Hooke's Law:
A temporary deformation if a metal is lightly stressed, presumably allowed through an elastic displacement of the atoms within the space lattice, takes place. Removal of the stress concludes within a gradual return of the metal to its original shape and dimensions. In the year of 1678 an English scientist named Robert Hooke ran experiments which provided data which showed that inside the elastic range of a material, strain is proportional to stress. The elongation of the bar is straightly proportional to the tensile force and the length of the bar and inversely proportional to the cross-sectional area and the modulus of elasticity.
Hooke's experimental law might be providing through Equation (1).
δ = Pl /AE (1)
This simple linear relationship among the force (stress) and the elongation (strain) was formulated using the subsequent notation.
P = force producing extension of bar (lbf)
l = length of bar (in.)
A = cross-sectional area of bar (in.2)
δ = total elongation of bar (in.)
E = elastic constant of the material and called the Modulus of Elasticity, or Young's Modulus (lbf/in.2)
A quantity E, the ratio of the unit stress to the unit strain, is the modulus of elasticity of the material in tension or compression and is frequently known as Young's Modulus.
Earlier, we learned in which tensile stress, or simply stress, was equated to the load per unit area or force applied per cross-sectional area perpendicular to the force measured within pounds force per square inch.
σ = P/A (2)
We also learned in that tensile strain or the elongation of a bar per unit length is determined through:
ε =δ/l (3)
Therefore, the conditions of the experiment defines above are adequately expressed through Hooke's Law for elastic materials. For materials under tension, strain (ε) is proportional to applied stress.
ε = σ/E (4)
where
E = Young's Modulus (lbf/in.2)
σ = stress (psi)
ε = strain (in. /in.)