Geoscience Reference
In-Depth Information
change dramatically with a number of parameters
including stress (strain-rate), temperature, pres-
sure, water content and grain-size. Consequently
rheological properties of planetary materials are
the key to the understanding of dynamics and
evolution of terrestrial planets.
However, studies of rheological properties are
far more complicated than those of other proper-
ties such as elastic properties (see Chapters 6 and
7, this volume, below) and electrical conductivity
(see Chapter 5, this volume), and consequently
there have been only limited constraints on rhe-
ological properties including effective viscosities
and on deformation microstructures from labora-
tory or theoretical studies. In these studies, one
needs a large extrapolation of laboratory data or of
theoretical calculations to infer rheological prop-
erties in the Earth and planetary interiors. In order
to make appropriate applications (extrapolation)
of these data, it is essential to understand the ba-
sic physics of plastic deformation. An extensive
reviewon these subjects was presented by (Karato,
2008). In this chapter, I will provide a brief review
of the fundamentals of plastic deformation with
the emphasis on the recent developments.
of atoms are unstable and when the stress is
removed, they go back to the original stable
positions immediately. Consequently, elastic
deformation is instantaneous (independent of the
timescale) and recoverable. The relation between
stress and strain is linear in most of elastic
deformation. Therefore once the proportional
coefficient (elastic constant) is measured or
calculated the elasticity is fully characterized.
Applications to seismological observations is
straightforward with a minor correction for the
influence of anelasticity (Karato, 1993).
Atomic processes involved in plastic deforma-
tion are different. Plastic deformation occurs by
the large atomic displacements over the next sta-
ble positions often helped by thermal activation
in a stochastic manner. Consequently, plastic
deformation is in most cases time-dependent and
nonrecoverable. This poses important challenges
for the study of rheological properties in the
geological context. First, timescales (strain-rates)
of laboratory experiments are always much
shorter (faster strain-rates) than those in the
Earth. Therefore a large extrapolation is needed
to apply laboratory results using a constitutive
relationship (a relationship between applied
stress and strain-rate). Second, because the con-
stitutive relationship is different among different
mechanisms of deformation, the applicability of
a constitutive relationship (either determined
by lab experiments or calculated by theory) to
deformation in the Earth's interior needs to be
examined. Consequently, one needs to make sure
that the mechanism of deformation studied in
the lab or by a theoretical study is the same as
the mechanism that may operate in the Earth
and planetary interiors.
Electrical conductivity involves large-scale
transport of charged species and has some
similarities to plastic deformation. Both plastic
deformation and electrical conductivity in min-
erals occurs via thermally activated motion of
atoms or electrons involving crystalline defects
(see Chapter 5, this volume). Therefore both
of these properties in minerals are sensitive
to temperature and in many cases sensitive to
impurities such as hydrogen. However, electrical
4.1.2 Differences between rheological
properties and other physical properties
Various physical properties are important in the
geophysical studies of the Earth and planetary
interiors, but the nature of these properties are
different that makes important differences in the
way materials science studies on these properties
should be made in the geophysical context. To
highlight some challenges in the studies of rhe-
ological properties, let me compare rheological
properties with elastic properties and electrical
conductivity.
Both elastic and rheological properties are
among the various mechanical properties rep-
resenting the response of a material to applied
stress. Elastic deformation occurs when a small
stress is applied to a material for a short period
(or at high frequencies). In these cases, atoms
in a material move their positions only slightly
from their stable positions. The new positions
