Lecture on Nanocomposites

1

Properties and Applications of Composites & Nanocomposites

PSCI 640 Elements of Nanosciences, November 9, 2009

Arya EbrahimpourProfessor, Civil and Environmental Engineering

Properties and Applications of Composites & Nanocomposites 2

Outline of the Lecture

Introduction Engineering Properties of Materials Composite Materials Carbon Molecules Nanocomposites Applications of Nanocomposites & Smart

Materials

Will use PowerPoint and the board


Introduction

Predictions involving applications of nanotechnology (Booker & Boysen): By 2012 significant products will be available

using nanotechnology (medical applications including cancer therapy and diagnosis, high density computer memory, …)

By 2015 advances in computer processing By 2020 new materials and composites By 2025 significant changes related to energy


Engineering Properties of Materials

Normal stress is the state leading to expansion or contraction. The formula for computing normal stress is:

Where, is the stress, P is the applied force; and A is the cross-sectional area. The units of stress are Newtons per square meter (N/m2 or Pascal, Pa). Tension is positive and compression is negative.

Normal strain is related to the deformation of a body under stress. The normal strain, , is defined as the change in length of a line, L, over it’s original length, L.

A

P

L

L

PP

L L

A


Engineering Properties, cont. Young's modulus of elasticity (E) is a measure of the stiffness of

the material. It is defined as the slope of the linear portion of the normal stress-strain curve of a tensile test conducted on a sample of the material.

Yield strength, y, and ultimate strength, u, are points shown on the stress-strain curve below.

For uniaxial loading (e.g., tension in one direction only): = E

1

E

Stress

Strain,

u

y

Rupture


Engineering Properties, cont.

Shear stress, , is the state leading to distortion of the material (i.e., the 90o angle changes). The corresponding change in angle, in Radians, is called shear strain, . The slope of the linear portion of the -is called shear modulus of elasticity, G.

1

G

Stress

Strain,



Poisson’s ratio, , is another property defined by the negative of the ratio of transverse strain, 2, over the longitudinal strain, 1, due to stress in the longitudical direction, 1.

2

11

Original shape

11

2

1

212


Engineering Properties, cont. Isotropic Materials have properties that do not depend on the

orientation of the coordinate system (xyz). That is,

E1 = E2 = E3, G23 = G31= G12, & 12 =21 =13 =31 …

Isotropic materials can be fully described with only two (2) of the three material constants (E, G, and ).

Examples of isotropic materials: steel, aluminum, …

1

2

3

)1(2 E

G



Anisotropic materials have different properties in different directions. In the most general case, they are defined by 21 independent constants. Special cases include: Orthotropic: wood and some composites Transversely isotropic: some continuous fiber reinforced

composites

Fibers


Engineering Properties, cont. Stresses and Strains in 3D:

Knowing that ij = ji, we have six independent stresses:

1, 2, 3, 23, 31 , and 12

For shear stresses, the first index is theplane number and the second is the direction.

Stresses in terms of strains or vice versa are given by:

Where, [C] is the stiffness matrix and the [S] is the compliance. matrix. Vectors {} and {} represent both normal and shear stresses and strains, respectively.

S

C

A 3D stress element


Engineering Properties, cont. Stresses in terms of strains:

Strains in terms of stresses:


Composite Materials

Composites consist of two or more materials in a structural unit. There are four types: Fibrous composites (fibers in a matrix)

Continuous fibers, woven fibers, chopped fibers Laminated composites (layers of various

materials) Particulate composites Combinations of some or all of the above


Composite Materials, cont. Engineering Applications: Composite materials have been used in

aerospace, automobile, and marine applications (see Figs. 1-3). Recently, composite materials have been increasingly considered in civil engineering structures. The latter applications include seismic retrofit of bridge columns (Fig. 4), replacements of deteriorated bridge decks (Fig. 5), and new bridge structures (Fig. 6).

Figure 1 Figure 2 Figure 3

Figure 4 Figure 5 Figure 6


Composite Materials, cont. Medical Applications: Stents are made with steel and more

recently with polymers with shape memory effects (Wache, et al.). The material is deformed within a temperature range of glass

transition temperature (Tg) of amorphous phase and melting temperature (Tm) of crystalline phase, then was cooled below Tg. After the material was reheated between Tg and Tm, the original structural shape was recovered. High dosage (up to 35% by weight) and at a high rate of release of medication were noted in this study.


Composite Materials, cont.

Fabrication Process

Open mold, hand lay-up Open mold, spray-up

Pultrusion process Roll-forming process



Fabrication Process Sheet-molding compounds (SMCs) are used extensively

in the automobile industry.

Machine for producing SMCs Compression molding process



Lamina: Basic building block of a laminate consisting of fibers in a thin layer of matrix.

Laminate: Bonded stack of laminae (plural of lamina) with various orientations.

Note: Unlike metals, with composites we can design the structure and the material that goes with it.



Glass fiber versus bulk glass:Strength Ratio = 3400/170 = 20

Griffith’s measurement of tensile strength as a function of fiber thickness (Gordon, J.E., The New Science of Strong Materials, 1976)

3400 MPa

170 MPa

< 1m



Behavior of orthotropic vs. anisotropic materials:In orthotropic (and special case of isotropic) materials, shear-extension coupling (SEC) and shear-shear coupling (SSC) terms are zero. That is, if you pull on the material, it will not distort.

For example, for an orthotropic material, if we let all stresses other than 1 be zero, then we have no shear strain, 12, as shown below:

= S161 + S26 2 + S36 3 + S4623 + S5631 + S6612 = S161 = 0



Taking advantage of coupling in composites: In the forward-swept wings of Grumman X-29 aircraft, bending and twisting coupling was used to eliminate the aerodynamic divergence (gross wing flapping that tears off the wings).



Orthotropic material compliance matrix can be expresses in terms of the previously defined materials properties Ei, Gij, and ij .

Note that the SEC and SSC terms are zero.

SEC

SSC3,2,1, ji

EE j

ji

i

ij

Because of symmetry, of the matrix, we have:



Example 1: Given: The unidirectionally-reinforced glass-epoxy lamina shown has the following properties: E1 = 53 GPa, E2 = 18 GPa, 12 = 0.25, G12 = 9 GPa. The load P is applied in the 1-direction. Note: This lamina is orthotropic.

Find:

a. Determine strains 1 and 2 under the force P.

b. What are reasonable values for E3 and 13?

c. Based on the values in Part (b), find 3.

d. What are the final dimensions of the lamina?



Predicting stiffness E1 using Rule of Mixtures

mmff VEVEE 1

)1 :(Note

matrix andfiber of fractions Volume and

matrix andfiber of elasticity of Modulus and

,Where

mf

mf

mf

VV

VV

EE



Predicting stiffness E1

Load sharing is analogous to a set of springs in parallel (see figure on the left)

Figure on the right shows the predicted vs. measured values



Predicting stiffness E2

fmmf

mf

VEVE

EEE

2



Predicting stiffness 12 and G12

mmff VV 12

fmmf

mf

VGVG

GGG

12

matrix andfiber of elasticity of modulusShear and

matrix andfiber of ratios sPoisson' and

,Where

mf

mf

GG



Example 2: Given: A unidirectional carbon/epoxy has the following properties:

Ef = 220 GPa, Em = 4 GPa, and Vf = 0.55

Find: a. Estimate the value of the composite longitudinal modulus E1

b. Estimate the value of the composite transverse modulus E2

c. If fiber Poisson’s ratio f = 0.25 and m = 0.35, find the lamina 12

d. Assuming that the fiber and the matrix behave individually as

isotropic materials, estimate G12

e. What Vf is needed to obtain composite E1 that matches stiffness

of aluminum (E = 69 GPa)?



Predicting Composite strength Function of individual stiffness, strength, and strain values at the

points of failure

Will go over an example, if time permits.


Carbon Molecules

Graphite versus Diamond Graphite: Used as lubricant and pencil lead is composed

of sheets of carbon atoms in a large molecule. Only weak van der Waals’ forces hold the sheets together. They slide easily over each other.

Diamond: Carbon atoms stacked in a three-dimensional array (or lattice), giving a very large molecule. This gives diamond its strength.

Graphite sheets Diamond structure


Carbon Molecules, cont.

Graphite sheet is a molecule of interlocking hexagonal carbon rings. Each carbon bonds covalently with three others, leaving one electron unused. The orbital for these “extra” electrons overlap, allowing electrons to freely move throughout the sheet. This is why graphite conducts electricity.

Structure of a sheet of graphite



Buckyballs were discovered by Smalley (Rice University), Kroto and Curl in 1985 by vaporizing carbon with a laser and allowing carbon atoms to condense.

A buckyball is short for buckmisterfullerene after Buckminster Fuller, an American architect and engineer, who proposed an arrangement of pentagons and hexagons for geodesic dome structures.

It has 60 carbon atoms in a ball shaped with 20 hexagons and 12 pentagons and has a diameter of about one nanometer.

A buckyball



In 1991, carbon nanotubes (CNTs) were discovered by Sumio Iijima of NEC Research Lab. After taking pictures of buckyballs in an electron microscope, he noticed needle shaped structures (i.e., cylindrical carbon molecules).

Single-wall carbon nanotubes (SWNTs) versus multiwalled carbon nanotubes (MWNTs)

The length of CNTs vary, but the smallest diameter seen in SWNTs is about one nm.

A single-walled carbon nanotube



A scanning electron microscope (SEM) image of a CNT hanging off the tip of an atomic force microscope (AFM) cantilever.

CNT



Strength (u), stiffness (E modulus), and density of common materials

Material Tensile Strength (MPa)

Tensile Modulus (GPa)

Density (g/cm3)

6061 Aluminum (bulk) 310 69 2.71

4340 Steel (bulk) 1,030 200 7.83

Nylon 6/6 (polymer) 75 2.8 1.14

Polycarbonate (polymer) 65 2.4 1.20

E-glass fiber 3,448 72 2.54

S-2 glass fiber 4,830 87 2.49

Kevlar 49 aramid fiber 3,792 131 1.44

T-1000G carbon fiber 6,370 294 1.80

Carbon nanotubes 30,000 1,000 1.90

From: Gibson, R.F., 2007


Nanocomposites, cont. Nanofibers and MWNTs: hollow tubular geometries with aspect

ratios (L/d) ranging in the thousands.

10 m

Scanning electron microscope image of vapor-grown carbon nanofibers in a polypropylene matrix

300 nm

Image of MWNTs in a polystyrene matrix

Material Diameter

(nm)

Length

(nm)

Young’s Modulus

(GPa)

Tensile Strength

(GPa)

Vapor-grown carbon nanofibers 10-200 30,000-100,000 400-600 2.7-7.0

SWNT ~ 1.3 500-40,000 320-1470 13-52

From: Gibson, R.F., 2007


Nanocomposites, cont. Challenge: Unlike fibers in conventional laminates, waviness

of the nanotubes and nanofiber reinforced materials complicates the material property calculations. Representative volume elements (RVEs) may be modeled as shown below:

Waviness is defined by the waviness factor,NTL

Aw


Nanocomposites, cont.

Predictions of the Young’s modulus of elasticity: The modulus of the RVE2 (the right diagram in the previous

page), Ex= ERVE2, and the effective modulus for randomly oriented nanotubes, E3D-RVE2, have complex formulas, but are both are functions of the waviness factor. E3D-RVE2 as functions of nanotube volume fraction and w, is shown below.



Combinations of nanoparticles and conventional continuous fibers:

Nanoparticle reinforced matrix

Conventional continuous fiber



Example 3: Given: A unidirectional carbon/epoxy lamina with Ef = 220 GPa, Em = 2 GPa, and Vf = 0.55 is also reinforced with randomly placed carbon nanotubes with volume fraction, VNT, equal to 25% of the matrix. Assume nanotube waviness factor of 0.05.

Find:

a. Estimate the value of the composite longitudinal modulus E1

b. Estimate the value of the composite transverse modulus E2

Hint: Use the given graph of E3D-RVE2 in place of the complicated formulas.



Strength prediction: In general, relations for predicting strength are complex. However, for randomly oriented fibers, an approximate equation may be used to estimate the tensile strength, as follows (Gibson, 2007):

strength tensilee transvers

strain failurefiber the toingcorrespond stressmatrix

strenghtshear

strenght tensilecomposite~Where,

T

mf

LT

x

S

S

S

2ln1

2~LT

mfT

mf

TLTx S

SS

S

SS


Applications of Nanocomposites & Smart Materials

Shape Memory Alloys (SMAs) are used in reconstructive surgery where sustained pressure is needed for faster healing process. Nickel and Titanium alloy developed by Naval Ordinance Laboratory (named Nitinol).

Shape memory phase changesSMA plate connected to a jaw bone



Tether between two space outposts for providing artificial gravity (Scientific American)



Carbon nanotube reinforced polymer composites for structural damping Application: large amplitude vibrations of space structures

Damping loss modulus values for polycarbonate with and without nanotube fillers (Ajayan, et al, 2006)


References University of Alberta’s Smart Material and Micromachines web site

(November 6, 2007), available from: http://www.cs.ualberta.ca/~database/MEMS/sma_mems/index2.html

Ajayan, P. M., Suhr, J., and Koratkar, N., (2006). “Utilizing interfaces in carbon nanotube reinforced polymer composites for structural damping, Journal of Material Science, 41, 7824-7829.

Suhr, J., Koratkar, N., Keblinski, P., and Ajayan, P. (2005). "Viscoelasticity in carbon nanotube composites,” Nature Materials Vol. 4.

Gibson, R. F., Principles of Composite Material Mechanics, Second Edition, CRC Press, 2007.

Jones, R. M., Mechanics of Composite Materials, Taylor and Francis, 1999. Advani, S. G., Processing and Properties of Nanocomposites, World

Sciences, 2007. Booker, R. and Boysen, E., Nanotechnology, Wiley Publishing, 2005. Scientific American, Understanding Nanotechnology, 2002.

Lecture on Nanocomposites

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