Messerschmidt U. Dislocation Dynamics During Plastic Deformation

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322 9 Intermetallic Alloys

by cross slip the leading partial returns onto a plane parallel to the original slip

plane as illustrated in Fig. 9.5. The model explains most of the experimental

results, including the strong work-hardening in the anomaly range.

A quite diﬀerent approach to the motion of a superdislocation with kinks

was taken in the simulations by Mills and Chrzan [523]. Dislocations are

pinned locally by random events with their probability depending on the local

orientation of the dislocation line. The distribution of the pinning agents turns

out not to be random but to consist of strongly pinned near-screw segments

connected by mobile superkinks. The dislocation moves by sidewise spread-

ing of the kinks at high velocities. Owing to ﬂuctuations in the density of the

kinks, whole segments may become immobile. Thus, the jerky motion observed

experimentally is not a consequence of locking and unlocking of long segments

but of the nonrandom distribution of the macrokinks. Several versions of such

models have been discussed in [524]. Petukhov [525], too, gave a statistical

treatment of the formation of pinning agents by cross slip and subsequent

unpinning.

In conclusion one can say, a number of reﬁned models have been developed

for estimating the ﬂow stress of intermetallic compounds with the L1

struc-

ture, particularly of the ﬂow stress anomaly. These models are based on the

dissociation of the superdislocations into superpartials connected by an APB.

The energy of the APB being lower on the cube cross slip plane than on the

octahedral glide plane, together with a shear stress component acting on the

cross slip plane lead to localized cross slip, which locks the cross-slipped dislo-

cation segments. Such models are exemplary also for intermetallics with other

crystal structures. However, as will be discussed in the following sections, the

ﬂow stress anomalies may have many other origins, too.

9.3 γ-TiAl

Titanium aluminides are prospective materials for structural applications at

intermediate temperatures owing to their light weight, their relatively good

corrosion resistance and, particularly, to their high ﬂow stress up to tempera-

tures above 650

◦

C. The latter is due to the occurrence of a ﬂow stress anomaly,

at least a constancy of the ﬂow stress with increasing temperature over a

wide range. Materials of technological interest based on Ti–Al are mostly

two-phase alloys consisting of the soft TiAl γ-phase having the L1

structure

and the harder Ti

Al α

-phase with the D0

structure. Single-phase γ-alloys

have some major disadvantages regarding their room temperature formability,

creep and also strength properties. However, in two-phase alloys, the major

part of the plastic deformation occurs in the γ-phase so that the single-phase

γ-alloys may serve as a model material of the plastic constituent of other TiAl

based materials. Comprehensive reviews on γ-TiAl based materials are given,

e.g., in [526–528].

9.3 γ-TiAl 323

The single-phase γ-alloys form on the Al-rich side of the stoichiomet-

ric TiAl composition, whereas the two-phase (α

+ γ) alloys occur on the

Ti-rich side. In the latter, diﬀerent microstructures may develop depending

on further alloying elements and the thermo-mechanical treatment. These

microstructures frequently involve a lamellar structure consisting of rela-

tively wide twin-related lamellae of the γ-phase and thin α

lamellae. These

microstructures essentially inﬂuence the macroscopic deformation properties

of the technical alloys. However, the present section is restricted to the dis-

location behavior and plastic properties of the γ-phase, in particular to the

deformation at room temperature and in the anomaly range. In Ti

Al, dis-

location dynamics was studied by in situ straining experiments in a TEM in

[529,530].

9.3.1 Crystal Structure and Slip Geometry

The L1

structure of the γ-phase of TiAl is an f.c.c. based structure with

a small tetragonality of c/a ≈ 1.02. It is characterized by lattice planes

alternately occupied by Al and Ti atoms as demonstrated in Fig. 9.7a. Con-

sequently, the {111} slip planes consist of separate rows of Al and Ti atoms

in 110 directions (Fig. 9.7b). The shift vector b

=0α =1/2110 does not

produce a planar fault, it corresponds to complete dislocations. Frequently,

the vectors in this tetragonal structure are also written as 1/2110] to indi-

cate that the third index may not be mixed up with the other two. However,

this is self-evident in the tetragonal structure. Dislocations with 1/2110

Burgers vectors are called simple or ordinary dislocations. The shift vector

=0β =1/2101 causes an APB and corresponds to a superpartial dislo-

cation. The complete superdislocation has the Burgers vector b

=0γ = 101.

[001]

[010]

[100]

(a)

[−210]

[−101]

[11−2]

[01−1]

[−110]

[−12−1]

(b)

Fig. 9.7. Unit cell with Burgers vectors b

and b

of ordinary and superdislocations

(a) and atomic arrangement on the {111} slip plane (b) of an AB compound with the

structure. Three layers of atoms a, b, c are stacked in the ...abcabc... sequence

and are drawn by circles of decreasing size

324 9 Intermetallic Alloys

In Fig. 9.7a, the Burgers vectors of ordinary and 101 superdislocations are

indicated. There exist also superdislocations with b

=1/2112,whichare

rare and are not considered further. The fault vectors 0δ and 0 produce a CSF

and an SISF. In addition to dislocation motion, γ-TiAl may also be deformed

by twinning of {111}11

2 type.

9.3.2 Microscopic Observations

The following observations are based on in situ straining experiments in an

HVEM on coarse-grained single-phase γ-Ti-52at%Al containing 750 at ppm of

oxygen [286], and on two-phase (α

+γ) Ti–47Al–2Cr–0.2Si (at%) [531] with a

so-called near-γ microstructure consisting of large γ grains with the α

-phase

located in the grain boundary pockets. In situ experiments in a conventional

TEM in [532, 533] yielded similar results.

Room Temperature

The room temperature deformation is mainly carried by dislocations, mostly

ordinary ones and occasionally 101 superdislocations as demonstrated in

Fig. 9.8 for the near-γ alloy. The ﬁgure shows the same specimen area under

diﬀerent imaging conditions so that in Fig. 9.8a only the ordinary dislocations

are imaged, and in Fig. 9.8b only the superdislocations. The majority of dis-

locations are of screw character and move on {111} planes. Most dislocations

move in slip bands. The dislocation density within these bands is of the order

of magnitude of 1 ×10

to 3 × 10

−2

The ordinary dislocations are of curly shape indicating that the dislocation

motion is impeded by obstacles between which the dislocation segments bow

out under stress. In most cases, the obstacle sites are not aligned accurately in

screw direction, instead they are distributed over the slip plane. To determine

the spatial arrangement of the bowed-out dislocation segments, some stereo

pairs of the dislocation structure were taken under load and in the unloaded

state after the in situ experiments. They reveal that most of the segments bow

out on a single slip plane, or on parallel planes, respectively. These observa-

tions are important for identifying the obstacle mechanism. The deep cusps

in the dislocation line are clearly due to jogs, some of which are marked by

J in Fig. 9.8a. The jogs trailing dipoles (dislocation debris) are marked by D.

Most of the dipoles are not arranged in edge direction. If the jogs are high

enough, both arms of the dipole may pass each other as at M, leading to

dislocation multiplication. There are only a few micrographs showing edge

dislocation segments. Under load, edge dislocations exhibit the same curly

shape as screw dislocations do, as is demonstrated in Fig. 9.9. Figure 9.8b

illustrates that superdislocations S are pinned like the ordinary ones. This is

shown more clearly in Fig. 9.10 at the head of a slip band of superdislocations.

However, their bowing is always less strong. Slip traces prove that these dis-

locations had moved during the in situ experiment. In conclusion, it may be

9.3 γ-TiAl 325

1µm

(a)

(b)

Fig. 9.8. Dislocations and a twin T under load during the in situ deformation of

near-γ TiAl at room temperature. Image normal [101]. (a) Ordinary dislocations

with b =1/2[

10] imaged with g =[

11]. Superdislocations with b =[0

1] are

extinguished. (b) The superdislocations are imaged with g =[

111], whereas the

ordinary dislocations are out of contrast. From the work in [531]

326 9 Intermetallic Alloys

1µm

b, g

Fig. 9.9. Slip band taken during in situ deformation of γ-TiAl at room temperature

showing ordinary mixed and edge dislocations. Diﬀraction vector g =[1

10]. b =

1/2[1

10] is the only possible Burgers vector of ordinary dislocations at the [110]

pole. The traces in [1

2] directions are from defects on (1

11) planes, probably twins.

The ordinary dislocations are created at these defects. From the work in [286]

1µm

Fig. 9.10. Head of a slip band of superdislocations during in situ deformation of γ-

TiAl at room temperature. b projection of [101] Burgers vector, g = [001] diﬀraction

vector near the [110] pole. From the work in [286]

9.3 γ-TiAl 327

(a) (b)

Fig. 9.11. Four successive frames from the ﬁrst part of Video 9.2 of the motion of

ordinary dislocations in γ-TiAl

pointed out that obstacles impede the motion of both ordinary dislocations

and superdislocations, independent of their character, i.e., screw or edge. Fig-

ure 9.8 shows also a twin lamella T. Below, a remark will be made about the

twinning dislocations.

Video recordings reveal the kinematic behavior of the moving dislocations.

Video 9.2. Motion of ordinary dislocations in γ-TiAl at room temperature: This

clip consists of two sequences showing the motion of individual ordinary screw dislo-

cations. In the ﬁrst clip, the dislocations move by jumps of individual segments over

areas comparable with the square of the obstacle distance. This is demonstrated

by the sequence of successive frames in Fig. 9.11. In (b)and(c) several positions

are superimposed due to the afterglow of the luminescence screen of the recording

system. In the second one, dislocations frequently move as a whole over distances

in the order of magnitude of the obstacle distance. They are curved also in the

intermediate states.

In slip bands of a higher density of dislocations, the dislocations frequently

move in a collective way, as demonstrated by the following video sequences.

Video 9.3. Motion of ordinary dislocations in slip bands in γ-TiAl at room tem-

perature: The video presents three clips of ordinary dislocations moving in slip

bands:

328 9 Intermetallic Alloys

1. A narrow band originates from a crack. The dislocations move in a jerky mode

over distances large compared to the obstacle distance along the dislocations,

frequently in a collective way.

2. This clip shows the head of a slip band mostly consisting of screw dislocations.

Partially, the leading dislocations overcome individual obstacles. Some of them

are jogs which, along the screw dislocations, are driven toward the edge com-

ponents. The edge segments are also locally pinned. Later on, dislocations are

driven by the stress ﬁeld of the succeeding dislocations and move over larger

distances.

3. In the interior of the band in 2., many dislocation segments are of near edge

character. Their mode of motion resembles that of the screw dislocations.

These sequences illustrate that the kinematic behavior of mixed and edge

ordinary dislocations is similar to that of screws, and that the dislocations in

dense bands move in a collective way, indicating the importance of long-range

elastic interactions between the dislocations.

Superdislocations mostly move in jumps over long distances. Only once

their motion has been recorded on video tape.

Video 9.4. Motion of 101 superdislocations in γ-TiAl at room temperature: The

video is from the same experiment as Fig. 9.10 is. The image normal is [110]. 1/2[

110]

is the only possible Burgers vector direction of ordinary dislocations, which is per-

pendicular to the [001] diﬀraction vector and the image normal. There are no

(screw) dislocations visible in this orientation. Thus, all dislocations in this video

are superdislocations. A few dislocations move almost simultaneously right of the

circular marks. The left ones belong to the (

111) slip plane, which is oriented edge-

on. The right one glides on the (111) plane, which is also the slip plane of Fig. 9.10.

Since the specimen normal is not identical with the image normal, the traces of the

slip plane in the video and in the ﬁgure are not perpendicular to the [001] g vector.

These superdislocations move over shorter distances in a jerky way.

Part of the plastic deformation of γ-TiAl is also carried by the formation

of deformation twins. This mechanism was brieﬂy introduced in Sect. 3.3.3.

The motion of twinning dislocations was recorded in the following video.

Video 9.5. Motion of twinning dislocations in γ-TiAl at room temperature:

Between obstacles, the twinning dislocations bow out like ordinary and superdis-

locations. However, owing to their low line tension, the bowing is very strong. The

jerky motion of the twinning dislocations is most similar to that of the ordinary

ones, including the collective behavior in the twinning lamella.

It may be concluded in a qualitative sense that all types of dislocations, ordi-

nary, super, and twinning dislocations, are impeded by similar obstacles and

that they move in a jerky way by jumps over diﬀerent distances, depending

on the average dislocation velocity.

To obtain quantitative data on the obstacle mechanism, the distances l

between the pinning points were measured along the dislocations. For ordi-

nary dislocations of all characters as well as for screw superdislocations the

9.3 γ-TiAl 329

average values are always around 100 nm. The histogram of the obstacle dis-

tances along ordinary screw dislocations is of the asymmetric shape typical of

localized obstacles as discussed in Sects. 4.5.1 and 7.2.2 (H(v) in Fig. 7.10b).

The eﬀective stress τ

∗

corresponding to an equilibrium curvature of the bowed-

out dislocation segments was determined by ﬁtting the shape of the segments

calculated by the line tension theory of elastically anisotropic materials to the

shape in the micrographs as described in Sect. 5.2.3 and by (5.18). The line

tension data used were calculated by Yoo [534]. While ordinary dislocations

are of almost circular shape, superdislocations are elliptic, with their screw

segments showing a very low curvature. Ordinary and superdislocations indi-

cate the same value of the eﬀective stress of τ

∗

≈ 40 MPa. It is important to

note that the dislocation bowing only slightly relaxes after unloading.

High Temperatures

Similarly to room temperature, deformation at intermediate temperatures

occurs by the motion of ordinary and superdislocations as well as by twin-

ning. Figure 9.12 shows ordinary dislocations moving during the deformation

at elevated temperatures of 360 and 575

◦

C. The diﬀerent widths of the slip

traces in Fig. 9.12a, e.g., of dislocations A and B, indicate that the disloca-

tions must contain large jogs. They cause a wide variation of the width of

the slip trails because of the ﬂat inclination of the slip planes. In spite of the

jogs, the dislocations are quite smooth, i.e., the extent of bowing is drastically

reduced compared to that at room temperature so that the cusps in the dis-

location line corresponding to the obstacles are scarcely visible. Nevertheless,

the average obstacle distance is still approximately equal to its room temper-

ature value. Most of the dislocations are additionally pinned at the surfaces

of the specimen, probably owing to an oxide layer. The kinematic behavior of

the dislocations is similar to that at room temperature. At 575

◦

C (Fig. 9.12),

the number of cusps is strongly decreased. The dislocations are pinned by only

a few jogs about 0.5–1 μmapart.

Compared to lower temperatures, in the high-temperature range, the shape

as well as the dynamic behavior of dislocations have changed strongly. The

obstacles, which aﬀect the motion of all dislocations at room temperature and

at intermediate ones, no longer act above about 600

◦

C. As demonstrated in

Fig. 9.13, the ordinary dislocations with 1/2[1

10] Burgers vectors are smoothly

bent with large radii of curvature. The spatial arrangement of the disloca-

tions was proved by stereo pairs taken after the in situ experiments at room

temperature. The observed nonplanar arrangement shows that their motion

is not restricted to their slip planes. In addition to the curved dislocation

segments being predominant, some segments are straight and arranged in

[10

1] direction. They are the only segments lying on the original (111) slip

plane.

The dynamic behavior of dislocations at high temperatures drastically

diﬀers from that at low and intermediate temperatures. On loading the

330 9 Intermetallic Alloys

1µm

1 µm

Fig. 9.12. Ordinary dislocations of mainly screw character moving during in situ

straining of γ-TiAl at elevated temperatures. (a) 360

◦

C, g = [101] diﬀraction vector,

b projection of 1/2[110] Burgers vector. (b) 575

◦

C, g =[1

10] diﬀraction vector, b

projection of 1/2[1

10] Burgers vector. From the work in [286]

9.3 γ-TiAl 331

1µm

Fig. 9.13. Ordinary dislocations under load during in situ deformation of γ-TiAl

at 655

◦

C. g = [111] diﬀraction vector, b projection of 1/2[1

10] Burgers vector, t

projection of [10

1]. From the work in [286]

specimens for the ﬁrst time during the in situ experiments above about 600

◦

large numbers of ordinary dislocations and some superdislocations usually

appear instantaneously after pronounced load drops like those demonstrated

in Fig. 9.39 for MoSi

single crystals. This avalanche-like multiplication has

never been recorded. If ordinary dislocations again start to move, their motion

is no longer jerky but smooth in a viscous way as illustrated by the following

video.

Video 9.6. Motion of ordinary dislocations in γ-TiAl at 655

◦

C: In the tempera-

ture range of the ﬂow stress anomaly, smoothly curved dislocations move in a viscous

way.

Superdislocations with 101 Burgers vectors occur less frequently at ele-

vated temperatures than simple dislocations do. Figure 9.14 shows that they

are characterized by long screw segments linked by superkinks. The movement

of these superdislocations has never been recorded. Obviously, they jump over

larger distances, adopt the screw orientation and get locked.

9.3.3 Macroscopic Deformation Parameters

The temperature dependence of the yield stress of γ-TiAl is demonstrated

in Fig. 9.15, together with two NiAl materials which will be described later.

In contrast to the NiAl materials, which do not show a ﬂow stress anomaly,

γ-TiAl exhibits a weak anomaly, with the yield stress slightly increasing up

to about 700

◦

The strain rate sensitivity of the ﬂow stress of γ-TiAl was studied over a

wide range of strain rates by stress relaxation experiments, where the depen-

dence of the strain rate sensitivity r on the strain rate ˙ε can be followed along