State Hooke's law of elasticity.

Explanation

Hooke.s low is for a small deformation, when the stress and strain are proportional to each other. it can be verified in a simple way by stretching a thin straight wire (stretches like spring) of length L and uniform cross sectional area A suspended from a fixed point O. A pan and a pointer are attached at the free and of the wire. The extension produced on the wire is measured using a vernier scale arrangement. the experiment shows that for a given load, the corresponding stretching force is F and the elongation produced on the the wire is`DeltaL`. It is directly proportional to the original length L and inversely proportional to the area of cross section A. A graph is plotted using F on the x-axis and `DeltaL`on the y-axis.
Therefore, `DeltaL = ("slope")F`
Multiplying and dividing by volume,
`V = AL`
`F("slope") = (AL)/(AL)`
Rearranging, we get `F/A = (L/(A("slope")))(DeltaL)/(L)`
Therefore, `F/A prop ((Delta L)/(L))`
Comparing with stress and strain equations, `sigma prop epsilon`. I.e., the stress is proportional to hte 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 analysed from the stress -strain profile.
(a) Portion OA: in this reason, stress is very small such that stress is proportional to strain, which means Hook.s law is valid. The point A is called limit of proportionality because above this point Hook.s law is not valid. The slope of the line OA gives the Young.s modulus of the wire.
(b) Portion AB: the reason is reached if the stress is increased by a very small amount. In this reason, stress is not proportional to the strain. But once the stretching force is hence, the point B is known as yield point (elastic limit). The elastic hebaviour of the material (here wire) in stress-strain curve is OAB.
(c ) Portion BC: if the wire is stretched beyond the point B (elastic limit), stress increases and the wire will not regain its original length after the removal of of stretching force.
(d) portion CD: with further increase in stress (beyond the point C), the stress increases rapidly and reaches the point D. Beyond D, the strain increases even when the load is removed and brakes (raptures) at the point E. Therefore the maximum stress (here D) beyond which the wire breaks is called breaking stress tensile strength. The corresponding point D is known as the fracture point. The reason BCDE represent the plastic .