Definition of
Modulus of Elusticity:
It is often difficult to precisely define yielding due to the wide variety
of
stress–strain curves exhibited
by real materials. In addition, there are several possible ways to define
yielding:
[1]
True
elastic limit: The lowest stress at which
dislocations
move. This definition is rarely used, since dislocations move at very low
stresses, and detecting such movement is very difficult.
Proportionality limit:Up
to this amount of stress, stress is proportional to strain (
Hooke's
law), so the stress-strain graph is a straight line, and the gradient will
be equal to the
elastic modulus of the material.
Elastic
limit (yield strength):Beyond the elastic limit, permanent
deformation will occur. The elastic limit is therefore the lowest stress at
which permanent deformation can be measured. This requires a manual load-unload
procedure, and the accuracy is critically dependent on the equipment used and
operator skill. For
elastomers, such as
rubber, the elastic
limit is much larger than the proportionality limit. Also, precise strain
measurements have shown that plastic strain begins at low stresses.
[2][3]
Yield
point:The point in the stress-strain curve at which the curve
levels off and plastic deformation begins to occur.
[4]
Offset
yield point (proof stress):When a yield point is not easily
defined based on the shape of the stress-strain curve an
offset yield point
is arbitrarily defined. The value for this is commonly set at 0.1 or 0.2% strain.
[5]
The offset value is given as a subscript, e.g., R
p0.2=310 MPa.
[6]
High strength steel and aluminum alloys do not exhibit a yield point, so this
offset yield point is used on these materials.
[5]
Upper and lower yield points:Some
metals, such as
mild steel, reach an upper yield point before dropping
rapidly to a lower yield point. The material response is linear up until the
upper yield point, but the lower yield point is used in structural engineering
as a conservative value. If a metal is only stressed to the upper yield point,
and beyond,
Lüders bands can develop.
[7]
