test. Also, ductile metal which is pulled in tension becomes unstable and necks
down during the course of the test. Because the cross-sectional area of the
specimen is decreasing rapidly at this stage in the test, the load required continuing
deformation falls off. The average stress based on original area like wise decreases,
and this produces the fall-off in the stress-strain curve beyond the point of
maximum load.
The engineering stress-strain curve does not give a true indication of the
deformation characteristics of a metal because it is based entirely on the original
dimensions of the specimen, and these dimensions change continuously during the
test. Also, ductile metal which is pulled in tension becomes unstable and necks
down during the course of the test. Because the cross-sectional area of the
specimen is decreasing rapidly at this stage in the test, the load required continuing
deformation falls off. The average stress based on original area likewise decreases,
and this produces the fall-off in the stress-strain curve beyond the point of
maximum load. Actually, the metal continues to strain-harden all the way up to
fracture, so that the stress required to produce further deformation should also
increase. If the true stress, based on the actual cross-sectional area of the specimen,
is used, it is found that the stress-strain curve increases continuously up to fracture.
If the strain measurement is also based on instantaneous measurements, the curve,
which is obtained, is known as a true-stress-true-strain curve. This is also known
as a flow curve since it represents the basic plastic-flow characteristics of the
material. Any point on the flow curve can be considered the yield stress for a metal
strained in tension by the amount shown on the curve. Thus, if the load is removed
at this point and then reapplied, the material will behave elastically throughout the
entire range of reloading. The true stress is expressed in terms of engineering
stress s by