EP015 Lecture 11L

Chapter 11

11.1 Stress & Strain.
11.2 Young’s Modulus.

11.3 Bulk Modulus.

CONCEPTUAL MAP : Deformation of Solid

CHAPTER 11 : DEFORMATION OF SOLID

11.0 INTRODUCTION

Matter is made up of many
particles called atoms or
molecules. Binding forces
(bonds) are holding atoms
or molecules together.

Matter consists of three
basic phase, i.e.
solids, liquids and gases.

LEARNING OUTCOMES : Deformation of Solid

11.1 STRESS & STRAIN

Forces not only cause
acceleration, but can also cause
changes in the inner structure of
solids (externally changes shape
or size). Such changes are
called “deformations”.

The effect of complex molecular
forces can be described by the
measurable quantities :
“stress” and “strain”.

11.1 STRESS & STRAIN

Stress,  :

It refers to the distorting
force acting on a unit cross-
section area of an object. It
defined as :

The basic unit for stress is
kgm-1s-2 or normally known
as Nm-2.

11.1 STRESS & STRAIN

There are 2 types of stress :
Tensile stress &
Compressive stress.

Tensile stress :
The wire is extended
horizontally by a pair
a pair of opposite force.

Compressive stress :
The wire is compressed
horizontally by a pair
a pair of opposite force.

11.1 STRESS & STRAIN

11.1 STRESS & STRAIN

Strain,  :

It refers to the extension
(elongation) per unit original
length of an object when
there is a distorting force
applied on it.

There is no unit for strain.

11.1 STRESS & STRAIN
ELASTIC STRESS - STRAIN GRAPH

When an external force is
stretching / compressing a
wire, the wire will be
elongated. In this process,
the attractive / repulsive
force between the atoms is
increased to oppose the
external force.

11.1 STRESS & STRAIN
ELASTIC STRESS - STRAIN GRAPH

Proportionality limit (Point A) :
= Maximum stress for which
Hooke’s law is still valid.

Elastic limit (Point B) :
= The maximum value by which
the wire can be stretched by a
distorting force and still regains
its original shape after the force
is removed.

11.1 STRESS & STRAIN
PLASTIC STRESS - STRAIN GRAPH

Applying external force
greater than the elastic limit
causes permanent
deformation, also called
“plastic deformation”.

The wire does not regain its
original shape after the force
is removed.

11.1 STRESS & STRAIN
PLASTIC STRESS - STRAIN GRAPH

The yield point (Point C) :
= The point where at a certain
strain begins to increase
rapidly with increasing stress.

Ultimate tensile strength,
UTS (Point E) :
= The largest stress at which
the body still does not rupture
(break).

11.1 STRESS & STRAIN
PLASTIC STRESS - STRAIN GRAPH

The ultimate tensile strength
of the wire is the stress at
which it breaks.

Ductile metals such as
copper can undergo a great
deal of plastic deformation
before they break.

11.1 STRESS & STRAIN
PLASTIC STRESS - STRAIN GRAPH

LEARNING OUTCOMES : Deformation of Solid

11.2 YOUNG’S MODULUS
Young’s Modulus, Y :
Young’s Modulus of a material (such as wire)

is defined as :

The unit for Y is the same as the stress, i.e. Nm-2.

11.2 YOUNG’S MODULUS

11.2 YOUNG’S MODULUS
STRAIN ENERGY

The strain energy :
= The energy stored by the
material when there is force to
compress or extend it.

11.2 YOUNG’S MODULUS
STRAIN ENERGY

Graphically, since the external
force exerted on the wire
increases uniformly, then :

11.2 YOUNG’S MODULUS
STRAIN ENERGY PER UNIT VOLUME

Then, the area under the stress-
strain graph is equal to the
energy stored per unit volume.

LEARNING OUTCOMES : Deformation of Solid

11.3 BULK MODULUS

11.3 BULK MODULUS

11.3 BULK MODULUS

11.3 BULK MODULUS

11.3 BULK MODULUS

LEARNING OUTCOMES : Deformation of Solid