Geology Reference
In-Depth Information
Relatively few dislocation sources are active and the dislocation density does not
increase markedly with strain, a trend with which the low strain-hardening rate of
the order of 10
-4
G is correlated.
Stage II: This stage begins with the onset of more obvious activity of secondary
slip systems intersecting the primary system. The primary system continues to
contribute most to the strain but with much shorter distances of travel of the
individual dislocations, as deduced from the lengths of slip traces at the surface,
and with a much increased rate of strain hardening, now of the order of G/300 to
G/200. The dislocation density increases markedly during this stage with the build-
up of the three-dimensional dislocation network. As a result of dislocation reac-
tions the network may contain many sessile segments. The flow stress in stage II
shows very little dependence on temperature but its extent depends on the stacking
fault energy (see stage III).
Stage III: As higher stresses are reached, the linear hardening regime of stage II
gives way to a further stage of more or less parabolic shape in which the strain
hardening rate steadily decreases toward values of the order of 10
-3
G or less. In
this third stage, the build-up of the dislocation network begins to be moderated by
dynamical recovery processes that relieve dislocation pile-ups or that lead to the
annihilation of dislocations or the sharper development of cell-like structures
(
Sect. 6.5.1
). The most important step in such recovery processes in metals at low
to moderate temperatures is widely thought to be cross-slip, which is evidenced in
the appearance of wavy slip traces. Since dissociated dislocations must recombine
to undergo cross-slip, a dependence on stacking fault energy can be introduced
into the stress-strain curve at this stage, as well as some temperature dependence;
in particular, the onset of stage III is earlier, and hence the length of stage II
shorter, for higher stacking fault energies. At higher temperatures, dislocation
climb becomes a potentially important dynamical recovery mechanism, intro-
ducing a stronger temperature and time dependence (
Sect. 6.6.6
).
In attempting to explain this athermal or only mildly temperature dependent
behavior in terms of mutual dislocation interaction two views have been taken of the
predominating characteristic of the interaction (
Sect. 6.3.4
). In the first, emphasis is
put on the role of the long-range elastic stress field associated with the dislocation
network. In the second, the short-range forest-cutting effect is emphasized.
According to models based on the effect of the long-range stress field, the flow
stress s is that which is required to counteract the internal stress s
i
due to the
dislocation network. Assuming that the interactions between parallel dislocations
are the most important and that the stress fields of all except the nearest dislocation
cancel to zero at a given point, and noting that the relevant shear stress at a point
due to a dislocation at a distance r is of the order of Gb
=
2pr (
Sect. 6.2.1
), then,
putting r
¼
q
2
;
we obtain the Taylor estimate of the internal stress,
s
i
¼
aGbq
2
ð
6
:
30
Þ
(Taylor
1934
; Weertman and Weertman
1983a
, p. 1281), where G is the shear
modulus, b the Burgers vector, q the dislocation density and a a numerical constant
