Virtual Lab Tension Test
ELASTIC DEFORMATION IN MATERIALS
True Stress
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This is defined as the ratio of the load to the instantaneous area supporting the load.
True strain is defined as:
Engineering strain is then
For small strains, the true strain 
and engineering strain 
are related by the above equation. For large strains, this equation does not hold, and only the true strain values must be used. For example, in metal working calculation true strain must be used. For large strains, the true strain can be calculated from the relation
that is, using the change in cross-sectional area at a point.
A typical curve from a tension test is shown below.
Unlike the engineering stress-strain curve, the slope above is always positive and the slope decreases with increasing strain. Although in the elastic range stress and strain are linearly related, the total curve is approximated by a power law.
When the true stress-strain curve is plotted on a log-log scale, a straight line is obtained as shown below, and the slope of the line is equal to the exponent of 
in the power law expression representing the curve.
Toughness is defined as the area under the entire true stress – strain curve.
Toughness = 
where 
is the true fracture strain
Toughness is energy per unit volume that has been dissipated up to the point of fracture. Note that this energy pertains only to the volume of material at the region of the neck. Volume of the material away from the neck undergoes less strain and hence dissipates less energy.
