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Carbon fibers are manufactured by treating organic fibers (precursors) with heat and tension, leading to a highly ordered carbon structure. The most commonly used precursors include rayon-base fibers, polyacrylonitrile (PAN), and pitch.

Carbon fibers

Carbon Material

Fiber Diamet

er(m)

Tensile modul

us (GPa)

Tensile streng

th (GPa)

Density (g/cm3)

Thermal Expansi

on Coeff.

(10-6 K-1)

High modulus PAN-based 6 - 8

290 - 590

2.5 – 3.9

1.70 –1.94

-1.0 to –1.2

High strength PAN-based

5 - 8 230 - 295

3.5 – 7.1

1.76 – 1.82

-0.4 to –1.0

High modulus Pitch-based

10 520 - 830

2.1 – 2.2

2.03 – 2.18

-1.4

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PAN and Rayon (=regenerated cellulose) made from the 1970s

Pitch-based process gives better properties and lower cost

“Graphite” is an abusive term – it means: heat-treatment at T where the crystalline order is similar to graphite (> 2000°C)

The structure of graphite is anisotropic (unlike glass)

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(Note on the length of the C-C bond)

Single bondParaffinic – 1.541 ÅDiamond – 1.544 Å

Partial double bondShortening of single bond in the presence of C=C double bond (example: aromatic ring) – 1.53 ÅGraphite – 1.421 Å

Double bond – 1.337 Å

Triple bond (C2H2) – 1.204 Å

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Within each graphene plane, each C atom shares 3 strong covalent bonds with its neighbors.

Between each graphene plane, weaker VDW bonding

This is the source of anisotropy in properties

Objective of fabrication processes: to create a preferential orientation of graphitic layers parallel to the fiber axis

Conversion from a precursor to high-modulus C fiber through (generally) 3 main steps: (1) stabilization of precursor to avoid extensive volatilization or partial melting, (2) longitudinal orientation of graphite-like structure, (3) development of crystalline ordering (graphitization)

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Step 1 – Zipper reaction (cyclization or transformation into a rigid ladder) – PAN is a stable linear polymer that is stable up to 180°C

PAN (stable up to 180C)

Rigid ladder (stable up to 345C)

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Step 2 - dehydrogenation T>300°C

Thermal treatment of PAN below 400°C

Step 3 - denitrogenation600-1300°C

Leads to 2D carbon sheets

+ 2 HCN

+ 2 N2

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Two types of fibers are normally prepared from PAN:

Type I – high stiffness, low strength

Type II – high strength

Even in Type I, only 40% of the modulus of graphite crystals is achieved because of misalignment, imperfections, defects etc.

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reactive peripheralatoms

reactive peripheralatomshe0alable faults

Defects and chemical reaction possibilities on a graphite lattice

Fibre Nominal Modulus (GPa)

LM 200

MM 380

HM 750

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Fibrillar model of carbon fibreaccording to Ruland

Lamellar model of carbon in cross-section

Model of skin-core organization in type I carbon fibres

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Anisotropic Mesophase Pitch Based Process

Petroleum or coal tar pitch is converted into a highly anisotropic mesophase or liquid crystal phase through heating. Melt spinning is performed, generating high shear stresses and molecular orientation is generated parallel to the fiber axis. This is followed by stabilization in air and carbonization/graphitization

Main advantages: (1) cheaper (2) no tension is required during stabilization or graphitization (unlike PAN-based process)

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Typical pitch molecule

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Pitch Based Process

pitch purification

mesophase formation

spinning

pitch precursor fiber

stabilization

carbonization

surface treatment

sizing

carbon fiber

stabilization

graphite-like structure

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Alignment of mesophase pitch into a

pitch filament

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Pitch-basedPAN-based

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16

17

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High-modulus high-strength organic fibers

• Theoretical estimates for covalently bonded organics show strength of 20-50 GPa (or more) and modulus of 200 – 300 GPa

• Serious processing problems• New fibers developed since the early 1970s: high axial

molecular orientation, highly planar, highly aromatic molecules

• Major fibers: Kevlar (polyaramid); Spectra (PE); polybenzoxazole (PBO) and polybenzothiazole (PBT).

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N H CH2 6 NH C

O

CH2 4 C

O

C

O

N H

N H

C

O C

O

H N

N H

N H

C

O

C

O

N H

N H

C

O

Nylon 6,6

Poly(m-phenylene isophthalamide) (Nomex)

Poly(p-phenylene terephtalamide)PPT (Kevlar)

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Aramid Fibers

• Aramid (aromatic polyamide) fibers = poly(paraphenylene terephthalamide)

• Kevlar behaves as a nematic liquid crystal in the melt which can be spun

• Prepared by solution polycondensation of p-phenylene diamine and terephthaloyl chloride at low temperatures. The fiber is spun by extrusion of a solution of the polymer in a suitable solvent (for example, sulphuric acid) followed by stretching and thermal annealing treatment

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Liquid crystal Conventional (PET)

Solution

Extrusion

Solidstate

Nematic structureLow entropy Random coil

High entropy

Extended chain structureHigh chain continuityHigh mechanical properties

Folded chain structureLow chain continuityLow mechanical properties

Schematic representation of structure formationduring spinning, contrasting PPT and PET behavior

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Producing Kevlar fibers

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Phase diagram of the anisotropic solution of PPT in 100% H2SO4

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•Various grades of Kevlar fibers: Kevlar-29, 49, and 149 (Kevlar-49 is the more commonly used in composite structures)

•X-ray diffraction: the structure of Kevlar-49 consists of rigid linear molecular chains that are highly oriented in the fiber axis direction, with the chains held together in the transverse direction by hydrogen bonds. Thus, the polymer molecules form rigid planar sheets.

•Strong covalent bonds in the fiber axis direction - high longitudinal strength•Weak hydrogen bonds in the transverse direction - low transverse strength.

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•Aramid fibers exhibit skin and core structures – Core = layers stacked perpendicular to the fiber axis, composed of rod-shaped crystallites with an average diameter of 50 nm. These crystallites are closely packed and held together with hydrogen bonds nearly in the radial direction of the fiber.

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0.51 nm

Schematic diagram of Kevlar® 49 fibershowing the radially arranged

pleated sheets

Microstructure of aramid fiber

Kevlar fibers

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Kevlar - High flexibility but poor compressive

performance

Also low shear performance, moisture-sensitive, UV-sensitive

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Twaron(Akzo)

Twaron

HM

Kevlar

29

Kevlar

49

Kevlar

149

HM-50(Teijin

)

Density, g/cm3 1.44 1.45 1.44 1.44 1.47 1.39

Tensile strength, GPa 2.8 2.8 2.8 2.8 2.8 3.0

Tensile modulus, GPa 80 125 62 124 186 74

Tensile strain, % 3.3 2.0 3.5 2.5 1.9 4.2

Coefficient of thermal expansion,

10-6oC

Longitudinal:

0 to 100 oC … … -2.0 … -- …

Radial:

0 to 100 oC … … 59 … -- …

The Aramid fiber family

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Kevlar/epoxy בא

Note the fibrillar structure of the fiber

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•Little creep only

•Excellent temperature resistance (does not melt, decomposes at ~500°C)

•Linear stress-strain curve until failure

•Low density : 1.44

•Negative CTE (why? mechanism?)

•Fiber diameter = 11.9 micron

•Fiber strength variability

Kevlar fiber

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Polyethylene fibers

The theoretical elastic modulus of the covalent C-Cbond in the fully extended PE molecule is 220 Gpa.

Experimental value in PE fibres - 170 Gpa.

Stretching

Entanglement network Fibrillar crystal

Dyneema or SpectraOrientation > 95%Crystallinity up to 85%

Normal PEOrientation lowCrystallinity < 60%

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Extended chain polyethylene

minimum chain folding

UHMPE fibre structure: (a) macrofibril consists of array of microfibrils;(b) microfibril; (c) orthorhombic unit cell; (d) view along chain axis

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•UHMWPE (Spectra or Dyneema) are highly anisotropic fibers

•Even higher specific properties than Kevlar because of lower density (0.98 g/cc)

•Limited to use below 120°C

•Creep problems; weak interfaces

•Applications – ballistic impact-resistant structures (however: very large strains are undesirable in ballistic applications)

UHMWPE

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UHMWPE (Spectra) – high flexibility and toughness, poor

interfacial bonding

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Poly(p-phenylene benzobisthiazole)

PBT or PBZT

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SiC

Cl Si Cl

CH3

CH3

n

Si

CH3

CH3

Si

CH3

CH3

Si

CH3

CH3

DimethylchlorosilaneNa

reaction

polysilane

polymerization

polycarbosilane

spinning

unfusing treatment

carbonization

SiC fiber

Na

+

CH3 CH3

Si

CH3

Si

CH3

CH3

SiH

CH3

CH3

Si

CH3

CH3

Si

CH3

CH3

Si

CH3

CH2

CH3

Si

CH3

CH2n

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39

40

41

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Kevlar

Spectra

Flexibility, compressibility, and limit performance of fibers

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FLEXIBILITY

Intense bending strains and stresses applied to fibers during manufacturing operations (weaving, knitting, filament winding, etc)

Definition of flexibility:

Bending of an elastic beam: M = (EI)/R = (EI)

Units: [N/m2][m4]/[m] = [N*m]

M = bending moment

I = second moment of area of cross-section

R = radius of curvature to the neutral surface of cross-section

dAyI 2

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E = Young’s modulus

EI = flexural rigidity (≈ resistance of beam to bending)

= curvature = 1/R

Intuitively: the flexibility of a fiber is the highest when:

o The radius of curvature is as small as possible (or the curvature is as large as possible)

o The bending moment necessary to reach a given curvature is as small as possible

o The appropriate parameter to focus on is = /M = 1/EI, which must be maximized for highest flexibility.

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b

hM M

12

3bhI

64

4dI

MM d

Moment of inertia

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Flexibility is thus defined as (for a circular fiber)

where E and d are the fiber bending modulus and diameter, respectively

As seen, the effect of size (diameter) on flexibility is dominant, and thus nanoscale reinforcement promotes high flexibility. Low modulus also promotes high flexibility.

Units of flexibility are [1/Nm2]

464 dE

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ASSUMING A CONSTANT DIAMETER:

material d (m) E (Pa) [N-1m-2]

E-glass 1.00E-05 72.0 E+9 28 E+9max

HM carbon 1.00E-05 750 E+9 2.7 E+9 min

HS carbon 1.00E-05 250 E+9 8.2 E+9

Kevlar 49 1.00E-05 130 E+9 16 E+9

Nicalon 1.00E-05 190 E+9 11 E+9

(Steel) 1.00E-05 210 E+9 9.7 E+9

Performing a ‘gedanken’ experiment:

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Using real diameters and moduli:

USING REAL DIAMETERS AND MODULI:

material d (m) E (GPa) [N-1m-2]

E-glass 1.10E-0572.0 E+9 19 E+9

HM carbon 8.00E-06 750 E+9 6.6 E+9

HS carbon 8.00E-06 250 E+9 20 E+9 max

Kevlar 49 1.20E-05 130 E+9 7.6 E+9

Nicalon 1.50E-05 190 E+9 2.1 E+9 min

SWNT 1.10E-091200 E+9

1.16E+25 !

Glass fibers are thus much more tolerant to bending than HM carbon fibers or even kevlar 49.

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Flexibility of carbon nanotubes

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Compressibility

• The compressive strength of single fibers is very difficult to measure and is usually inferred from the behavior of composites including the fibers.

• Euler buckling is one possible mode of compressive failure: it occurs when a fiber under compression becomes unstable against lateral movement of its central region. Displacements are relatively small.

• When displacements grow very large: theory of the elastica

• NOTE: All the following methods can be used to measure the (bending) Young’s modulus of a fiber (or a long & thin beam)

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Definitions: • ℓ – length of the bar• EI – flexural rigidity of the bar• P – load• A – area of cross section of

the bar

1. Small deflections - Euler buckling of slender bar

xδ

Y

P

REDRAW THIS !!

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Assumptions:

a) The stress is below proportional limit

b) The deflection δ is (relatively) small

Objective: to find the minimum load at which the beam bends sidewise.

Equation to solve:

)(2

2

yPdx

ydEI δ

curvatureBending moment

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After solving and applying specific boundary conditions the following result is obtained:

2

2

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EI

Pcr

Dividing by the cross-sectional area and substituting r (radius of gyration, which for a hollow cylinder, taken as an example, is the radius of the cylinder), the critical stress is:

A

Ir

2

2

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/ r

E

A

Pcrcr

thus

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EIkPcr 2

2

EULER’s THEORY OF BUCKLING

A long and slender column has a low critical stress, whereas a short and broad column will buckle at a high stress.

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2. Large deflections – The Elastica

x

yP

θ

s

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• For small deflections, an approximate expression for the curvature of the bar was used (d2y/dx2). For large deflections, it is necessary to introduce the exact expression for the curvature of the bar: dθ/ds (s is the distance along the bar, θ is the deflection angle at each point).

• Equation to be solved:

• After solving and applying boundary conditions the following result is obtained:

Pyds

dEI

θ

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2

2)(4

l

EIpKPcr

where p = sin(/2) ( is the deflection at the upper end of the bar) and K(p) is the complete elliptic integral of the first kind (values are tabulated numerically in handbooks).

Note: In the previous (Euler, small deformations) solution the bar could have any value of deflection, provided the deflection remained small. Now we have a connection between the load and the deflection. At small values of (small deflections) the solution approaches the critical load given by Euler solution.

The stress is:

2

2

/

)(

rl

EpK

A

Pcrcr

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Cantilever

xδ

Y

P

3

3

EI

Pδ

(small deflections)