Steels_ Metallurgy and Applications, Third Edition

28 Steels: Metallurgy and Applications

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Strain-hardening exponent n

(a)

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Strain-hardening exponent n

(b)

Figure 1.27 Calculated (a) polar thickness strain (absolute value) and (b) polar height
at instability versus strain-hardening exponent n for several values of r (After Wang 46)

Forming limit diagrams

In 1963, Backhofen and Keeler 48 introduced the concept of a forming limit
diagram (FLD) which gives a plot of the major and minor strains that may
be obtained by deformation. This diagram enables the strains that are obtained
across any commercial pressing to be compared with the maximum strains that
could be sustained by the material without necking or splitting. These maximum
strains are defined by a line called the forming limit curve which separates the
strains that would give an unsatisfactory pressing from those that would give a
satisfactory pressing. The forming limit line for any material may be measured
experimentally, as indicated below, and its position on the diagram depends on
the properties of the steel and its thickness. It usually has the general shape
illustrated in Figure 1.28. The fight-hand side of the diagram covers stretching
when both the major and the minor strains are positive, whereas the left-hand side
covers drawing for which, as mentioned previously, one of the strains is negative.
The strains to be plotted on a forming limit diagram may be measured by first
etching a grid pattern, consisting of an array of circles about 2 mm in diameter,
onto the steel surface prior to forming. This is done using a stencil and an electro-
chemical or photographic marking technique. On forming, the circles change in
size and shape and usually become elliptical, depending on the local strain at each
point over the pressing. The circles and ellipses plotted in Figure 1.28 indicate
the nature of the strain produced by deformation in different areas of the diagram.
The major component of strain plotted vertically is obtained by measuring the
long axis of the ellipse, whereas the other component is obtained from the minor
axis. A comparison of strains on a component may be made with those for the
forming limit curve. It is usually considered that if the plotted strains are well
away from the forming limit line, the pressing is likely to be made without risk
of necking or splitting. If the strains are close to the forming limit line, however,