Steels_ Metallurgy and Applications, Third Edition

20 Steels: Metallurgy and Applications

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(a) (b)

Figure 1.16 (a) Deep drawing; (b) stretch forming

A simple measure of the stretchability of a steel may be obtained by using
a hemispherical punch to form a circular dome, as indicated in Figure 1.16(b).
The flange of the circular blank is prevented from being pulled in by the use of
a draw bead or by using sufficient blank holder pressure. The maximum ratio of
dome height to dome diameter at the moment of necking or splitting is a measure
of the stretchability of the steel. A similar test, called a hydraulic bulge test, may
be used, employing oil under pressure to form the dome. In this case, the result
would not be influenced by friction. In these tests in which the shape of the dome
is circular, the strain at the top of the dome is almost the same in two directions
at fight angles. The strain, therefore, is said to be balanced biaxial strain.

Work-hardening coefficients and normal anisotropy

The formability of sheet steels may also be assessed using parameters that may be
measured directly from a conventional tensile test, provided suitable length and
width extensometers are available. The first parameter is the strain ratio which
was originally devised by Lankford and others 38 and is usually called the r value.
It gives a measure of the drawability of the steel but also gives a measure of the
resistance to thinning resulting from the orientation of the slip systems that are
active during drawing. The second parameter is the work-hardening coefficient,
designated the n value which is closely related to the stretchability of the steel.
The uniform and total elongation measured in a tensile test are also related
to the stretchability of a steel, but it is necessary to introduce the concepts of
true stress and true strain before the r value and the n value may be defined
precisely.

True stress and true strain

The stress used in a conventional tensile test, often called the engineering stress,

is defined as the load at any moment during the test divided by the original

cross-sectional area of the test piece. During the test, the load increases up to the

point of maximum load which defines the tensile strength of the material and then

decreases as the specimen undergoes local necking. The true stress, however, is

defined as the load at any moment during the test divided by the current cross-

sectional area at the same moment. Thus, as illustrated in Figure 1.17, the true