Properties of Metals
This chapter discusses the mathematical method used to calculate the elongation
of a material under tensile force and elasticity of a material.
STATE Hooke's Law.
DEFINE Young's Modulus (Elastic Modulus) as it relates to
Given the values of the associated material properties,
CALCULATE the elongation of a material using Hooke's Law.
If a metal is lightly stressed, a temporary deformation, presumably permitted by an elastic
displacement of the atoms in the space lattice, takes place. Removal of the stress results in a
gradual return of the metal to its original shape and dimensions. In 1678 an English scientist
named Robert Hooke ran experiments that provided data that showed that in the elastic range of
a material, strain is proportional to stress. The elongation of the bar is directly 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 may be given by Equation (2-3).
This simple linear relationship between the force (stress) and the elongation (strain) was
formulated using the following notation.
force producing extension of bar (lbf)
length of bar (in.)
cross-sectional area of bar (in.2)
total elongation of bar (in.)
elastic constant of the material, called the Modulus of Elasticity, or
Young's Modulus (lbf/in.2)
The 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 often called Young's Modulus.