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Tensile (Load) Tests and Stress-Strain Curves | Up
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Figure 4 Typical Brittle Material Stress-Strain Curve |
Properties of Metals
DOE-HDBK-1017/1-93
STRESS-STRAIN RELATIONSHIP
A graph of the results is made from the tabulated data. Some testing machines are equipped with
an autographic attachment that draws the graph during the test. (The operator need not record
any load or elongation readings except the maximum for each.) The coordinate axes of the graph
are strain for the x-axis or scale of abscissae, and stress for the y-axis or scale of ordinates. The
ordinate for each point plotted on the graph is found by dividing each of the tabulated loads by
the original cross-sectional area of the sample; the corresponding abscissa of each point is found
by dividing the increase in gage length by the original gage length. These two calculations are
made as follows.
Stress =
= psi or lb/in.2
(2-9)
load
area of original cross section
P
Ao
Strain =
(2-10)
instantaneous gage length original
original gage length
elongation
original gage length
=
= inches per inch x 100 = percent elongation
(2-11)
L Lo
Lo
Stress and strain, as computed here, are sometimes called "engineering stress and strain." They
are not true stress and strain, which can be computed on the basis of the area and the gage length
that exist for each increment of load and deformation. For example, true strain is the natural log
of the elongation (ln (L/Lo)), and true stress is P/A, where A is area. The latter values are usually
used for scientific investigations, but the engineering values are useful for determining the load-
carrying values of a material. Below the elastic limit, engineering stress and true stress are
almost identical.
Figure 3 Typical Ductile Material
Stress-Strain Curve
The graphic results, or stress-strain diagram, of
a typical tension test for structural steel is
shown in Figure 3. The ratio of stress to strain,
or the gradient of the stress-strain graph, is
called the Modulus of Elasticity or Elastic
Modulus. The slope of the portion of the curve
where stress is proportional to strain (between
Points 1 and 2) is referred to as Young's
Modulus and Hooke's Law applies.
The following observations are illustrated in
Figure 3:
Hooke's Law applies between
Points 1 and 2.
Hooke's Law becomes questionable between Points 2 and 3 and strain increases
more rapidly.
Rev. 0
Page 17
MS-02
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