Page 256 - Materials Science and Engineering An Introduction

228 • Chapter 7 / Dislocations and Strengthening Mechanisms

Polished surface

Twin plane Twin plane
(a) (b)

Figure 7.12 Schematic diagram showing how twinning results from an applied shear stress t. In (b), open circles
represent atoms that did not change position; dashed and solid circles represent original and final atom positions,
respectively.
(From G. E. Dieter, Mechanical Metallurgy, 3rd edition. Copyright © 1986 by McGraw-Hill Book Company, New York. Reproduced
with permission of McGraw-Hill Book Company.)

7.7 DEFORMATION BY TWINNING
In addition to slip, plastic deformation in some metallic materials can occur by the
formation of mechanical twins, or twinning. The concept of a twin was introduced in
Section 4.6—that is, a shear force can produce atomic displacements such that on one
side of a plane (the twin boundary), atoms are located in mirror-image positions of
atoms on the other side. The manner in which this is accomplished is demonstrated
in Figure 7.12. Here, open circles represent atoms that did not move, and dashed and
solid circles represent original and final positions, respectively, of atoms within the
twinned region. As may be noted in this figure, the displacement magnitude within the
twin region (indicated by arrows) is proportional to the distance from the twin plane.
Furthermore, twinning occurs on a definite crystallographic plane and in a specific direc-
tion that depend on crystal structure. For example, for BCC metals, the twin plane and
direction are (112) and [111], respectively.
Slip and twinning deformations are compared in Figure 7.13 for a single crystal that
is subjected to a shear stress t. Slip ledges are shown in Figure 7.13a; their formation was
described in Section 7.5. For twinning, the shear deformation is homogeneous (Figure
7.13b). These two processes differ from each other in several respects. First, for slip, the
crystallographic orientation above and below the slip plane is the same both before and
after the deformation; for twinning, there is a reorientation across the twin plane. In ad-
dition, slip occurs in distinct atomic spacing multiples, whereas the atomic displacement
for twinning is less than the interatomic separation.
Mechanical twinning occurs in metals that have BCC and HCP crystal structures,
at low temperatures, and at high rates of loading (shock loading), conditions under
which the slip process is restricted—that is, there are few operable slip systems. The
amount of bulk plastic deformation from twinning is normally small relative to that
resulting from slip. However, the real importance of twinning lies with the accompa-
nying crystallographic reorientations; twinning may place new slip systems in orienta-
tions that are favorable relative to the stress axis such that the slip process can now
take place.