Page 49 - Global Tectonics

36 CHAPTER 2

results from repeated shear fracturing, which acts to Power-law creep (also known as dislocation creep)
reduce the grain size of the rock, and by the sliding or takes place at temperatures in excess of 0.55 T m . In this
rolling of grains over each other. form of creep the strain rate is proportional to the nth
power of the stress, where n ≥ 3. Power-law creep is
similar to plastic flow, where deformation takes place

2.10.3 Ductile deformation by dislocation glide. However, in addition, the diffusion
of atoms and of sites unoccupied by atoms called
The mechanisms of ductile flow in crystalline solids vacancies is permitted by the higher temperatures (Fig.

2.24). This diffusive process, termed dislocation climb,
have been deduced from studies of metals, which have

the advantage that they flow easily at low temperatures allows barriers to dislocation movement to be removed
as they form. As a result work-hardening does not
and pressures. In general, where the temperature of a
material is less than about half its melting temperature occur and steady state creep is facilitated. This balance
results in dynamic recrystallization whereby new crystal
(T m in Kelvin), materials react to low stresses by fl owing
slowly, or creeping, in the solid state. At high tempera- grains form from old grains. Because of the higher
temperature the yield strength is lower than for plastic

tures and pressures, the strength and flow of silicate

minerals that characterize the crust (Tullis, 2002) and flow, and strain results from lower stresses. Power-law
creep is believed to be an important form of deforma-
mantle (Li et al., 2004) have been studied using experi-
mental apparatus. tion in the upper mantle where it governs convective
flow (Weertman, 1978). Newman & White (1997)

There are several types of ductile flow that may
occur in the crust and mantle (Ashby & Verrall, 1977). suggest that the rheology of continental lithosphere is
controlled by power-law creep with a stress exponent
All are dependent upon the ambient temperature and,
less markedly, pressure. Increased temperature acts to of three.
Diffusion creep dominates as temperatures exceed
lower the apparent viscosity and increase the strain rate,
while increased pressure produces a more sluggish fl ow. 0.85 T m , and results from the migration of individual
atoms and vacancies in a stress gradient (Fig. 2.25).
In general, for ductile flow, the differential stress (Δσ)

and the strain rate (δε/δτ) are related through a fl ow Where the migration occurs through a crystal lattice it
is known as Nabarro–Herring creep. Where it occurs
law of the form:
along crystal boundaries it is known as Coble creep. In
1/n
Δσ = [(δε/δτ)/A] exp[E/nRT], both forms of creep the strain rate (δε/δτ) is propor-
tional to the differential stress (Δσ) with the constant of
where E is the activation energy of the assumed creep proportionality being the dynamic viscosity (η). This
process, T is temperature, R is the universal gas con- relationship is given by:
stant, n is an integer, and A is an experimentally deter-
mined constant. Δσ = 2η(δε/δτ)
Plastic flow occurs when the yield strength of the

material is exceeded. Movement takes place by the The viscosity increases as the square of the grain radius
gliding motions of large numbers of defects in the so that a reduction in grain size is expected to result in
crystal lattices of minerals. Slip within a crystal lattice rheological weakening. Diffusion creep is believed to
occurs as the individual bonds of neighboring atoms occur in the asthenosphere (Section 2.12) and in the
break and reform across glide planes (Fig. 2.23). This lower mantle (Section 2.10.6).
process results in linear defects, called dislocations, that Superplastic creep has been observed in metals and
separate slipped from unslipped parts of the crystal. may also occur in some rocks. This type of creep results
The yield strength of materials deforming in this way from the coherent sliding of crystals along grain bound-
is controlled by the magnitude of the stresses required aries where the movement occurs without opening up
to overcome the resistance of the crystal framework gaps between grains. The sliding may be accommo-
to the movement of the dislocations. The strain pro- dated by both diffusion and dislocation mechanisms.
duced tends to be limited by the density of disloca- Superplastic creep is characterized by a power-law rhe-

tions. The higher the density, the more difficult it is ology with a stress exponent of one or two and is asso-
for dislocations to move in a process known as strain- ciated with high strain rates. Some studies (e.g. Karato,
or work-hardening. 1998) have inferred that superplastic creep contributes