l

  2

  l τ π dl  

  c i c

  W =  

  p , ave

  l

  24  

  probability for pullout energy required for pullout

  Energy for Fiber Pullout vs Fiber Length(l) If l < l , fiber pullout distance increases with increasing length l.

  c

  2

  → W increases, with increasing length l. ∝ l W

  p ( p ) If l > l , fiber fracture tendency increases with increasing length l. c

  1   → W decreases, with increasing length l. ∝ l = constant  W  p

p c

l  

  W becomes maximum, when l l .

  ≈

  6 " 77 " 6 & % % %

  , % ) % 2' * % % ( % % % .' 1' ! $ 5 % ' ( % % %

  ! 3 !

  : diameter fiber d

  V V Energy d fracture of f m

  2    

   

∝

τ

∝

i d Energy fracture of p p d fracture

  W W W W ≈ + =

  σ σ

  σ ^yy

  σ xx

  8 →

  % →

  ! 5 % 9 % % →

  → !

  σ ^xx

• (:

  6 ) % → ; $ % ' ( % 5 $ % ' ( & %

  ; → → < = > ? "

  5 β − 1 β

  f σ = L αβσ exp − L ασ

  ( ) ( )

  f σ

  ( )

• %

  α , β

  9 σ d + σ σ

• (@ %

  A % !

  → ) 9 % %

• ( % ( % ! B%

  ! % →

  ! $ ; ' → ) 6 & % % % %

  =

  ( ( % , 5 % 6 % &

  ! % % ( $∵

  ' 5 % $ ! ' % ( $∵

  ' ( & + * & 3 B* B*

  % & →

  ( & + ) % $;B6 6 .

  C

  1 B6 6 .

  C

  1 B '

• " ! ) %

  ( ! 6 % % % & % 6 %

  ( % %

  6 %

• & ! ,

  & & & % = % % % B% 9 % %

  ! 5 5 % & ' * !

  ' 5 % '

  )

  

σ

  C ) ) σ _{2 n max} 1 dE  σ  _max

  σ _m

  A − =

   ^{2 } E dN E ( 1 − E / E )

    time

  σ _min

  > % > % %

  D σ _max

  !

  6

  2  1 dE   σ  max log − vs log plot 

  2   

  →

E dN E ( 1 − E / E )    

  E % % % &

  % →

• (F , % % , , % % % ! % ! % % ! ! % $α'

  % %

  ! ! % % ! % *

  ! % 0 ! % & % ! % T

  σ ∝ ' α ⋅ ' / ! ! % ! % ! ! % !

  % / % % ! ! % ! % ! % ! / & % % ! B% ! !

  ! ! % ! ! % ! % % % ! ! % % % ! % % ! ! ! B% ! % %

  ! ! % % !