Geology Reference
In-Depth Information
With increasing plastic strain there are several possible effects consequent upon
the accumulation of residual dislocation loops around bypassed particles that lead
to more complex strain-hardening behavior in the bypassing case than in the
particle-cutting case (normal strain hardening accompanying dislocation multi-
plication will be discussed in the next section). The residual loops themselves
become involved in mutual dislocation interactions, or the accumulating internal
stress around the particle may lead to prismatic punching (possibly initiated by the
reorientation of the Orowan loop itself through cross-slip or climb) which also
increases the dislocation density, or secondary slip systems may be activated in the
vicinity of the particles. These various processes, reviewed by Martin (
1980
, p. 72)
and Strudel (
1983
), are additional to the normal dislocation multiplication effects,
as observed in pure metals and which are effective in a similar way in precipitation
hardened materials. Thus, the strain hardening of particle-bearing materials
through the effects of internal stress, over and above the precipitation hardening
effect, tends to be a very complex phenomenon, leading to predicted shapes of
stress-strain curve varying from linear to quadratic—see Strudel (
1983
) who
discusses at some length the concept of internal stress as applied in the theory of
the flow stress for particle-strengthened materials.
Order hardening. Where short-range ordering exists, there is a local resistance
to the motion of a dislocation having a Burgers vector of the disordered structure
because of the work done locally in destroying the ordering across the slip plane.
An additional local stress of c
=
b is then needed, where c is the antiphase boundary
energy per unit area, and so the crystal shows an effect analogous to a precipitation
hardening in which the force F for cutting through the barriers derives from this
local stress (Friedel
1964
, p. 383).
When long-range ordering exists (
Sect. 1.2.3
)
, the independent movement of
ordinary dislocations having a Burgers vector of the disordered structure will tend
to be difficult and super dislocations (
Sect. 6.2.5
) will move much more readily,
unless a high Peierls stress intervenes. The properties associated with the motion
of the super dislocations will be analogous in many respects to those of extended
dislocations except that the joining strip of antiphase boundary can more readily
exist in arbitrary planes compared with the stacking fault strip in extended dis-
locations. Although the super dislocations may be able, in principle, to move
locally without resistance from order destruction, there will be some hardening
associated with the domain structure of the ordering, corresponding to an addi-
tional stress component of the order of c
=
a
;
or somewhat less when the finite
thickness of domain walls is taken into account, where a is the domain size and c is
of the order of SDE
=
b
2
;
S being the Bragg-Williams order parameter defined by
(
1.1
) and DE the reduction in energy per unit cell due to the ordering (Friedel
1964
, p. 384; Haasen
1983
, p. 1392; Hirth and Lothe
1982
, p. 685). Also various
yield point and aging phenomena can appear, for example, due to segregation
effects, and the hardening may tend to peak before complete ordering is reached
(Haasen
1983
).
