Composite Materials & Structures

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Unit 2.

Composite materials
and structures:
Professor C Bhaskaran

Methods of analysis:

Micro mechanics mechanics of materials

approach, elasticity approach to determine
material properties.
Macromechanics - stress-strain relations,
with respect to natural axis, arbitrary axis
- determination of material properties.
Experimental characterization of lamina.

NIET

Syllabus
Unit 3. Laminated Plates:
Objective:
To understand the design and
fabrication of composite materials
and structures.

Unit 1.

Stress-strain Relation:

Introduction - Advantages and

applications of composite materials,
reinforcements and matrices
Generalized Hookes law
Elastic constants for anisotropic,
orthotropic and isotropic materials.

Prepared By Prof. C Bhaskaran

Governing differential equation for a

general laminate,
angle ply and cross ply laminates.
Failure criteria for composites.

Unit 4. Sandwich Constructions:

Basic design concepts of sandwich
construction
-Materials used for sandwich
construction
- Failure modes of sandwich panels.

Composite Materials & Structures

Unit 5. Fabrication process:

Various open and closed mould
processes.
Manufacture of fibres .
Types of resins and properties and
applications
- Netting analysis.

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Composite materials and structures:

Unit 1. Stress-strain Relation:
Introduction- Advantages and application
of composite materials, reinforcements
and matrices Generallized Hookes lawElastic constants for anisotropic,
orthotropic and isotropic materials.

Books:
1. Calcote L.R., The analysis of laminated composite structures
Von Nostrand Reinhold company, New York.
2. Jones R M., Mechanics of composite materials McGraw-Hill.
3. M. Mukopadhyay Mechanics of composite materials and
structures Universities Press.
4. Isaac M Daniel & Ori Ishai
Engineering Mechanics of
composite materials Oxford University Press.
5. Avtar K Kaw. Mechanics of composite materials crc press.
6. Krishan K Chawla Composite materials: Science and Engg.
References:
1. Agarwal B D & Broutman L J The analysis and performance
of Fibre composites. John Wiley and sons.
2. Lubin G. Handbook of Advanced Plastics and Fibre glass
- Von Nostrand Reinhold Co., New York.
3.
Dowling
Mechanical Behaviour of Materials.

Definitions:
A composite material is a material system
composed of two or more physically
distinct phases whose combination
produce aggregate properties that are
different from those of its constituents.

A composite material may be defined as one which

satisfies the following conditions:
1. It is manufactured.

Blank page

2. It consists of two or more physically and/or

chemically distinct, suitably arranged or distributed
phases with an interface separating them.
3.It has characteristics that are not depicted by
any of the components in isolation.
[Ref: J F Schier and R F Juergens (sept. 1983)
Astronautics and Aeronautics]

Prepared By Prof. C Bhaskaran

Composite Materials & Structures

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Ceramic-metal composites

Metal- polymer
composites

Natural composites:

metals

1. Coconut palm leaf : concept of fibre

reinforcement
2. Wood : Cellulose fibres in a lignin matrix
3. Bone : short and soft collagen fibres in a
mineral matrix called apatite

ceramics

polymers

ceramic -polymer composites

What is a composite?
A composite is a structural material which consists of
two or more constituents. The constituents are
combined at a macroscopic level and are not soluble in
each other. One constituent is called the reinforcing
phase and the other in which it is embedded is called
the matrix. The reinforcing phase material may be in
the form of fibres, particles or flakes. The matrix phase
materials are generally continuous.
Example:
Concrete reinforced with steel,
Epoxy reinforced with graphite fibres.

Difference between an alloy and a composite

material?
Composite material is, in effect, a mixture of
two or more materials(e.g., concrete, a mixture
of cement and aggregate Whereas an alloy is a
solid solution of alloying elements in t he host
metal. The atoms of the alloying elements take
positions in the crystal structure, as impurities,
whereby the metal gets strengthened, known
as, solid solution strengthening .

Prepared By Prof. C Bhaskaran

structural Composite materials

The Two phases:
matrix

- plastics(polymers),
metals, or ceramics
and

reinforcements

- Fibre or particles

Composite materials
examples:

Wood, plywood, concrete

reinforced rubber
fibre reinforced plastics
fibre reinforced metals
and so on

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Classification
Based on
i) the Matrix Material
ii) the Shape of reinforcement

Based on matrix material

PMC - Polymer Matrix Composites

MMC - Metal Matrix Composites
CMC - Ceramic Matrix Composites

Based on reinforcement shape.

Fibre composites
and particulate composites.
Particulate composites can have
small particles or flakes as
reinforcements.

Reinforcements:
(metal, polymer or ceramic)

Composite materials
PMC

MMC

fibre

CMC
particle

Prepared By Prof. C Bhaskaran

flake

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A-glass has good resistance to chemicals.

E-glass is a non-conductor of electricity.
Though economical, glass fibre is
relatively heavy. Of the common synthetic
reinforcements, it has the least efficient
strength-to-weight ratio.

Types of fibre-reinforced composites

Type

Fibre

Polymer

Metal

Ceramic

Carbon

Glass, Carbon,
Aramid (Kevlar),
Boron
Boron, Carbon,
Borosic,
Silicon carbide,
Alumina
Silicon carbide,
Alumina,
Silicon nitride.
Carbon

Matrix

Epoxy, Polyester,
Polyimide
Polysulfones,
Aluminium,
Magnesium,
Copper, Titanium.
Silicon carbide,
Alumina,
Glass-ceramic,
silicon nitride
Carbon

Glass fibres come in several varieties.

Designated S-, A-, C-, or E-glass.
Each variety has special characteristics.
S-glass is exceptionally strong.
C-glass is extremely resistant to
corrosion and chemical attack.

Prepared By Prof. C Bhaskaran

Aramid Fibre resists impact. It is used

extensively in bulletproof vests and body
armor. Racing drivers wear aramid suits that
help protect them from burns in fiery, highspeed crashes. Aramid is commonly known as
Kevlar, produced by DuPont. Aramid fibres
cost is between glass and carbon. Aramid is
more difficult to work with than glass and has
a tendency to absorb moisture.

Carbon Fiber is a very strong fiber and

extremely stiff. It is lighter in weight than
glass fiber. Carbon fibers come in several
varieties and strengths and are the most
expensive kind of fiber reinforcements. They
are typically used in airplanes and spacecraft.
Carbon fiber reinforced composites are also
used in products such as bicycle frames,
tennis rackets, skis, and golf club shafts.

Composite Materials & Structures

Boron is an extremely hard natural element

and
ceramics are hard materials that can
withstand high heat and harsh chemicals.

Ceramic material is a compound containing metallic and

non-metallic elements.
Oxygen, nitrogen, carbon are the major
non-metallic elements.
Examples:
-clay : Traditional ceramics,
consisting of fine particles of hydrous
aluminum silicates and other minerals.
-silica : SiO2 , basic for all glassy materials.
-Alumina : Al2O3.
-silicon carbide: SiC.
-carbides and nitrides: such as Tungsten carbide (WC),
Titanium carbide (TiC),
Titanium nitride, Boron nitride.

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What are advanced composites?

Advanced composites are composite materials
traditionally used in aerospace industry. These have
high performance reinforcements of a thin diameter in
a matrix material such as epoxy and Aluminum.
Example: graphite/epoxy, kevlar /epoxy, and
boron/ aluminum composites.

What are the advantages of composite materials ?

--have high specific strength and specific stiffness.
-- Fatigue properties are better than common
engineering materials
- Tailorability of physical properties to suit specific applications.
-Low maintenance
-Corrosion resistance
-Self lubrication (specialized composites)
-Long life (if UV protected)
-Low weight (compared to the alternatives)
-better appearance and surface finish.
-Radar-invisible
-Low thermal signature

Disadvantages:

Different fibers can be combined to make a

composite to cost less or perform better.
Composites that are made of more than one
fibre/resins are called hybrid composites.
Fibers with special characteristics are used
when a composite must be exceptionally
strong or heat-resistant;
--for high-performance military aircraft and
aerospace applications.

Prepared By Prof. C Bhaskaran

Disadvantages:
- poor reliability and repeatability.
- Anisotropic
- PMCs are liable to be attacked by chemicals and
solvents
- generally expensive and man intensive .

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Polymer:
Materials
solid, liquid, gas
Metallic and non-metallic materials
Organic and inorganic materials

Metals

Is a compound formed of repeating

structural units called mers, whose
atoms share electrons to form very
large molecules.
Polymers usually consist of carbon plus
one or more other elements such as
hydrogen, oxygen, nitrogen, and
chlorine. Theses are organic polymers.

Ferrous and Non-ferrous metals

Ferrous metals:
Iron, Steel, steel alloys, cast iron.

Non-ferrous metals:
Aluminium (Al), Copper (Cu),
Magnesium (Mg), Manganese (Mn),
Gold (Au), Silver (Ag),
Tin (Sn), Titanium (Ti), Zinc (Zn), etc

Inorganic polymers are those

without carbon atom. Eg., glass ,
silicon rubber.

Non-metallic materials:

Cotton, silk, wool and rubber are natural

polymers.

Boron, Carbon, Silicon, Sulfur,

phosphorus, oxygen, nitrogen

Polyethylene, PVC (Poly Vinyl Chloride),

Nylon, Terylene are synthetic polymers,
synthesised from low molecular weight
compounds.

Prepared By Prof. C Bhaskaran

Composite Materials & Structures

Polymers:
can be divided in to

Thermosetting polymers
and Thermoplastic polymers
(and also elastomers).

Thermoplastic polymers:
These materials gets softened when
heated and can be formed in to various
shapes, which will be retained on cooling.
Can be subjected to several cycles of
heating and cooling.
Polyethylene, PVC, Nylon, Polystyrene, etc.

[ C H2-CH2 ]n
Polyethylene monomer
0000000000000000
chain formation in making a polymer

Prepared By Prof. C Bhaskaran

9/24/2013

Thermosetting Polymers:
some of the polymers undergo some
chemical change on heating and convert
them in to a rigid structure. They are like
the yolk of the egg, which on heating sets
into a mass, and , once set can not be
reshaped. Such polymers are called
thermosetting polymers.
Eg., Phenolics, Amino resins, Epoxies.

Elastomers:
Polymers that exhibit significant elastic
behaviour is termed as elastomers.
Eg., Natural rubber, Neoprene, Polyurethane.

Plastics, elastomers, Fibres and Liquid Resins:

Depending on its ultimate form and use, a polymer
can be classified as plastic, elastomer, fibre or liquid
resin.
When a polymer is shaped in to hard and tough
utility articles by the application of heat and pressure,
it is used as a plastic. Typical examples are
:Polystyrene, PVC, Polymethyl methacrylate.
When vulcanised in to rubbery products exhibiting
good strength and elongation, polymers are used as
elastomers. Eg., Natural rubber, Synthetic rubber,
Silicone rubber.

Composite Materials & Structures

If drawn into long filament like materials,

whose length is at least 100 times its
diameter, polymers are said to have been
converted in to fibres. Typical examples
are Nylon and Terylene.
Polymers are used as adhesives, potting
compounds, sealants etc., in a liquid form
are described as liquid resins. Typical
examples are: commercially available
epoxy adhesives and polysulphide sealants.

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Hybrid composites:
Different fibers can be combined to
make a composite to cost less or
perform better. Composites that are
made of more than one type of fibre
or resin are called hybrid composites.

Ceramics- a compound containing metallic

and non-metallic elements.
Oxygen, nitrogen, carbon are the major nonmetallic elements.
Examples:
-clay : Traditional ceramics, consisting of fine
particles of hydrous aluminum silicates
and other minerals.
-silica : SiO2 , basic for all glassy materials.
-Alumina : Al2O3.
-silicon carbide: SiC.
-carbides and nitrides: such as Tungsten
carbide (WC), Titanium carbide (TiC),
Titanium nitride, Boron nitride.

Carbon fibre cloth used to make

composites

Prepared By Prof. C Bhaskaran

Applications:
1. Aircraft, Aerospace & Military
2. Marine field
3. Automotive
4. Sporting Goods
5. others.

Aircraft and Aerospace and military

applications:
Optimally an Aircraft, missile, satellite launch
vehicle and satellite requires a minimum weight
design to attain greater speeds and increased
payload and fibre - reinforced composites have
been found to be ideal for this purpose. Carbon
fibre or kevlar fibre reinforced polymer (FRP)
composites are being extensively used in the
production of aircrafts, nowadays. Civil and
military aircraft wings, fuselage, empennage
components are being designed and built using
these composites.
-contd-

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-Continued-

For Missiles and Launch vehicles, interstage

structures, solid motor cases, liquid storage
tanks etc., uses composite materials very
successfully. Satellites also use composite
materials in the form of sandwich structures for
main body and other structural components.
Carbon fibre composites are vey useful in the
design of dish antennas, especially for
temperature stability.

The popularity of GFRP with boat builders

lies in its competitive low cost ( in
comparison to wooden hulls), a troublefree performance, low maintenance cost
and aesthetics.
Military and commercial hovercrafts also
uses GFRP. Fast patrol boats are made of
hybrid glass/carbon laminates in place of
steel and aluminum.

-continued-

-cotinued-

Strength and stiffness of composites are major

considerations for the aircraft, missile and
launch vehicles, while stiffness and low (or zero)
coefficient of thermal expansion are the major
requirements for space (satellite) applications.
FRP is used for the construction of antennas,
booms, support trusses and struts.

Marine field applications:

Potential applications in the marine field range
from small components such as radar domes,
masts and piping to large-scale structures,
submersibles and off-shore structure modules.
Glass reinforced plastics (GFRP) are used in the
construction of boat hulls, including yachts, life
boats, dinghies, canoes, speed boats, fishing
boats, and passenger boats.

Prepared By Prof. C Bhaskaran

Automotive field:
FRPs are being used to make many parts
of cars. Exterior parts of the cars, such as
canopy, door etc are made of composites.
Chassis components leaf spring is made of
FRP.

Sporting goods:
Because of the reduction in weight
many sports goods are being made
using composite materials.
Tennis rackets, fishing rods, archery
bows, bicycle frames, sail boats and
kayaks, oars, paddles, canoe hulls,
javelins, helmets, golf clubs, hockey
sticks, athletic shoes surf boards etc.

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Composite Materials & Structures

The Soldiers Load and Life Expectancy:

The humble soldiers life expectancy is increased
not only by Kevlar vests but by composite
helmets, advanced composite goggles, gloves
and more effective, lighter weaponry using
composites in their construction. The general
weight reduction of standard equipment has not
lessened his (or her) load though one just has
to carry additional equipment.
However what has changed is that there are
many soldiers alive today who would be dead
were it not for advanced composite armor and
flak jackets.

Hookes law:
States that the deformation is directly
proportional to the load or strain is
directly proportional to the stress up
to elastic limit, for a linearly elastic
material.
{} = [1/E] {},
where E is the proportionality
constant, called Youngs modulus.

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STRESS STRAIN
STRENGTH
STIFFNESS
TOUGHNESS

Stress is the load which we apply and strain is

the effect. Stress can be normal stress( tensile or
compressive) and/or shear stress. And the strain
can be normal strain and/or shear strain.
Stress and strain are related through Hookes law.
Stiffness is the load required to produce unit
deformation, in the direction of the load.
Toughness is the energy absorbed by the
material before it breaks.
The area under the stress-strain diagram gives
the energy per unit volume .

Anisotropic, orthotropic, isotropic

materials:
Definitions:
Isotropy: properties at a point are
same in all directions.
Orthotropy: Three planes of symmetry
exists. Equality of property
in each plane, in one direction.
Anisotropy: properties are different
everywhere, any direction.

Prepared By Prof. C Bhaskaran

Generalized Hookes Law

Hookes law gives the stress-strain relations
for engineering materials.
The connecting parameters are the elastic
constants through engineering constants
for the materials.

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In the most general case the stress

strain components are related by the
generalized Hookes law, as given in the
following equations, in the matrix form.
There are 81 elastic constants

Or
we can also have the strain-stress relation as,
ij = Sijkl kl
where, Sijkl are compliance
or flexibility coefficients.

( figure showing the stresses, on face 1)

the above can be written in indicial form as:

ij = Cijkl kl ,
where, (i,j,k,l = 1,2,3)
and Cijkl are known as Stiffness coefficients.

12
11
13

Identification of stress, strain components:

11, 22, 33 are normal stresses.
12 etc are shear stresses.

Stress and strain tensors are required to

be symmetric, that is,
ij =ji, ij = ji .

1, 2, 3 are normal stresses.

4 = 23, 5 = 31
and 6 = 12, are shear stresses.

This reduces the number of elastic

constants to 36.

Similarly strains also. Replace with

we can write the stress- strain relations or

the constitutive relations as follows:

Stress strain relation for an anisotropic material

Prepared By Prof. C Bhaskaran

stress-strain relations for an anisotropic material 3-D,

considering stress symmetry

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i = Cijj

S11

similarly,
i = Sijj

S12

S12
S22

S13
S23

S14
S24

S15
S25

S16
S26

S13

S 23

S33

S34

S35

S36

S14

S24

S34

S44

S45

S46

S15

S25

S35

S45

S55

S56

S16

S26

S36

S46

S56

S66

i=j=1 to 6
Compliance or flexibility matrix
3- Dimensional

It can be seen that, as per the requirement

of energy considerations,
Cij=Cji and Sij=Sji.
And hence the number of independent
elastic constants for an anisotropic
material reduces to 21.

C11 C12

C13

C14

C15

C16

C12 C22

C23

C24

C25

C26

C13

C23 C33

C34

C35

C36

C14

C24

C34 C44

C45

C46

C15

C25

C35

C45 C55

C56

C16

C26

C36

C46

C66

C56

We can write Hookes law, in the expanded

form, for strain, as,
1 = s111 + s122 + s133+s144+s155+s166
2 = s121+s222+s233+s244+s255+s266
-------- etc.
S11 to S66 and C11 to C66, the elements of the
compliance and stiffness matrices respectively
are the elastic constants.
So we need 21 elastic constants to study an
anisotropic material, at the minimum.

Orthotrpy is that the material has three

planes of symmetry.
If 1, 2, 3 are the coordinate axes
normal to these planes and the load is
acting along these directions, then we can
write the relations :

stiffness coefficients for anisotropic materials

(symmetric about diagonal) (3-D)
Similarly compliance matrix [Sij] also.

Prepared By Prof. C Bhaskaran

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C11

C12

C13

C12

C22

C23

C13

C23

C33

C44

C55

C66

Constants for Isotropic materials:

S11= S22= S33= 1/E,
and
S12 = -/E = S13 = S23
S44 = S55 = S66 = 1/G = 2(1+)/E
Needs only two elastic constants, S11 and S12.

Stiffness matrix for orthotropic materials 3-D

Needs two engineering constants to be

evaluated, given by E and G or .

Elastic constants for various epoxy matrix

composites:
1
S11 S12 S13 0
2
S12 S22 S23 0
3 = S13 S23 S33 0
23
0 0
0 S44
31
0
0
0 0
12
0
0
0
0

0
0
0
0
S55
0

0
0
0
0
0
S66

1
2
3
23
31
12

Hookes law for 3-D orthotropic material

(Strain-stress relation)

C11

C12

C12

C22

C66

Stiffness matrix for orthotropic materials 2-D

Needs FOUR (4) elastic constants.

Prepared By Prof. C Bhaskaran

(Fibres along x-axis)

Exx
GPa

Eyy
GPa

Gxy
GPa

xy

yx

Vf

Sp.
Gravity

Graphite 181

10.3

7.17

0.28

.016

0.7

1.6

Material

Boron

204

18.5

5.59

0.23

0.5

2.0

Glass

38.6

8.27

4.14

0.26

0.45

1.8

Kevlar

76

5.5

2.3

0.34

0.6

1.46

Now, the elements of the compliance

and flexibility matrices are formed by
engineering constants or elastic properties
of the material, such as,
Youngs modulus E,
shear modulus G
and Poissons ratio .

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Determination of elastic constants for

1

s11 S12 S13 0

Most often the material properties are

S12 S22 S23 0

determined in the laboratories in terms of the

S13 S23 S33 0

23
31

orthotropic materials:

engineering constants, E, G, . These are

23 = 0

S44 0

measured using simple tests like uniaxial tension

31

S55 0

test, pure shear, torsion test etc.

12

S66 12

Initially, apply 1, keeping other forces zero, then

we have all the elements in the stress matrix as
zeroes, except 1.
1 = S111 ----(1)
2 = S121 ------(2)
3 = s131 ------(3)
23 = 31 = 12 = 0
The youngs modulus in direction (1) is E1 and is
defined as E1=1/1 = 1/S11.

The engineering constants for an

orthotropic materials are, E1, E2, E3,
12, 21, 23, 32, 31, 13,
G12, G23, and G31.
But six Poissons ratios are not
independent, only three are required.

Poissons ratio:
In general terms Poissons ratio, ij,
is defined as the ratio of the negative of
the normal strain in the direction j to the
normal strain in the direction i, when the
only normal load applied is in direction i.

The strain-stress relation for an orthotropic

material is:

Prepared By Prof. C Bhaskaran

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Composite Materials & Structures

The Poisson's ratio 12 is defined as,

12 =-2/1 = -S12/S11.
The Poissons ratio 13 is defined as
13 = -3/1 = -S13/S11

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In the above expressions, twelve

engineering constants have been defined
as follows:
E1, E2, E3 in each material axes,
Six Poissons ratios 12, 21,23,32,13, and 31,
two for each plane, and three shear modulii for
each plane, G23, G31 and G12.
However, Six Poissons ratios are not
independent of each other.

Similarly apply load in the direction 2 only, and

get,
E2 = 1/S22,
21 = -S12/S22
23 = -S23/S22
Similarly apply load in the direction 3 only,
and get,
E3 = 1/S33,
31 = -S13/S33
32 = -S32/S33

Now apply,23, keeping others zero.

Then, 23 = S44 23.
Shear modulus in plane 2-3 is defined as,
G23= 23/23 = 1/S44.

From the above expressions, we have,

E1 = 1/1 = 1/S11
E2 = 2/2 = 1/S22
12 = -2/1 = -S12/S11
21 = -1/2 = -S12/S22
12/21 = (-S12/S11) / (-S12/S22)
= (S22/S11) = E1/E2

or, we may write,

(12/E1) = (21/E2)-------(i)
(13/E1) = (31/E3)-------(ii)
(23/E2) = (32/E3)-------(iii)
These are known as
Reciprocal Poissons ratio equations.

similarly, G31 = 1/S55

and

G12 = 1/S66.

Prepared By Prof. C Bhaskaran

Thus there are Nine (9) elastic constants to be

evaluated through Nine(9) material properties.

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The stiffness matrix elements can be

obtained by inverting the flexibility or the
compliance matrix, as ,
C11 = (S22S33-S232)/S
C22 = (S11S33-S132)/S
C33 = (S11S22-S122)/S
C12 = (S13S23-S12S33)/S
C23 = (S11S13-S23S11)/S
C13 = (S12S23-S13S22)/S
C44 = 1/S44, C55 = 1/S55, C66 = 1/S66

Where,

s=

S11

S12

S13

S21
S31

S22
S32

S23
S33

End of unit 1

Macromechanics:
Macromechanics deals with the establishment
of the stress- strain relationship and the
strength and stiffness of the composite material
applying the average properties established
through micromechanics analysis.
Stress and strain relations for uni-directional
and bi-directional lamina are developed using
the lamina properties. Methods for the
evaluation of the properties of the angle lamina
are established and the strength and stiffness of
the laminate are arrived at.

Note:
Crystalline and amorphous nature of
materials,
lattice structure,
grains and grain boundaries.
Long order and short order arrangement of
atoms and molecules.
Solid, Liquid, Gas.
Slurry ( mixture of liquid and solid)

Assignment-1:
1. Write down the generalized Hookes law.
2. Write the stress- strain relation for an orthotropic
material (3-D) and state the flexibility and stiffness
matrices in terms of the engineering constants, Es,
s and Gs.
3. Explain what are anisotropic, orthotropic,
monoclinic, transversely isotropic and isotropic
materials.
Date of submission: 12/8/13

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Prepared By Prof. C Bhaskaran

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