slides on composites

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MSE 280: Introduction to Engineering Materials

I ddReading: Callister Ch. 15

CompositesIssues to address… • What are composites?• Classification of composites.• Why composites?

MSE280© 2007, 2008 Moonsub Shim1

• Mechanical properties of composites.• Applications.

Composites: definition & examples- Multiphase materials with chemically different phases and distinct interfaces.

- Properties of the resultant combination of materials are- Properties of the resultant combination of materials are superior to the properties of the individual components.

- Advantages: High-strength/light-weight, low cost, environmentally resistant…

- Natural composites:-Wood: strong & flexible cellulose fibers in stiffer lignin (surrounds the fibers).B t b t ft ll ( t i ) ithi h d b t b ittl tit


-Bone: strong but soft collagen (protein) within hard but brittle apatite (mineral).-Certain types of rocks can also be considered as composites.

-Synthetic composites: fiberglass, concrete, carbon-carbon composites….

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Bicycle forksBraided and

High Strength

unidirectional S-2 Glass and carbon fibers are used to produce forks with different stiffness


High StrengthWeight ReductionDesign FlexibilityCost Performance

From http://matse101.mse.uiuc.edu/

Lightweight - low density

Pole-vaultingg t e g t o de s ty

Buckling resistance - stiffness Strong - yield strength Minimal twisting Cost


Glass fiber web/epoxy Glass fiber ringsLongitudinal carbon fibers/epoxy


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Boeing 757-200Rudder (graphite) Fixed trailing edge

panels graphiteFlap support fairings Fwd segment (graphite/Kevlar

Aft flaps Outboard (graphite) Inboard (graphite/fiberglass)

Fixed trailing edge panels Graphite/Kevlar + non-woven

Fixed trailing edge panels upper (graphite /fiberglass), lower (graphite /Kevlar + non-woven Kevlar mat)

Elevators (graphite)

Auxiliary power inlet

graphiteEnvironmental control system ducts (Kevlar)

Engine strut fairings (Kevlar/fiberglass)

Ailerons (graphite)

Tip fairings (fiberglass)

panels graphite /Kevlar + non-woven Kevlar mat)

Fwd segment (graphite/Kevlar + non-woven Kevlar mat Aft segment (graphite/fiberglass)


Wing leading edge lower panel Kevlar/fiberglass

Kevlar matSpoilers (graphite)

Cowl components (graphite)

Body main landing gear doors (graphite) Trunnion fairings and wing landing gear doors (graphite/Kevlar) Brakes( structural carbon)

Wing to body fairings (graphite/Kevlar/Fiberglass and Graphite/Kevlar + non-woven Kevlar mat

Nose landing gear doors (graphite)


Terminology• Matrix:

– softer, more flexible and continuous part that surrounds the other phase.– transfer stress to other phases– protect phases from environment

• Reinforcement (dispersed phase):– stiffer, high strength part (particles or fibers are the most common).– enhances matrix properties

C fibers: very stiff very strongC matrix:


fibers lie in plane

view onto plane

C matrix: less stiff less strong

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Composite characteristicsDepends on:

- properties of the matrixconcentration size shapeproperties of the matrix

material.

- properties of reinforcement material.

- ratio of matrix to reinforcement. distribution

orientation


- matrix-reinforcement bonding/adhesion.

- mode of fabrication.

Classification of Composites• Matrix-based:

– Metal Matrix Composites (MMC)Metal Matrix Composites (MMC) – Ceramic Matrix Composites (CMC)– Polymer Matrix Composites (PMC)


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• CMCs: Increased toughness • PMCs: Increased E/ρ

E(GPa)10 210 3

PMCs

ceramicsparticle-reinf

Force

COMPOSITE BENEFITS

10-46061 Al1

G=3E/8K=E

Density, ρ [Mg/m 3].1 .3 1 3 10 30

.01.1

110

10metal/ metal alloys

polymers

fiber -reinf

un-reinf

Bend d isplacement


• MMCs:Increasedcreepresistance

20 30 50 10 0 20010-10

10-8

10-66061 Al

6061 Al w/SiC whiskers σ(MPa)

εss (s -1 )Adapted from T.G. Nieh, "Creep rupture of a silicon-carbide reinforced aluminum composite", Metall. Trans. A Vol. 15(1), pp. 139-146, 1984. Used with permission.

From Callister resources CD

Reinforcement-based

dparticle>100nm

dparticle< 100nm


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Particle-reinforced Fiber -reinforced Structural• Examples:

-Spheroidite matrix: particles: Adapted from Fig.

COMPOSITE SURVEY: Particle-I

p steel ferrite ( α)

(ductile)cementite(Fe 3C) (brittle)

-WC/Co cemented carbide

matrix: cobalt (ductile)

particles: WC (brittle, hard)

60 μm

Vm:

10.10, Callister 6e. (Fig. 10.10 is copyright United States Steel Corporation, 1971.)

Adapted from Fig. 16.4, Callister 6e. (Fig. 16.4 is courtesy Carboloy Systems, Department, General Electric Company )


hard)

-Automobile tires

matrix: rubber (compliant)

particles: C (stiffer)

Vm: 10-15vol%! 600 μm

0.75 μm

Electric Company.)

Adapted from Fig. 16.5, Callister 6e. (Fig. 16.5 is courtesy Goodyear Tire and Rubber Company.)


• Elastic modulus, Ec, of composites:two approaches

Fiber -reinforced StructuralParticle-reinforced

COMPOSITE SURVEY: Particle-II

-- two approaches.

Data: Cu matrix w/tungsten particles

15020 025030 0350

E(GPa)

lower limit:1

Ec= Vm

Em+

VpEp

c m m

upper limit:E = V E + VpEp

“rule of mixtures”

Adapted from Fig. 16.3, Callister 6e. (Fig. 16.3 is from R.H. Krock, ASTM Proc, Vol. 63, 1963.)


• Application to other properties:-- Electrical conductivity, σe: Replace E by σe.-- Thermal conductivity, k: Replace E by k.

0 20 40 60 80 10 0 vol% tungsten(Cu) (W)


Analogy to resistors in series vs. parallel…

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Fiber-reinforced composites


Continuous & aligned

Discontinuous & aligned

Discontinuous & random

Fiber-reinforced compositesThe Fiber Phase

Smaller diameter fiber is stronger than bulk in most materials ( i ll b i l ) Wh ?(especially brittle ones). Why? Flaws!

Whiskers:• very thin single crystals that have extremely large aspect ratios.• high degree of crystallinity and virtually flaw free – exceptionally high strength.• usually extremely expensive.• some whisker materials: graphite, SiC, silicon nitride, aluminum oxide.Fibers:


Fibers:• polycrystalline or amorphous.• typically: polymers or ceramics (polymer aramids, glass, carbon, boron, SiC…Fine Wires:• relatively large diameter, often metal wires.• e.g. steel, molybdenum, tungsten…

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Fiber-reinforced compositesThe Matrix Phase• can be metal polymers or ceramics• can be metal, polymers, or ceramics.

• typically metals and polymer because some ductility is often desired.

• main functions of the matrix:

-Hold fibers together.

-Transmit and distribute external stress to the fibers.


-Protect fibers from surface damage: abrasions, chemical reactions…

• in CMCs, reinforcements are usually added to improve fracture toughness .


1. Molecular entanglement (interdiffusion):• Entanglement of molecules at the interface.

The Fiber-Matrix Interface

Entanglement of molecules at the interface.• Especially important in fibers that are pre-

coated with polymers.• Molecular conformation/structural and

chemical aspects.2. Electrostatic attraction

• Depends on surface charge density.• e.g. glass fibers, polymers with chargeable

groups.3. Covalent bonding

• Usually the strongest fiber matrix

+ + + + + + + - - - - - - -

- - - - - - -+

-

+

-

+

-

+

-

+

-

+

-


• Usually the strongest fiber-matrix interaction.

• The most important in many composites.4. Mechanical adhesion

• Interlocking of 2 rough surfaces• e.g. thermosetting resins

AB

AB

AB

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Fiber-reinforced compositesProperties depend on LENGTH and ORIENTATION of the fibers (as well as isolated properties of each of the components)!

*Critical fiber length

c

fc

dl

τσ2

*

==fσ Fiber tensile strength

=d Fiber diameter

=cτ Smaller of:• fiber-matrix bond strength• matrix shear yield strength.

Possible failure modes:

Continuous when fiber length >> lcDiscontinuous when fiber length < 15 lc


1) fiber breaking.2) matrix breaking.3) fiber pullout (interface between fiber and matrix fails)


σ(x)σ(x)

Short fibersLong fibers


Poorer fiber efficiency Better fiber efficiency

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Aligned fibers

Elastic Modulus

Continuous when fiber length >> lcDiscontinuous when fiber length < 15 lc

Not so detrimental since:1) Not all fibers fail at the same time2) Matrix still intact

E

0o


0o 90o

σ

max min

Aligned Continuous fibersFiber-reinforcedParticle-reinforced Structural

COMPOSITE SURVEY: Fiber-I

• Examples:

fracture surface

matrix: α (Mo) (ductile)

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

--Glass w/SiC fibersformed by glass slurryEglass = 76GPa; ESiC = 400GPa.

(a)


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

surface

fibers: γ’ (Ni3Al) (brittle)

2μm From F.L. Matthews and R.L. Rawlings, Composite Materials; Engineering and Science, 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 CRCPress, Boca Raton, FL.

(b)


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Continuous-aligned fibersConsider a composite with fibers having square rod geometry with stress in the longitudinal direction…

fiber

L

B

B

Matrix

b

l

σ σ

When l >> l (typically l > 15 l ) we can simplify to:


b

When l >> lc (typically l > 15 lc), we can simplify to:

σ σB

l thenl

Ll

Ll

L matrixfibercomposite Δ=

Δ=

Δ

since ,lLΔ

≡ε matrixfibercomposite εεε ==

ISOSTRAIN

Continuous-aligned fibersWhat about elastic modulus? σ σ

B

l

Total force on the composite is simply the sum of

Longitudinal loading

b

fibermatrixcomposite FFF +=Total force on the composite is simply the sum of forces on matrix and fibers:

sinceAF

=σ or , we have: AF σ= ffmmcc AAA σσσ +=

Recall stress-strain relation: εσ E= Sub-in for stresses…

AEAE


fffmmmccc AEAEAE εεε +=

Imposing isostrain condition ,mfc εεε ==cc

fff

cc

mmmc A

AEA

AEEεε

εε

+=rearrange

c

ff

c

mmc A

AE

AAEE +=

“Area fractions”Prefer volume fractions….

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Continuous-aligned fibers

σ σB

l

Total area = Bb

Af = number of fibers x area of each fiber = Nb2


bThen we have:

BNb

AA

c

f = Also,

BNb

AA

AAor

AAA

c

f

c

m

fcm

−=−=

−=

11For volume fractions:

lNbV

BblV

f

c2=

=


Then:c

f

c

ff A

AB

NbBbl

lNbVV

v ====2

same as “area fraction”

c

mm A

Av =Similarly, ffmmcl EvEvE +=Longitudinal elastic modulus(upper bound for Ec)


σ σB

l

?fFWhat about the load on the matrix and the fibers?


b?=m

f

F AF σ=

mm

ff

mm

ff

m

f

vv

AA

FF

σσ

σσ

==

With εσ E=


mmm

fff

m

f

vEvE

FF

εε

=Isostrain conditions

mm

ff

m

f

vEvE

FF

=

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Continuous-aligned fibersσ

B

lTransverse loading

Stress, rather than strain, is the same in this case:

b

σ

B

mfc σσσ == ISOSTRESS condition

The total elongation will be the sum of elongation of the components:

mfc LLL Δ+Δ=Δ

mfcc L

LLL

LL Δ

+Δ

=Δ

=ε Where Lc = length of the composite along the direction of stress = BStrain =


ccc LLL along the direction of stress B

Again, to express in terms of volume fractions:

BNb

LL

NbL

c

f

f

=

=

Same as what we derived for volume fraction

fv=Rearrange

f

fc v

LL = Similarly,

m

mc v

LL =


B

lTransverse loading

mfcc L

LLL

LL Δ

+Δ

=Δ

=ε

b

σ

B

m

mm

f

ff

mm

m

ff

f

LLv

LL

vvL

LvL

L Δ+

Δ=

Δ+

Δ=

//

ccc LLL

fε mε

ffmmc vv εεε +=Lower bound for E


From stress-strain relation;Eσε =

f

ff

m

mm

c

c

Ev

Ev

Eσσσ

+=

Applying isostress condition and rearranging gives mffm

fmct EvEv

EEE

+=

Lower bound for Ec(transverse modulus)

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B

lMany properties follow these upper and lower bound relations for continuous-aligned fiber composities.

b

BIn general:

ffmmupperccl vv χχχχ +==


mffm

fmlowercct vv χχ

χχχχ

+==

Continuous-aligned fibers: example1. Calculate the longitudinal and transverse modulus and

thermal conductivity for polyester reinforced with 60% volume fraction of glass fiber (E-glass).volume fraction of glass fiber (E glass).

2. Calculate longitudinal specific stiffness.

3. Calculate the percentage of the load on the fibers for longitudinal loading.


E(GPa) K(W/mK) Specific gravity

Polyester 6.3 0.17 1.46

E-glass 72.4 0.97 2.58

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Continuous-aligned fibers: example Mixed Fibers

• A two-fiber composite (continuous aligned) i d f th f ll i tis composed of the following components.

E(GPa) Vol. fraction

Kevlar fiber 131 30%

E-glass fiber 72.5 20%

Epoxy matrix 2.41 50%


• Calculate the longitudinal elastic modulus.


B

l

Tensile strengthTensile strengthLongitudinal: *'*

ffl vv σσσ +=

Similar to elastic modulus

bffmmcl vv σσσ +This is assuming that the fiber fails prior to the matrix.

='mσ Stress in the matrix at failure

=*fσ Tensile strength of the reinforcement fiber

Transverse: more complex due to many factors that affect it(e.g. matrix & fiber properties, fiber-matrix bond strength,

presence of voids etc…)


In general, stronger along longitudinal direction

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Discontinuous & aligned fibersDiscontinuous when fiber length < 15 lc

If l > lc

mmc

ffcd vl

lv '**

21 σσσ +⎟

⎠⎞

⎜⎝⎛ −= Similar to continuous case,

except for the length factor.

If l < l


mmfc

cd vvd

l '*' στσ +=

=cτ Smaller of:• fiber-matrix bond strength• matrix shear yield strength.

If l < lc

Discontinuous, random 2D fibers• Example: Carbon-Carbon

--process: fiber/pitch, then

C fibers: very stiff very strong

Discontinuous & random fibers

burn out at up to 2500C.--uses: disk brakes, gas

turbine exhaust flaps, nosecones. fibers lie

in plane

view onto plane

y gC matrix: less stiff less strong

(b)

(a)

Ec = EmVm + KEf Vf



efficiency factor (depends on vf and Ef/Em):--aligned 1D: K = 1 (anisotropic)--random 2D: K = 3/8 (2D isotropy)--random 3D: K = 1/5 (3D isotropy)

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Polymer matrix composites• Glass fiber-reinforced

polymer (GFRP) it fib lcomposites: fiberglass

– Some reasons for using glass as fibers:

• Easy to draw fibers from molten state.

• Strength.• Readily available/economic.• Chemical inertness (e.g.

non-corrosive).


)– Applications: automotive &

marine bodies, storage containers, industrial flooring…

Polymer matrix composites• Carbon fiber-reinforced polymer (CFRP)

composites:composites:– Some reason for using C-fibers:

• Highest specific modulus and specific strength of all reinforcing fiber materials.

• Retain high modulus and TS at elevated T (chemical oxidation may be a problem).

• At or near RT, very inert.• Can engineer specific mechanical and physical properties


• Can engineer specific mechanical and physical properties.– Some applications: fishing rods, golf clubs, bicycles,

military and commercial aircraft structural components…

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Polymer matrix composites• Aramid (e.g. Kevlar) fiber-reinforced polymer composites:

– High strength, high modulus.Much better strength to weight than metals– Much better strength-to-weight than metals.

– Stable to relatively high T (high mechanical properties maintained from ~ - 200 to 200oC).

– Relatively inert chemically (except strong acids).– Uses: bullet-proof vests, tires, ropes, missile cases, parts for automotive

brake, clutch lining and gaskets…


Carbon-carbon composites• Carbon fiber reinforced carbon matrix

composites.p– High modulus & TS (retained to T > 2000oC).– Resistant to creep.– Large fracture toughness.– Small thermal expansion coefficient.– High thermal conductivity.– Uses: rocket motors, friction material for aircraft and

hi h f t bil b k t f


high-performance automobile brakes, components for turbine engines…

– Very expensive mainly due to relatively complex processing.

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Carbon nanotube composite

Carbon matrixMaterial Young’s Modulus

Aluminum 72 GPa

1μm

Aluminum alloys

72 GPa

Steel 200 GPa

Tungsten 400 GPa

Carbon Nanotube

>1000 GPa


Ajayan et al.

Nanotube bundles

Processing of fiber-reinforced composites

Pultrusion

Prepreg production process


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Processing of fiber-reinforced composites

Filament winding


Design exampleF

Requirements - at F = 890N, deflection < 0.33mm

- Circumferential winding with θ = 15o

A) Which fiber(s), if embedded in epoxy matrix, meet the these criteria?

B) D id th t t ff ti fib


B) Decide on the most cost-effective fiber.

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Concepts to remember…• Matrix & reinforcement.• What composite characteristics depend on.

Cl ifi ti t i b d MMC CMC PMC• Classification: matrix-based – MMC, CMC, PMC; reinforcement-based.

• Particle reinforced composites: upper and lower bound for E (rule of mixtures).

• Fiber-reinforced composites– Continuous-aligned, discontinuous-aligned &

discontinuous-random cases.C i i l l h


– Critical length.– Longitudinal & transverse properties.– Isostrain & isostress cases.

• Structural composites.

slides on composites

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