Environmental Engineering Reference
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proceeds at a constant rate. Elsewhere, the dependence of creep rate on
time was described by a power series
5
∑
ε
=
n
−
i
,
a
i
t
[3.2 ]
i
where
is the creep rate,
a
i
and
n
i
are functions of both temperature and
stress. The primary stage of a normal creep curve, namely curve A, can be
described by Equation [3.2] when
n
attains a value of 2/3. In such a case, the
time dependence of creep strain (
ε
ε
) is described by
13
εε β
[3.3 ]
=+
ε
0
t
/
,
where
is a constant and
t
is time. Equation
[3.3] is in accordance with the time law of creep proposed by Andrade,
1
known as Andrade's
ε
0
is the instantaneous strain,
β
-fl ow.
For steady-state creep,
n
= 0. The creep curve is then described by
β
ε
0
s
t
,
=+
[3.4 ]
εε ε
where
ε
s
is the steady-state creep rate. The total creep curve consisting of
the primary, secondary and tertiary region can be then described by
13
3
εε β
ε
[3.5 ]
=+
ε
ε
t
+
t
γ
,
0
s
where
t
3
describes the tertiary component of the creep curve. There were
several other time-creep law equations proposed to describe creep data. A
major objection to the Andrade's
γ
-fl ow equation is that it predicts infi nite
creep-rate at the instant of loading (i.e. as
t
approaches 0) which is consid-
ered to be unrealistic.
4
Garofalo
6
proposed the following equation:
β
(
)
rt
1
s
,
e
−
rt
)
+
t
[3.6 ]
εε ε
=+
ε
ε
ε
0
t
s
where
t
is the limit for transient creep and
r
is the rate of exhaustion of
th
e
transient creep that is a function of the ratio of initial creep strain rate
ε
t
→0
4
An extension of the Garofalo equation that further includes the
tertiary creep regime, would be
7
:
.
(
)
(
)
p
(
rt
[3.7 ]
1
−
e
−
rt
)
+
ε
t
εε ε
=+
ε
ε
ε
+
ε
e
s
+
ε
L
,
0
t
s
where
L
is a constant equal to the smallest strain deviation from steady
state at the onset of tertiary creep,
p
is a constant and
t
ot
is the time for onset
of tertiary creep.
ε
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