Deformation, stress and strain - Introducing Tectonics, Rock Structures and Mountain Belts - page 28

in pulling the block along the surface at
a uniform speed; the amount of strain
is represented by the distance travelled
by the block. The initial force applied
to move the block is analogous to what
is known as the yield strength of a ma-
terial - the point at which permanent
strain commences. For ideal plastic
strain, only this size of force is required;
a larger initial force would produce
accelerated strain leading to failure.
The concept of viscosity is usually
applied to the behaviour of liquids
although, by analogy, it can be extended
to rock materials undergoing solid-state
flow. The term viscosity is defined as
the rate of flow of material subjected
to a stress; in the case of liquids, it is
measured by the rate of flow through
a narrow tube, subjected, for example,
to gravitational force. Ideal viscous
behaviour can be represented using
the familiar analogy of the piston, as
in the shock absorber of an automo-
bile (Figure 4.10C). Here, the rate of
flow (i.e. the strain rate ) is propor-
tional to the magnitude of the stress;
in viscous strain, therefore, it is the
rate of increase of the strain that is
proportional to the size of the stress.
Since viscosity is measured as rate
of flow (or strain rate) divided by stress,
the larger the value of the viscosity,
the more slowly the material deforms.
Thus a material with a high viscosity,
like rock, deforms more slowly than
one of low viscosity, such as oil. The
terms plastic and viscous are com-
monly used interchangeably although,
strictly speaking, plastic strain in a
given material should exhibit a single
strain rate, whereas with viscous strain,
a range of strain rates is possible,
depending on the size of the stress.

Real rock material deforms usually
in a more complex way than these
idealised elastic, plastic and viscous
models. A closer approximation to
the behaviour of real materials is the
visco-elastic model, which combines
an initial period of elastic strain with a
period of viscous strain (Figure 4.10D).
To simulate the geological conditions
under which permanent strain occurs in
rocks, such as in the formation of folds,
a smaller stress has to be applied for
a very long period of time. The result-
ing variable visco-elastic behaviour is
usually known as creep . Figure 4.10D
shows a typical creep curve of the kind
that represents the deformation of real
rock materials in laboratory experi-
ments. In this type of behaviour, an
initial short period of visco-elastic strain
is followed by a much longer period of
steady plastic or viscous strain, which
may end, after a period of accelerating
viscous deformation, in failure. Under
geological conditions, the behaviour
of rocks will generally fall into two cat-
egories: high values of stress lead to an
accelerating strain rate and failure after
relatively short periods of time, whereas
low values of stress lead to long-term,
steady, viscous creep at low strain rates.
It is possible to demonstrate creep
behaviour of rock in a relatively short
time span by suspending a thin slab
of rock, such as sandstone, between
two supports at each end of the slab.
After a period of perhaps months, or
even years, depending on the strength
of the slab, it will bend downwards
and eventually fracture under con-
stant gravitational force. If the amount
of downwards displacement (i.e. the
strain) is measured over time, it should
correspond to a typical creep curve.

Brittle and ductile behaviour
Materials that fail (fracture) after there
has been no, or very little, plastic or
viscous deformation when a stress is
applied are said to be brittle , whereas
those that experience considerable
plastic or viscous flow are said to be
ductile. These terms are relative and
somewhat subjective, and materials
that are brittle at low temperatures
become ductile at higher tempera-
tures. It follows that, in general terms,
brittle behaviour characterises fault-
ing and ductile behaviour, folding.

Effects of temperature, lithostatic
pressure and pore-fluid pressure
An increase in temperature has a
marked effect on the way a rock
deforms, since it decreases the yield
strength of the material, so that per-
manent deformation will commence
at a lower stress and the strain rate
will increase for a given stress level.
Thus an increase in temperature
makes a rock more ductile. Increas-
ing the lithostatic pressure , however,
has the opposite effect, by raising the
yield strength of the material, and
thus requiring a larger directed stress
to achieve permanent deformation.
The effect of raising the lithostatic
pressure can be counteracted by the
effect of pore fluids. In a rock with a high
proportion of pore fluid, the pressure of
this fluid (the hydrostatic pressure ) will
approach that of the lithostatic pressure
(since the fluid is subject to the same
gravitational pressure as the surround-
ing rock). Thus in rocks at a consider-
able depth in the crust, the effective
pressure consists of the lithostatic pres-
sure minus the pore fluid (hydrostatic)
pressure . This means that, at a given