Question

Why the material does not experience uniform elongation after necking tensile test

Answer 1

The strain associated with this uniform elongation is called uniform strain. Note that the uniform strain will have both elastic and plastic components. After the tensile strength has been reached, the specimen will undergo non-uniform strain. Most of the remainder of the deformation will be highly localized in a phenomenon known as necking.

During non-uniform deformation, the minimum cross-sectional area decreases as the test proceeds, so the engineering stress (force divided by the original cross-sectional area) falls off as the strain increases. The engineering stress continues to decrease until the sudden fracture at the conclusion of the test. Note that on an engineering stress-strain curve, the fracture strength is actually lower than the tensile strength. On a true stress-strain curve, the stress will continue to increase to failure.

Until the neck forms, the deformation is essentially uniform throughout the specimen, but after necking all subsequent deformation takes place in the neck. The neck becomes smaller and smaller, local true stress increasing all the time, until the specimen fails. This will be the failure mode for most ductile metals. As the neck shrinks, the nonuniform geometry there alters the uniaxial stress state to a complex one involving shear components as well as normal stresses. The specimen often fails finally with a “cup and cone” geometry in which the outer regions fail in shear and the interior in tension. When the specimen fractures, the engineering strain at break will include the deformation in the necked region and the unnecked region together. Since the true strain in the neck is larger than that in the unnecked material, the value of engineering strain will depend on the fraction of the gage length that has necked.

These equations can be used to derive the true stress-strain curve from the engineering curve, up to the strain at which necking begins. Beyond necking, the strain is nonuniform in the gage length and to compute the true stressstrain curve for greater engineering strains would not be meaningful. However, a complete true stress-strain curve could be drawn if the neck area were monitored throughout the tensile test, since for logarithmic strain we have

now it is no more linear relation.