
structure, it is found that it falls into two subcategories,
both having GNBs aligned with {111} planes but with
different systematic small deviations from the ideal slip
plane. These deviations are by rotations of a few degrees
(up to 10 deg) around a specific crystallographic axis,
which may be either a 112
hi
or a 110
hi
axis.
[27]
The
existence of these two subcategories implies an under-
lying difference in slip systems, which is the basis for
definition of two different slip classes. Detailed analysis
of a number of cases concludes that the difference lies in
the number of active slip systems on the slip plane so
that deviations around 112
hi
axes result from one active
system while the 110
hi
axes originate from activation of
two systems in the same slip plane (in the following,
referred to as coplanar systems).
[33]
For the type 2 structure, the common feature of the
slip systems is the activation of codirectional pairs of slip
systems, i.e., two systems on two different slip planes but
with the same slip direction. When comparing different
cases, it is concluded that at least two sets of codirec-
tional slip systems (i.e., a total of four systems) must be
activated to produce type 2. The sign of the dislocations
gliding on the slip systems also plays a role (Reference
33 provides more details).
For the type 3 structure, the number of subcategories
is the highest and the difference between subcategories is
much larger than for type 1. Table I lists the different
GNB planes observed and divides them into two
subcategories, each of which is associated with activa-
tion of a slip class. Please note that in all cases the GNB
planes lie far from a slip plane, in agreement with the
definition of the type 3 structure. The two slip classes
consist of the following combinations of slip systems.
(1) One set of codirectional slip systems. The GNBs
align with a plane containing the common slip
direction and bisecting the angle between the two
slip planes. The GNB lies closer to the more active
slip plane and the signs of the slip systems control
whether the GNB bisects the acute or obtuse angle
between the slip planes.
(2) So-called dependent coplanar and codirectional
slip, which is a combination of three systems on
two slip planes where one system is codirectional
and coplanar to the other two, respectively. Sev-
eral such slip system combinations may be acti-
vated in the same grain, possibly sharing some of
the slip systems, which gives rise to a number of
characteristic GNB planes. For more details, see
Reference 33.
The relations between slip classes and structure types
are of universal nature in the sense that they are not
restricted to any deformation mode or grain orientation.
The identification of these relations establishes a new
framework for the analysis and interpretation of struc-
tures, as exemplified in Sections IV–B, V,andVI–B.
B. Applica tion of Slip Classes
By means of the slip class concept, some of the
fluctuations observed between grains of similar orienta-
tion or within a grain can be better understood. The
occurrence of both type 1 and 3 boundaries a long the b
fiber of the rolling texture
[28]
is, for example, due to
activation of both a coplanar set of slip systems and a
codirectional set, leading to type 1 and 3 boundaries,
respectively. It is often observed that either the type 1 or
3 boundary is more clearly developed. In most cases,
however, the second set can also be detected. These
variations are attributed to local variations in the
relative activities of the slip systems, possibly caused
by minor strain variations or ambiguities. Analogously,
one or two sets of type 1 GNBs are found in grains of
Goss or Brass
[28]
orientation, depending on the activities
on the two slip planes with which the GNBs align. It is,
however, emphasized that these variations have their
origin in fluctuations in the relative activities of a fixed
set of slip systems, which can be pred icted based on the
grain orientation, rather than activation of new syst ems,
which can only be predicted based on detailed interac-
tions with neighboring grains.
Of course, the relations can also be used to predict the
structure based on the slip systems. For example, the
relations have been applie d to predict the dominant
alignment of the structure after torsion for the major
stable texture components, giving good agreement with
experimental observations.
[33]
This further served as a
demonstration of the uni versality by being a prediction
for a deformation mode other than tension and rolling.
The ability to predict the structure type is also vital for the
modeling of mechanical properties, as demonstrated in
Section VI.
V. SINGLE VS POLYCRYSTALS
The classification into three main types of structures,
of which types 1 and 3 can be subdivided further
according to the exact plane of the GNBs, has been
presented and analyzed above for grains in polycrystals.
Table I. Relations between Slip Classes and Dislocation Structures (Reference 33 Provides More Details)
Slip Class Crystallographic GNB Plane Structure Type
Single slip {111} type 1
Coplanar slip {111} type 1
Two sets of codirectional slip no GNBs, only cells type 2
One set of codirectional slip
symmetric
{101} or {010}* type 3
Dependent coplanar and directional slip {315}, {441}, or {115} type 3
*Depending on the signs of the Schmid factors. Asymmetric codirectional slip brings the GNB plane closer to the more active slip plane.
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 42A, MARCH 2011—621