Messerschmidt U. Dislocation Dynamics During Plastic Deformation
Подождите немного. Документ загружается.
342 9 Intermetallic Alloys
0.5 μm
g,b
0.5 μm
(a) (b)
g,b
Fig. 9.19. Dislocations with 100 Burgers vectors on {010} planes under load
during in situ deformation at room temperature. (a) NiAl single crystal in a soft
orientation. (b) NiAl-0.2at%Ta polycrystal. Image normal (110), diffraction vector
g =[
¯
110], b projection of [010] Burgers vector. From the works in [287, 565]
Fig. 9.20. Equilibrium shape of a dislocation with [100] Burgers vector on a (011)
plane in units of E
s
/(τb) calculated within the framework of the line tension model
using anisotropic elasticity. Elastic constants for room temperature from [567]
instability occurs on {110} planes too. It also holds for other planes, leading
to the sharp “knee” at the screw parts and to the dominance of mixed dislo-
cation characters as in Fig. 9.19. At about 45
◦
, E has a minimum, whereas Γ
exhibits a maximum. The local effective shear stress τ
∗
can be estimated from
9.4 NiAl 343
the size of the calculated loops fitting the images of bowed-out dislocation
segments by the method described in Sect. 5.2.3 using (5.18). The average
value of the minor half axis x
0
of the loops, taken from relatively long
bowed-out segments, is 95 nm, which has to be considered a rough estimate
because of the angular shape of the segments. For NiAl-0.2at%Ta, the size x
0
could not be estimated unambiguously. A lower limit is x
0
= l/2=75nm.
The detailed analysis of the video recordings enabled the obstacles imped-
ing the motion of screw dislocations to be identified as jogs. This is demon-
strated in the following video clip.
Video 9.7. Motion of dislocations with 100 Burgers vectors in an NiAl single
crystal at room temperature: The clip consists of three parts. The first one shows the
typical movement of dislocations with large screw components by shifting jogs along
the dislocation line. Selected frames are reproduced in Fig. 9.21. The dislocation
moves on a {210} plane as indicated by the [
¯
112] trace t on the (110) surface. Some
major positions of the dislocation are summarized in Fig. 9.22. These positions are
not identical with those of Fig. 9.21. At 0 s, the dislocation under consideration is
anchored by two jogs, J
1
and J
2
. Because of the greater length of the central segment,
the jogs are subjected to an outward tangential force, initiating the outward motion
of the jogs. At 6.16 s, the central segment bows out extraordinarily wide. In the
next frame of the figure, two positions of the lower part of the dislocation appear
in weak contrast due to a quick motion during the exposure of the frame. Thereby,
the dislocation produced a debris D and acquired a new jog J
3
by cross slip. Later
on, J
3
is shifted along the dislocation in the Burgers vector direction. The most
prominent feature of this kind of motion is the formation of long segments by the
lateral spreading of the limiting jogs leading to very large bow-outs as at 6.16 s.
These large bow-outs cannot be explained by the action of localized obstacles like
precipitates, since the moving dislocation segment has a high probability to contact
the next obstacle after sweeping an area of the square of the square lattice distance
(see Sect. 4.5.1). The steps in the outer traces in the compilation of positions in
Fig. 9.22 reveal that the dislocation undergoes cross slip during its motion.
Between their stable positions, the dislocations move in a viscous way at a veloc-
ity that can be resolved by the video recording. This suggests that a lattice friction
mechanism is also active, in agreement with the fact that the segments bowed-out
under load do not remarkably relax when the specimen is unloaded.
In the second video sequence, part of a dislocation annihilates with another one,
which is arranged on another plane, as indicated by the different lengths of both
dislocations. The third part presents the motion of edge segments. They have a
zig-zag shape, too, owing to the elastic equilibrium shape demonstrated in Fig. 9.20.
Video 9.8. Motion of dislocations with 100 Burgers vectors in NiAl-0.2at%Ta
at room temperature: Dislocations move in a slip band originating at a crack. The
elementary processes of motion are not well resolved but are similar to those in pure
NiAl.
The activated slip planes are identified from slip traces, from points where
the dislocations emerge through the surface and from the path of these points
344 9 Intermetallic Alloys
0s 2.2s 5.48s 6.16s
6.56s 8.64s 9.04s 9.28s
t
b
J
2
J
1
J
3
D
Fig. 9.21. Sequence of frames from Video 9.7 showing the motion of a dislocation
with a 100 Burgers vector with the projection b by shifting the jogs along the
screw direction. The line t =[
¯
112] is the trace of the {210} slip plane. From the
work in [287]
Fig. 9.22. Schematic drawing of different stages of the motion of the dislocation in
NiAl shown in Fig. 9.21. The stages are not the same as those in Fig. 9.21
during motion, recorded in the videos. According to that, the dislocations
glide on {100}, {110},and{210} planes, with frequent cross slip events
between these planes. That cross slip is easy was observed earlier in [569,570].
Accordingly, many short dislocation dipoles are created forming the debris
shown earlier in Fig. 5.19. The dislocation mobility does not remarkably differ
between the different planes.
At elevated temperatures, the concentration of jogs on dislocations with
100 Burgers vectors is drastically reduced. Figure 9.23 demonstrates that
the shape of the dislocation segments is still controlled by the line tension
9.4 NiAl 345
0.5 µm
t1
t2
Fig. 9.23. Dislocation motion in an NiAl single crystal during in situ deformation
at 475
◦
C. The dislocation marked by an arrow has cross slipped from a {100} plane
with trace t1 onto a {110} plane with trace t2. From the work in [287]
with the typical knee in the dislocation line at the elastically unstable screw
orientation. The average size of the fitting theoretical loops amounts to about
x
0
= 560 nm. The following video is characteristic also of higher temperatures.
Video 9.9. Motion of dislocations with 100 Burgers vectors in an NiAl single
crystal at 475
◦
C: At elevated temperatures, the dislocations of mixed character near
screw orientation move viscously at different velocities depending on the long-range
interactions with other dislocations. During the motion, the shape of dislocations
governed by the line tension is preserved. Dislocations frequently cross slip from
a {100} plane onto a {110} plane as marked in Fig. 9.23. Two of such events are
labeled by violet circles just before the dislocations emerge at the right edge of the
frame. The slip traces are mostly relatively straight, but sometimes also serrated as
indicated by CS, which also hints at cross slip. The short second part of the video
presents a dislocation moving quickly on the (vertically running) plane with frequent
cross slips.
At 475
◦
C, slip appears preferentially still on {100} and {110} planes with
frequent cross slips between these planes. At higher temperatures, the slip
trails become noncrystallographic so that probably climb, too, contributes to
the dislocation motion. Some features of the motion of edge dislocations are
presented in Video 9.10.
Video 9.10. Motion of dislocations with 100 Burgers vectors in an NiAl single
crystal at 565
◦
C: The band of dislocations with dominating edge character is emitted
at a crack tip. The dislocations are slightly bowed. The dislocation right of the violet
346 9 Intermetallic Alloys
label drags a prismatic half-loop behind. Another prismatic half-loop at P is moved
forward and backward on its glide cylinder by the interaction with the passing
dislocations of the band.
In NiAl-0.2at%Ta, dislocations with 110 Burgers vectors were activated
in grains in the hard orientation. Their shape strongly depends on their glide
plane. Figure 9.24a shows such dislocations marked A, moving on {111}planes
and trailing slip traces. Segments parallel to the surfaces along [0
¯
11] seem to
be quite immobile. The moving parts show preferred orientations along [12
¯
1]
directions, which do not correspond to the edge and screw orientations. They
can also not be explained by the elastic equilibrium shape and may therefore
be determined by an anisotropic glide resistance. Video records show that
these dislocations move in a continuous viscous way. Figure 9.24a also exhibits
a large number of dislocations like B of the same type of Burgers vectors which
are not located on {111} slip planes and which are difficult to interpret.
Figure 9.24b demonstrates that the morphology of dislocations with 110
Burgers vectors greatly differs when they move on {110} planes. They consist
of very straight segments in 111 orientations, i.e., they are neither of screw
nor of edge character. This observation was confirmed by post-mortem TEM
of Ni-44at%Al single crystals deformed in the hard orientation [571]. The
straight shape can also not be interpreted by the elastic equilibrium shape,
which is quite smooth without instabilities. The segments are connected by
small arcs. The following video exhibits the motion of these dislocations.
Video 9.11. Motion of dislocations with 110 Burgers vectors on {110} planes in
NiAl-0.2at%Ta at 475
◦
C: At elevated temperatures, the straight dislocations with
110 Burgers vectors move in a viscous way on {110} planes.
The core structure of edge dislocations with 100 and 110 Burgers vec-
tors was studied by Mills and Miracle [572] by high-resolution TEM. According
to that, the cores of the 100 dislocations are compact but have large elastic
strains corresponding to the relatively large Burgers vectors. The 110 dis-
locations may dissociate into two partial dislocations with 1/2111 Burgers
vectors including an APB, or they decompose into two dislocations with 100
Burgers vectors. The decomposition was proved also for dislocations along
111 directions with a decomposition distance of only 2 nm [571]. For edge
dislocations, it is larger. The consequences of such a kind of decomposition
will be discussed in Sect. 9.4.4.
9.4.3 Macroscopic Deformation Parameters
As shown in Fig. 9.15, stoichiometric NiAl single crystals strained along a soft
orientation, which are deformed by 100 dislocations, do not exhibit a flow
stress anomaly. The NiAl-0.2at%Ta polycrystals not only show much higher
flow stresses but also a normal temperature dependence. In contrast to the
in situ straining experiments above, where at high temperatures only grains
in the hard orientation were observed, mainly dislocations with 100 Burgers
9.4 NiAl 347
1µm
g
b
A
A
A
B
(a)
0.5 µm
b
11-1
111
g
(b)
Fig. 9.24. Dislocations with 110 Burgers vectors during in situ deformation of
NiAl-0.2at%Ta at 475
◦
C. (a) Dislocations A moving on {111} planes and trailing slip
traces and those moving on other planes B. Diffraction vector g =[0
¯
11], b projection
of [
¯
110] or [
¯
1
¯
10] Burgers vectors. (b) Dislocations moving on {110} planes. Indicated
are the projections of the [11
¯
1] and [111] directions and of the [110] Burgers vector
onto the image plane and the imaging vector g =[0
¯
11]. From the work in [565]
348 9 Intermetallic Alloys
(a)
(b)
Fig. 9.25. Dependence of the strain rate sensitivity of the flow stress on the loga-
rithm of the strain rate in (a) NiAl single crystals deformed along 421 and in (b)
NiAl-0.2at%Ta polycrystals. Data from [573]
vectors will carry the deformation. As reviewed in [562], crystals deformed in
the hard orientation show a weak flow stress anomaly with a plateau, where a
transition occurs between glide on the {112}111 system below about 325
◦
C
and {110}110 above that temperature. Thus, the in situ straining experi-
ments with 110 dislocations belong to the range where these dislocations
control the deformation in the hard orientation.
The dependence of the strain rate sensitivity r on the logarithm of the
strain rate ˙ε is plotted in Fig. 9.25a for the NiAl single crystals. At all the three
temperatures selected, there is a positive dependence corresponding to normal
obstacle behavior. An exception is the highest temperature where r is high
at very low strain rates due to recovery. In NiAl–Ta, however, the behavior
of the strain rate sensitivity is normal only at room temperature (Fig. 9.25b).
At elevated temperatures, this material exhibits an inverse dependence of r
on log ˙ε.
9.4.4 Deformation Mechanisms
Like in TiAl, different mechanisms control the dislocation mobility in NiAl
at room temperature and at high temperatures. At room temperature, the
dislocations have configurations with bowed-out segments and are moving in
a jerky way. At high temperatures, they are smooth and move viscously.
Room Temperature
The static configurations and especially the details of the mode of forward
motion described earlier (Fig. 9.19, Video 9.7) suggest that the obstacles which
pin the dislocations with 100 Burgers vectors at room temperature are jogs.
Thus, these dislocations are clearly an example of the jog mechanism sug-
gested by Sriram et al. [549] for γ-TiAl. However, as proved in NiAl in soft
orientations, the jog mechanism does not cause a flow stress anomaly. The jogs
9.4 NiAl 349
Table 9.2. Deformation data of NiAl materials at room temperature. Data rom
[287, 565]
Material σ
y
(MPa) r (MPa) V/b
3
l/b x
0
(nm) τ
∗
(MPa)
NiAl 421 220 2.5 215 260 95 90
NiAl-0.2at%Ta 380 9.3 57 520 >75 <110
are created by double-cross slip as proposed for dislocation multiplication in
the Koehler–Orowan mechanism described in Sect. 5.1.1. The high frequency
of cross slip in NiAl is quite strange since only screw segments can cross slip.
However, this orientation is unstable and does not exist in equilibrium con-
figurations of the dislocations. Before cross slip, first a screw segment has
to be created, the energy of which is about 9% higher than that of the sta-
ble branches adjoining the knee at the screw orientation. Apparently, stress
components on the cross slip plane assist this process.
As several times before in this book, via (5.18) the (shear) back-stress
can be calculated resulting from the bowing-out of dislocation segments
pinned between obstacles. Table 9.2 lists the results together with other defor-
mation data, using the values of the minor half-axis x
0
of the bowed-out
segments and the relevant constants. These values are large fractions of the
total yield stresses σ
y
if average orientation factors are considered. Thus,
the jog mechanism contributes essentially to the total flow stress at room
temperature.
Comparing the activation volume V following from the strain rate sensitiv-
ity r with the obstacle distance l from the in situ straining experiments yields
for NiAl an activation distance Δd of about b if (4.4) and the data of Table
9.2 are used. Unfortunately, there does not exist a theory of the activation
parameters of the motion of screw dislocations by the sidewise shifting of jogs
so that this value cannot be interpreted microscopically. For NiAl-0.2Ta, Δd
roughly equals only about 0.1 b. The corresponding small activation volume
should result from the solution hardening of the Ta additions. In [565], based
on the theory of Mott statistics described in Sect. 4.5.2 it is argued that solu-
tion hardening may explain both the increased flow stress of NiAl-0.2Ta with
respect to pure NiAl as well as the corresponding decrease of the activation
volume. A further contribution to the flow stress certainly originates from
the Peierls mechanism. If there were no lattice friction, the jogs would easily
glide along the screw direction so that long segments became unstable and
the dislocations would easily proceed forward.
High Temperatures
For the 100 dislocations in NiAl at 475
◦
C, the effective stress τ
∗
≈ 20 MPa
measured from the dislocation bowing is only about 20% of the macroscopic
flow stress. Viscous motion of dislocations at these temperatures was described
before for TiAl (Sect. 9.3). It cannot be explained by the Peierls mechanism
350 9 Intermetallic Alloys
based on the data of the low-temperature increase of the flow stress. According
to standard theory, thermally activated processes controlling the dislocation
mobility at low temperatures should not be active above specific temperatures.
Apparently, like in TiAl, diffusion-controlled processes are important also in
NiAl. At high temperatures, climb is indicated by noncrystallographic slip
trails. Because of the low mobility of vacancies, characterized by a migration
enthalpy of 2.1 eV [560], diffusion processes may become evident only in the
temperature range of the viscous dislocation motion.
As estimated in [565], the solution hardening of the Ta additions in NiAl-
0.2Ta will rather quickly decrease with increasing temperature, in contrast
to the weak normal temperature dependence of the yield stress in Fig. 9.15.
It may therefore be concluded that the Ta additions contribute to the flow
stress at higher temperatures through the formation of impurity atmospheres
around the dislocations. This is in agreement with the inverse dependence
of the strain rate sensitivity on the strain rate, which is observed in NiAl–Ta
but not in pure NiAl, as documented in Fig. 9.25. Corresponding strain ageing
effects were observed in NiAl materials containing additions of Ti, Zr, and Hf
[574].
The formation of point defect atmospheres can explain the viscous motion
of dislocations at high temperatures and also the occurrence of a flow stress
anomaly. However, it does not explain that the dislocations with 110 Burgers
vectors arrange in very straight configurations along the mixed 111 ori-
entation as in Fig. 9.24 and Video 9.11. Apparently, in NiAl single crystals
deformed in the hard 100 orientation the situation is quite complex. Dis-
locations with 100 Burgers vectors are not activated because of their zero
orientation factor. Below a certain transition temperature, the material is
deformed by dislocations with 111 Burgers vectors (e.g., [568, 575]) at a
very high resolved shear stress of 600 MPa. Above the transition temperature,
the deformation occurs either by kinking via 100 dislocations [576] or by slip
of 110 dislocations [577]. In [578,579], for instance, it is suggested that the
slip transition is achieved by decomposition of the 111 dislocations according
to
[111] → [110] + [001].
This reaction is energetically favorable for dislocations with near-edge orienta-
tion on (
¯
110) planes [580]. By atomistic calculations, Srinivasan et al. [581,582]
have shown that the 111 dislocations may occupy a metastable state along
the mixed 111 orientation. These dislocations can move as a whole but if the
components are separated wide enough, they may decompose completely. All
reaction products are then arranged parallel to the 111 mixed orientations
of the parent dislocations. The components with 100 Burgers vectors expe-
rience no shear stress. Thus, the 110 components have to move away. This
is possible only at sufficient mobility, i.e., if the temperature is high enough.
As mentioned in Sect. 9.4.2, edge dislocations with
110 Burgers vectors
are observed to have a decomposed core after the reaction [572]
9.4 NiAl 351
(110)
(010)
(100)
b = [–110]
b = [–100]
b=[010]
Fig. 9.26. Decomposition of an edge dislocation of [
¯
110] Burgers vector as suggested
in [583]
[110](1
¯
10) → [100](010) + [010](100). (9.3)
The indexes in parentheses mark the slip planes of the respective dislocations.
Based on the microstructural observations, the reaction is studied by elastic
and atomistic calculations in more detail by Mills, Srinivasan and Daw [583].
It may occur by glide of the product dislocations on their (010) and (100) glide
planes as outlined in Fig. 9.26. It is favored for edge dislocations since their line
orientation is contained in the glide plane of the parent dislocation as well as in
low-index glide planes of both product dislocations. From calculations of the
elastic energy, the reaction is neutral, i.e., there is no radial force between the
product dislocations. Taking the elastic interaction energy into account, the
reaction yields a gain in energy. Atomistic calculations by the embedded atom
method (EAM) show that the decomposition takes place under a shear stress
on the parent dislocation. In its decomposed state, the dislocation cannot
glide. However, it can move in upward direction indicated by the arrow at the
parent dislocation in Fig. 9.26 by a vacancy flux from the [100] dislocation to
the [010] dislocation as indicated by the open square with the arrow. This
process requires only short-range diffusion, but no lattice diffusion over larger
distances. It is called conservative climb.
In Fig. 9.24, Video 9.11 and in the TEM study on Ni-44at%Al in [571],
the dislocations with 110 Burgers vectors on {110} planes are mostly ori-
ented along the mixed 111 directions. Line tension calculations within the
framework of anisotropic elasticity yield a smooth equilibrium shape of 110
dislocations without elastic instabilities. Besides, static relaxation and molec-
ular dynamics calculations by the EAM at 0 K do not show higher Peierls
stresses for particular orientations [571]. Thus, the straight oriented course of
the mixed dislocations may be explained by the same decomposition reaction
as (9.3), which now reads
[110](
¯
110) → [100](0
¯
11) + [010](10
¯
1). (9.4)
The {110} planes on which the decomposition may take place are also low-
index planes, they are preferred slip planes of the 100 dislocations. Besides,
the 111 preference orientation of the dislocations is contained in the slip
planes of both the parent dislocation and of the reaction products.