Deformation Mechanisms: Crystal Plasticity - Materials Science for Structural Geology - page 188

This heterogeneity has been observed directly in, for example, alpha-beta brass
and nickel-silver alloys (Honeycombe and Boas 1948 ; Petrovic and Vasudevan
1978 ). Such a strain heterogeneity has also been observed in the thermal regime in
oolitic limestone in which the finer-grained oolites are weaker than the coarser-
grained matrix (Schmid and Paterson 1977 ) and finite-element calculations have
been made for such cases (Ankem and Margolin 1982 ; Horowitz et al. 1981 ).
A self-consistent scheme for treating multiphase materials has been given by
Berveiller et al. ( 1981 ).
6.9 The Role of Pressure
6.9.1 General
Since plastic deformation is primarily a change of shape of a body without
appreciable change of volume, only work terms involving shear stress are expected
to be important in determining plastic behavior. Accordingly, plastic flow criteria
for multiaxial stress states, such as the von Mises and Tresca criteria ( Sect. 4.5 ) ,
are expressed in terms of deviatoric stresses, with omission of any influence of the
hydrostatic component of the stress. There is a similar omission in the Schmid law
for the yield of single crystals ( Sect. 6.1 ). Such a view is well supported experi-
mentally in situations in which the hydrostatic component of the stress does not
markedly exceed the deviatoric components. However, when the hydrostatic
component of the stress is large or when second order effects are being considered,
the influence of the hydrostatic component must also be taken into account and the
associated changes in volume, or dilatancy, discussed. This topic is commonly
referred to as the influence of the pressure on plastic flow and will be dealt with in
its athermal and thermal aspects in Sects. 6.9.2 and 6.9.3 .
In the ensuing discussion, the term ''pressure'' should, strictly, be taken as
referring to the hydrostatic component of the stress, that is, the mean stress, since
the effect of the pressure is associated, in a thermodynamic sense, with work done
in volume changes. However, in practice, especially in the literature on experi-
mental rock deformation and in geophysical applications, the term is commonly
identified, somewhat loosely, with the confining pressure ( Sect. 4.2 ) or the litho-
static pressure at a given depth in the Earth. The error incurred in this identification
becomes less serious the larger the ''pressure'' is relative to the stress difference or
the deviatoric component of the stress.
In the case of single crystals, the theoretical questions center on the influence of
pressure on the various interactions that impede dislocation motion and on the rate
of growth of dislocation populations. In the case of polycrystals, similar effects
arise within grains and at grain boundaries. In addition, the initial structure of a
polycrystal may be modified by the application of pressure, with further influence
on the deformation behavior. This modification may involve effects associated