Environmental Engineering Reference
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strain, instantaneous plastic strain and time-dependent strain component
from primary and secondary creep regimes:
(
)
rt
s
,
[1.5 ]
1
−
=+
ε
e
rt
)
+
t
εε ε
ε
ε
0
t
s
where
ε
0
is the instantaneous strain (the majority from elastic deforma-
tion),
t
is the extent of primary creep strain,
r
is the rate at which strain
decreases with time during primary creep regime and subscript '
s
' stands for
steady-state creep rate. The steady-state creep rate is a unique function of
the applied stress and temperature for a given material
ε
QRT
/
n
,
[1.6 ]
ε
A
−
σ
Q
e
s
where
Q
c
is the activation energy for creep,
n
is the stress exponent,
R
is the
gas constant and
T
is absolute temperature. The activation energy for creep
can generally be matched with that for self diffusion and the above relation-
ship can be rewritten as
n
,
[1.7 ]
AD
′
ε
σ
s
where
D
stands for appropriate diffusion coeffi cient and
A
could be grain
size dependent (see Chapter 3 for details). In general, lattice diffusion is
temperature dependent:
′
β
α
6
2
QRT
Q
/
Dv Ce
D
C
,
[1.8a ]
−
and
Q
Ce
V
/
RT
,
[1.8b ]
−
V
is the atomic jump distance, ν
D
is
Debye frequency,
C
V
is vacancy concentration and
Q
m
and
Q
V
are the acti-
vation energies for migration and formation of a vacancy, respectively. It
should be noted that higher stress increases the diffusion and leads to higher
creep rate with reduced rupture time.
where
β
is the coordination number,
α
1.2.3 Fracture toughness
All structural materials contain some types of fl aw in them, the size of which
can range from microscopic to mesoscopic in scale; these defects promote
stress to concentrate locally around them leading to premature failure of
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