The Difference Between True Stress and Engineering Stress
Think about pulling a bar in tension. Load
divided by cross-sectional area is force, or stress. But what
cross section are you considering? Before starting pull, the
bar had a known cross-section of (lets say) 0.5" wide x metal
thickness. It's easy to measure these, since it is your
starting material. At any load, the engineering stress is the
load divided by this initial cross- area. While you are
pulling, the length increases, but the width and thickness
shrink. At any load, the true stress is the load divided by the
cross-area at that instant. Unless thickness and width are
being monitored continuously during the test, you cannot
calculate true stress. It is, however, a much better
representation of how the material behaves as it is being
deformed, which explains its use in forming simulations. In
circle grid analysis, engineering strain is the % expansion of
the circle compared to the initial diameter of the circle. The
relationships between engineering values and true values are:
σ = s (1+e) ε =
ln (1+e)
Where "s" and "e" are the engineering stress and strain,
respectively, and "
" and "
" are the true stress and strain,
respectively.