Steels_ Metallurgy and Applications, Third Edition

Low-carbon strip steels 25

e

25

~" 45o

0

0 ~ 90 ~

troughs ~?

-15 a I i ~ ~!!! I I I J

-0.6 -0.2 0.2 0.6 1.0 1.4 1.8

Figure 1.23 The relationship between earing and Ar (After Wilson and Butler 43)

high parts of the rim and the bottom of the troughs. The relationship between
Ar/rm and eating is illustrated in Figure 1.23. For this figure, ears in the rolling
and transverse directions are regarded as positive eating and ears in the diagonal
direction are regarded as negative earing. The punch and blank diameters (P and
B) used to make a cup also influence ear height and for a given material, the ear
height is given with reasonable accuracy by the following equation: 44

Ear height = M. (B 2 - P2)(B- p)l.5/p2.5

where M is a dimensionless eating parameter related mainly to the r and Ar
values of the steel but also influenced a little by cup drawing conditions. Ears
are clearly more noticeable on a simple cup than on a more complicated pressing,
but the equivalent effect on strain distribution is obtained on all pressings, unless
the steel is specially manufactured to give a low earing tendency.

The work-hardening coefficient n

Any stress/strain curve may be regarded as approximately conforming to an
equation of the type:

cr = kt~ n

where a and ~ are the true stresses and the true strains measured throughout a
tensile test as defined above and n is a constant. It follows that:

loglo a = n. log10 e + logl0 K

The coefficient n is, therefore, defined as the slope of a true stress- true strain
curve plotted on a logarithmic scale. It determines, therefore, how quickly the
true stress builds up with increasing true strain and is, therefore, referred to as
the work-hardening coefficient. In practice, it is found that the above logarithmic
plot is not always a perfect straight line. The n value is then said to vary with
strain and more than one value is sometimes quoted from a single tensile test,
corresponding to different ranges of strain.