Steels_ Metallurgy and Applications, Third Edition

Low-carbon strip steels 13

RD

TD

e{111) <112>

0{111} <110>

"{100} <011>

A{211} <011>

Figure 1.7 (200) pole figure for cold-rolled steel showing important orientations
(Hutchinson 2~

z(NO)

[O~)z 1] ~ ~,-rot

irot

(RO) ,/x /~ "YlTD)

Figure 1.8 Diagram illustrating the relationship between the crystal coordinate system
[1001, [010], [O01l and the rolling, transverse and normal directions by means of the
Euler angles ~l, ~, ~z

and ~ relate the crystal coordinate system [ 100], [010] and [001] to the physical
reference frame RD, TD, ND (the rolling transverse and normal directions) by
three rotations taken in order. These rotations are illustrated in Figure 1.8 and are
further illustrated on a stereographic projection in Figure 1.9. This figure uses a
(111)[ 121 ] orientation as a particular example.
An outline orientation distribution function giving the positions of some
important orientations is given in Figure 1.10. It is useful to note that any