
230 
Direct 
strip 
casting 
of 
metals 
and 
alloys 
4.0,----------------------, 
(? 
9 3 0 
IJ 
J:f.I 
.. 
........ 
.  Steel 
...... 
0 
... 
~ 
l:/:> 
.... 
C::::::
r 
...... 
·.. 
Titanium 
~ 
~~~~T~ 
.!: 
2.0 
L  ....... 
~........ 
v 
0... 
0 
~ 
...... 
.. 
~ 
Copper 
'0 
Zinc 
Brass 
~ 
Aluminium 
c:: 
1.0 
:;:; 
'E 
:::i 
O~~I----~I--~I----~I------~I-----I~--~I~ 
0.2 
0.4 
0.6 
1.0  2.0  4.0  6.0 
Normal anisotropy (f) 
Figure 6.29. Relationship between normal anisotropy, 
r, 
and 
limiting drawing ratio, 
LDR, 
for a wide range of sheet metals, after Atkinson (1967). 
6.7.1.3 
Relationship 
between 
microstructure, 
texture 
and 
formability 
From a fundamental viewpoint, good deep drawability requires a 
high 
r -value 
(Eq. 
6.6);  a  parameter intimately  associated 
with 
grains  oriented  such  that 
certain  crystallographic  directions 
«111>  in  cubic  metals)  are  aligned 
perpendicular to the plane of the sheet.  However, low planar anisotropy is also 
important,  which  requires  that the  grains  also 
be 
randomly oriented 
in 
the 
plane of the sheet. 
The preferred orientation of grains in cubic metals that leads to high normal 
anisotropy  is  usually  termed  the  <111>//NO 
or 
r-fibre 
(§B.3.3), 
and 
the 
production of this texture, 
and 
therefore highly formable sheet products, is  a 
major aim of industrial steel processing (Ray 
et 
al. 
1994).  Since good drawability 
of cubic metals is associated with <111>//NO textures and poor drawability with 
<OOI>//NO 
textures (Hutchinson 
1984), 
the ratio of the intensities of the 
111 
and 
200 X-ray reflections from a rolling plane specimen 
(1111 
/1
200
) 
is a useful measure 
of formability and it correlates very well with 
r (Figure 6.30). 
As indicated in §6.6.3,  the cold rolling 
and 
annealing textures that develop 
in 
metals are affected 
by 
a host of parameters relating to the material itself 
and 
the 
entire  processing  history. 
It 
is  the  combination of  these  parameters which 
ensures that any particular material will possess the final microstructure 
and 
texture  for  superior  formability.  Table  6.3  provides 
data 
of  formability 
parameters 
(n, 
r, f:"r, 
LOR 
& % Earing) for a range of strip-cast aluminium and 
iron alloys; the range is restricted since reliable 
data 
is 
not 
openly available for 
other materials.  In general, the 
r -values for iron alloys are low and less than