Sha W., Malinov S. Titanium Alloys: Modelling of Microstructure, Properties and Applications

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Titanium alloys: modelling of microstructure278

The analysis allows us to determine all possible microcrack planes for

crystals 1–3 (Fig. 11.4a–c and Table 11.2). The plane of the macrocrack

shown in Fig. 11.4a, coincides with the

(1 123)

plane, and the planes of its

cleavage microfacets are the (0001) and

(0112)

planes, respectively. Crack

II in Fig. 11.4b contains cleavage microfacets in the basal plane and pyramidal

(0111)

plane. In Fig. 11.4c, Crack I propagates along the

(2113)

plane, and

Crack II is formed by cleavage microfacets in the

(0111)

planes and in

(0112)

(1123)

(1213)

(1101)

planes.

Figure 11.6 shows the microstructure near the top of the microcrack stopped

in the crystal bulk. The crack has a stepped path with the straight segments

parallel to the rough slip bands in the basal plane (0001). The regions in

which the crack trace has a zigzag path due to the plastic zone formation in

the prism plane

(1100)

are marked by the arrows in Fig. 11.6a. The crack

shifts from one basal plane to a parallel one. The region where the crack

stops within the bulk of the crystal is marked with the arrow in Fig. 11.6b.

The high dislocation density in the prism plane is very pronounced. Therefore,

the stepped nature of the cracks in (0001),

{1012}

and

{1011}

planes is

0001

1123

2113

1102

0112

101 1

11.5

Stereographic projection for the DO

lattice. The traces and

planes of crack openings are presented.

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Crystallographic and fracture behaviour of titanium aluminide 279

stipulated by their stopping and blunting as a result of plastic zone formation

in the prism slip systems.

The above presents the geometry of micro- and macrocracks in a single

crystal Ti

Al with an orientation where basal slip is operative. Most of the

cracks observed have a stepped path. The indexes of the traces on straight

fragments of microcracks are determined using a statistical method. The

directions determined are shown by crosses on the stereographic projection

(Fig. 11.5). They can be divided into several groups which belong to the

pyramidal planes of different types. Therefore, we have proved, experimentally,

that the stepped-like macrocleavage surface is formed by microcracks of

shear type along the basal planes, bound with the opening fracture mode

cracks in the pyramidal planes. The analysis shows that the cleavage microfacets

of the cracks are formed by the (0001),

{1012}

{1011}

and,

{1 123}

planes.

The fracture on the pyramidal planes of

{1011}

type is observed. The most

frequently observed planes of main cracks are the pyramidal planes of

{1 123}

type, while the planes (0001),

{1012}

and

{1011}

form short cleavage

microfacets.

11.4 Transmission electron microscopy

Straight lines of slip band traces (Figs. 11.7 and 11.8) are parallel to the

[1010]

direction. We can see only dot contrast of dislocations, which belong

to the slip bands (pointed by arrows in Fig. 11.7), and a projection of the

dislocation line coincides with the

[1010]

direction. One can suppose,

therefore, that the slip bands are perpendicular to the surface of the image,

while its normal coincides with the [0001] direction. The experimentally

(0001)

{1 100}

(a)

(b)

11.6

Bright-field TEM images of the microstructure of a single crystal

Al after compression deformation (Crystal 1).

0.2 µm

0.5 µm

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Titanium alloys: modelling of microstructure280

11.7

Bright-field TEM image of microstructure of a single crystal

Al after deformation.

(a)

(b)

(101 0)

(0001)

(101 2)

(0002)

11.8

(a) Electron diffraction pattern of deformed Ti

Al, and (b) the

corresponding reciprocal lattice plane

(1210)

with selected directions

indicated.

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Crystallographic and fracture behaviour of titanium aluminide 281

observed basal slip is in agreement with calculated values of Schmid factors

(Table 11.1), because the choice of compression axis orientation defines the

maximum Schmid factor to correspond to basal slip.

The dislocations located in between the slip bands are in Fig. 11.7 besides

the dislocations in basal plane. The number density of these dislocations is

higher near the basal planes. A part of the dislocations is located in short slip

bands in the

(1010)

prism plane, which initiate at basal planes. The prism

slip was observed before for the material oriented for basal slip. The short

bands of prism slip form and initiate at more coarse basal slip bands, having

zero Schmid factor. Why these short traces of prism slip form, initiated by

basal slip, is not clear.

The microstructure near a basal slip plane shows quite noticeable prism

slip. The macrocleavage surface is stepped-like, as it consists of microcracks

of shear type along the basal planes (0001), and decohesion in some other

planes. Ti

Al single crystals are soft and quite deformable with respect to

prism slip. The reason why the macrocleavage surface is stepped-like might

be the stopping and blunting of microcracks of shear type along basal slip

planes due to the previously mentioned prism slip.

11.5 A model for microcracks nucleation

in basal slip

The main experimental facts on basal slip study in a single crystal of Ti

are: (i) quite low yield stress; (ii) coarse bands of basal slip with fine short

bands of prism slip formation; (iii) low strain to failure with formation of

shear cracks in a basal plane. A theoretical model on deformation behaviour

of Ti

Al for basal slip has to explain all the above experimental facts.

Yakovenkova et al. (2003b) have determined the structure and energies of

a-superdislocations of different orientations with

1120〈〉

Burgers vector in

the basal plane by molecular dynamics calculations, having N-atom interaction

potentials for Ti

Al found by the embedded atom method (Kar’kina et al.,

2002; Yakovenkova et al., 2000). The analysis of the results from computer

modelling of screw, 30°, 60° and edge superdislocations in the basal plane,

separated by an anti-phase boundary (APB), shows that the changes in partial

core structure are to be observed only for superdislocations of screw orientation

(Fig. 11.9a and b). The core of each Shockley partial with

1100〈〉

Burgers

vector, confining a complex stacking fault (CSF), acquires quite pronounced

displacement in the

{1100}

prism plane, propagated on 2–3 interplanar

spacing. The analogous core structure for a screw a-superdislocation, split

into Shockley partials in the basal plane is proved to have the minimal

energy value (Fig. 11.3). The increasing of Peierls stress for Shockley

superpartials slip is stipulated by the core structure of nonplanar partial

dislocations in the basal plane. It also explains the experimental observation

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Titanium alloys: modelling of microstructure282

that the yield stress in the basal plane is higher than in the prism plane. A

sufficiently high Peierls stress for the motion of the

2110〈〉

superpartial

dislocation was also reported, and it was shown that the motion of the a-

superdislocation connected by APB in the basal plane occurs jump-wise and

is characterised by a sufficiently high Peierls stress for the motion of the

2110〈〉

superpartial dislocation.

On the basis of available experimental data, a model for shear microcracks

nucleation in the basal slip band is introduced here, taking into account the

processes of cross-slip into the prism plane. A dislocation might undergo

cross-slip only in case that its axis is parallel to an intersection line of initial

slip plane and cross-slip plane. The basal and prism planes intersect along

[0001]

[011 0]

(a)

(b)

APB

CSF

[1 010]

[1 100]

11.9

(a) Core structure of the

2110〈〉

screw dislocation in basal

plane after relaxation, and (b) scheme of split dislocation.

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Crystallographic and fracture behaviour of titanium aluminide 283

the

〈〉2110

direction, which is the axis of a 60° or screw a-superdislocation.

The energy advantage of the reactions is estimated with the use of the

expressions for the dislocation interaction energy, adjusted to the unit of its

length. In Fig. 11.10, the consecutive stages of microcracks nucleation in the

slip bands of the basal plane are depicted, taking into account the long-

distance elastic interaction of a-superdislocations and all superpartial

dislocations taking part in the reaction. If we examine the analogous scheme

for 60° orientated a-superdislocations, we will find that the rearrangement of

a superdislocation with cross-slip into the prism plane is energetically

unfavourable. Thus, the nucleation of a microcrack of shear type is possible

only on screw dislocations.

Figure 11.10a presents a fragment of two interacting split a-superdislocations

with

[2110]

Burgers vector of screw orientation. The superdislocation is

split into two superpartials with

[2110]

Burgers vector with APB formation:

(0001)

[2110] [2110] + APB + [2110]→

[11.1a]

Each of the superpartial dislocations further dissociates, with the formation

of a CSF:

(0001)

[2110] [1100] + CSF + [1010]→

[11.1b]

In Fig. 11.10a, the Dislocations 1 and 2 move in the slip plane under the

orientation of the external stress.

Figure 11.10b shows the result of a rearrangement of Shockley dislocations

with

[1100] and [1010]

Burgers vectors, which belong to Superdislocation

1 in a stress field of Superdislocation 2. As a result of the rearrangement, the

splitting of each Shockley dislocation occurs in the prism plane with SF

band formation, confined by the partial with

[2110]

Burgers vector:

(0110)

[1010] [2110] + SF + [0110]→

[11.2a]

(0110)

[1100] [2110] + SF + [0110]→

[11.2b]

The reactions of splitting, Eqs. [11.2a] and [11.2b], are energy indifferent,

and their realisation is possible only due to the repulsion of the partials

belonging to other superdislocations in the slip band, as mentioned above.

Experimentally, the splitting of a a/2-superdislocation into two partials in

the prism plane was observed, but the Burgers vector magnitudes of the

partials were not determined. As a result of computer modelling (Yakovenkova

et al., 2000), the Burgers vectors of the partial dislocations were found to be

equal to

[2110]

. These Burgers vectors are used in reactions Eqs. [11.2a]

and [11.2b].

The dislocation configuration formed (Fig. 11.10b) is not stable, because

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Titanium alloys: modelling of microstructure284

(a)

[1 010]

[1 100]

[1 010]

[1 100]

(b)

[1 010]

[1 100]

[01 10]

[2110]

[011 0]

[2110]

(c)

[1 010]

[1 100]

[2110]

11.10

Scheme of a shear microcrack formation.

1+2

(d)

[1 010]

[1 100]

[2110]

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Crystallographic and fracture behaviour of titanium aluminide 285

1+2

(e)

[1 010]

[011 0]

[2110]

1+2

(f)

[2110]

1+2

(g)

11.10

Continued

APB

(0001)

;

APB ;

( 1100)

CSF

(0001)

;

( 1100)

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Titanium alloys: modelling of microstructure286

the partials with

[0110]

and

[0110]

Burgers vectors belonging to the

Superdislocation 1, attract in the basal plane and can recombine with the

formation of the configuration shown in Fig. 11.10c. As a result of these

dislocation rearrangements for Superdislocation 1, there is no partial along

the intersection of the basal and prism planes to prevent superdislocation

approaching. The partial dislocations

[2110]

of Superdislocation 1 do not

interact with the partial dislocation

[1100]

and thus do not hamper the

coalescence of Superdislocations 2 and 1. The configuration shown in Fig.

11.10d becomes possible under the action of the external stress and the stress

imposed by other superdislocations of the slip band. The total Burgers vector

of the configuration is twice as big in this case.

Consecutive stages of internal dislocation rearrangements of the 1+2

configuration (Fig. 11.10d) are shown in Fig. 11.10e–g. As a result of these

rearrangements, the total energy of the configuration decreases because of

the reactions occurring between attracting partials (the dislocations with the

Burgers vectors

[0110]

and

[1010]

in Fig. 11.10e). When the change of

the configuration of Fig. 11.10d to the configuration of Fig. 11.10e occurs,

the energy decreases due to the change of a planar defect type (CSF

(0001)

→

APB

(0001)

), because the energy of complex SF is lower than the energy of

APB in the basal plane (Yakovenkova et al., 2000). Similarly, the decrease

of energy while the configuration of Fig. 11.10f changes to configuration of

Fig. 11.10g is due to the

SF APB

(1100) (1 100)

→

change. The final configuration

(Fig. 11.10g) is stable. It consists of bands of anti-phase boundaries in the

initial basal plane and in the planes of cross slip – the prism planes. The

considerable anisotropy in anti-phase boundaries energies for prism and

basal planes

(APB APB )

(0110)

(0001)

is characteristic of Ti

Al, and is the

consequence of DO

superstructure features (Yakovenkova et al., 2003a).

Thus, we have examined the sequence of dislocation transformations (Fig.

11.10a–g) on Superdislocations 1 and 2, as a result of which the configuration

with total Burgers vector of 2a magnitude is formed. An interaction of this

configuration with following a-superdislocation coalescence may be described

with the help of the same chain of dislocation transformations. This will

result in total Burgers vector magnitude being equal to 3a, etc. The configuration

developed may be considered as a microcrack nucleus of shear type because

the total Burgers vector of the configuration lies on the basal plane. The

number of dislocations which form a microcrack depends on both the number

of dislocations in an array and their distribution in the slip band. This may

lead to a microcrack nucleation in different places of the slip band.

Kar’kina et al. (2002) have shown an a-superdislocation to be split into

two superpartial dislocations with Burgers vector

[2110]

connected by an

APB band. The atom arrangement of the neighbouring layers in the basal

plane of DO

superstructure is equivalent to the one in the octahedron plane

of the L1

superstructure. This allows us to compare the results on the

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Crystallographic and fracture behaviour of titanium aluminide 287

computer modelling of the core structure of the superdislocations

2110〈〉

and <110> in these two superstructures. A superdislocation with the Burgers

vector <110> splits in the octahedral plane into four Shockley partial

dislocations, connected by APB bands and CSF, similarly to the

superdislocations

2110〈〉

in the basal plane. The core structure of Shockley

partial dislocations differs essentially in these cases. For a screw

superdislocation in Ti

Al, the core of a Shockley partial dislocation is nonplanar,

and noticeable displacements take place in the prism plane (Fig. 11.9), whereas

for L1

superstructure the displacements near the core of Shockley superpartial

dislocations are localised in the octahedron plane. This makes the configuration

considered to be a gliding one for L1

superstructure, while the motion of a

superpartial dislocation is impeded for DO

superstructure. The stress field

of other a-superdislocations in a slip band of the basal plane causes the

lowering of Peierls stress, and, apparently, results in coarse slip band formation

in this plane.

External stress and the stress imposed on a dislocation in the slip band

might change the core structure of the dislocation. For instance, in L1

superstructure, the stress imposed by the array dislocations might promote

the Shockley partial dislocations recombination, as a result of a decreasing

of the distance between the partial dislocations, and facilitate the process of

cross-slip of screw superdislocations. For Ti

Al, this stress can both promote

and impede the process recombination and cross-slip of a superpartial

dislocation, depending on the relation between the components of stress

effective in the basal and prism planes. If stress, caused by the other dislocations

in the slip band, promotes the widening of Shockley partial dislocation splitting

in the prism plane, the processes of recombination and cross-slip become

difficult, but coalescence of a-superdislocations with microcracks nucleation

by the mechanism introduced here is easy to initiate. If the stress in the prism

plane is small, it is possible to activate thermally the process of a-

superdislocations cross-slip. Thus, in the slip band both processes of shear

microcracks nucleation and slip-cross process might take place. In fact, the

cross-slip of the a-superdislocations into the prism plane in a slip band when

the basal slip is operative has been observed experimentally, along with

shear microcrack nucleation.

In Section 11.2, the surface of macrocleavage is shown to be stepped. One

of the steps is parallel to the basal plane; the trace of the other one on the

crystal surface

(1011)

coincides with

[1210]

line direction (Fig. 11.3b).

Thus, the cleavage-like crack propagation might be due to consecutive processes

of shear along the basal plane and decohesion in the

(1210)

prism plane. It

might be suggested that the microcracks of shear type nucleate first in the

basal planes. These microcracks nucleate in the places of high concentration

of local stress in one or several parallel slip bands. When the density of shear

microcracks is comparatively high, the macrocrack is nucleated due to some

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