YOUNG'S MODULUS
DOE-HDBK-1017/1-93
Properties of Metals
Previously, we learned that 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 in pounds force per
square inch.
(2-4)
s
P
A
We also learned that tensile strain, or the elongation of a bar per unit length, is determined by:
(2-5)
e
d
Thus, the conditions of the experiment described above are adequately expressed by Hooke's Law
for elastic materials. For materials under tension, strain (e) is proportional to applied stress s.
(2-6)
e
s
E
where
E
=
Young's Modulus (lbf/in.2)
s
=
stress (psi)
e
=
strain (in./in.)
Young's Modulus (sometimes referred to as Modulus of Elasticity, meaning "measure" of
elasticity) is an extremely important characteristic of a material. It is the numerical evaluation
of Hooke's Law, namely the ratio of stress to strain (the measure of resistance to elastic
deformation). To calculate Young's Modulus, stress (at any point) below the proportional limit
is divided by corresponding strain. It can also be calculated as the slope of the straight-line
portion of the stress-strain curve. (The positioning on a stress-strain curve will be discussed
later.)
E = Elastic Modulus =
stress
strain
psi
in./in.
psi
or
(2-7)
E
s
e
MS-02
Page 12
Rev. 0
