Work-hardening in ordered alloys (see Figure 8.10). The dislocation density increases

7.6.2.5 Work-hardening in ordered alloys (see Figure 8.10). The dislocation density increases

A characteristic feature of alloys with long-range order very rapidly with strain because the particles produce

is that they work-harden more rapidly than in the

11 for Fe-Al with a B2 ordered them. The dislocations gliding in the matrix leave

a turbulent and complex deformation pattern around

loops around particles either by bowing between the greater than a typical fcc or bcc metal. However, particles or by cross-slipping around them; both these

the density of secondary dislocations in Stage II is mechanisms are discussed in Chapter 8. The stresses in

relatively low and only about 1/100 of that of the and around particles may also be relieved by activating

primary dislocations. One mechanism for the increase secondary slip systems in the matrix. All these dislo-

in work-hardening rate is thought to arise from the cations spread out from the particle as strain proceeds

generation of antiphase domain boundary (apb) tubes. and, by intersecting the primary glide plane, hinder

A possible geometry is shown in Figure 7.43a; the primary dislocation motion and lead to intense work-

superdislocation partials shown each contain a jog hardening. A dense tangle of dislocations is built up

produced, for example, by intersection with a forest at the particle and a cell structure is formed with the

dislocation, which are nonaligned along the direction particles predominantly in the cell walls.

of the Burgers vector. When the dislocation glides At small strains ⊲ 1%⊳ work-hardening probably

and the jogs move nonconservatively a tube of apbs arises from the back-stress exerted by the few Orowan

is generated. Direct evidence for the existence of loops around the particles, as described by Fisher, Hart

tubes from weak-beam electron microscope studies and Pry. The stress–strain curve is reasonably linear

was first reported for Fe-30 at.% Al. The micrographs with strain ε according to

show faint lines along h1 1 1i, the Burgers vector

3/2 i

ε direction, and are about 3 nm in width. The images are expected to be weak, since the contrast arises

with the work-hardening depending only on f, the vol- from two closely spaced overlapping faults, the second ume fraction of particles. At larger strains the ‘geomet-

effectively cancelling the displacement caused by the rically necessary’ dislocations stored to accommodate

first, and are visible only when superlattice reflections

232 Modern Physical Metallurgy and Materials Engineering

Figure 7.43 Schematic diagram of superdislocation (a) with non-aligned jogs, which, after glide, produce an apb-tube and (b) cross-slipped onto the cube plane to form a Kear–Wilsdorf (K–W) lock .

are excited. APB tubes have since been observed in increasing temperature. This could account for the other compounds.

increase in yield stress with temperature, while the Theory suggests that jogs in superdislocations in

onset of cube slip at elevated temperatures could screw orientations provide a potent hardening mecha-

account for the peak in the flow stress. nism, estimated to be about eight times as strong as that

Cube cross-slip and cube slip has now been observed resulting from pulling out of apb tubes on non-aligned

in a number of L1 2 compounds by TEM. There is some jogs on edge dislocations. The major contributions to

TEM evidence that the apb energy on the cube plane is

lower than that on the ⊲1 1 1⊳ plane (see Chapter 9) to generate point defects or tubes, and (2) the interaction

s , the stress to

favour cross-slip which would be aided by the torque,

3 s arising from elastic anisotropy, exerted between the i

i with dislocations on neighbouring slip planes,

f p ⊳ε . Thus, with ˛ s

D 1.3 and

components of the screw dislocation pair.

f p is constant and small, linear hardening with the observed rate is obtained.

In crystals with A 3 B order only one rapid stage

7.6.3 Development of preferred orientation

of hardening is observed compared with the normal

7.6.3.1 Crystallographic aspects three-stage hardening of fcc metals. Moreover, the

When a polycrystalline metal is plastically deformed perature and peaks at ¾0.4T m . It has been argued

11 increases with tem-

the individual grains tend to rotate into a common that the apb tube model is unable to explain why

orientation. This preferred orientation is developed anomalously high work-hardening rates are observed

gradually with increasing deformation, and although for those single crystal orientations favourable for sin-

it becomes extensive above about 90% reduction in gle slip on f1 1 1g planes alone. An alternative model

area, it is still inferior to that of a good single crystal. to apb tubes has been proposed based on cross-slip of

The degree of texture produced by a given deformation the leading unit dislocation of the superdislocation. If

is readily shown on a monochromatic X-ray transmis- the second unit dislocation cannot follow exactly in

sion photograph, since the grains no longer reflect uni- the wake of the first, both will be pinned.

formly into the diffraction rings but only into certain For alloys with L1 2 structure the cross-slip of a

1 segments of them. The results are usually described in

terms of an ideal orientation, such as [u, v , w] for the ⊲ 1 1 1⊳ plane to the ⊲0 1 0⊳ plane was first proposed by

screw superpartial with b D 2 [10 1] from the primary

fibre texture developed by drawing or swaging, and

fhklghu v wi for a rolling texture for which a plane of on the ⊲1 1 1⊳ plane and the other on the ⊲0 1 0⊳ plane,

Kear and Wilsdorf. The two 1 2 [10 1] superpartials, one

the form (hkl ) lies parallel to the rolling plane and a are of course dissociated into h1 1 2i-type partials and

direction of the type hu v wi is parallel to the rolling the whole configuration is sessile. This dislocation

direction. However, the scatter about the ideal orienta- arrangement is known as a Kear–Wilsdorf (K–W)

tion can only be represented by means of a pole-figure lock and is shown in Figure 7.43b. Since cross-slip

which describes the spread of orientation about the is thermally activated, the number of locks and there-

ideal orientation for a particular set of (hkl ) poles (see fore the resistance to ⊲1 1 1⊳ glide will increase with

Figure 7.44).

Mechanical behaviour of materials 233

Figure 7.44 (1 1 1 ) pole figures from (a) copper, and (b) ˛-brass after 95% deformation (intensities in arbitrary units) . In tension, the grains rotate in such a way that the

developed, as may be appreciated by consideration movement of the applied stress axis is towards the

of the twinning modes, and it is also possible that operative slip direction as discussed in Section 7.3.5

solid solution elements alter the relative values of and for compression the applied stress moves towards

critical resolved shear stress for different deformation the slip plane normal. By considering the deformation

modes. Processing variables are also capable of giving process in terms of the particular stresses operating and

a degree of control in hexagonal metals. No texture, applying the appropriate grain rotations it is possible to

stable to further deformation, is found in hexagonal predict the stable end-grain orientation and hence the

metals and the angle of inclination of the basal planes texture developed by extensive deformation. Table 7.3

to the sheet plane varies continuously with deforma- shows the predominant textures found in different

tion. In general, the basal plane lies at a small angle metal structures for both wires and sheet.

⊲< 45 ° ⊳ to the rolling plane, tilted either towards the For fcc metals a marked transition in deformation

rolling direction (Zn, Mg) or towards the transverse texture can be effected either by lowering the defor-

direction (Ti, Zr, Be, Hf).

mation temperature or by adding solid solution alloy- The deformation texture cannot, in general, be elim- ing elements which lower the stacking fault energy.

inated by an annealing operation even when such a The transition relates to the effect on deformation

treatment causes recrystallization. Instead, the forma- modes of reducing stacking fault energy or thermal

tion of a new annealing texture usually results, which energy, deformation banding and twinning becoming

is related to the deformation texture by standard lattice more prevalent and cross-slip less important at lower

rotations.

temperatures and stacking fault energies. This texture transition can be achieved in most fcc metals by alloy- ing additions and by altering the rolling temperature.