Geology Reference
In-Depth Information
there has been little discussion of the role of twinning in deformation in thermal
regimes. However, under the assumption that the nucleation will be rate-control-
ling, Frost and Ashby (
1982
, p. 10) have proposed a rate equation for twinning,
analogous to (
6.47a
), which can be written in the form
=
RT
1
s
s
0
c
¼
c
0
m
0
exp
E
N
ð
6
:
54
Þ
where c
0
is a term containing the density of nucleation sites and the strain resulting
from each nucleation event, m
0
an attempt frequency, E
N
the (Gibbs) activation
energy for nucleation, s
0
the stress needed to initiate the twinning athermally, and
s the applied stress; c is the strain rate, T the temperature, and R the gas constant.
Such an expression can only be expected to be relevant where thermally activated
nucleation of twinning is significant, for example, possibly when the Burgers
vector of the twinning dislocation is very small. An extensive discussion of
thermal and athermal twin nucleation is given by Christian (
1965
, p. 777 et seq.).
Shear transformations, such as orthoenstatite-clinoenstatite, can be expected to
involve similar factors to those involved in mechanical twinning. However, in
addition, the dynamics of shear transformation will be influenced by the change in
Gibbs energy accompanying the phase change. The influence of the latter will
presumably be equivalent to the superposition of an internal stress assisting the
process of transformation (or opposing it if the thermodynamic conditions still fall
in the stability field of the first phase), but the magnitude of this effect will also
depend on the value of the shear stress itself if the equilibrium boundary is affected
by nonhydrostatic stress (Coe
1970
).
Because of the finite plastic strain in a twin or transformation lamella, there may
be elastic accommodation strains required to maintain continuity with the sur-
rounding untwined or untransformed material, depending on the geometry involved.
These requirements are especially obvious in the grains in a polycrystalline aggre-
gate, the general consideration of which follows in the next section (
Sect. 6.8
). One
of the consequences of the compatibility requirements is seen in the commonly
lenticular shape of mechanical twins in polycrystals, the aspect ratio of the lenticles
being higher the larger the twinning strain. A case of interlamellar stresses arising
from shear transformation in feldspar is discussed by Yund and Tullis (
1983
).
6.8 Crystal Plasticity in Polycrystalline Aggregates
6.8.1 Introduction: The Compatibility Problem
Having considered at some length the various aspects of the crystal plasticity of
individual crystals, we now discuss the deformation of polycrystalline aggregates
in which the constituent grains are deforming by crystal plasticity processes. The
deformation properties of the aggregate cannot be derived by a simple averaging
