Messerschmidt U. Dislocation Dynamics During Plastic Deformation
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292 8 Metallic Alloys
dislocations, however, D
2
/l
2
=0.049, which is consistent with the model and
also with the few micrographs showing edge dislocations.
The disagreement between the behavior of screw dislocations and the sim-
ple theory can be explained by assuming that in addition to order hardening
a further mechanism contributes to the interaction between dislocations and
precipitates, which also acts on the trailing dislocations. It is suggested that
this mechanism is modulus hardening. The difference between the shear mod-
ulus of the particles and the matrix amounts to 6.7 GPa or about 22% [470].
Estimations on the basis of (4.70) of the model in Sect. 4.7 yield an increase
of about 50% of the strength F
0
of the precipitates, but only slight change
in the total activation energy. As the particles are overcome in an athermal
way, the behavior of the dislocation pairs can be explained by a combination
of APB and modulus hardening.
The local effective stress τ
∗
is approximately equal for the leading screw
dislocations in pairs and single screw dislocations. This can be expected if
dislocations in both arrangements have to cut the same type of obstacles
and to create the antiphase boundaries. The applied stress in the respective
regions, however, is drastically different, which is certainly connected with the
necessity for the pair mechanism to create dislocations in pairs. This topic will
be touched again in Sect. 8.2.
In polycrystals, planar slip frequently occurs. The dislocations can be
generated by Franck–Read sources in the grain boundaries. In this case, all
dislocations automatically move on exactly the same plane. Planar slip should
also be favored for energetic reasons, as the slip resistance of the precipitates is
reduced if many dislocations shear the particles on the same plane, thus dimin-
ishing the cutting area. In the present study, planar slip has been observed
most rarely. An example is given in Fig. 8.7. It shows dislocations emitted
apparently from a localized source. In agreement with the model, only the
1 µ
m
Fig. 8.7. Planar slip of dislocation pairs and single dislocations in Al–Li. From the
work in [284]
8.2 Dislocation Generation in Metals 293
first dislocations, visible on the left of the figure, move in pairs until the par-
ticles are fully sheared. The following single dislocations should not bow out
if the particles interact solely by order hardening. This is a further indication
of the action of an additional hardening mechanism.
8.1.4 Summary
Three examples were presented of precipitation hardening in aluminium alloys.
Only in Al–Li, the obstacle distances agreed satisfactorily with those predicted
from the concentration and size of the particles. In Al–Zn–Mg, far more obsta-
cles controlled the dislocation motion than those considered before based on
conventional methods. The opposite case occurred in Al–Ag, where only part
of the precipitates visible in conventional and high-resolution TEM impede
the dislocation motion.
As demonstrated in Table 8.1, the normalized effective stress τ
is always
high in these alloys, between 0.45 and 0.87, where the lower values belong
to the under-aged alloys. The high values indicate that the situation is close
to the Orowan case. It should be remembered that in a line tension analo-
gon Orowan looping appears for τ
< 1 if the self-stress of the interacting
dislocation segments is taken into account.
A problem is the calculation of the effective stress τ
∗
from the curvature
measure S, which requires the knowledge of the dislocation line energy. There
is great uncertainty because of the constant C in formulae like (3.45), (5.17),
or (5.18). The measurements of the dependence of the curvature of dislocation
segments on their length in Al–Zn–Mg and Al–Li confirm the value of C dis-
cussed in Sect. 3.2.7 for MgO, leading to very low line energies. Nevertheless,
the values of τ
∗
quoted in this section on aluminium alloys were based on the
theoretical value of C. This may be kept in mind if some of the effective stress
data appear unrealistically high.
8.2 Dislocation Generation in Metals
This section presents several video sequences of the creation of new dis-
locations in metals, thus supplementing the experimental observations of
Sect. 5.1.2. In many metals, the dislocations are generated by the double-
cross slip mechanism. A further example from Al–Ag described in Sect. 8.1.2
is given in the following video.
Video 8.3. Loop generation and opening in an Al–Ag single crystal: The video
clip shows the very sudden generation of large dislocation loops and their opening
resulting in the generation of new dislocations moving away. The places of events
are marked by green circles. After the second labeling, the shift of the upper loop
downwards is caused by a reaction with a dislocation moving very quickly from the
lower center of the image to the left, thereby annihilating parts of the loop. All
processes take place very quickly.
294 8 Metallic Alloys
1 µm
L
L
Fig. 8.8. α-like dislocation configurations indicating dislocation generation by the
double-cross slip mechanism in Al–Li. From the work in [284]
The very sudden appearance of the loops and their opening underline that
dislocation multiplication is controlled mainly by long-range dislocation pro-
cesses. It is therefore of athermal character.
A special situation occurs in the Al–Li alloy treated in Sect. 8.1.3, where
the dislocations move in pairs and are spread over relatively wide slip bands as
in Fig. 8.4. This loose arrangement again hints at the operation of the double-
cross slip mechanism. But, to multiply in pairs, both dislocations of the pair
have to cross slip together onto a cross slip plane and afterwards to cross slip
again together back to a plane parallel to the original one. This is astonishing
in so far as the dislocations of the pair do not attract but repel each other,
and as they are not coupled together by a continuous planar fault. The APB
faults exist only inside the precipitates. Nevertheless, the dislocations multiply
in pairs as documented by the α-like dislocation configurations marked by
arrows in Fig. 8.8. There are also small loops and half-loops L consisting of
dislocation pairs.
A material in which dislocations are created during plastic deformation
in a dispersed way by the double-cross slip mechanism as well as in localized
repeatedly operating (Frank–Read) sources is a titanium alloy with 6 wt% alu-
minium. The α-phase has the h.c.p. crystal structure. The dislocations with
a-type Burgers vectors b = a/311
¯
2 move preferentially on prismatic and
basal planes. The flow stress depends on annealing treatments. The responsi-
ble solution hardening is supposed to result from the formation of short-range
8.2 Dislocation Generation in Metals 295
order [471, 472]. The order is partially destroyed by the moving dislocations.
This requires energy, which causes a friction stress for the dislocations. Fur-
ther, dislocations moving on the same plane move in a less ordered region
and consequently experience a lower friction stress. This favors planar slip.
The specimens shown in the following video sequences were produced in coop-
eration with M. Mills and T. Neeraj. The crystals were all homogenized at
900
◦
C for 24 h and then either air-cooled or annealed at 600
◦
C for another
24 h followed by ice water quenching (step-annealed). Both treatments cause
the formation of different degrees of short-range order. The first two videos
present several examples of the creation of dislocations by the double-cross
slip mechanism.
Video 8.4. Creation and opening of dislocation loops in air-cooled Ti-6 wt% Al at
room temperature: This video consists of three sequences, in which many events
show the creation of dislocation loops and their opening to new dislocations as well
as the annihilation of screw dislocations of opposite sign. In the first sequence, a
small loop L is annihilated by a dislocation gliding nearby. The second sequence
shows the opening of several loops to form pairs of dislocations. The dislocation
at J acquires a jog, which trails a dipole growing to a loop and finally also to two
new dislocations. In the third sequence, at D two screw dislocations of opposite sign
trap each other to form a dipole. A dislocation loop expands at L to form two new
dislocations. The right one annihilates with another dislocation of opposite sign so
that only a small debris remains, which later on grows to a loop. At A, the left
dislocation moves to the screw dislocation dipole formed before and annihilates one
dislocation of the dipole so that only a single dislocation remains. This underlines
the dynamic character of dislocation multipoles as discussed in Sect. 5.1.3.
Video 8.5. Dislocation generation at a jog in step-annealed Ti-6 wt% Al at room
temperature: A jog in a screw dislocation trailing a short dipole is labeled J. The
dipole opens to a loop, which is growing until the edge segments emerge at the
surface so that two new dislocations are formed.
The next video shows several localized dislocation sources.
Video 8.6. Localized (Frank–Read) sources in step-annealed Ti-6 wt% Al at room
temperature: In contrast to the preceding videos, here dislocations are generated by
localized (Frank–Read) sources. One source is marked by a green circle. It consists of
a half-loop, which is pinned by a high jog J at the lower end, as shown in Fig. 8.9. The
jog causes a shift of the emergence points of the two dislocation branches through the
surface with respect to the trace of the slip plane marked by the dashed line. One arm
of the dislocation rotates around the jog, thereby always emitting one dislocation
moving to the right and another one moving to the left. Two further sources are
located at the left edge of the frame. The dislocations emitted from these sources
are pinned temporarily at a dislocation of opposite sign forming a screw dislocation
dipole. All the emitted dislocations moving to the right form a pile-up, the back
stress of which blocks the sources. They operate again only after the dislocations
of the pile-up have moved far enough away. This behavior was described before in
Sect. 5.1.2 and is typical of all localized dislocation sources.
296 8 Metallic Alloys
J
Fig. 8.9. Frank–Read source in Ti-6 wt% Al consisting of a half loop with a high
jog. From a cooperation with M. Mills and T. Neeraj
As a consequence, dislocations with a high screw component are effectively
pinned by high jogs. These jogs may trail a dipole, which opens to a dislocation
loop, or one branch rotates around the jog, thus emitting a greater number
of dislocations. The occurrence of localized dislocation sources in Ti-6Al is a
prerequisite to planar slip taking place in this material. The slip localization
is favored by the strain softening due to the destruction of the short-range
order.
A two-phase material with different mechanisms of dislocation generation
in the two phases is duplex steel. It consists of grains of b.c.c. (α) ferrite with
{110}1/2111 slip systems and of f.c.c. (γ) austenite with {111}1/2110
slip systems. The Burgers vectors in the two phases correspond to each other.
While the dislocations in the ferrite grains multiply by the double-cross slip
mechanism, localized (Frank–Read) sources operate in the austenite grains,
as demonstrated by the two following video clips.
Video 8.7. Dislocation multiplication in a ferrite grain during the deformation of
duplex steel at room temperature: In the two-phase material, slip has to be transferred
between grains of the same phase and of different phases. In the present example, slip
in a grain in the middle of the left side of the frame is transferred to the bright grain
on the right side. Thus, many dislocations emerge from the phase or grain boundary.
In addition, the clip contains a number of α-like dislocation configurations, which
are characteristic for dislocation multiplication and which develop to loops and later
on to two isolated dislocations. At J, a jog trailing a short debris dipole is shifted
conservatively along the dislocation until it disappears at the surface. The α-like
configuration at L opens to a loop that expands to two dislocations.
Video 8.8. Frank–Read source in an austenite grain during the deformation of
duplex steel at room temperature: The video clip presents the operation of a localized
dislocation source in an austenite grain. The nature of the pinning agent is not clear.
8.3 Oxide Dispersion Strengthened Materials 297
A connection of the source dislocation with the dislocation network is not obvious.
It can be extinguished under the present contrast conditions, or the pinning agent is
a high jog in the dislocation as in the preceding example of a localized source. The
moving branch rotates quite fast because of the athermal character of the dislocation
motion. After one dislocation is emitted, the source stops due to the back stress of the
emitted dislocations, which pile up against the grain or phase boundaries. When the
outer dislocation breaks through the boundaries, part of the back stress is released
and a new dislocation can be generated.
In summarizing, it may be stated that both mechanisms of dislocation gen-
eration are quite similar and may operate simultaneously in a single material.
If cross slip is easy, many sources may be created, the jogs may move con-
servatively along the multiplying screw dislocations after one new dislocation
loop has been created. Thus, slip spreads easily over the crystal volume. If
cross slip is restricted, the jogs may remain in their positions, and the sources
may operate repeatedly. Localized sources emitting many dislocations always
occur when the pinning agents are nodes of the dislocation network.
8.3 Oxide Dispersion Strengthened Materials
Hard incoherent particles can be incorporated into a metal matrix to improve
the creep resistance of alloys at high temperatures. Frequently, the parti-
cles are oxides, leading to oxide dispersion strengthened (ODS) alloys. At
low temperatures, such particles have to be bypassed by Orowan looping
(Sect. 4.7). At high temperatures, the dispersoids are easily overcome by
climb [473]. Nevertheless, there exists a well-defined threshold stress for creep,
below which the ODS alloys exhibit very low creep rates. The interpretation
of the threshold stress is based on an attractive interaction, which causes
the pinning of the moving dislocations on the departure side of the par-
ticles [474]. It was stated that if the interfaces between the particles and
the matrix do not transfer shear strains, the stress field of the dislocations
may partly relax at the interface leading to a reduced dislocation energy
[475, 476], which causes the attractive interaction. Most experimental data
on the creep behavior of ODS alloys are interpreted in terms of the respec-
tive model by Arzt and R¨osler [477] or its variant including the thermally
activated detachment from the particles [478] (Arzt–R¨osler model). Recently,
Xiang and Srolovitz [479] simulated the overcoming of penetrable and impene-
trable particles without and with misfit by combined glide and climb applying
linear relations between the glide and climb velocities and the respective stress
components. It turned out that during overcoming the particles, the disloca-
tions may assume a great variety of configurations depending on the actual
parameters. There is some transmission electron microscope evidence of dis-
locations pinned to particles (e.g., [480, 481]), but there was no direct proof
that the dislocations spend most of their time in the respective configurations
on the departure side of the particles. In situ straining experiments in an
298 8 Metallic Alloys
HVEM were performed to study the dislocation dynamics and the interaction
between dislocations and particles in the ODS alloy INCOLOY MA956 [482]
and the ODS superalloy INCONEL MA754 [483]. The studied alloys consist of
Fe-19.9Cr-4.6Al-0.38Ti-0.51Y-0.019C-0.014N-0.19O and Ni-20Cr-0.3Al-0.5Ti-
1Fe-0.05C-0.6Y
2
O
3
(wt%). The activated slip planes were determined from
the traces the moving dislocations generated on the specimen surfaces. The
Burgers vectors are of a/2111 type for MA956 and a/2110 for MA754.
8.3.1 Microscopic Observations
in Oxide Dispersion Strengthened Alloys
Experimental results are mainly described for MA956. They are supplemented
by those of MA754. At room temperature, slip was observed only on {110}
planes. At the beginning of the in situ experiments, slip occurs in relatively
narrow slip bands, as shown in Fig. 8.10. The slip plane is inclined by about 65
◦
to the image plane so that the dislocations appear only in a narrow projection.
Resting dislocations are mainly of screw character, being quite straight then.
Only edge or mixed segments bow out strongly. With increasing strain, the
dislocations cross slip onto another {110} plane, with the slip bands broaden-
ing until the whole volume is filled with dislocations. Many small dislocation
loops occur in the slip bands.
1 µm
b
Fig. 8.10. Dislocations moving on {011} slip planes during in situ deformation of
MA956 at room temperature. From the work in [482]
8.3 Oxide Dispersion Strengthened Materials 299
The dynamic behavior of dislocations at room temperature is shown in
the video.
Video 8.9. Dislocation motion in INCOLOY MA956 at room temperature: At
room temperature, the dislocations move in a very jerky way over distances longer
than those between the oxide particles.
The jerky motion hints at the athermal character of the deformation at room
temperature.
At elevated temperatures, slip occurs in MA956 on {110}, {112},and
{123} planes often including cross slip between these planes. Most experiments
were made at 700
◦
C. A typical example is presented in the following video.
Video 8.10. Dislocation motion in MA956 at 700
◦
C: This video clip consists of
two sequences. The dislocations move in a smooth and viscous way. At the particles,
a cusp develops, with the adjoining dislocation segments bowing out. When the
maximum bowing is reached, that is, when the maximum force acts, the particles
are mostly overcome without long waiting times in the equilibrium positions.
In the second video sequence, dislocations move on a {112} plane. The slip plane
is inclined by about 25
◦
with respect to the image plane so that the width of the slip
plane is about 1 μm. The average dislocation velocity is 10–15 nm s
−1
,whichisslow
enough to resolve different stages of overcoming the dispersoids. The dislocation
velocity was approximately equal for screw and edge dislocations. The first part of
this sequence shows several stages of surmounting a single strong obstacle, marked
by a green dot above it. Selected frames are presented in Fig. 8.11. In the first frame
taken at a time of 0 s, the obstacle is first contacted. Afterwards, the dislocation
moves from the arrival side to the departure side of the obstacle in about 7 s forming
only a weak cusp at the obstacle. It then slowly bows out reaching its equilibrium
bowing after a total time of 21 s. In this configuration, the dislocation forms a
sharp cusp on the departure side. It remains in this position for less than 1 s. At
21.6 s, the dislocation starts to detach from the obstacle. At 22.7 s, it has left the
particle completely, the strong bowing has disappeared, and the dislocation moves
in a viscous way. While traveling to the next particle, which takes about 10 s, most
of the dislocation is quite straight. Certainly, the particle that had been overcome
during the first 22 s was a particularly large one. Nevertheless, the process is very
much the same also for smaller particles, which are not imaged in the HVEM, but
which cause the formation of cusps along the dislocation line.
To increase the particle size, some specimens were annealed. An example
is presented in the following video.
Video 8.11. Dislocation motion in annealed MA956 at 700
◦
C: This clip of the
annealed alloy with particles of larger size confirms the observation made above
that the dislocations detach from the pinning centers without long waiting times
in the equilibrium configurations. The dislocation moving upwards undergoes cross
slip onto a plane with an inclined trace.
In conclusion, one can say that around 700
◦
C the four following stages of
dislocationmotioninanarrayofincoherent particles can be distinguished.
300 8 Metallic Alloys
0.2 µm
[042]
b
[200]
18 s
21 s
21.6 s
22.7 s
24.3 s
27.8 s
1 s
7 s
16 s
0 s
Fig. 8.11. Sections of a video sequence showing a dislocation in MA956 moving at
700
◦
Cona{112} plane overcoming a large oxide particle. The plane is inclined by
about 25
◦
with respect to the image plane. From the work in [482]
1. The dislocations move in a viscous way between configurations in which
they are locally pinned. This points to a frictional force acting on the
moving dislocations.
2. After contacting a particle, the dislocation moves to the departure side in
rather a short time, with a relatively small force acting.
3. The dislocation gets pinned on the departure side of the particle while
the adjacent segments in the matrix slowly bow out until they reach their
elastic equilibrium configurations. This process of bowing out between
the particles takes a relatively long time. The back stress of the bowed
segments reduces the stress available for the viscous motion, causing a
8.3 Oxide Dispersion Strengthened Materials 301
lower velocity before the equilibrium bowing is reached. This back stress,
which reduces the applied stress temporarily, is supposed to be the main
strengthening effect of the particles around 700
◦
C.
4. After a short lifetime of the equilibrium configuration, the dislocation
detaches from the particle, straightens, and glides to the next obstacle as
described under 1.
Dislocation configurations at other temperatures resemble those at 700
◦
C.
The dislocation motion at lower temperatures is viscous between the sta-
ble configurations. The slip distances after overcoming the particles are not
much greater than the particle distances. A different situation holds for higher
temperatures as verified by the following two video clips.
Video 8.12. Dislocation motion in MA956 at 1010
◦
C: At this high temperature,
the dislocation motion becomes quite jerky.
Video 8.13. Collective dislocation motion in MA956 at 1010
◦
C: The video clip
comprises two sequences taken from a narrow slip band. In the band, the dislocations
move in a collective way where the dislocations are approximately equally spaced.
The dislocation motion is quite jerky at this temperature. Many dislocations are
pinned at the same particles so that successive configurations resemble each other.
In the second clip, many dislocations pass a very large particle almost in the
center of the frame. The course of the dislocations while passing the particle can be
followed.
The jerky motion at high velocities between the particles suggests that the
frictional forces, which act at temperatures around 700
◦
C, disappear at higher
temperatures. In addition, the slip distances become larger than a micrometer.
Near 1000
◦
C, the dislocations mostly move in a collective way. This suggests
that long-range elastic interactions between the dislocations play an important
role.
Quantitative data on the dislocation dynamics can be derived from
the micrographs and video recordings. Some efforts were made to measure the
obstacle distance l at 700
◦
C. First, the distances were determined between the
cusps in all bowed-out positions that were recorded during a 3-minute obser-
vation of the second part of the dynamic Video 8.10. In a second approach,
video frames were selected randomly for determining the pinning point dis-
tances of a larger number of segments. Finally, l can be estimated from the
size and density of the dispersoids. It follows from all three measurements that
the segment length between such obstacles which effectively impede the dis-
location motion at about 700
◦
C amounts to about 200 nm. Similar estimates
were made for MA754. The results are summarized in Table 8.3.
The stress acting on individual bowed-out dislocation segments was mea-
sured from the dislocation curvature determined by matching calculated
dislocation shapes with the dislocation images as described in Sect. 5.2.3 and
by applying (5.18). The elastic constants for MA956 were taken from [484]
for the alloy PM 2000, which should be similar to INCOLOY MA956. As no