Geology Reference
In-Depth Information
Although it is of practical and conceptual convenience to identify linearly
additive instantaneous, transient and steady-state terms in the creep function (
4.5
),
this procedure may eventually prove to be an artificial, and even possibly invalid,
one from a theoretical or mechanistic point of view. Thus, as Amin et al. (
1970
),
Mukherjee (
1975
), and Poirier (
1976
) point out, the primary creep stage, the
behavior in which is normally treated as being dominated by the transient creep
term B
ðÞ
in (
4.5
), should probably be regarded more accurately as a transitional
stage of structural evolution in which the mechanisms of deformation are being
established. The nature of these mechanisms may well not change fundamentally
during the course of the deformation, but the strain rate that they contribute may be
expected to change as the structural details evolve until some sort of dynamic
equilibrium or saturation is reached at the steady state. Moreover, the nonelastic
strain occurring prior to the recorded primary stage is somewhat artificially
divorced from it by experimental limitations and probably should be treated
separately from the elastic strain calculated using a dynamically determined,
unrelaxed elastic modulus (cf. Eq.
4.4
). Any fully developed theory is therefore
more likely to yield, in addition to the elastic strain, a single unified creep function,
probably of complex form and representing within itself the several aspects of
preliminary nonelastic strain, the measured primary stage and the asymptotic
approach to a steady state to be expected in the secondary stage if a tertiary stage
or instability is sufficiently delayed.
The concept of steady-state creep calls for brief comment at this point. At the
present experimental or empirical level, it embodies the notion of behavior that is
independent of the strain. Care should be taken in any attempt to attribute deeper
significance to it than this, for two reasons. On the one hand, the experiments are
often limited to moderate amounts of strain and the demonstration of the constancy
of creep rate is an approximate one, described as such for convenience in analysis
but which might not be justifiably so designated if a larger strain interval were
explored (as in torsion experiments, Paterson and Olgaard
2000
). On the other
hand, one may be tempted to infer from the existence of a steady-state creep rate
that, under the given values of the independent macroscopic variables, the spec-
imen is now in a stationary state in the sense used in the thermodynamics of
irreversible processes (for example, Prigogine
1967
,
Chap. 6
) and that this state
would correspond to the optimization of a dissipation potential or entropy pro-
duction rate (for example, Ziegler
1977
,
Chap. 15
). However, Rice (
1970
) has
concluded that, except in special cases, ''no firm basis… is available for a sta-
tionary creep potential'', such as would give the steady-state strain rate when
differentiated with respect to the stress; that is, in general, the steady-state strain
rate cannot be expected to be a function of state that is determined completely by
the instantaneous values of the macroscopic variables, independently of history,
but that additional internal variables (such as uncontrolled structure parameters)
will be needed to define fully the state of the specimen.
In spite of a lack of fundamental significance for a steady state in creep
deformation, the concept has been widely used in discussions of the rheology of
rocks in geological contexts. It simplifies theoretical analysis by eliminating one
