11.3 Deformation Mechanisms of Nanocrystalline Materials 259
Figure 11.13 Influence of the deformation mode, dislocation gliding or climbing, on the
shape of a single-crystal specimen after deformation.
Gliding
Climbing
DeformaƟon by dislocaƟon
Before
deformaƟon
AŌer
deformaƟon
Box 11.1 The Frank–Reed Mechanism as the Origin of Dislocations
The most important source of dislocations is the Frank–Reed source. To operate
such a Frank–Reed source within a slip plane of one grain, one needs a dislocation, anchored at two fixed nodes. These nodes may be positioned within one
grain, or at the grain boundary. Because of their high elastic energy, dislocations are connected to a line tension. Therefore, any dislocation has the tendency to shorten. An applied external stress bows the dislocation out. This leads
to a change of its radius of curvature until the line tension is in equilibrium
with the applied stress. Further increasing the line stress beyond a point where
the dislocation is semicircular, creates a situation where the dislocation no
longer has an equilibrium position. Therefore, the dislocation expands rapidly
and rotates around the nodes until the loops meet each other forming a complete dislocation loop and a new line source between the nodes. Now this
process may start again. This generation and movement of dislocations is connected to plastic deformation. This temporal sequence of the dislocation loop of
a Frank–Reed source is, in three different time steps, depicted in Figure 11.14.
The stress necessary to activate a Frank–Reed source is given by
τ =
Gb
l
.
(11.8)
In Eq. (11.8), τ stands for the shear stress in the plane of the dislocation, G
the shear modulus and l the distance between the two nodes. The Burgers
vector b, is characteristic of the type of dislocation and the crystal lattice;
numerically, it is in the range of a few tenths of a nanometer. The shear stress
necessary to activate a Frank–Reed source is, according to Eq. (11.8) indirectly
proportional to the distance between the pinning points (nodes). The maximum
possible distance between the pinning points is the grain size. Rewriting Eq.
Figure 11.13 Influence of the deformation mode, dislocation gliding or climbing, on the
shape of a single-crystal specimen after deformation.
Gliding
Climbing
DeformaƟon by dislocaƟon
Before
deformaƟon
AŌer
deformaƟon
Box 11.1 The Frank–Reed Mechanism as the Origin of Dislocations
The most important source of dislocations is the Frank–Reed source. To operate
such a Frank–Reed source within a slip plane of one grain, one needs a dislocation, anchored at two fixed nodes. These nodes may be positioned within one
grain, or at the grain boundary. Because of their high elastic energy, dislocations are connected to a line tension. Therefore, any dislocation has the tendency to shorten. An applied external stress bows the dislocation out. This leads
to a change of its radius of curvature until the line tension is in equilibrium
with the applied stress. Further increasing the line stress beyond a point where
the dislocation is semicircular, creates a situation where the dislocation no
longer has an equilibrium position. Therefore, the dislocation expands rapidly
and rotates around the nodes until the loops meet each other forming a complete dislocation loop and a new line source between the nodes. Now this
process may start again. This generation and movement of dislocations is connected to plastic deformation. This temporal sequence of the dislocation loop of
a Frank–Reed source is, in three different time steps, depicted in Figure 11.14.
The stress necessary to activate a Frank–Reed source is given by
τ =
Gb
l
.
(11.8)
In Eq. (11.8), τ stands for the shear stress in the plane of the dislocation, G
the shear modulus and l the distance between the two nodes. The Burgers
vector b, is characteristic of the type of dislocation and the crystal lattice;
numerically, it is in the range of a few tenths of a nanometer. The shear stress
necessary to activate a Frank–Reed source is, according to Eq. (11.8) indirectly
proportional to the distance between the pinning points (nodes). The maximum
possible distance between the pinning points is the grain size. Rewriting Eq.