Geology Reference
In-Depth Information
be then described by the stress difference r and the strain by the relative change of
length e or the natural strain e
;
as defined in
Sect. 4.2
.
Athermal or temperature-insensitive ductile behavior is characterized by a
stress-strain relationship r
¼
re; e
;
T
;
..
ð Þ
where the dependences on strain rate
e
;
temperature T
;
etc., are relatively weak. The main aspects of athermal behavior
are therefore represented in the stress-strain curve, where it is convenient to treat
the strain as the independent variable, following the usual testing procedure. There
is usually a fairly distinct initial elastic region, terminated at a more or less well
defined level of stress called the initial yield stress r
y
:
Unloading beyond this point
will reveal that the specimen has undergone permanent or plastic strain. On
reloading, a stress of approximately the same level as previously reached must be
applied before yielding again occurs and plastic flow continues; hence, the stress at
any point on the stress-strain curve beyond the initial yield stress can be called the
flow stress. Commonly, the flow stress increases as straining progresses, a phe-
nomenon called strain hardening or work hardening, characterized by the slope
c
¼
or
=
oe of the stress-strain curve. If c
¼
0orc\0
;
the material is said to be
perfectly plastic or strain softening, respectively. The existence of strain hardening
or softening indicates that there is continual change within the material during
plastic straining whereby its ability to support stress is changed.
The initial states are commonly not at thermodynamic equilibrium, nor is the
strain-hardened state, and so there is very limited scope for thermodynamic dis-
cussion of plastic behavior in the temperature-insensitive field. If the deformed
material is subsequently heated sufficiently, that is, annealed, the strain hardening
is removed, partially in the case of recovery (
Sect. 3.3.2
) or more or less fully in
the case of recrystallization (
Sect. 3.3.3
).
4.3.2 Low Temperature Creep
Although the main interest in the athermal field centers on the stress-strain curve
and time or rate effects play a secondary role, the latter effects are sometimes of
interest, as in the case of creep in bodies held under stress for long periods of time.
In the creep test, the strain e is measured as a function of elapsed time t at constant
stress. In the relatively low-temperature field, the creep relation e
¼
e
ðÞ
is widely
found to have the form
e
¼
e
0
þ
a ln 1
þ
mt
ð
Þ
ð
4
:
2
Þ
where e
0
is the initial strain and a
;
m are constants that depend on stress and
temperature. Such behavior is called logarithmic creep. As indicated by mea-
surements on various rocks by Misra and Murrell (
1965
) under conditions for
logarithmic creep, typical values of a are 10
-4
to 10
-6
and of m are 10
-2
to 1s
-1
and
sometimes larger. Thus over most of the time span of creep experiments, at least
after a few minutes, mt
1 and the relation (
4.2
) can be written in the form
