the object, in other words, strain measures the degree of deformation. As an example, in one dimension, consider a rod of length L when it stretches to a new length ∆ L then Strain, ε = Changeinsize Originalsize = ∆ L L ( . ) ε is a dimensionless quantity and has no unit. Strain is classified into three types.
( ) Longitudinal strain When a rod of length L is pulled by equal and opposite forces, the longitudinal strain is defined as ε l = Increaseinlengthof therod Originalornaturallengthof therod = ∆ L ( . ) Longitudinal strain can be classified into two types - - - - Unit Properties of matter Figure . (b) Variation of ∆L with F Stretching force (F) Slope m = Extension( L) F Therefore, ∆ L = (slope)F Multiplying and dividing by volume, V = A L, F (slope) = AL AL D Rearranging, we get F A slope ∆ ( ) Therefore, F ∝ ∆ Comparing with equation ( . ) and equation ( .
), we get equation ( . ) as σ ∝ ε i.e., the stress is proportional to the strain in the elastic limit. Stress – Strain profile curve: The stress versus strain profile is a plot in which stress and strain are noted for each load and a graph is drawn taking strain along the X-axis and stress along the Y-axis. The elastic characteristics of the materials can be analyzed from the stress-strain profile.
Figure . Stress-Strain profile B C D Stress Strain o OA : Proportional limit OB : Elastic behaviour BCDE : Plastic behaviour B : Elastic limit D : Ultimate stress point E : Breaking or rupture point removal of deforming force is called the elastic limit. If the deforming force exceeds the elastic limit, the body acquires a permanent deformation. For example, rubber band loses its elasticity if pulled apart too much.
It changes its size and becomes misfit to be used again. . . Hooke’s law and its experimental verification Hooke’s law states that for a small deformation within the elastic limit, the strain