Is the assumption on commonly used conversion between true and engineering stress for tensile testing wrong?
When I Google conversion between engineering and true stress conversion, I found a ton of webpages using the following formula:
True strain = ln(1 + engineering strain)
True stress = (engineering stress) * exp(true strain) = (engineering stress) * (1 + engineering strain)
However, this stress conversion is only true when the material is fully incompressible (Poisson's ratio = .5). For plastics of Possion's ratio often around 0.3, current area * current length ≠ original area * original length, and therefore this equation is quite problematic.
Am I thinking wrong, or that this equation (that has been long used by the industry) wrong?
Thanks,
Shawn
Indeed the formula you mentioned is with the assumption of volume conservation during plastic deformation. For metals (mostly) plastic deformation is independent of hydro-static stress (J2 plasticity). In metals, the volume changes during elastic deformation according to the Poisson ratio (mostly 0.29-0.33) but the plastic strains show volume conservation. Generally, Poisson's ratio is defined for elastic deformation.
In case the plasticity is hydro-static stress dependent (such as concrete or rocks etc) then the above mentioned formula for true stress is indeed not valid because then you get an irrecoverable volume change.
Just FYI, another requirement for the validity of above mentioned formula is that the strain must remain uniform in the tensile specimen (i.e. the formula is valid up to maximum force).
Dear Wang,
This confusion always exist. But there is a very minor difference between the engineering strain and true strain at less deformation and at low temperature. But it show more difference for large deformation and high temperatures. Please refer Mechanical metallurgy book by Dieter for more information
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