6.5 Hooke's Law
The statement regarding strain & stress being proportional
to each other in the elastic region is known as Hooke's law. "Within Elastic
limit stress and strain are directly proportional to each other".
i.e., Stress a Strain within elastic limit.
The constant ratio of stress to strain within elastic limit is called elastic
Note : Unit of Elastic modules is same as that of stress (as strain
has no limit) viz. n/m2.
The behavior of an elastic object, with increasing stress is represented
in the Stress - Strain Curve shown below.
OP = Linear Elastic region
PQ = Rising Fatigue region
QR = Total Yield, with breaking into pieces
P = Elastic limit
Q = Yield Point
Linear Elastic region
In this region if stress is increased from O to A & is
decreased back from A to O then, the strain increases in direct proportion from,
O to C and decreases from C to O in the same proportion. In this region the
object retain its elasticity, strain is the directly proportional to strain.
The limit point 'P' of this region is called elastic limit.
Rising Fatigue region
In this strain region increases with the same amount as, the
increase in stress; eventually the substance looses its elasticity partially,
and therefore becomes partially plastic. This deformation remains permanent,
even if the stress is reduced back from B to A and then from A to O. The end
point of this region 'Q' is called the Yield Point.
The total yield region
The region QR, represents infinitely large increase in strain
produced when stress is increased even by small amount; the substance has completely
lost its elasticity & has become completely plastic; hence it yields completely
to deforming forces. The substance in this region can be broken into pieces.