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deformation is modified by the presence of a
liquid phase. Various processes may affect the
plastic properties of such a solid-liquid mixture
including (i) chemical reaction between solid
and liquid (dissolution-precipitation), (ii) fast
diffusional mass transport through liquid phase,
and (iii) stress concentration.
The influence of chemical reaction (dissolution-
precipitation) has been studied extensively in
relation to so-called ''pressure-solution'' creep
(e.g., Rutter, 1976; Shimizu, 1994; Spiers
et al
.,
2004). This mechanism is essentially the same
as grain-boundary diffusion creep (Coble creep),
but because diffusion is fast in the liquid, the
rate of deformation is often controlled by the
rate of chemical reaction at the grain-liquid
interface (Spiers
et al
., 2004). The influence of
processes (ii) and (iii) were analyzed by Cooper
and Kohlstedt (1986); Kohlstedt (2002). They
showed that the presence of partial melt has
only modest influence on creep rate (see a later
part of this chapter). In contrast, Takei and
Holtzman (2009a,b,c) presented a more sophisti-
cated analysis of stress states at grain-boundaries
and concluded that the influence of partial
melting is stronger, a factor of
4.2.6 Deformation mechanism map
Because of the presence of multiple mechanisms
of plastic deformation, it is convenient to use
some diagrams to illustrate the parameter space
where one mechanism dominates over others.
Such a diagram is called a deformation mecha-
nism map (Frost & Ashby, 1982). In many cases,
the competing mechanisms are independent, so
these diagrams simply show the mechanisms
with the largest strain-rate under various condi-
tions. Because strain-rate depends on a number of
parameters (temperature (
T
), pressure (
P
), grain-
size (
L
), stress (
σ
), water content (
C
W
)), such a
diagram must in general be presented in a multi-
dimensional space. However, a two-dimensional
diagram is easy to use for practical purposes,
and therefore in most cases, such a diagram is
usually constructed on a two-dimensional space
keeping other parameters fixed. An example of de-
formation mechanismmap is shown in Figure 4.4
10
4
10
3
Peierls mechanism
1
10
3
10
−
3
5 reduction in
viscosity even at a small melt fraction, 10
−
3
%
(see Chapter 3, this volume). The reason for this
discrepancy is not well understood. Modeling
diffusion creep is complicated because the stress
state and diffusional flux have strong interaction
and these two must be solved self-consistently as
shown by Raj and Ashby (1971). For dislocation
creep, there is no mechanism to enhance creep
significantly at a small melt fraction. The same
is true for diffusion creep controlled by volume
diffusion. In some Earth sciences literatures,
boundary diffusion controlled diffusion creep is
exclusively considered (e.g., Mei & Kohlstedt,
2000a; Hirth & Kohlstedt, 1995a; Kohlstedt,
2002). However, interplay between volume and
boundary diffusion is complicated in ionic solids
and both boundary diffusion-controlled and
volume diffusion-controlled creep behaviors are
found in many oxides depending on the grain-size
and temperature (e.g., Cannon & Coble, 1975;
Gordon, 1973; Li
et al
., 1996).
∼
lab
10
2
10
−
6
•
=
10
−
9
s
−
1
10
1
Power-law creep
diffusion creep
10
−
12
10
0
Earth
10
−
15
10
−
1
10
−
2
10
−
4
10
−
3
10
−
2
10
−
1
10
2
1
10
Grain-size, mm
Fig. 4.4
A deformation mechanism map for olivine
(after Karato, 2010b) P
=
7GPaandT
=
1700 K
(
300 km depth), dry condition. Dominant defor-
mation mechanisms in the hot mantle are either
diffusion or power-law (dislocation) creep although in
the laboratory conditions many mechanisms may
compete depending on the precise conditions. A similar
conclusion is obtained for other minerals (see Karato,
1998b). Reproduced with permission of Elsevier.
∼
