Geology Reference
In-Depth Information
11
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slip systems in holohedral cubic crystals but only two are indepen-
dent; the activity of a third system does not make possible any deformation that
cannot be achieved with the first two. The inadequacy of the 11
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slip
systems for producing a general deformation is illustrated by the impossibility of
achieving change of length parallel to any 11
hi
direction with such systems.
The von Mises criterion of five independent slip systems has been widely
evoked as a necessary condition for the ductility of polycrystalline aggregates.
Thus, in polycrystalline NaCl-structure materials, the transition from brittleness to
ductility at elevated temperatures has been correlated with the onset of 10
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slip in addition to the normal 11
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slip, an addition which raises the total
number of available independent slip systems from two to five (Copley and Pask
1965
; Groves and Kelly
1963
; Pratt
1967
). The criterion is, of course, not in itself a
sufficient condition for ductility since there must also be adequate mobility of the
dislocations and interpenetrability of the slip activity.
The von Mises criterion refers to a deformation that is homogeneous at the
microscopic or grain scale. When the heterogeneity of deformation at this scale is
taken into account, the question arises as to how far the criterion can be relaxed as
a result of the additional scope for maintaining the mutual fit between grains
through compensating local deformations. Thus, if grains of a particular small
range of orientations were incapable of undergoing the required strain for lack of
suitable slip systems, the remaining majority of grains might be able to undergo
additional compensating deformation so that the undeformable grains could be
accommodated as hard inclusions. The possibility of such an effect has been
demonstrated by Hutchinson (
1977
) in a self-consistent numerical treatment of a
polycrystalline aggregate of hexagonal material having active basal and prismatic
slip systems (which comprise four independent slip systems) but lacking the
pyramidal slip systems that would permit normal strain parallel to the c axis (see
Sect. 6.8.4
). Thus, it can be concluded that, in practice, not more than four
independent slip systems are necessary for the deformation of a polycrystalline
aggregate solely by intragranular slip. Whether this requirement can be reduced to
three is not clear but the calculation of Hutchinson (
1976
) for NaCl-structure
materials (discussed further in
Sect. 6.8.4
) suggests that this may not be possible.
Nevertheless, intuitively, it would seem that with three independent slip systems
active, the amount of activity needed of any fourth, accommodating micro
mechanisms would, at least, be relatively small.
In many nonmetallic materials, especially in rocks, the grains are often of
relatively low crystallographic symmetry and the number of available independent
slip systems is therefore often small. For example, olivine has only three inde-
pendent slip systems and one of these is relatively strong, while feldspars probably
have even fewer (quartz and calcite do not present the same problem provided that
more than one of their known sets of slip systems is active). Nevertheless, these
substances can be deformed in polycrystalline form, suggesting that other micro
mechanisms are active. Some possibilities for the latter are:
