Environmental Engineering Reference
In-Depth Information
h
FR
L
Barrier
3.12
Schematic of dislocation glide-climb event.
encountered which it has to climb so that another dislocation can be gener-
ated by the source.
A rather simple way of deriving the relation between the strain rate and
the applied stress and temperature is given by referring to Fig. 3.12: thus the
total strain is given by,
Δ
γ
= strain during glide-climb event =
Δ
γ
g
+
Δ
γ
c
≈
Δ
γ
g
=
ρ
b L
h
t
= time of glide-climb event =
t
g
+
t
c
≈
t
c
=
,
v
c
= climb velocity
v
c
Δ
bL
ρ
hv
L
h
v
γρ
γ
b
ρ
=
=
=
,
c
t
/
c
where
v
c
∝
Δ
C
v
e
−E
m
/kT
,
E
m
= activation energy for vacancy migration
⎛
⎜
⎞
⎟
L
V
kT
σ
k
−
0
V
kT
0
+
−
σ
γρ
=
bv
, where
Δ
CC
+
Ce
−
C
2
inh
⎛
⎝
⎞
⎠
ρ
Δ
CCC
=
+
Ce
e
σ
V
kT
C
s
=
σ
V
/
=
C
v
CC
C
v
c
v
v v
CC
C
v
C
v
h
b
L
h
v
L
h
Ce
⎛
⎜
⎞
⎟
V
kT
σ
EkT
m
0
sinh
so that
εαρ
b
−
2
⎛
⎝
⎞
⎠
[3.30 ]
α ρ
/
α ρ
c
α ρ
b
h
C
v
.
α ρ
At
low
stresses,
sinh
(
σ
V
/
kT
)
≈
σ
V
/
kT
so
that
EkT
m
(
)
(
)
ε
Ab
ρ
Ce
v
o
−
ρ
/
σ
1
L
V
L
σ
[3.31 ]
ε
Ab
ρ
D
A
D
L
ρσ
≈
1
ρ
L
≈
≈
A
A
ρσ
h
D
b
D
.
ρ
h
kT
h
kT
h
Assuming that the dislocation density (
ρ
) varies as stress is raised to the
power 2 (
σ
2
), we fi nd that
[3.32 ]
3
AD
σ
ε
σ
.
L
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