Volume Fraction in Large Particle Composites

(1)

FILLER AND MATRIX

Nurun Nayiroh, M.Si

Pertemuan ke#3 & 4

Mata Kuliah Komposit

Sub Pokok Materi

(Bahan Pengisi/penguat):

b. Kekuatan dari Reinforcement: Stabilitas Thermal, Compressive Strength, Fibre Fracture and flexibility, a statistical treatment of fibre strength

c. Matrices: Polimer Matrices, Metal Matrices, Ceramic matrices

Metals

Polymers

Ceramics

Composites

–

Keuntungan dari komposit yang disusun oleh

a) Kekuatan lebih seragam pada berbagai arah

b) Dapat digunakan untuk meningkatkan kekuatan dan meningkatkan kekerasan material

c) Cara penguatan dan pengerasan oleh partikulat adalah dengan menghalangi pergerakan dislokasi.

Proses produksi pada komposit yang disusun oleh berbentuk partikel

a) Metalurgi Serbuk b) Stir Casting c) Infiltration Process d) Spray Deposition e) In#Situ Process

Ukuran partikel dibedakan menjadi dua, yaitu !

" # $

a) Fraksi partikulat sangat kecil, jarang lebih dari 3%. b) Ukuran yang lebih kecil yaitu sekitar 10#250 nm.

1) Large particle

Interaksi antara partikel dan matrik terjadi tidak dalam skala atomik atau molekular

Partikel seharusnya berukuran kecil dan terdistribusi merata

(2)

• Other examples:

Adapted from Fig.

10.19, %.

(Fig. 10.19 is copyright United States Steel Corporation, 1971.)

# Spheroidite steel

Adapted from Fig.

16.4, %.

(Fig. 16.4 is courtesy Carboloy Systems, Department, General Electric Company.)

Adapted from Fig.

16.5, %.

(Fig. 16.5 is courtesy Goodyear Tire and Rubber Company.)

# Automobile tires

Volume Fraction

in Large Particle Composites

• Elastic modulus is dependent on the volume

fraction

• “Rule of mixtures” equation

– E# elastic modulus, V# volume fraction, m# matrix, p# particulate

– upper bound (iso#strain)

– lower bound (iso#stress)

=

+

=

+

Rule of Mixtures

conc. of particulates

E

• All three material types

– metals, ceramics, and polymers

• CERMET (ceramic#metal composite)

– cemented carbide (WC, TiC embedded in Cu

or Ni)

– cutting tools (ceramic hard particles to cut, but

a ductile metal matrix to withstand stresses)

– large volume fractions are used (up to 90%!)

2) Dispersion Strengthened particle

• Metals and metal alloys

– hardened by uniform dispersion of fine particles of a very hard material (usually ceramic)

• Strengthening occurs through the

interactions of dislocations and the

particulates

• Examples

• Thoria in Ni

• Al/Al2O3sintered aluminum powder SAP

• GP zones in Al

!

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"

#

$

#

$

• Penjepit fiber

• Melindungi fiber dari kerusakan permukaan

• Pemisah antara fiber dan juga mencegah

timbulnya perambatan crack dari suatu fiber ke

fiber lain

• Berfungsi sebagai medium dimana eksternal

stress yang diaplikasikan ke komposit,

ditransmisikan dan didistribusikan ke fiber.

Ultimate Tensile Strength (UTS) (kuat tarik

utama), sering disingkat menjadi Tensile Strength

(TS) atau Ultimate Strength, adalah tegangan

maksimum dimana material dapat menahan

ketika sedang diregangkan atau ditarik sebelum

necking (ketika penampang spesimen mulai

berkontraksi secara signifikan). Kekuatan tarik

(TS) adalah kebalikan dari kuat tekan dan nilai#

nilainya bisa sangat berbeda.

%

#

$

%

• Ductile

• Lower E than for fiber

• Bonding forces between fiber and

matrix must be high

– otherwise fiber will just “pull#out” of matrix

• Generally, only polymers and metals

are used as matrix material (they are

ductile)

Fiber yang digunakan sebagai reinforced harus memiliki syarat sebagai berikut :

a) Mempunyai diameter yang lebih kecil dari diameter bulknya (matriksnya) namun harus lebih kuat dari bulknya. b) Harus mempunyai tensile strength yang tinggi

Parameter fiber dalam pembuatan komposit, yaitu sebagai berikut :

a) Distribusi b) Konsentrasi c) Orientasi d) Bentuk e) ukuran

#

a. Short(discontinuous) fiber reinforced composites

Aligned Random

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Aligned Fibers

• &%

$

– properties of material are highly anisotropic

– modulus in direction of alignment is a function

of the volume fraction of the E of the fiber and

matrix

– modulus perpendicular to direction of

alignment is considerably less (the fibers do

not contribute)

Fiber Alignment

aligned continuous

aligned random discontinuous

Adapted from Fig.

16.8, %.

Randomly Oriented Fibers

• Properties are isotropic

– not dependent on direction

• Ultimate tensile strength is less than for

aligned fibers

• May be desirable to sacrifice strength for

the isotropic nature of the composite

Berdasarkan penempatannya terdapat beberapa tipe serat pada komposit, yaitu:

Continuous atau uni#directional, mempunyai susunan serat panjang dan lurus, membentuk lamina diantara matriksnya. Jenis komposit ini paling banyak digunakan. Kekurangan tipe ini adalah lemahnya kekuatan antar antar lapisan. Hal ini dikarenakan kekuatan antar lapisan dipengaruhi oleh matriksnya.

b) ) * + '

Komposit ini tidak mudah terpengaruh pemisahan antar lapisan karena susunan seratnya juga mengikat antar lapisan. Akan tetapi susunan serat memanjangnya yang tidak begitu lurus mengakibatkan kekuatan dan kekakuan tidak sebaik tipe continuous fiber.

c) # + $

Komposit dengan tipe serat pendek masih dibedakan lagi menjadi : 1) Aligned discontinuous fiber

2) Off#axis aligned discontinuous fiber 3) Randomly oriented discontinuous fiber

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d)

,-Hybrid fiber composite merupakan

komposit gabungan antara tipe serat lurus

dengan serat acak. Pertimbangannya

supaya dapat mengeliminir kekurangan

sifat dari kedua tipe dan dapat

menggabungkan kelebihannya.

' %

$

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(!

) *

– $ $ # + $ % %

$ $ $ $ # #

#

–, % -. ) /. 0 1

2 + + "$+ 3 + !

–" $ $ # # $

–* $ $ #

–' $ # # $+ # + +

% $

Sifat#Sifatnya

• Densitynya cukup rendah ( sekitar 2.55 g/cc)

• Tensile strengthnya cukup tinggi (sekitar 1.8

GPa)

• Biasanya stiffnessnya rendah (70GPa)

• Stabilitas dimensinya baik

• Resisten terhadap panas

• Resisten terhadap dingin

• Tahan korosi

Keuntungan :

• Biaya murah • Tahan korosi

• Biayanya relative lebih rendah dari komposit lainnya

Kerugian

• Kekuatannya relative rendah • Elongasi tinggi

• Keuatan dan beratnya sedang (moderate)

Jenis#jenisnya antara lain

:

– E#Glass # electrical, cheaper – S#Glass # high strength

!

• Densitaskarbon cukup ringan yaitu sekitar 2.3

g/cc

• Struktur grafit yang digunakan untuk membuat

fiber berbentuk seperti kristal intan.

• Karakteristik komposit dengan serat karbon :

– ringan;

– kekuatan yang sangat tinggi; – kekakuan (modulus elastisitas) tinggi.

• Diproduksi dari poliakrilonitril (PAN), melalui tiga

tahap proses :

• Stabilisasi = peregangan dan oksidasi;

• Karbonisasi= pemanasan untuk mengurangi O, H, N;

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• Proses produksi pada

'

-1. Open Mold Process

a. Hand Lay#Up

b. Spray Lay#Up

c. Vacuum Bag Moulding

d. Filament Winding

2. Closed Mold Process

a. Resin Film Infusion

b. Pultrusion

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(7)

Composite Strength: Longitudinal Loading

Continuous fibers

#

Estimate fiber#reinforced

composite strength for long continuous fibers in a matrix

• Longitudinal deformation

σ

:

σ

;

σ

but

ε

εε

ε

:

ε

εε

ε

:

ε

εε

ε

volume fraction isostrain

∴ . = . & + . & longitudinal (extensional) corresponds to the “upper bound” for particulate composites

Elastic Behavior Derivation

(Longitudinal Loading)

Consider longitudinal loading of continuous fibers, with good fiber/matrix bonding. under these conditions matrix strain = fiber strain (isostrain condition).

εm= εf = εc

The total load on the composite, Fc, is then equal to loads carried by the matrix and the fibers

Fc= Fm+ Ff Substituting for the stresses

σcAc= σmAm+ σfAf Rearranging

σc= σm Am/Ac+ σf Af /Ac

were Am/Ac and Af /Acare the area fractions of matrix and fibers, respectively. If the fiber length are all equal than then these terms are equivalent to the volume fractions

Vf = Af /Ac & Vm = Am /Ac

σc= σm Vm+ σf V Using the isostrain constraint and Hookes Law, σ= εE

=

+

Can also show ratio of load carried by fiber and matrix: Ff/Fm= EfVf/EmVm

Fc= Ff+ Fm

Composite Strength: Transverse Loading

• In transverse loading the fibers carry less of

the load and are in a state of ‘isostress’

σ and note, this model corresponds to the “lower bound” for particulate composites

Elastic Behavior Derivation

(Transverse Loading)

Consider transverse loading of continuous fibers, with good fiber/matrix bonding. under these conditions matrix strain = fiber strain (isostress condition).

σm= σf = σc = σ

The total strain of the composite is given by εc= εm Vm = εf Vf

Using Hookes Law ε= σ/E and the isostress constraint σ/Ec= (σ/Em) Vm+ (σ/Ef) Vf

Dividing by σ, Algebraically this becomes

=

+

An Example:

Note: (for ease of conversion)

UTS, SI Modulus, SI

57.9 MPa 3.8 GPa

2.4 GPa 399.9 GPa

(241.5 GPa)

(9.34 GPa)

• Estimate of . and / for discontinuous fibers:

## valid when

## Elastic modulus in fiber direction:

##/ in fiber direction:

efficiency factor:

## aligned 1D: 0= 1 (aligned ) (Source for Table 16.3 is H. Krenchel, , Copenhagen: Akademisk Forlag, 1964.)

Composite Strength

Particle#reinforced Fiber#reinforced Structural

(/ ) = (/ ) & + (/ )&

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• Aligned Continuousfibers

• Examples:

From W. Funk and E. Blank, “Creep deformation of Ni3Al#Mo in#situ composites", / Vol. 19(4), pp. 987#998, 1988. Used with permission.

##Metal: γ'(Ni3Al)#α(Mo) by eutectic solidification.

Composite Survey: Fiber

matrix: α (Mo) (ductile)

fibers:γ’ (Ni3Al) (brittle)

2 m

##Ceramic: Glass w/SiC fibers formed by glass slurry

.glass = 76 GPa; .SiC = 400 GPa.

(a)

(b)

fracture surface

From F.L. Matthews and R.L.

Rawlings, 1

. , Reprint

ed., CRC Press, Boca Raton, FL, 2000. (a) Fig. 4.22, p. 145 (photo by J. Davies); (b) Fig. 11.20, p. 349 (micrograph by H.S. Kim, P.S. Rodgers, and R.D. Rawlings). Used with permission of CRC Press, Boca Raton, FL.

• Discontinuous, random 2Dfibers

• Example: Carbon#Carbon ## process: fiber/pitch, then burn out at up to 2500ºC. ## uses: disk brakes, gas

turbine exhaust flaps, nose cones.

• Other variations: ##Discontinuous, random 3D

##Discontinuous, 1D

Composite Survey: Fiber

(b)

fibers lie in plane view onto plane

C fibers: very stiff very strong C matrix: less stiff less strong

(a)

efficiency factor:

## random 2D: 0= 3/8 (2D isotropy) ## random 3D: 0= 1/5 (3D isotropy)

. = . & + 0. &

Influence of Fiber Length

• Mechanical properties depend on:

• mechanical properties of the fiber

• how much load the matrix can transmit to the fiber

– depends on the interfacial bond between the fiber and the matrix

• Critical fiber length # depends on

• fiber diameter, fiber tensile strength • fiber/matrix bond strength

Influence of Fiber Length

• Critical fiber length #

l

_c

– “Continuous” fibers l >> 15 lc

– “Short” fibers are anything shorter 15 lc

l

c

=

σ

f

d/2

τ

c

where

d = fiber diameter τc= fiber#matrix bond strength

σf= fiber yield strength

No Reinforcement

Influence of Fiber Orientation

• Fiber parameters

– arrangement with respect to each other – distribution

– concentration

• Fiber orientation

– parallel to each other – totally random – some combination

Example

• Calculate the composite modulus for

polyester reinforced with 60 vol% E#glass

under iso#strain conditions.

• Epolyester= 6.9 x 103MPa

• E_E#glass= 72.4 x 10 3_MPa

E_c= (0.4)(6.9x103_{MPa) + (0.6)(72.4x10}3_MPa)

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Home work

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Other Composite Properties

• In general, the rule of mixtures (for

upper and lower bounds) can be used

for any property X

c

# thermal

conductivity, density, electrical

conductivityTetc.

X

c

= X

m

V

m

+ X

f

V

f

X

_c

= X

_m

X

_f

/(V

_m

X

_f

+ V

_f

V

_m

)

Tensile Strength

• In longitudinal direction, the tensile strength is given by the equation below if we assume the fibers will fail before the matrix: