CMS Unit 1

Composite Materials & Structures 9/24/2013

Prepared By Prof. C Bhaskaran 1

Composite materials

and structures:

Professor C Bhaskaran

NIET

Syllabus

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 Hooke’s law –

Elastic constants for anisotropic,

orthotropic and isotropic materials.

Unit 2. 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.

Unit 3. Laminated Plates:

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.



Unit 5. Fabrication process:

Various open and closed mould

processes.

Manufacture of fibres .

Types of resins and properties and

applications

- Netting analysis.

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”.

Blank page

Composite materials and structures:

Unit 1. Stress-strain Relation:

Introduction- Advantages and application

of composite materials, reinforcements

and matrices – Generallized Hooke’s law-

Elastic constants for anisotropic,

orthotropic and isotropic 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.

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]



Natural composites:

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

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 .

metals

ceramics polymers

Ceramic-metal composites Metal- polymer

composites

ceramic -polymer composites

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



Classification

Based on

i) the Matrix Material

ii) the Shape of reinforcement

Based on matrix material

Composite materials

PMC MMC CMC

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)

fibre

particle flake



Types of fibre-reinforced composites

Type Fibre Matrix

Polymer Glass, Carbon,

Aramid (Kevlar),

Boron

Epoxy, Polyester,

Polyimide

Polysulfones,

Metal Boron, Carbon,

Borosic,

Silicon carbide,

Alumina

Aluminium,

Magnesium,

Copper, Titanium.

Ceramic Silicon carbide,

Alumina,

Silicon nitride.

Silicon carbide,

Alumina,

Glass-ceramic,

silicon nitride

Carbon Carbon 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.

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.

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, high-

speed crashes. Aramid is commonly known as

Kevlar, produced by DuPont. Aramid fibre’s

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.



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.

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.

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:

Disadvantages:

- poor reliability and repeatability.

- Anisotropic

- PMC’s are liable to be attacked by chemicals and

solvents

- generally expensive and man intensive .



Materials

solid, liquid, gas

Metallic and non-metallic materials

Organic and inorganic materials

Metals – 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

Non-metallic materials:

Boron, Carbon, Silicon, Sulfur,

phosphorus, oxygen, nitrogen

Polymer: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.

Inorganic polymers are those

without carbon atom. Eg., glass ,

silicon rubber.

Cotton, silk, wool and rubber are natural

polymers.

Polyethylene, PVC (Poly Vinyl Chloride),

Nylon, Terylene are synthetic polymers,

synthesised from low molecular weight

compounds.



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

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.



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.

Ceramics- 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.

Carbon fibre cloth used to make

composites

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.

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-



-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.

-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.

The popularity of GFRP with boat builders

lies in its competitive low cost ( in

comparison to wooden hulls), a trouble-

free 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.

Automotive field:

FRP’s 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.



The Soldier’s Load and Life Expectancy:

The humble soldier’s 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.

Hooke’s 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.

{ε} = [1/E] {σ},

where E is the proportionality

constant, called Young’s modulus.

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.

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 Hooke’s 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 .

Generalized Hooke’s Law

Hooke’s law gives the stress-strain relations

for engineering materials.

The connecting parameters are the elastic

constants through engineering constants

for the materials.



In the most general case the stress –

strain components are related by the

generalized Hooke’s law, as given in the

following equations, in the matrix form.

There are 81 elastic constants

( figure showing the stresses, on face 1)

2 σ12

σ11

σ13

3 1

Identification of stress, strain components:

σ11, σ22, σ33 are normal stresses.

σ12 etc are shear stresses.

σ1, σ2, σ3 are normal stresses.

σ4 = τ23, σ5 = τ31

and σ6 = τ12, are shear stresses.

Similarly strains also. Replace σ with ε

Stress – strain relation for an anisotropic material

the above can be written in indicial form as:

σij = Cijkl εkl ,

where, (i,j,k,l = 1,2,3)

and Cijkl are known as Stiffness coefficients.

Or

we can also have the strain-stress relation as,

εij = Sijkl σkl

where, Sijkl are compliance

or flexibility coefficients.

Stress and strain tensors are required to

be symmetric, that is,

σij =σji, εij = εji .

This reduces the number of elastic

constants to 36.

we can write the stress- strain relations or

the constitutive relations as follows:

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

considering stress symmetry



σi = Ʃ Cijεj

similarly,

εi = Ʃ Sijσj

i=j=1 to 6

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.

stiffness coefficients for anisotropic materials

(symmetric about diagonal) (3-D)

Similarly compliance matrix [Sij] also.

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 C56 C66

Compliance or flexibility matrix

3- Dimensional

S11 S12 S13 S14 S15 S16

S12 S22 S23 S24 S25 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

We can write Hooke’s law, in the expanded

form, for strain, as,

ε1 = s11σ1 + s12σ2 + s13σ3+s14σ4+s15σ5+s16σ6

ε2 = s12σ1+s22σ2+s23σ3+s24σ4+s25σ5+s26σ6

-------- 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 matrix for orthotropic materials 3-D

C11 C12 C13 0 0 0

C12 C22 C23 0 0 0

C13 C23 C33 0 0 0

0 0 0 C44 0 0

0 0 0 0 C55 0

0 0 0 0 0 C66

ε1 S11 S12 S13 0 0 0 σ1

ε2 S12 S22 S23 0 0 0 σ2

ε3 = S13 S23 S33 0 0 0 σ3

γ23 0 0 0 S44 0 0 τ23

γ31 0 0 0 0 S55 0 τ31

γ12 0 0 0 0 0 S66 τ12

Hooke’s law for 3-D orthotropic material

(Strain-stress relation)

Stiffness matrix for orthotropic materials 2-D

Needs FOUR (4) elastic constants.

C11 C12 0

C12 C22 0

0 0 C66

Constants for Isotropic materials:

S11= S22= S33= 1/E,

and S12 = -ν/E = S13 = S23

S44 = S55 = S66 = 1/G = 2(1+ν)/E

Needs only two elastic constants, S11 and S12.

Needs two engineering constants to be

evaluated, given by E and G or ν.

Elastic constants for various epoxy matrix

composites:(Fibres along x-axis)

Material Exx

GPa

Eyy

GPa

Gxy

GPa

νxy νyx VfSp.

Gravity

Graphite 181 10.3 7.17 0.28 .016 0.7 1.6

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,

Young’s modulus E,

shear modulus G

and Poisson’s ratio ν.



Determination of elastic constants for

orthotropic materials:

Most often the material properties are

determined in the laboratories in terms of the

engineering constants, E, G, ν. These are

measured using simple tests like uniaxial tension

test, pure shear, torsion test etc.

The engineering constants for an

orthotropic materials are, E1, E2, E3,

ν12, ν21, ν23, ν32, ν31, ν13,

G12, G23, and G31.

But six Poisson’s ratios are not

independent, only three are required.

The strain-stress relation for an orthotropic

material is:

ε1 s11 S12 S13 0 0 0 σ1

ε2 S12 S22 S23 0 0 0 σ2

ε3 S13 S23 S33 0 0 0 σ3

γγγγ23 = 0 0 0 S44 0 0 ττττ23

γγγγ31 0 0 0 0 S55 0 ττττ31

γγγγ12 0 0 0 0 0 S66 ττττ12

Initially, apply σ1, keeping other forces zero, then

we have all the elements in the stress matrix as

zeroes, except σ1.

ε1 = S11σ1 ----(1)

ε2 = S12σ1 ------(2)

ε3 = s13σ1 ------(3)

γ23 = γ31 = γ12 = 0

The young’s modulus in direction (1) is E1 and is

defined as E1=σ1/ε1 = 1/S11.

Poisson’s ratio:

In general terms Poisson’s ratio, νij,

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 Poisson's ratio ν12 is defined as,

ν12 =-ε2/ε1 = -S12/S11.

The Poisson’s ratio ν13 is defined as

ν13 = -ε3/ε1 = -S13/S11

Similarly apply load in the direction 2 only, and

get,

E2 = 1/S22,

ν21 = -S12/S22

ν23 = -S23/S22

Similarly apply load in the direction 3 only,

and get,

E3 = 1/S33,

ν31 = -S13/S33

ν32 = -S32/S33

Now apply,τ23, keeping others zero.

Then, γ23 = S44 τ23.

Shear modulus in plane 2-3 is defined as,

G23= τ23/γ23 = 1/S44.

similarly, G31 = 1/S55

and G12 = 1/S66.

In the above expressions, twelve

engineering constants have been defined

as follows:

E1, E2, E3 in each material axes,

Six Poisson’s ratios ν12, ν21,ν23,ν32,ν13, and ν31,two for each plane, and three shear modulii for

each plane, G23, G31 and G12.

However, Six Poisson’s ratios are not

independent of each other.

From the above expressions, we have,

E1 = σ1/ε1 = 1/S11

E2 = σ2/ε2 = 1/S22

ν12 = -ε2/ε1 = -S12/S11

ν21 = -ε1/ε2 = -S12/S22

ν12/ν21 = (-S12/S11) / (-S12/S22)

= (S22/S11) = E1/E2

or, we may write,

(ν12/E1) = (ν21/E2)-------(i)

(ν13/E1) = (ν31/E3)-------(ii)

(ν23/E2) = (ν32/E3)-------(iii)

These are known as

Reciprocal Poisson’s ratio equations.

Thus there are Nine (9) elastic constants to be

evaluated through Nine(9) material properties.



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 =

End of unit 1

S11 S12 S13

S21 S22 S23

S31 S32 S33

Assignment-1:

1. Write down the generalized Hooke’s 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, E’s,

ν’s and G’s.

3. Explain what are anisotropic, orthotropic,

monoclinic, transversely isotropic and isotropic

materials.Date of submission: 12/8/13

-------0000--------

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)

CMS Unit 1

Documents

chawla composite materials

isotropic materials

blank pagecomposite

material properties

structures universities

material system

structural material

stressstrain relation