Resilience is the
ability of a material to absorb energy when it is deformed elastically, and
release that energy upon unloading. The modulus of resilience is defined as the
maximum energy that can be absorbed per unit volume without creating a
permanent distortion. It can be calculated by integrating the stress-strain curve from
zero to the elastic limit. In uniaxial tension,
.
.
References
1. Campbell,
Flake C. (2008). Elements of
Metallurgy and Engineering Alloys. ASM International. p. 206. ISBN 9780871708670.
Young's
modulus , also known as the tensile
modulus , is a measure of the stiffness of an elastic material
and is a quantity used to characterize materials. It is defined as the ratio of the
uniaxial stress over
the uniaxial strain in
the range of stress in which Hooke's lawholds. [ 1 ] In solid mechanics , the slope of the stress-strain curve at any point is called the tangent modulus . The
tangent modulus of the initial, linear portion of a stress-strain curve is
called Young's modulus . It
can be experimentally determined from the slope of astress-strain curve created during tensile tests conducted
on a sample of the material. In anisotropic materials,
Young's modulus may have different values depending on the direction of the
applied force with respect to the material's structure.
It is
also commonly called the elastic modulus or modulus
of elasticity , because
Young's modulus is the most common elastic modulus used, but there are other
elastic moduli measured, too, such as the bulk modulus and
the shear modulus .
Young's
modulus is named after Thomas Young , the 19th century British scientist. However, the concept was developed in
1727 byLeonhard Euler , and the first experiments that used
the concept of Young's modulus in its current form were performed by the
Italian scientist Giordano Riccati in 1782, predating Young's work by 25
years. [ 2 ]
Young's modulus, E ,
can be calculated by dividing the tensile stress by
the tensile strain in the
elastic (initial, linear) portion of thestress-strain curve :
Where :
E is the Young's modulus
(modulus of elasticity)
F is the force exerted on an
object under tension;
A 0 is the
original cross-sectional area through which the force is applied;
ΔL is the amount by which the
length of the object changes;
L 0 is the
original length of the object.
|
Material
|
lbf/in² (psi)
|
|
|
Steel (ASTM-A36)
|
200[ 3 ]
|
29,000,000
|
References
1. ^ Nic, M.; Jirat, J.; Kosata,
B., eds. (2006–). "modulus of elasticity (Young's modulus), E " . IUPAC Compendium of Chemical Terminology (Online
ed.). doi :10.1351/goldbook.M03966 . ISBN 0-9678550-9-8 .
2. ^ The Rational Mechanics of
Flexible or Elastic Bodies, 1638–1788 : Introduction to Leonhardi
Euleri Opera Omnia, vol. X and XI, Seriei Secundae. Orell Fussli.
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