This document discusses the properties of elasticity and plasticity in materials. It defines elasticity as the ability of a material to return to its original shape and size after an applied force is removed, while plasticity means a material does not return to its original shape after force removal. Stress and strain are also defined, along with Hooke's law which states stress is proportional to strain within a material's elastic limit. The different types of moduli - Young's, rigidity, and bulk - are explained. Factors that impact a material's elastic properties, like temperature, purity, and crystal structure are outlined. Poisson's ratio and stress-strain diagrams are also introduced.

1. UNIT - I
PROPERTIES OF MATTER

2. OVERVIEW
ELASTICITY
STRESS, STRAIN AND ITS TYPES
HOOKE’S LAW
MODULII OF ELASTICITY
POISSON’S RATIO
STRESS STRAIN DIAGRAM
FACTORS AFFECTING ELASTICITY

3. UNIT I
PROPERTIES OF MATTER
Elasticity:
When an external force is applied to a body there will be
some change in its length, shape and volume. When the external
force is removed, if the body regains its original shape and size,
then the body is said to be a perfectly elastic body. This property
is known as elasticity.
Example: Quartz fiber
Definition:
The property by virtue of which the body regains its
original shape and size on the removal of the external force is
called elasticity and the deformation caused is known as elastic
deformation.

4. Plasticity:
If the body does not regain its original shape or size, when
the applied force is removed, then it is a perfect plastic body (or
inelastic body). This property is called plasticity.
Example: Chewing gum, ordinary putty and wax
Definition:
The property by which the body does not regain its
original shape and size on the removal of the external force is
called plasticity and the deformation caused is known as plastic
deformation.

5. STRESS:
Stress is defined as the restoring force acting per unit
area. The restoring force is equal and opposite to the applied
force(F).
TYPES OF STRESS:
(i) Linear or Longitudinal or normal stress
1. Tensile Stress
2. Compressive Stress
(ii) Shearing or tangential stress
(iii)Volume or Bulk stress

6. Types of stresses:
(i) Linear or Longitudinal or normal stress
When the force applied is perpendicular(or normal)
to the surface of the body, then the stress applied is called as
normal stress.
tensile stress - stress that tends to stretch
or lengthen the material - acts normal to the
stressed area
compressive stress - stress that tends to
compress or shorten the material - acts normal
to the stressed area

7. Types of stresses:
(ii) Shearing or tangential stress
When the force is applied along the
surface of the body, then the stress applied is
called as shearing stress.
(iii) Volume or Bulk stress
When a body is subjected to normal
external forces from all sides, then the stress
applied is called as volume stress.

8. STRAIN:
Strain is defined as the ratio of change in dimension
produced by the external force on the body to its original
dimension.
Since it is the ratio of two similar quantities, it has no unit
or dimension.
Types of strain:
(i)Linear strain or Longitudinal Strain =
change in length
original length
(ii)Shearing strain or Tangential Strain=θ (Angular
deformation produced due to the application of external tangential force)
(iii)Volume or Bulk strain =
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑉𝑜𝑙𝑢𝑚𝑒
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑉𝑜𝑙𝑢𝑚𝑒

11. HOOKE’S LAW
Robert Hooke stated
that stress is directly
proportional to the strain
produced, within the elastic
limit.
ELASTIC LIMIT:
The maximum stress upto which a body can able
to regain its original shape or size after the removal of
deforming force is called elastic limit.

12. HOOKE’S LAW
Robert Hooke stated that “within the elastic
limit, stress developed in a body is directly
proportional to the strain produced in it.
Stress α Strain
Stress = a constant(E) x Strain
Where E is a constant of proportionality called elastic
modulus(or) modulus of elasticity. It depends on
nature of the materials. It’s unit is Nm-2 or Pa.

13. CLASSIFICATION OF ELASTIC MODULUS
Three kinds of elastic moduli are possible
based on three types of stress and strain.
1. Young’s Modulus
2. Rigidity Modulus
3. Bulk Modulus

14. YOUNG’S MODULUS
Young’s modulus is the ratio of the longitudinal
stress to the longitudinal strain, within the elastic limit
and is usually represented by Y.
Longitudinal stress =
Longitudinal force
area
=
Linear or Longitudinal strain=
change in length
original length
=

15. RIGIDITY MODULUS
The rigidity modulus is defined as the ratio
between shearing stress to shearing strain, within the
elastic limit.
Rigidity modulus(n) =
Tangential stress
Shearing strain
Shearing stress =
Shearing Strain = θ =
𝐴𝐴′
𝐴𝐹
=
𝑙
𝐿
Rigidity Modulus =
𝐹
𝐴θ
=
𝐹𝐿
𝐴𝑙
Unit: 𝑁𝑚−2

16. BULK MODULUS
The ratio of the volume stress to volume strain,
within the elastic limit is called the bulk modulus of
elasticity and is usually denoted by the symbol K.
Bulk modulus(K) =
Bulk stress
Bulk strain
Bulk stress =
Bulk Strain =
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑉𝑜𝑙𝑢𝑚𝑒
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑉𝑜𝑙𝑢𝑚𝑒
=
𝑣
𝑉
Bulk Modulus =
𝐹𝑉
𝐴𝑣
Unit: 𝑁𝑚−2

17. STRESS STRAIN DIAGRAM
A-Proportional Limit
B-Elastic Limit
Sy-Yield Strength
D-Tensile Strength
E-Fracture Point

18. USES OF STRESS STRAIN DIAGRAM
 It is used to measure the elastic strength, yield
strength, ultimate tensile strength and breaking point
of the materials.
 It is used to estimate the working stress and safety
factor of an engineering material.
It is used to identify the ductile and brittle materials.

19. Stress-strain behavior of brittle and ductile material
DUCTILE MATERIALS
If a material can acquire a large permanent
deformation, without fracture or rupture, it is said
to be ductile. Examples of ductile substances are
aluminium, gold, silver, brass, annealed copper
and low-carbon steel.
BRITTLE MATERIALS
A brittle substance is one which ruptures
without any appreciable amount of permanent
deformation being produced in it. Examples of
brittle materials are glass, stone, ceramics, cast
iron and high carbon steel.
SAFETY FACTOR
The ratio between the ultimate tensile stress and the working stress is
called safety factor.
 The working stress of a body is kept far below the ultimate tensile stress and
it is never allowed to cross the elastic limit.
 For steel structures, the safety factor is about 4 since the steel is a very good
engineering material. But for brick structures, it is about 10 since it is not a
very good elastic material.

20. FACTORS AFFECTING ELASTIC MODULUS
AND TENSILE STRENGTH
1. Effect of temperature
2. Effect of annealing
3. Effect of hammering and rolling
4. Presence of impurities
5. Due to the nature of crystals
6. Effect of constant stress

21. EFFECT OF TEMPERATURE
A rise in temperature usually decreases elasticity.
With rise in temperature, the distance between atoms also
increases and so the elastic restoring force decreases. This in
turn decreases the elasticity.
Examples
1. The elastic property of lead increases when the
temperature is decreased.
2. The carbon filament becomes plastic at higher
temperatures.

22. EFFECT OF ANNEALING
Annealing is a process by which the material is
heated to a very high temperature and then it is slowly
cooled. While annealing constituent crystals are uniformly
oriented and form larger crystal grains. This results in
decrease in their elastic properties.
EFFECT OF HAMMERING AND ROLLING
While being hammered or rolled larger crystal
grains break into smaller grains resulting in increasing of
their elastic properties.

23. EFFECT OF IMPURITIES
The addition of impurities produces variation in the
elastic property of the materials. The increase and decrease
of elasticity depends upon the type of impurity added to it.
Examples:
1. When potassium is added to gold, the elastic property
of gold increases.
2. When carbon is added to molten iron, the elastic
property of iron decreases provided the carbon content
should be more than 1% in iron.

24. EFFECT OF NATURE OF CRYSTALS
The elasticity also depends on the types of the
crystals, whether it is a single crystal or poly crystals. For a
single crystal, the elasticity is more and for a poly crystal ,
the elasticity is less. The metal of smaller grains has better
elasticity than the same metal of larger grains.
EFFECT OF CONSTANT STRESS
When a material is subjected to large number of
cycles of stresses, it loses its elastic property even within the
elastic limit.

25. POISSON’S RATIO
Poisson’s ratio of a given material can be defined as the
ratio between the lateral strain to longitudinal strain within
the elastic limits.

26. Poisson’s Ratio (σ) has no units and dimensions.
Theoretically σ lies between -1 and +
1
2
. Practically σ lies
between 0 and +
1
2

27. PROBLEMS
1.
2.