In the use of metal for
mechanical engineering purposes, a given state of stress
usually exists in a considerable volume of the material.
Reaction of the atomic structure will manifest itself on a
macroscopic scale. Therefore, whenever a stress (no matter
how small) is applied to a metal, a proportional dimensional
change or distortion must take place.
Such a proportional
dimensional change (intensity or degree of the distortion) is
called strain and is measured as the total elongation
per unit length of material due to some applied stress.The equation below illustrates this proportion or distortion.
strain (in./in., mm/mm)
δ = total
elongation or change of length after force applied (in., mm)
L = original length (in., mm)
Types of Strain
Strain may take two forms;
elastic strain and plastic deformation.
Elastic strain is a
transitory dimensional change that exists only while the
initiating stress is applied and disappears immediately upon
removal of the stress. Elastic strain is also called elastic
deformation. The applied stresses cause the atoms in a
crystal to move from their equilibrium position. All the
atoms are displaced the same amount and still maintain their
relative geometry. When the stresses are removed, all the
atoms return to their original positions and no permanent deformation occurs.
Plastic deformation (or
plastic strain) is a dimensional change that does not
disappear when the initiating stress is removed. It is
usually accompanied by some elastic strain. The phenomenon of
elastic strain and plastic deformation in a material are
called elasticity and plasticity, respectively.
At room temperature, most metals have some elasticity, which
manifests itself as soon as the slightest stress is applied.
Usually, they also possess some plasticity, but this may not
become apparent until the stress has been raised appreciably.
The magnitude of plastic strain, when it does appear, is
likely to be much greater than that of the elastic strain for
a given stress increment. Metals are likely to exhibit less
elasticity and more plasticity at elevated temperatures. A
few pure unalloyed metals (notably aluminum, copper and gold)
show little, if any, elasticity when stressed in the annealed
(heated and then cooled slowly to prevent brittleness)
condition at room temperature, but do exhibit marked
plasticity. Some unalloyed metals and many alloys have marked
elasticity at room temperature, but no plasticity.
The state of stress just
before plastic strain begins to appear is known as the proportional
limit, or elastic limit, and is defined by the stress
level and the corresponding value of elastic strain. The
proportional limit is expressed in pounds per square inch.
For load intensities beyond the proportional limit, the
deformation consists of both elastic and plastic strains. As
mentioned previously in this chapter, strain measures the
proportional dimensional change with no load applied. Such
values of strain are easily determined and only cease to be
sufficiently accurate when plastic strain becomes dominant.