Geology Reference
In-Depth Information
The transient creep term B
ðÞ
tends to predominate in the primary stage of the
creep test. A number of empirical forms have been used for B
ðÞ:
These include:
1. B
ðÞ¼
a ln 1
þ
m
ð Þ
or a ln t
;
analogous to the form mentioned above for rep-
resenting the whole of the time-dependent strain in the athermal field. This
form has not found much application at high temperatures.
2. B
ðÞ¼
bt
m
;
where b and m are constants (m\1). The transient creep behavior
of a wide variety of materials can be fitted to a rough approximation with
m
¼
1
=
3
:
The term Andrade creep is often then applied to this form, after
Andrade (
1910
), although Andrade actually proposed B
ðÞ¼
ln 1
þ
bt
1
=
3
;
which is equivalent to bt
1
=
3
for small transient creep strains (i.e. \\1). By
allowing both parameters b and m to vary, better fits can, of course, be
achieved, in which case values of m varying from 0.03 to nearly 1 are found
(Garofalo
1965
, p. 16). The variation with stress can often be expressed by
putting b
/
r
n
0
;
so that B
ðÞ¼
C
0
r
n
0
t
m
where n
0
and C
0
are constants. Differ-
entiation then leads to a primary creep rate of
e
¼
Cr
n
e
p
where C
¼
mC
ð
1
=
m
;
n
¼
n
0
m and p
¼
1
=
m
1
:
These expressions are commonly
used in engineering design, being also treated as covering the whole of the creep
strain when there is no marked secondary or tertiary stages. Both the logarithmic
and bt
m
forms of B
ðÞ
have the property that the ''transient'' creep component of
the strain increases indefinitely as t increases.
;
where e
t
and t
0
are constants. This is identical to the
anelastic form (
4.4
), but now applied to substantial plastic strains. It often gives
better fits than the bt
m
form (Garofalo
1965
, p. 16). It also implies that there is
an upper limit to the contribution of the transient creep term, represented by the
constant e
t
:
The constant t
0
can then be viewed as an empirical relaxation time
for the transient creep. Studies on high-temperature transient creep in metals
(Amin et al.
1970
) suggest that, in the absence of significant grain boundary
sliding, the influence of stress and temperature is mainly reflected in the
parameter t
0
and that the product t
0
e
s
is a constant of the order of 100, not
varying greatly from one material to another.
3. B
ðÞ¼
e
t
1
e
t
=
t
0
The steady-state creep term e
s
t in (
4.5
) tends to predominate in the secondary
stage of the creep rate. It should be emphasized that the observed minimum creep
rate is not necessarily equal to the steady-state creep rate e
s
but only represents an
upper limit to it since there may still be some contribution from the transient creep
term up to the onset of tertiary creep; however, in the absence of a tertiary
instability, the expression (
4.5
) represents a total strain rate that decreases con-
tinuously with increasing time and asymptotically approaches the steady-state
creep rate e
s
:
