Elasticity
Elasticity is a measure of the deformation of an object when a force is applied.
Referred Video:
https://www.youtube.com/watch?v=GhUGNBuBfFA or
https://www.youtube.com/watch?v=XRKkjm4cuFE
Stress:
Stress is force over area.
𝜎=
𝐹
𝐴
Where
For Area of Wire
A = Area in 𝑚2
r= Radius in m
D=Diameter in m
For Force
𝐴 = 𝜋𝑟 2
𝐷
𝑟=
2
𝐹 = 𝑊 = 𝑚𝑔
Where
𝑔 = 9.8 𝑚⁄𝑠
Types of Stress
Tensile Stress
If the deforming force or applied
force results in the increase in the
object’s length then the resulting
stress is termed as tensile stress. For
example: When a rod or wire is
stretched by pulling it with equal and
opposite forces (outwards) at both
ends.
Volumetric Stress
When the deforming force or
applied force acts from all
dimensions resulting in the
change of volume of the object
then such stress in called
volumetric stress or Bulk stress.
In short, when the volume of
body changes due to the
deforming force it is termed as
Volume stress.
Shear Stress
When the direction of the
deforming force or external
force is parallel to the crosssectional area, the stress
experienced by the object is
called shearing stress or
tangential stress. This
results in the change in the
shape of the body
Strain:
Strain is change in length over original length.
𝑆𝑡𝑟𝑎𝑖𝑛 =
Tensile Strain
X=l
𝛥𝑥
𝑥
Volumetric Strain
X=V
Shear Strain
Modulus of Elasticity:
it is a measure of how easily any material can be bent or stretched.
λ=
Elastic Modulus
Young's modulus (Y)
Bulk modulus (B)
Shear modulus or Rigidity modulus (S)
𝑆𝑡𝑟𝑒𝑠𝑠
𝑆𝑡𝑟𝑎𝑖𝑛
Definition
Tensile strain
Bulk strain
Shear strain
Nature of strain
Change of shape and size
Change of size but not shape
Change of shape but not size
Hooke’s Law
Hooke's law states that the strain of the material is proportional to the applied stress within the
elastic limit of that material.
Stress-Strain Curve:
Referred Link, https://www.youtube.com/watch?v=OdU4t6JD6aE
Material Property:
The term "property" is a qualitative or quantitative measure of response of materials to
externally imposed conditions like forces and temperature.
Following are the properties w.r.t Stress and Strain (Elaborate both Topics)
Referred Video: https://www.youtube.com/watch?v=9qcqfp5d6aA
Term
ELASTICITY
Definition
The ability of a material to return to its original shape
after being stretched or compressed Example: Steel,
Spring‫۔‬
PLASTICITY
The ability of a material to permanently change its
shape without breaking when a force is applied. Ex:
Rubber band.
Strength
The ability of a material to withstand external forces
without breaking or deforming.
STIFFNESS
The resistance of a material to bending or deformation
when subjected to a force.
E.g. Steel beam is more stiffer or more rigid than
aluminum beam.
DUCTILITY
The ability of a material to be stretched into a wire or
thread without breaking. Ex: Platinum, Iron, Copper,
Aluminum and Zinc.
Malleability
The ability of a material to be shaped or formed into
various shapes without breaking. E.g Lead can be
readily rolled and hammered into thin sheets but can
be drawn into wire.
RESILIENCE
The ability of a material to absorb energy when
subjected to stress and then release it when the force is
removed, without permanent deformation.
Hardness
Ability of the material to withstand plastic
deformation or indentations (‫ )کھوکھیل‬produced in the
material.
BRITTLENESS The tendency of a material to break or fracture under
stress, without significant deformation. Ex: glass
Creep
The slow and gradual deformation of a material over
time when subjected to a constant load or stress.
Fatigue
The weakening or failure of a material over time due
to repeated or cyclic loading.
Slogan
Gain Orignal Shape
Permanently change
Hard to broken
Hard to deformed
To make wire
To make sheets
To absorb energy
Resist plastic deformation
Tendency to Break
Deformation over time
Weakening over time