Volume Fraction in Large Particle Composites

  Sub Pokok Materi

  Pertemuan ke#3 & 4 (Bahan Pengisi/penguat):

FILLER AND MATRIX

  b. Kekuatan dari Reinforcement: Stabilitas Thermal, Compressive Strength, Fibre Fracture and flexibility, a

  Nurun Nayiroh, M.Si

  statistical treatment of fibre strength

  c. Matrices: Polimer Matrices, Metal Matrices, Ceramic matrices Mata Kuliah Komposit

  Metals Polymers

• – – Ceramics
• – Composites

  1) Large particle

  Keuntungan dari komposit yang disusun oleh Interaksi antara partikel dan matrik terjadi tidak dalam skala atomik atau molekular

  a) Kekuatan lebih seragam pada berbagai arah Partikel seharusnya berukuran kecil dan terdistribusi

  b) Dapat digunakan untuk meningkatkan kekuatan dan meningkatkan merata kekerasan material Partikelnya kurang lebih harus sama sumbu.

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

  Volume fraction dependent on desired properties.

  Proses produksi pada komposit yang disusun oleh Contoh dari large particle composit: cement dengan berbentuk partikel sand atau gravel, cement sebagai matriks dan sand

  a) Metalurgi Serbuk sebagai partikel

  b) Stir Casting _{Ukuran partikel dibedakan menjadi dua, yaitu}

  c) Infiltration Process _!

  d) Spray Deposition _{a) Fraksi partikulat sangat kecil, jarang lebih dari 3%. " # $}

  e) In#Situ Process _{b) Ukuran yang lebih kecil yaitu sekitar 10#250 nm.}

  Volume Fraction

• Other examples: _{Adapted from Fig.}

  # Spheroidite particles: in Large Particle Composites

  matrix: _{10.19, % .} cementite

  steel ferrite (α) (Fig. 10.19 is _{copyright United}

  (ductile) (Fe3C) _{States Steel Corporation, 1971.)} • Elastic modulus is dependent on the volume (brittle) 60 m

  fraction _{16.4, % . Adapted from Fig.} • “Rule of mixtures” equation # WC/Co Matrix :

  particles: _{(Fig. 16.4 is courtesy} – E# elastic modulus, V# volume fraction, m# matrix, p# cobalt

  cemented WC _{Carboloy Systems,}

  particulate (ductile) Department, General

  (brittle,

  carbide _{Electric Company.)} & : hard)

  (CERMET)

  5#12 vol%! 600 m

• – upper bound _{Adapted from Fig. 16.5, % .}

  = +

  (iso#strain)

  # Automobile (Fig. 16.5 is courtesy

  matrix: particles: _{Goodyear Tire and}

  tires rubber

  C _{Rubber Company.)}

• – lower bound

  (compliant)

  =

  (stiffer)

• (iso#stress)

  0.75 m

  Bahan Komposit ! '( Rule of Mixtures

• All three material types

  Actual Values

• – metals, ceramics, and polymers
• CERMET (ceramic#metal composite)

  te la

• – cemented carbide (WC, TiC embedded in Cu

  u ix ic tr or Ni) rt a a m p # – cutting tools (ceramic hard particles to cut, but # E E a ductile metal matrix to withstand stresses) conc. of particulates – large volume fractions are used (up to 90%!)

   ! 2) Dispersion Strengthened particle Fungsi utama dari serat adalah sebagai

• Metals and metal alloys penopang kekuatan dari komposit,
• – hardened by uniform dispersion of fine particles of a very hard material (usually ceramic)

  sehingga tinggi rendahnya kekuatan komposit sangat tergantung dari serat

• Strengthening occurs through the interactions of dislocations and the yang digunakan, karena tegangan yang particulates dikenakan pada komposit mulanya diterima oleh matrik akan diteruskan
• Examples kepada serat, sehingga serat
• Thoria in Ni • Al/Al O sintered aluminum powder SAP
_{2 3}

  menahan beban sampai beban

• GP zones in Al maksimum.

  " # $ # $ Ultimate Tensile Strength (UTS) (kuat tarik

  $ $ utama), sering disingkat menjadi Tensile Strength

• Penjepit fiber (TS) atau Ultimate Strength, adalah tegangan
• Melindungi fiber dari kerusakan permukaan maksimum dimana material dapat menahan
• Pemisah antara fiber dan juga mencegah ketika sedang diregangkan atau ditarik sebelum timbulnya perambatan crack dari suatu fiber ke necking (ketika penampang spesimen mulai fiber lain

  berkontraksi secara signifikan). Kekuatan tarik

• Berfungsi sebagai medium dimana eksternal (TS) adalah kebalikan dari kuat tekan dan nilai# stress yang diaplikasikan ke komposit, nilainya bisa sangat berbeda.

  ditransmisikan dan didistribusikan ke fiber.

  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.

• Ductile

  b) Harus mempunyai tensile strength yang tinggi

• Lower E than for fiber

  Parameter fiber dalam pembuatan komposit, yaitu sebagai

• Bonding forces between fiber and

  berikut :

  matrix must be high

  a) Distribusi

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

  b) Konsentrasi

• Generally, only polymers and metals

  c) Orientasi

  d) Bentuk

  are used as matrix material (they are

  e) ukuran

  ductile)

  a. Short(discontinuous) fiber reinforced composites Aligned Random

  b. Continuous fiber (long fiber) reinforced composites

  #

  Fiber Alignment Aligned Fibers _{16.8, % . Adapted from Fig.}

• &% $
• – 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)

  aligned aligned random continuous discontinuous Berdasarkan penempatannya terdapat beberapa tipe serat pada komposit, yaitu:

  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

  c) # + $ Komposit dengan tipe serat pendek masih dibedakan lagi menjadi : 1) Aligned discontinuous fiber

  Continuous atau uni#directional, mempunyai susunan 2) Off#axis aligned discontinuous fiber serat panjang dan lurus, membentuk lamina diantara

  3) Randomly oriented discontinuous fiber matriksnya. Jenis komposit ini paling banyak digunakan.

  Randomly oriented discontinuous fiber merupakan komposit Kekurangan tipe ini adalah lemahnya kekuatan antar dengan serat pendek yang tersebar secara acak diantara antar lapisan. Hal ini dikarenakan kekuatan antar matriksnya. Tipe acak sering digunakan pada produksi dengan lapisan dipengaruhi oleh matriksnya. volume besar karena faktor biaya manufakturnya yang lebih murah.

  Kekurangan dari jenis serat acak adalah sifat mekanik yang masih dibawah dari penguatan dengan serat lurus pada jenis serat yang b) ) * + ' sama.

  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.

  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.

  ' % $ $ # (! ) *

• – $ $ # + $ % %

  $ $ $ $ # # #

• – , % -. ) /. 0
• – " $ $ # # $
• – * $ $ #
• – ' $ # # $+ # + +

  1 2 + + "$+ 3 + !

  % $ Sifat#Sifatnya

  Keuntungan :

• Biaya murah
• Tahan korosi
• Biayanya relative lebih rendah dari komposit lainnya
• 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

  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 pros
• Stabilisasi = peregangan dan oksidasi;
• Karbonisasi= pemanasan untuk mengurangi O, H,

  N; • Grafitisasi = meningkatkan modulus elastisitas.

• 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 ' # # # + # ##

  4

  5 (! &% # ! 5! & &67 ,8 # # $$ $ $ $ 4 $9 $ $ ! 2# # $ # + # $# # # $$ + % $$ # #

  9 $ % $ $$ →

  → → →

  # % $ $ # ! " # # + % # 4 $ # # % $ $ % ! + # % # $ # 4 $ $ ! % % # % $ + # # + # + # ! 7'8 % # $ # # ! " # #+ + # + # + + # + # # ! &7 8 # $ ! % 4 + + $ ! & $ # $ + + ! 5! % " Elastic Behavior Derivation Composite Strength: Longitudinal Loading _{Consider longitudinal loading of continuous fibers, with good fiber/matrix bonding.} (Longitudinal Loading)

  Estimate fiber#reinforced

  Continuous fibers # _{under these conditions matrix strain = fiber strain (isostrain condition).}

  composite strength for long continuous fibers in a _{ε = ε = ε m f c} matrix ^{The total load on the composite, F , is then equal to loads carried by the matrix and} _{the fibers c}

• Longitudinal deformation _{Substituting for the stresses} ^{F = F + F} _{c m f}

  σ σ σ σ σ σ σ σ σ σ σ σ εε ε ε ε εε ε εε ε ε : ; but : : _{Rearranging σ c c m m f f A = σ A + σ A}

  volume fraction isostrain _{were A /A and A /A are the area fractions of matrix and fibers, respectively. If the m c f c σ = σ A /A + σ A /A c m m c f f c} ^{fiber length are all equal than then these terms are equivalent to the volume}

• ∴ . = . & . & longitudinal (extensional) _fractions modulus _{and note, this model Remembering: E = σ/ε V = A /A & V = A /A f f c m m c = σ V + σ}
_V

  . & _{corresponds to the Can also show ratio of load} ^σ _{c m m f} = fiber

  = _{“upper bound” for Using the isostrain constraint and Hookes Law, σ = εE carried by fiber and matrix:}

  . & = matrix _{particulate composites F /F = E f m f f m m V /E V}

• = ^{F = F + F c f m}

  Elastic Behavior Derivation Composite Strength: Transverse Loading

  (Transverse Loading)

• In transverse loading the fibers carry less of

  Consider transverse loading of continuous fibers, with good fiber/matrix

  the load and are in a state of ‘isostress’

  bonding. under these conditions matrix strain = fiber strain (isostress condition).

  σ σ σ σ σ σ σ ε ε ε ε ε ε σ = σ = σ = σ σ σ : σ σ : σ σ : σ σ σ εε : εε ; εε m f c

  The total strain of the composite is given by ε = ε _{c m m f f} V = ε

  V

  1 & & Using Hookes Law ε = σ/E and the isostress constraint

  ∴ = +

  transverse modulus

  = (σ/E ) V + (σ/E ) V σ/E c m m f f . . .

  Dividing by σ, Algebraically this becomes Remembering: E = σ/ε and note, this model

  =

• corresponds to the “lower bound” for particulate composites

  Composite Strength An Example: Particle#reinforced

  Fiber#reinforced Structural _{UTS, SI Modulus, SI} • Estimate of . and / for discontinuous fibers: _{57.9 MPa 3.8 GPa ## valid when fiber length > 15} σ _{2.4 GPa 399.9 GPa} τ ## Elastic modulus in fiber direction: . = . & + 0 . &

  (241.5 GPa)

  efficiency factor : _{Values from Table 16.3, % .}

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

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

  ## / in fiber direction: (aligned 1D) _{(for ease of conversion)} + (/ ) = (/ ) & (/ ) &

  Note: ₂ 6870 N/m per psi!

  Composite Survey: Fiber Composite Survey: Fiber Particle#reinforced Fiber#reinforced Structural Particle#reinforced

  Fiber#reinforced Structural

• Aligned Continuous fibers Discontinuous, random 2D fibers

  Examples: Example: Carbon#Carbon

₃ C fibers: ## Metal : γ'(Ni Al)#α(Mo) ## Ceramic : Glass w/SiC fibers ## process: fiber/pitch, then very stiff formed by glass slurry by eutectic solidification. burn out at up to 2500ºC. _(b) very strong . glass = 76 GPa; . SiC = 400 GPa. matrix: α (Mo) (ductile)

  ## uses: disk brakes, gas C matrix: turbine exhaust flaps, nose less stiff view onto plane cones. _{(a) fracture} less strong _surface • Other variations: fibers lie

  ## Discontinuous, random 3D (a) _{From F.L. Matthews and R.L.} in plane _{Rawlings, 1} ## Discontinuous, 1D

  2 m _{. , Reprint ed., CRC Press, Boca Raton, FL,}

  fibers: γ’ (Ni ^{3 Al) (brittle) 2000. (a) Fig. 4.22, p. 145 (photo by} _{composites", / Vol. 19(4), pp. From W. Funk and E. Blank, “Creep deformation of Ni3Al#Mo in#situ (b) with permission of CRC Rodgers, and R.D. Rawlings). Used efficiency factor : (micrograph by H.S. Kim, P.S. J. Davies); (b) Fig. 11.20, p. 349} . = . & + 0 . & _{987#998, 1988. Used with permission. Press, Boca Raton, FL.} ## random 2D: 0 = 3/8 (2D isotropy) ## random 3D: 0 = 1/5 (3D isotropy)

  Influence of Fiber Length Influence of Fiber Length

• Mechanical properties depend>mechanical properties of the f>Critical fiber leng
• how much load the matrix can transmit to the

  l c

  fiber

• – “Continuous” fibers l >>
• – depends on the interfacial bond between the fiber 15 l _c and the ma
• – “Short” fibers are anything shorter 15 l c _No

  l = σ d/2τ c f c _{Reinforcement} where d = fiber diameter

• Critical fiber length # depends on

  τ = fiber#matrix bond _c

• fiber diameter, fiber tensile strength

  strength

• fiber/matrix bond strength σ _{f = fiber yield strength}

  Influence of Fiber Orientation Example

• Fiber parameters • Calculate the composite modulus for
• – arrangement with respect to each other

  polyester reinforced with 60 vol% E#glass

• – distribution under iso#strain conditions.
3<
• – concentration
• E polyester = 6.9 x 10 MPa
3<>E E#glass = 72.4 x 10
• Fiber orientation
• – parallel to each other
• – totally random
_{3 3} E = (0.4)(6.9x10 MPa) + (0.6)(72.4x10 MPa) c<
• – some combination
₃

  = 46.2 x 10 MPa

  

Home work Other Composite Properties

• In general, the rule of mixtures (for upper and lower bounds) can be used

  ! " ! #$ $ for any property X # thermal c

  % &amp; conductivity, density, electrical

  $ ₎ conductivityTetc. % ' ( )* * + !

  X = X V + X

  V c m m f f

  $ X = X X /(V X + V V ) c m f m f f m

  % , Tensile Strength Discontinuous Fibers

• Ali
• In longitudinal
_{∗ ∗} ^’ σ _{c = σ f}

  V f (1#l c /2l) + σ m V m for l &gt; l c direction, the _{∗ ’} σ _{c c f m m c} = (lτ /d)V + σ V for l &lt; l tensile strength is given by the

• Random

  equation below if E c = KE f V f + E m V m where K ~ 0.1 to we assume the

  0.6 fibers will fail before the matrix: _{∗ 3/8} σ σ- . / σ- . _1/5

  3. Structural Reinforced# Laminar Composites Composites

• Defini
• Two dimensional sheets or panels with a preferred high#
• – composed of both homogeneous and

  strength direction

  composite materials

• Q. What is a natural example of
• – properties depend on constituent materials this?
• A. Wood

  and on geometrical design of the elements

• Q. What is a man made example
• A. Plywood # Layers are sta
• Types

  and subsequently bonded together so that the high strength direction

• – laminar composites

  varies

• – sandwich panels

  Sandwich Panel

  Sandwich Panels

• Two strong outer sheets (called faces) separated by a layer of less dense material or core (which has lower E and lower strength)
• Core
• – separates faces
• – resists deformation perpendicular to the faces
• – often honeycomb structures
• Used in roofs, walls, wings