STEEL - Materials for Civil and Construction Engineers - page 114

FIGURE 3.12 Tension test on a round steel specimen showing
grips and an extensometer with an LVDT.

True stress
and strain

Engineering
stress and strain

Yield
point

Rupture

Ultimate
strength

Proportional
limit

FIGURE 3.13 Typical stress-strain behavior of mild steel.

cross-sectional area and gauge length. If the stress and stains are calculated
based on the instantaneous cross-sectional area and gauge length, a true
stress-strain curve is obtained, which is different than the engineering
stress-strain curve (Figure 3.13).
As shown in Figure 3.13, the true stress is larger than the engineering
stress, because of the reduced cross-sectional area at the neck. Also, the
true strain is larger than the engineering strain, since the increase in length
at the vicinity of the neck is much larger than the increase in length out-
side of the neck. The specimen experiences the largest deformation (con-
traction of the cross-sectional area and increase in length) at the regions
closest to the neck, due to the nonuniform distribution of the deformation.