Geology Reference
In-Depth Information
Mecking
1980
; Kocks and Canova
1981
). This effect may be important when large
strains (say, [0.3-0.5) lead to inequant grain shape or when grains tend to form
initially in platy or needle-like form, as in the case of minerals such as mica and
sillimanite. The effect has been explored in copper by Tomé et al. (
1984
), who
show that it may lead to a geometric softening at large strains.
Another effect of plastic strain is to produce a crystallographic preferred orien-
tation. When this effect is strongly developed, the properties of the aggregate
approach in some degree those of a single crystal and again the requirement on the
number of independent slip systems may be reduced to some extent. The pattern of
preferred orientation can be calculated by direct extension of the calculation of the
stress-strain curve (previous subsection), proceeding incrementally, with the
weighting of the distribution of orientations being updated at each increment. Such
calculations, using the Taylor model applied to cases of geological interest, were
carried out by Lister and coworkers (Lister et al.
1978
, Lister and Paterson
1979
,
Lister and Hobbs
1980
); for recent papers on the measurement and analysis of
crystallographic preferred orientation, see Wenk (
1985
). Asaro and Needleman
(
1985
) set out a more sophisticated development of the Taylor model, based on single
crystal constitutive relations formulated by Peirce et al. (
1982
,
1983
) and aimed at
treating large deformations with arbitrary histories and predicting preferred orien-
tations. They demonstrate another form of geometrical softening of the aggregate,
which is associated with the development of crystallographic preferred orientation
and which is additional to the effect of Tomé et al. (
1984
), mentioned previously.
Structural inhomogeneities or instabilities have been observed to develop in
polycrystals at large strains, generally in the form of ''shear bands'', that is, regions
in which large shear strains have been concentrated (for example, Grewen et al.
1977
; Hatherly
1978
; Hatherly and Malin
1979
; Gil Sevillano et al.
1980
; Hecker
and Stout
1984
). The development of these features is usually related to a lack of
the stabilizing effect of strain hardening, arising both from a saturation in local
strain hardening within the grains and from geometric softening effects (Asaro and
Needleman
1984
,
1985
; Mecking
1980
,
1981a
; Tomé et al.
1984
).
Dynamic recrystallization (
Sect. 6.5.3
) is another important process in poly-
crystals deformed at higher temperatures. It has been studied especially in hot
working of metals at strain rates greater than, say, 10
-3
s
-1
; see review by Roberts
(
1984
) but it can also occur in creep. It has, of course, important consequences for
preferred orientation development.
6.8.6 Polyphase Aggregates
In this subsection, we are concerned primarily with polyphase materials in which
the grains of the individual phases are comparable in size and volume fraction and
more or less equiaxed in shape. The influence of small volume fractions of finely
dispersed particles or precipitates on the crystal plasticity of the enclosing matrix
has already been considered in the context of single crystal behavior (
Sects. 6.6.2
