202663872-Lecture-on-Nanocomposites.pptx

1
Properties and Applications of
Composites & Nanocomposites
PSCI 640 Elements of Nanosciences, November 9, 2009
Arya Ebrahimpour
Professor, 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, s 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, e, is defined as the change in
length of a line, DL, over it’s original length, L.
A
P

s
L
L
D

e
P
P
L DL
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, sy, and ultimate strength, su, are points shown on
the stress-strain curve below.
 For uniaxial loading (e.g., tension in one direction only): s = E e
s
s
1
E
Stress, s
Strain, e
su
sy
Rupture

 Shear stress, t, 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, g. The
slope of the linear portion of the t-g is called shear modulus
of elasticity, G.
g
t
t
t
t
1
G
Stress, t
Strain, g

 Poisson’s ratio, n, is another property defined by
the negative of the ratio of transverse strain, e2,
over the longitudinal strain, e1, due to stress in the
longitudical direction, s1.
e2
e1
s1
Original shape
s1
1
2
1
2
12
e
e
 


 Isotropic Materials have properties that do not depend on the
orientation of the coordinate system (xyz). That is,
E1 = E2 = E3, G23 = G31= G12, & n12 =n21 =n13 =n31 …
 Isotropic materials can be fully described with only two (2) of the
three material constants (E, G, and n).
 Examples of isotropic materials: steel, aluminum, …
1
2
3
)
1
(
2 n


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

 Stresses and Strains in 3D:
Knowing that tij = tji, we have six
independent stresses:
s1, s2, s3, t23, t31 , and t12
For shear stresses, the first index is the
plane 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 {s} and {e} represent both normal and shear stresses
and strains, respectively.
    
s
e S

    
e
s C

s1
t12
s2
s3
t13
t23
t32
t21
t31
A 3D stress element

 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

 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.

 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
< 1mm

 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
s1 be zero, then we have no shear strain, g12, as shown below:
g12 = S16s1 + S26 s2 + S36 s3 + S46t23 + S56t31 + S66t12 = S16s1 = 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 nij .
Note that the SEC and SSC terms are zero.
SEC
SSC
3
,
2
,
1
, 
 j
i
E
E j
ji
i
ij n
n
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, n12 = 0.25, G12 = 9 GPa. The
load P is applied in the 1-direction. Note: This lamina is orthotropic.
Find:
a. Determine strains e1 and e2 under the force P.
b. What are reasonable values for E3 and n13?
c. Based on the values in Part (b), find e3.
d. What are the final dimensions of the lamina?

 Predicting stiffness E1 using Rule of Mixtures
m
m
f
f V
E
V
E
E 

1
)
1
:
(Note
matrix
and
fiber
of
fractions
Volume
and
matrix
and
fiber
of
elasticity
of
Modulus
and
,
Where




m
f
m
f
m
f
V
V
V
V
E
E

 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
f
m
m
f
m
f
V
E
V
E
E
E
E


2

 Predicting stiffness n12 and G12
m
m
f
f V
V n
n
n 

12
f
m
m
f
m
f
V
G
V
G
G
G
G


12
matrix
and
fiber
of
elasticity
of
modulus
Shear
and
matrix
and
fiber
of
ratios
s
Poisson'
and
,
Where


m
f
m
f
G
G
n
n

 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 nf = 0.25 and nm = 0.35, find the lamina n12
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 (su), 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 mm
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

 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,
NT
L
A
w 

 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
tensile
e
transvers
strain
failure
fiber
the
to
ing
correspond
stress
matrix
strenght
shear
strenght
tensile
composite
~
Where,




T
mf
LT
x
S
S
S
s








 2
ln
1
2
~
LT
mf
T
mf
T
LT
x
S
S
S
S
S
S

s

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 changes
SMA 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.

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