Environmental Engineering Reference
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with the viscous glide creep discussed earlier which occurs along with climb
creep in class-A alloys. For the sake of the reader, we present a small exam-
ple of how the temperature and stress boundaries of different mechanisms
can be determined in a given material. If we assume Coble creep and N-H
creep as competing mechanisms for a given grain size, then Coble creep will
be dominant when
.
>
[3.45 ]
ε
ε
H
e
ε
N
Cobl
−
From the relevant equations for Coble and N-H creep mechanisms, this
would imply
D
δσ
B
Ω
B
D
Ω
σ
BB
L
c
[3.46 ]
B
>
H
3
B
H
2
kT
.
dkT
kT
d
π
d
Cancelling the common terms we obtain
K
D
D
B
L
>
5
,
[3.47 ]
d
where
K
5
is a constant. At a constant grain size, and after expanding
D
B
and
D
L
, the above equation will turn out to be
(
)
D
Q
RT
D
B
Q
[3.48 ]
K
>
5
,
(
RT
)
D
Q
D
L
Q
where
K
5
is a constant. Clearly the transition from Coble to N-H creep
is temperature dependent and independent of stress. The transition is only
dependent on the activation energies for grain boundary and lattice diffu-
sivities. The temperature dependence of this cross-over is captured by the
map where we can observe that a line parallel to the stress axis separates the
Coble creep and N-H creep fi elds.
An alternate way of representing the deformation mechanism maps was
proposed by Mohamed and Langdon.
80
Since grain size is an important
factor which governs the deformation behavior of materials, the mecha-
nism map can also be plotted for normalized grain size (
d/b
) against nor-
malized stress (
/G
) for a given temperature (Fig. 3.18). As the plot shows,
smaller grain sizes are favorable for Coble creep and as we increase the
grain size N-H and H-D creep mechanisms become dominant. Since dis-
location creep is independent of grain size, transitions from dislocation
creep to other mechanisms are represented by lines parallel to the grain
size axis. The climb-glide mechanisms are noted for larger grain sizes with
σ
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