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

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Titanium alloys: modelling of microstructure268

predictions of materials properties with a reduced level of empiricism. Almost

all the important phenomena associated with DRX are taken into account in

the quantitative model. More realistic relationships are proposed to determine

accurately the nucleation rate, growth kinetics, and the effect of processing

parameters, such as strain rate and the temperature. The model enables both

quantitative and topographic simulations of microstructure evolution during

DRX. The growth kinetics of each recrystallised grain (R-grain), including

variation of its dislocation density, growth velocity, grain topology, and

direction of growth, can be calculated and tracked during the entire deformation

process. The flow stress–strain curve is determined directly from the averaged

current dislocation density of all the grains in the considered field. The

growth direction and the shape of each R-grain are determined using the CA

method, and the equiaxed growth behaviour of R-grains can be predicted.

The simulated microstructure closely resembles the actual DRX microstructure.

10.11

Predicted variation of the dislocation density with strain under

different deformation conditions, (a) at different strain rates (0.02–

1 s

–1

) and a fixed temperature of 1000 °C, (b) at different

temperatures (1000–1150 °C) and a fixed strain rate of 0.1 s

–l

Dislocation density (×10

)

0 0.01 0.02 0.03 0.04 0.05 0.06

Strain

(a)

T: 1000 °C

1.0

0.5

0.1

0.05

0.02

Dislocation density (×10

)

0 0.01 0.02 0.03 0.04 0.05 0.06

Strain

(b)

: 0.1 s

–1

1000

1050

1100

1150

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

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Cellular automata method for microstructural evolution 269

Predictions for the Ti-6Al-4V alloy agree well with the corresponding

experimental findings, including the microstructure evolution and the plastic

flow behaviour at a range of thermomechanical processing conditions.

10.7 References

Ding R and Guo Z X (2001), ‘Coupled quantitative simulation of microstructural evolution

and plastic flow during dynamic recrystallization’, Acta Mater, 49 (16), 3163–75.

Ding R and Guo Z X (2002), ‘Microstructural modelling of dynamic recrystallisation

using an extended cellular automaton approach’, Comp Mater Sci, 23 (1–4), 209–18.

Ding R, Guo Z X and Wilson A (2002), ‘Microstructural evolution of a Ti–6Al–4V alloy

during thermomechanical processing’, Mater Sci Eng A, 327 (2), 233–45.

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270

Crystallographic and fracture behaviour

of titanium aluminide

Abstract: The chapter presents a crystallogeometrical analysis of the

geometry of micro- and macrocracks in a Ti

Al single crystal with an

orientation where the basal slip is operative. The basal and

{1011}

{1012}

{1 123}

pyramidal planes are the planes of micro- and

macrocracks facets. The coalescence of shear microcracks in the basal plane

leads to the zigzag crack formation on the fracture surface. A model for

shear microcrack nucleation with screw a-superdislocations interacting in the

slip band of the basal planes is described. The macrocracks path behaviour

in the Ti

Al single crystal is discussed based on the model.

Key words: titanium aluminides based on Ti

Al, fracture, dislocation

geometry and arrangement, defects, superdislocations.

11.1 Introduction

In Ti

Al single crystals, there is a strong dependence of the yield stress on

the orientation, complex slip geometry, and dislocation structure. The difference

in temperature dependence of the deformation characteristic is evident, namely:

(i) normal behaviour of shear stress σ

(T) for the basal and prism slip planes,

and (ii) anomalous dependence with a maximum in the σ

(T) curve for the

pyramidal slip plane. The orientation dependence of the fracture behaviour

of the Ti

Al single crystals has also been discovered: the deformation before

fracture reaches a value of about 250% for prism slip, while for basal slip

brittle fracture happens immediately after loading, even in compression. The

phase plays a major role in fracture processes of α

/γ alloys with lamellar

structure.

For an orientation where basal slip is operative, the slip lines are rough

and widely spaced. Electron microscopy reveals microcracks of shear type

along the basal slip planes. When loaded with a notch cut along the planes

close to the (0001) plane, brittle fracture occurs not only along the basal

plane, but also along the

{1102}

and

{1 123}

pyramidal planes. The reasons

for such low plasticity and brittle fracture in the (0001) basal plane compared

with the high plasticity and ductile fracture of Ti

Al in the prism plane

{1100}

need to be investigated, although in both cases the deformation is

accomplished by moving of a-superdislocations with Burgers vector

1120〈〉

In order to understand the nature of the brittle fracture of a Ti

Al single

crystal with basal slip, it is necessary to reveal the correlation between the

type and planes of brittle cleavage with micro- and macro-experimental

findings.

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Crystallographic and fracture behaviour of titanium aluminide 271

This chapter presents both experimental and theoretical findings of the

deformation morphology, geometry, and the peculiarities of micro- and

macrocracks in a Ti

Al single crystal with the deformation axis orientated

for a basal slip. Statistical treatment allows us to recognise the most probable

types of macrocleavage and microcrack planes. TEM study on the deformed

material helps us to determine the cause of the step-like macrocleavage

surface forming. Establishing the decohesion plane types allows us to better

understand the reasons for brittle fracture in a single crystal Ti

Al with an

orientation where basal slip is operative.

11.2 Single crystal characteristic

The alloy under study has a composition of Ti-28.4Al (at.%). Single crystals

of the alloy were grown from a master ingot using a floating zone furnace

under an argon gas flow. Figure 11.1 shows a typical micrograph. The central

part of a cylinder (diameter about 7 mm and height 0.4 mm) consists of large

single crystal grains (average size 3–5 mm), while the periphery consists of

grains with smaller size and large angle boundaries.

X-ray diffraction analysis proves that the material in its as-grown state is

mostly in a single crystal state with

(1011)

orientation, i.e.

(1011)

plane

perpendicular to the cylinder axis which is also the direction of compression

500 µm

11.1

Optical microscope image of the microstructure of as-grown

Al single crystal.

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Titanium alloys: modelling of microstructure272

deformation, with a small number of grains of other orientations (Fig. 11.2a).

To study the peculiarities of deformation and fracture for basal slip, the

single crystals with

(1011)

orientation are chosen.

The maximum intensity of diffraction peaks decreases with increasing

deformation (Fig. 11.2b–d). At the same time, the peak width increases as a

result of the defect density increase in the material. The formation of small

angle grain boundaries in the single crystal manifests itself in the appearance

of two additional peaks,

{2023}

and

{2021}

, of noticeable intensity along

with the main

{2022}

peak. One can also see the formation of the grains of

(0001) orientation, (0002) peaks in Fig. 11.2b–d, which is a pronounced

deviation from the initial orientation of a single crystal. The compression

axis is rotated towards the [0001] direction for the single crystals with

(1011)

orientation (the maximum Schmid factor for this orientation corresponds to

the

[1 120]

(0001) and the

[21 10]

(0001) slip systems, f = 0.43). The

11.2

X-ray diffraction patterns for (a) an as-grown state Ti

Al single

crystal and (b–d) three deformed crystals, respectively. For clarity, the

diffraction patterns are shifted with respect to each other along the

vertical axis.

20 30 40 50 60 70 80 90

2θ (°)

Intensity (c.p.s.)

16000

14000

12000

10000

8000

6000

4000

2000

{011 1}

{0221}

{0222}

{0223}

{0002}

(0221)

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Crystallographic and fracture behaviour of titanium aluminide 273

formation of grains with this orientation is observed experimentally in deformed

crystals (Fig. 11.2).

For the chosen orientation, the operating slip system with maximum Schmid

factor would be the (0001)

[1210]

and the (0001)

[2110]

basal slip systems

(Table 11.1). Yakovenkova et al. (2003b) show that orientations in the range

of 24–60° from [0001] direction are those where basal slip is preferred, i.e.

maximum Schmid factors correspond to basal slip systems. The orientation

chosen here for the single crystal Ti

Al lies within this range.

11.3 Crack path analyses

Figure 11.3 shows the fracture surface, deformed by compression perpendicular

to the

(1011)

plane. The basal slip, which has the maximum Schmid factor

for this orientation (Table 11.1), is coarse with big distances between slip

lines. The coarse basal slip lines result in the formation of deep microcracks

in the basal slip planes. In Fig. 11.3b, the microcracks of shear type are just

the extension of coarse slip bands. Consecutive coalescence of microcracks

in the basal plane results in macrocrack nucleation. The fracture surface is

stepped and the average fracture surface does not coincide with the basal

plane. The plane of the picture in Fig. 11.3b is parallel to the

(1011)

plane.

The line direction

[1210]

is parallel to a projection of the basal plane into the

(1010)

plane. As in Fig. 11.3a, along the

[1210]

line direction there are

coarse basal slip lines. The fracture trace, on average, coincides with the

[1321]

direction. The stepped nature of this surface is very pronounced,

with the zigzag projection into the

(1011)

plane parallel to the

[1210]

and

[1012]

line directions.

A crystallogeometrical analysis of microcracks formed after deformation

will be shown for grains with orientations close to the

(1011)

(2023)

and

(2021)

planes. The deformation in these grains occurs in the basal slip

systems. Table 11.1 presents the maximum Schmid factors for the chosen

deformation axis. In basal slip systems (0001)

[2110]

and (0001)

[1 120]

the Schmid factor is maximum for

(1011)

and

(2021)

orientations. For

(2023)

orientation, the Schmid factor (f = 0.46) is maximum in the case of

pyramidal slip systems. Deformation in these slip systems occurs when a

deformation axis is orientated close to the [0001] direction and the Schmid

factors in the basal and prism slip systems are close to zero. An analysis of

slip traces shows that for all the orientations included in Table 11.1, the main

operating slip system is the basal one. Optical micrographs (Fig. 11.4) show

the pronounced rough traces of basal slip on the polished surface, which are

formed during deformation. The chosen grain orientations (Table 11.1) makes

it possible to obtain a representative set of micro- and macrocleavage paths,

which are formed in presence of basal slip.

A macrocrack, shown in Fig. 11.4a, has a stepped path. The several straight

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Titanium alloys: modelling of microstructure274

Table 11.1

Maximum Schmid factor for basal, prism and pyramid slip systems

Plane, compression Basal slip Schmid Prism slip Schmid Pyramid slip Schmid factor

axis factor factor

(10 11), [101 2]

(0001)

[2110]

0.43

(0 110)[2 1 1 0]

0.23

( 1 1 21)[1126]

0.37

(0001)

[ 1 1 20]

(1 100)[ 1 1 20]

(2111)[21 1 6]

(1211)[1 1 26]

0.34

(2021), [6067]

(0001)

[2110]

0.36

(0 110)[2 1 1 0]

0.33

( 1 1 21)[1126]

0.32

(0001)[

[ 1 1 20]

(1 100)[ 1 1 20]

(2111)[21 1 6]

(2023), [2027]

(0001)

[2110]

0.39

(0 110)[2 1 1 0]

0.12

( 1 1 21)[1126]

0.46

(0001)

[ 1 1 20]

(1 100)[ 1 1 20]

(2111)[21 1 6]

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Crystallographic and fracture behaviour of titanium aluminide 275

(a)

(b)

[1210]

[1321]

(0001)

11.3

Focused ion beam (FIB) image of the surface of a Ti

Al single

crystal after deformation, showing (a) the basal slip lines (arrows)

and (b) crystallogeometry of the shear type microcrack.



Titanium alloys: modelling of microstructure276

[4513]

[231 1]

[1210]

[1 012]

200 µm

(a)

[2 1 34]

[1321]

[1210]

(b)

200 µm

[2 1 34]

[01 11]

[1210]

(c)

200 µm

11.4

Optical microscope image of the surface of deformed Ti

single crystals at

(101 1)

planes: (a) crystal 1; (b) crystal 2 and



Crystallographic and fracture behaviour of titanium aluminide 277

segments of the crack lie along the

[1210]

direction and form consecutive

steps of (0001) plane traces. The main crack path lies close to the

[2311]

direction. These segments are connected by comparatively short parallel

cracks with traces approximately

[4513]

(Table 11.2).

Figure 11.4b shows one of the fragments of the crystal surface, which

contains Crack I and Crack II, consisting of short straight segments. The

Crack I trace is parallel to the

[1321]

direction (Table 11.2). For Crack II,

part of the segments is parallel to the

[1210]

direction (Segment 1 in Fig.

11.4b), i.e. lies in the basal plane, and the other part of the segments is

parallel approximately to the

[2134]

direction (Segment 2 in Fig. 11.4b).

In Fig. 11.4c, two intersecting main cracks are marked as Crack I and

Crack II. The trace of Crack I on average is parallel to the

[1321]

direction,

and contains several microcracks (marked by arrows in Fig. 11.4c) in the

basal plane (the trace along the

[1210]

direction). Crack II contains several

straight segments. One of the straight segments (marked as 1 in Fig. 11.4c)

is formed by a crack which has a trace parallel approximately to the

[2134]

direction; the other straight segment (marked as 2 in Fig. 11.4c) is parallel

approximately to the

[0111]

direction (Table 11.2).

In Fig. 11.5, the hatched region corresponds to the orientation of the

grains. The solid line is the trace of the

(1011)

plane. The directions

corresponding to the traces of the 20 cracks are marked with crosses (some

cracks shown in Fig. 11.4). Dashed lines, traversing the crosses correspond

to the planes in which the traces of the microcracks lie (within the limits of

2–5°). The indexes of the cracks’ planes

(0112)

(1 123),

(2113),

(1102)

(0111)

are depicted by solid dots. The main crack planes of

{0112}

and

{1 123}

type have been observed before, where the crystals were loaded

with a notch cut.

Table 11.2

Typical experimentally observed traces of micro- and

macrocracks on the

(10 11)

plane

Sample number Crack trace on Crack plane

(10 11)

plane

[1210]

(0001)

[4513]

(0 112)

[2311]

( 1 1 23)

[1210]

(0001)

[2 1 34]

(01 11)

[1321]

(2113)

[1210]

(0001)

[0 111]

(0112), (1123), (1213)

[1321]

(2113)

[2 1 34]

(01 11)

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