Geoscience Reference
In-Depth Information
Fig. 4.2
Cartoons illustrating physical processes of
plastic deformation. (a) Diffusion creep. When
grain-boundaries are weak, grain-boundary sliding
occurs upon applying a stress. This leads to the
variation in the normal stress at grain-boundaries
with different orientation, which in turn causes the
concentration gradient in vacancies. Diffusive mass
transport occurs due to this concentration gradient in
vacancies that leads to plastic deformation.
Diffusional mass transport relaxes stress
concentration, and steady-state creep occurs
corresponding to the steady-state relaxed stress
distribution. Diffusional mass transport occurs both
inside of grains and along grain-boundaries.
(b) dislocation creep (
diffusional
flux
(a)
dislocation
climb/glide
indicates a dislocation).
Crystal dislocations are generated in a crystal and the
propagation of crystal dislocations results in finite
strain of a crystal. The rate of deformation by this
mechanism is proportional to dislocation density and
its mobility and hence in general a non-linear
function of stress. Dislocations move only along
certain crystallographic orientations. Therefore plastic
deformation by dislocation motion is anisotropic.
⊥
(b)
the driving force for diffusion creep is the
grain-scale heterogeneity in the normal stress at
grain-boundaries, the driving force for diffusional
flux is inversely proportional to grain-size. The
strain caused by diffusional mass flux is also
inversely proportional to grain-size. Therefore
the flow law for diffusion creep is written as
(and pressure). When grain-size reduction occurs,
then viscosity will be reduced. Diffusion coef-
ficients depend on temperature and pressure as
D
=
D
o
exp
(
E
∗
D
: activation energy for
diffusion,
V
D
: activation volume for diffusion)
and therefore the strain-rate corresponding to dif-
fusion creep depends on temperature, pressure,
grain-size and stress as
E
∗
D
+
PV
D
RT
−
A
diff
D
V
+
L
D
B
σ
3
δ
ε
diff
=
L
2
RT
,
(4.3)
L
b
−
2
exp
E
VD
+
PV
VD
RT
ε
diff
=
A
diff
·
·
−
where
A
diff
is a nondimensional parameter,
D
V
is a diffusion coefficient in the grain (volume
diffusion coefficient),
D
B
is a diffusion coeffi-
cient along grain-boundaries,
L
is grain-size,
δ
is the thickness of grain-boundary (
σ
μ
·
for volume diffusion
(4.4a)
∼
b
),
is the
L
b
−
3
exp
E
BD
+
PV
BD
RT
3
δ
b
·
b
3
). In this case, the strain-
rate is linearly proportional to stress, and the
viscosity (
η
=
molar volume (
∼
ε
diff
=
A
diff
·
·
−
σ
μ
σ
˙
ε
) is independent of stress or strain-
rate, but depends on grain-size and temperature
·
for boundary diffusion,
(4.4b)
