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In
order to facilitate comparisons between different samples, the load-displacement
data is converted
into
the sample-size independent quantities stress and strain. For most engineering
applications, stress is obtained from the applied force by normalizing
it with the initial cross-sectional area of the sample:
s
= F/A0
, and strain is obtained from the measured elongation of the sample by
normalizing this by the original length of the sample: e
= DL/L0
. In the elastic range, these quantities are related by Hooke's law such
that: s
=Ee,
where E is Young's Modulus, an elastic constant which is a material property.
At
larger values of DL
the material departs from this elastic behavior and remains permanently
deformed when the applied force is removed. The transition point between
elastic and plastic behavior is known as the yield stress, sy
, and applied stresses on a component during use should remain below this
value.
Loading
a material in compression will also give rise to a similar elastic-plastic
behavior, however, for
some
shapes the sample may buckle before it reaches the plastic deformation
range. This buckling
occurs
at a critical load that depends upon the shape of the sample. For a given
sample length, thin
samples
buckle at lower applied loads than thick samples. For a given cross-sectional
area, long samples buckle at lower applied loads than short samples. The
distribution of material in the structure under test is also important.
For a sample of given mass, a tubular shape will have a higher buckling
threshold than a rod. This is related to the moment of inertia of the cross
section. |
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