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Stress
is a force normalized by the area to which it is applied. If a force, DF,
acts on a small rectangular parallepiped across a face of area, DA,
the stress at the center of the parallepiped is defined by: s
= LimDA
-> 0
( DF/DA).
The stress acts in the direction of the applied force.
For
many engineering applications, an applied uniaxial force is normalized
by the initial cross-sectional area, A0,
of the sample to define a nominal or engineering stress:
Engineering
Stress = (F/A0) =
sN
The
true stress under the same conditions is determined by normalizing the
applied force with the actual area of the sample, Ai
:
True
Stress = (F/Ai) =
sT
In
the plastic deformation range before necking A0L0
= AiLi, so that the expression for true stress may
be written in terms of the engineering stress:
True
Stress = (F/A0L0/Li)
= sN(1
+ eN) |
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