Crystallography of twinning

7.5.1 Crystallography of twinning

Mechanical twinning plays only a minor part in the deformation of the common metals such as copper

Figure 7.33 Crystallography of twinning .

222 Modern Physical Metallurgy and Materials Engineering

deformation temperature is lowered the critical shear of planes) is homogeneously sheared by 0.707 in a

in which a particular set of f1 1 2g planes (the k 1 set

stress for slip increases, and then, because the general

h 1 direction). The same atomic stress level will be high, the process of deformation arrangement may be visualized by a shear of 1.414 in

twinning is more likely.

the reverse h1 1 1i direction, but this larger shear has Twinning is most easily achieved in metals of cph never been observed.

structure where, because of the limited number of slip systems, twinning is an essential and unavoidable

mechanism of deformation in polycrystalline speci- During the development of mechanical twins, thin

7.5.2 Nucleation and growth of twins

mens (see Section 7.4.11), but in single crystals the lamellae appear very quickly (³ speed of sound) and

orientation of the specimen, the stress level and the these thicken with increasing stress by the steady

temperature of deformation are all important factors movement of the twin interface. New twins are usually

in the twinning process. In metals of the bcc structure formed in bursts and are sometimes accompanied by a

twinning may be induced by impact at room tempera- sharp audible click which coincides with the appear-

ture or with more normal strain rates at low tempera- ance of irregularities in the stress–strain curve, as

ture where the critical shear stress for slip is very high. shown in Figure 7.34. The rapid production of clicks is

In contrast, only a few fcc metals have been made to responsible for the so-called twinning cry (e.g. in tin).

twin, even at low temperatures. Although most metals show a general reluctance

In zinc single crystals it is observed that there is no to twin, when tested under suitable conditions they

well-defined critical resolved shear stress for twinning can usually be made to do so. As mentioned in

such as exists for slip, and that a very high stress Section 7.3.1, the shear process involved in twinning

indeed is necessary to nucleate twins. In most crystals, must occur by the movement of partial dislocations

slip usually occurs first and twin nuclei are then created and, consequently, the stress to cause twinning will

by means of the very high stress concentration which depend not only on the line tension of the source dis-

exists at dislocation pile-ups. Once formed, the twins location, as in the case of slip, but also on the surface

can propagate provided the resolved shear stress is tension of the twin boundary. The stress to cause twin-

higher than a critical value, because the stress to ning is, therefore, usually greater than that required for

propagate a twin is much lower than that to nucleate slip and at room temperature deformation will nearly

it. This can be demonstrated by deforming a crystal always occur by slip in preference to twinning. As the

oriented in such a way that basal slip is excluded,

Figure 7.34 (a) Effect of grain size on the stress–strain curves of specimens of niobium extended at a rate of 2 .02 ð 10

s at 20 K; (1) grain size 2 d D 1 .414 mm, (2) grain size 2 d D 0 .312 mm, (3) grain size 2 d D 0 .0951 mm, (4) grain size 2 d D 0 .0476 mm. (b) Deformation twins in specimen 1 and specimen 3 extended to fracture. Etched in 95% HNO 3 C 5 % HF (after Adams, Roberts and Smallman, 1960).

Mechanical behaviour of materials 223

i.e. when the basal planes are nearly parallel to the effect with stacking fault energy and it has been specimen axis. Even in such an oriented crystal it is

shown that the twinning stress of copper-based alloys found that the stress to cause twinning is higher than

increases with increasing stacking fault energy. Twin- that for slip on non-basal planes. In this case, non-

ning is also favoured by solid solution alloying in basal slip occurs first so that when a dislocation pile-up

bcc metals, and alloys of Mo–Re, W–Re and Nb–V arises and a twin is formed, the applied stress is so high

readily twin at room temperature. In this case it that an avalanche or burst of twins results.

has been suggested that the lattice frictional stress It is also believed that in the bcc metals twin

is increased and the ability to cross-slip reduced by nucleation is more difficult than twin propagation. One

alloying, thereby confining slip dislocations to bands possible mechanism is that nucleation is brought about

where stress multiplication conducive to twin nucle- by the stress concentration at the head of a piled-up

ation occurs.

array of dislocations produced by a burst of slip as

a Frank–Read source operates. Such a behaviour is

7.5.4 Effect of prestrain on twinning

favoured by impact loading, and it is well known that twin lamellae known as Neumann bands are produced

Twinning can be suppressed in most metals by a cer- this way in ˛-iron at room temperature. At normal

tain amount of prestrain; the ability to twin may be strain rates, however, it should be easier to produce

restored by an ageing treatment. It has been suggested

a slip burst suitable for twin nucleation in a material that the effect may be due to the differing dislocation with strongly locked dislocations, i.e. one with a large

distribution produced under different conditions. For k

C, when which the dislocation locking is relatively slight (small

value (as defined by equation (7.19)) than one in

a heterogeneous arrangement of elongated screw dis- k values). In this context it is interesting to note

locations capable of creating the necessary stress con- that both niobium and tantalum have a small k value

centrations are formed. Room temperature prestrain, and, although they can be made to twin, do so with

however, inhibits twin formation as the regular net- reluctance compared, for example, with ˛-iron.

work of dislocations produced provides more mobile In all the bcc metals the flow stress increases so

dislocations and homogenizes the deformation. rapidly with decreasing temperature (see Figure 7.30),

that even with moderate strain rates ⊲10 s ⊳˛ -iron

7.5.5 Dislocation mechanism of twinning

will twin at 77 K, while niobium with its smaller value In contrast to slip, the shear involved in the twinning of k twins at 20 K. The type of stress–strain behaviour

process is homogeneous throughout the entire twinning for niobium is shown in Figure 7.34a. The pattern of

region, and each atom plane parallel to the twinning behaviour is characterized by small amounts of slip

plane moves over the one below it by only a fraction interspersed between extensive bursts of twinning in

of a lattice spacing in the twinning direction. Never- the early stages of deformation. Twins, once formed,

theless, mechanical twinning is thought to take place may themselves act as barriers, allowing further dislo-

by a dislocation mechanism for the same reasons as cation pile-up and further twin nucleation. The action

slip but the dislocations that cause twinning are partial of twins as barriers to slip dislocations could presum-

and not unit dislocations. From the crystallography of ably account for the rapid work-hardening observed

the process it can be shown that twinning in the cph at 20 K.

lattice, in addition to a simple shear on the twinning Fcc metals do not readily deform by twinning but

it can occur at low temperatures, and even at 0 °

plane, must be accompanied by a localized rearrange-

ment of the atoms, and furthermore, only in the bcc favourably oriented crystals. The apparent restriction

C, in

lattice does the process of twinning consist of a simple of twinning to certain orientations and low tempera-

shear on the twinning plane (e.g. a twinned structure tures may be ascribed to the high shear stress attained

p in tests on crystals with these orientations, since the

2 in stress necessary to produce twinning is high. Twinning

in this lattice can be produced by a shear of 1/

a h1 1 1i direction on a f1 1 2g plane). has been confirmed in heavily rolled copper. The exact

An examination of Figure 7.9 shows that the main mechanism for this twinning is not known, except that

problem facing any theory of twinning is to explain it must occur by the propagation of a half-dislocation

how twinning develops homogeneously through suc- and its associated stacking fault across each plane of a

cessive planes of the lattice. This could be accom- set of parallel ⊲1 1 1⊳ planes. For this process the half-

plished by the movement of a single twinning (par- dislocation must climb onto successive twin planes, as

tial) dislocation successively from plane to plane. One below for bcc iron.

suggestion, similar in principle to the crystal growth mechanism, is the pole-mechanism proposed by Cot-

7.5.3 Effect of impurities on twinning

trell and Bilby illustrated in Figure 7.35a. Here, OA, OB, and OC are dislocation lines. The twinning dis-

It is well established that solid solution alloying location is OC, which produces the correct shear as it favours twinning in fcc metals. For example, sil-

sweeps through the twin plane about its point of emer- ver–gold alloys twin far more readily than the pure

gence O, and OA and OB form the pole dislocation, metals. Attempts have been made to correlate this

being partly or wholly of screw character with a pitch

224 Modern Physical Metallurgy and Materials Engineering

Figure 7.35 (a) Diagram illustrating the pole mechanism of twinning. (b) The formation of a crack at a twin intersection in silicon–iron (after Hull, 1960) .

equal to the spacing of the twinning layers. The twin- crack has developed along one of the twins in a zigzag ning dislocation rotates round the pole dislocation and

manner while still retaining f0 0 1g cleavage facets. in doing so, not only produces a monolayer sheet of

In tests at low temperature on bcc and cph metals twinned crystal but also climbs up the ‘pole’ to the

both twinning and fracture readily occur, and this next layer. The process is repeated and a thick layer

has led to two conflicting views. First, that twins are of twin is built up.

nucleated by the high stress concentrations associated The dislocation reaction involved is as follows. The

with fracture, and second, that the formation of twins line AOB represents a unit dislocation with a Burgers

actually initiates the fracture. It is probable that both vector a/2[1 1 1] and that part OB of the line lies

effects occur.

in the ⊲1 1 2⊳ plane. Then, under the action of stress dissociation of this dislocation can occur according to the reaction

7.6 Strengthening and hardening

a/

mechanisms

The dislocation with vector a/6[1 1 1] forms a line

7.6.1 Point defect hardening

OC lying in one of the other f1 1 2g twin planes (e.g. The introduction of point defects into materials to pro- the ⊲1 2 1⊳ plane) and produces the correct twinning

duce an excess concentration of either vacancies or shear. The line OB is left with a Burgers vector

interstitials often gives rise to a significant change in a/ 3[1 1 2] which is of pure edge type and sessile in

mechanical properties (Figures 7.36 and 7.37). For alu- the ⊲1 1 2⊳ plane.

minium the shape of the stress–strain curve is very dependent on the rate of cooling and a large increase in the yield stress may occur after quenching. We

have already seen in Chapter 4 that quenched-in vacan- It has been suggested that a twin, like a grain boundary,

7.5.6 Twinning and fracture

cies result in clustered vacancy defects and these may may present a strong barrier to slip and that a crack

harden the material. Similarly, irradiation by high- can be initiated by the pile-up of slip dislocations at

energy particles may produce irradiation-hardening the twin interface (see Figure 8.32). In addition, cracks

(see Figure 7.37). Information on the mechanisms of may be initiated by the intersection of twins, and

hardening can be obtained from observation of the examples are common in molybdenum, silicon–iron

dependence of the lower yield stress on grain size. (bcc) and zinc (cph). Figure 7.35b shows a very good

The results, reproduced in Figure 7.37b, show that the example of crack nucleation in 3% silicon–iron; the

i C k y d , which is a general relation crack has formed along an f0 0 1g cleavage plane at

describing the propagation of yielding in materials, is the intersection of two f1 1 2g twins, and part of the

obeyed.

Mechanical behaviour of materials 225

Figure 7.36 Effect of quenching on the stress–strain curves from (a) aluminium (after Maddin and Cottrell, 1955), and (b) gold (after Adams and Smallman, unpublished) .

Figure 7.37 (a) Stress–strain curves for unirradiated and irradiated fine-grained polycrystalline copper, tested at 20 ° C ; (b) variation of yield stress with grain size and neutron dose (after Adams and Higgins, 1959) .

whereby loops and tetrahedra give rise to an increased size indicates that the hardening produced by point

y , on grain

flow stress is still controversial. Vacancy clusters are defects introduced by quenching or irradiation, is of

believed to be formed in situ by the disturbance intro- two types: (1) an initial dislocation source hardening

duced by the primary collision, and hence it is not and (2) a general lattice hardening which persists after

surprising that neutron irradiation at 4 K hardens the the initial yielding. The k y term would seem to indicate

material, and that thermal activation is not essential. that the pinning of dislocations may be attributed to

Unlike dispersion-hardened alloys, the deformation point defects in the form of coarsely spaced jogs,

of irradiated or quenched metals is characterized by a and the electron-microscope observations of jogged

low initial rate of work hardening (see Figure 7.36). dislocations would seem to confirm this.

This has been shown to be due to the sweeping out

of loops and defect clusters by the glide disloca- ble for the general level of the stress–strain curve

i is clearly responsi-

tions, leading to the formation of cleared channels. after yielding and arises from the large density of

Diffusion-controlled mechanisms are not thought to be dislocation defects. However, the exact mechanisms

important since defect-free channels are produced by

226 Modern Physical Metallurgy and Materials Engineering deformation at 4 K. The removal of prismatic loops

both unfaulted and faulted and tetrahedra can occur as a result of the strong coalescence interactions with screws to form helical configurations and jogged dislo- cations when the gliding dislocations and defects make contact. Clearly, the sweeping-up process occurs only if the helical and jogged configurations can glide eas- ily. Resistance to glide will arise from jogs not lying in slip planes and also from the formation of sessile jogs (e.g. Lomer–Cottrell dislocations in fcc crystals).