MECHANICAL
PROPERTIES OF SOLIDS
Elasticity- The property of a body, by virtue
of which it tends to regain its original size and shape when the applied force
is removed, is known as elasticity and the deformation caused is known as
elastic deformation.
Plasticity-if you apply force to a lump of
putty or mud, they have no gross tendency to regain their previous shape, and
they get permanently deformed. Such substances are called plastic and this
property is called plasticity.
Plasticity-if you apply force to a lump of
putty or mud, they have no gross tendency to regain their previous shape, and
they get permanently deformed. Such substances are called plastic and this
property is called plasticity.
If you try to displace any ball from its equilibrium
position, the spring system tries to restore the ball back to its original
position. Thus elastic behaviour of solids can be explained in terms of
microscopic nature of the solid.
Robert Hooke, an English physicist (1635 - 1703
A.D) performed experiments on springs and found that the elongation (change in
the length) produced in a body is proportional to the applied force or load.
In 1676, he presented his law of elasticity, now called Hooke’s law.
Stress- When a body is subjected to a deforming force, a
restoring force is developed in the body. This restoring force is equal in
magnitude but opposite in direction to the applied force. The restoring force
per unit area is known as stress.
{ If F is the force applied and A is the area of cross
section of the body, Magnitude of the stress = F/A}
SI Unit- N m–2 or
pascal (Pa)
Dimensional formula- [ ML–1T–2 ]
The restoring force per unit area in this case is called tensile stress.
Tensile or compressive stress can also be termed as longitudinal stress.
The change in the length ΔL to the original length L of the body is known as longitudinal strain.
The restoring force per unit area developed due to the applied tangential force is known as tangential or shearing stress
As a result of applied tangential force, there is a relative
displacement Δx between opposite faces of the cylinder as shown in the. The
strain so produced is known as shearing strain.
The internal restoring force per unit area in this case is
known as hydraulic stress and in magnitude is equal to the hydraulic
pressure (applied force per unit area).
The strain produced by a hydraulic pressure is called volume
strain and is defined as the ratio of change in volume (ΔV) to the original
volume (V).
HOOKE’S LAW-
Stress and strain take different forms in the situations
depicted . For small deformations the stress and strain are proportional to
each other. This is known as Hooke’s law.
Thus,
stress ∝ strain
stress = k × strain
where k is the proportionality constant and is known as
modulus of elasticity.
Hooke’s law is an empirical law and is found to be valid for
most materials. However, there are some materials which do not exhibits this
linear relationship.
ELASTIC MODULI
The ratio of stress and strain, called modulus of
elasticity.
1.
Young’s Modulus
The ratio of tensile (or compressive) stress (σ) to the
longitudinal strain (ε) is defined as Young’s modulus and is denoted by the
symbol Y.
2.
Bulk Modules
The ratio of hydraulic stress to the corresponding hydraulic strain is called bulk modulus. It is denoted by symbol B.
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