The significance of particle explain this, Mott and Nabarro consider the extent to deformability

8.2.3.1 The significance of particle explain this, Mott and Nabarro consider the extent to deformability

which a dislocation can bow round a particle under The strength of an age-hardening alloy is governed by

Frank–Read source this is given by the interaction of moving dislocations and precipitates.

The obstacles in precipitation-hardening alloys which (8.3) hinder the motion of dislocations may be either (1) the strains around GP zones, (2) the zones or precipitates

where r is the radius of curvature to which the dislo- themselves, or both. Clearly, if it is the zones them-

cation is bent which is related to the particle spacing. selves which are important, it will be necessary for

Hence, in the hardest age-hardened alloys where the the moving dislocations either to cut through them or

go round them. Thus, merely from elementary reason- ing, it would appear that there are at least three causes of hardening, namely: (1) coherency strain hardening, (2) chemical hardening, i.e. when the dislocation cuts through the precipitate, or (3) dispersion hardening, i.e. when the dislocation goes round or over the precipitate.

The relative contributions will depend on the particular alloy system but, generally, there is a critical dispersion at which the strengthening is a maximum, as shown in Figure 8.7. In the small-particle regime the precipitates, or particles, are coherent and deformable as the dislocations cut through them, while in the larger-particle regime the particles are incoherent and non-deformable as the dislocations bypass them. For deformable particles, when the dislocations pass through the particle, the intrinsic properties of the particle are of importance and alloy strength varies

Figure 8.7 Variation of strength with particle size, defining only weakly with particle size. For non-deformable

the deformable and non-deformable particle regimes .

266 Modern Physical Metallurgy and Materials Engineering

to a radius of curvature of about 100 atomic spac- ings, and since the distance between particles is of the same order it would appear that the dislocation can avoid the obstacles and take a form like that shown in Figure 8.8a. With a dislocation line taking up such a configuration, in order to produce glide, each section of the dislocation line has to be taken over the adverse region of internal stress without any help from other sections of the line — the alloy is then hard. If the precipitate is dispersed on too fine a scale (e.g. when the alloy has been freshly quenched or lightly aged) the dislocation is unable or bend sufficiently to lie entirely in the regions of low internal stress. As a result, the internal stresses acting on the dislocation line largely cancel and the force resisting its move- ment is small — the alloy then appears soft. When the dispersion is on a coarse scale, the dislocation line is able to move between the particles, as shown in Figure 8.8b, and the hardening is again small.

For coherency strain hardening the flow stress depends on the ability of the dislocation to bend and

Figure 8.8 Schematic representation of a dislocation (a) thus experience more regions of adverse stress than of

curling round the stress fields from precipitates and (b) aiding stress. The flow stress therefore depends on the

passing between widely spaced precipitates (Orowan treatment of averaging the stress, and recent attempts

looping) .

separate the behaviour of small and large coherent par- ticles. For small coherent particles the flow stress is

through the particle where the stacking fault energy given by

differs from the matrix (e.g. Al –Ag where  SF ¾ 3/2 f 1/2 ⊲r/b⊳ 1/2

100 mJ/m 2 between Ag zones and Al matrix) so that which predicts a greater strengthening than the sim-

(8.8) ple arithmetic average of equation (8.2). For large

SF /b

Usually 1 < apb and so 1 can be neglected, but the coherent particles

ordering within the particle requires the dislocations to 1/2 ⊲εb 3 /r 3 ⊳ 1/4

glide in pairs. This leads to a strengthening given by

apb / 2b⊳[4 apb

8.2.3.3 Chemical hardening where T is the dislocation line tension. When a dislocation actually passes through a zone

as shown in Figure 8.9 a change in the number of

8.2.3.4 Dispersion-hardening solvent –solute near-neighbours occurs across the slip

In dispersion-hardening it is assumed that the precipi- plane. This tends to reverse the process of cluster-

tates do not deform with the matrix and that the yield ing and, hence, additional work must be done by the

stress is the stress necessary to expand a loop of dislo- applied stress to bring this about. This process, known

cation between the precipitates. This will be given by as chemical hardening, provides a short-range interac-

the Orowan stress

tion between dislocations and precipitates and arises from three possible causes: (1) the energy required

(8.10) to create an additional particle/matrix interface with

where L is the separation of the precipitates. As dis- energy 1 per unit area which is provided by a stress

cussed above, this process will be important in the later 3/2 ⊲fr⊳ 1/2

stages of precipitation when the precipitate becomes incoherent and the misfit strains disappear. A mov-

where ˛ is a numerical constant, (2) the additional ing dislocation is then able to bypass the obstacles, as work required to create an antiphase boundary inside

shown in Figure 8.8b, by moving in the clean pieces the particle with ordered structure, given by

of crystal between the precipitated particles. The yield stress decreases as the distance between the obsta-

cles increases in the over-aged condition. However, even when the dispersion of the precipitate is coarse

where ˇ is a numerical constant, and (3) the change

a greater applied stress is necessary to force a dislo- in width of a dissociated dislocation as it passes

cation past the obstacles than would be the case if the

Strengthening and toughening 267

Figure 8.9 Ordered particle (a) cut by dislocations in (b) to produce new interface and apb .

obstruction were not there. Some particle or precipitate 4%) alloy in various structural states. The curves were strengthening remains but the majority of the strength-

obtained by testing crystals of approximately the same ening arises from the dislocation debris left around the

orientation, but the stress–strain curves from crystals particles giving rise to high work-hardening.

containing GP [1] and GP [2] zones are quite different

8.2.3.5 Hardening mechanisms in Al–Cu alloys When the crystals contain either GP [1] or GP [2] The actual hardening mechanism which operates in a

zones, the stress–strain curves are very similar to those given alloy will depend on several factors, such as

of pure aluminium crystals, except that there is a two- the type of particle precipitated (e.g. whether zone,

or threefold increase in the yield stress. In contrast, intermediate precipitate or stable phase), the mag-

nitude of the strain and the testing temperature. In yield stress is less than for crystals containing zones, the earlier stages of ageing (i.e. before over-ageing)

but the initial rate of work-hardening is extremely the coherent zones are cut by dislocations moving

rapid. In fact, the stress–strain curves bear no simi- through the matrix and hence both coherency strain

larity to those of a pure aluminium crystal. It is also hardening and chemical hardening will be important,

e.g. in such alloys as aluminium–copper, copper- deformation does not take place on a single slip sys- beryllium and iron–vanadium–carbon. In alloys such

tem but on several systems; the crystal then deforms, as aluminium–silver and aluminium–zinc, however,

more nearly as a polycrystal does and the X-ray pattern the zones possess no strain field, so that chemical

develops extensive asterism. These factors are consis- hardening will be the most important contribution. In

tent with the high rate of work-hardening observed in the important high-temperature creep-resistant nickel

alloys the precipitate is of the Ni 3 Al form which has

The separation of the precipitates cutting any slip

a low particle/matrix misfit and hence chemical hard- plane can be deduced from both X-ray and electron- ening due to dislocations cutting the particles is again

microscope observations. For the crystals, relating to predominant. To illustrate that more than one mech-

Figure 8.10, containing GP [1] zones this value is anism of hardening is in operation in a given alloy

15 nm and for GP [2] zones it is 25 nm. It then follows system, let us examine the mechanical behaviour of

from equation (8.3) that to avoid these precipitates the an aluminium–copper alloy in more detail.

dislocations would have to bow to a radius of cur- Figure 8.10 shows the deformation characteristics

vature of about 10 nm. To do this requires a stress of single crystals of an aluminium–copper (nominally

several times greater than the observed flow stress and,

Figure 8.10 Stress–strain curves from single crystals of aluminium–4% copper containing GP [1] zones, GP [2], zones,

268 Modern Physical Metallurgy and Materials Engineering in consequence, it must be assumed that the disloca-

over-aged condition and the hardening to dispersion- tions are forced through the zones. Furthermore, if we substitute the observed values of the flow stress in the

0 , being somewhat greater than 1 µ m and the initial flow stress is very low. In both cases,

mechanism is unlikely to operate unless the particles however, the subsequent rate of hardening is high are about 60 nm apart. This is confirmed by electron-

because, as suggested by Fisher, Hart and Pry, the microscope observations which show that dislocations

gliding dislocation interacts with the dislocation loops pass through GP zones and coherent precipitates, but

in the vicinity of the particles (see Figure 8.8b). The bypass non-coherent particles. Once a dislocation has

stress–strain curves show, however, that the rate of cut through a zone, however, the path for subsequent

work-hardening falls to a low value after a few per dislocations on the same slip plane will be easier,

cent strain, and these authors attribute the maximum so that the work-hardening rate of crystals containing

in the strain-hardening curve to the shearing of the zones should be low, as shown in Figure 8.10. The

particles. This process is not observed in crystals con- straight, well-defined slip bands observed on the sur-

faces of crystals containing GP [1] zones also support sequently, it seems more likely that the particles will

be avoided by cross-slip. If this is so, prismatic loops this interpretation.

of dislocation will be formed at the particles, by the If the zones possess no strain field, as in alu-

mechanism shown in Figure 8.11, and these will give minium–silver or aluminium-zinc alloys, the flow

approximately the same mean internal stress as that stress would be entirely governed by the chemical

calculated by Fisher, Hart and Pry, but a reduced stress hardening effect. However, the zones in aluminium

on the particle. The maximum in the work-hardening copper alloys do possess strain fields, as shown in

curve would then correspond to the stress necessary to Figure 8.4, and, consequently, the stresses around a

expand these loops; this stress will be of the order of zone will also affect the flow stress. Each dislocation

µ b/r where r is the radius of the loop which is some- will be subjected to the stresses due to a zone at a

what greater than the particle size. At low temperatures small distance from the zone.

cross-slip is difficult and the stress may be relieved It will be remembered from Chapter 7 that temper-

either by initiating secondary slip or by fracture. ature profoundly affects the flow stress if the barrier which the dislocations have to overcome is of a short-

8.2.4 Vacancies and precipitation

range nature. For this reason, the flow stress of crystals It is clear that because precipitation is controlled by the containing GP [1] zones will have a larger dependence

rate of atomic migration in the alloy, temperature will on temperature than that of those containing GP [2]

have a pronounced effect on the process. Moreover, zones. Thus, while it is generally supposed that the

since precipitation is a thermally activated process, strengthening effect of GP [2] zones is greater than

other variables such as time of annealing, composition, that of GP [1], and this is true at normal tempera-

grain size and prior cold work are also important. tures (see Figure 8.10), at very low temperatures it

However, the basic treatment of age-hardening alloys is probable that GP [1] zones will have the greater

is solution treatment followed by quenching, and the strengthening effect due to the short-range interactions

introduction of vacancies by the latter process must between zones and dislocations.

0 play an important role in the kinetic behaviour. It has been recognized that near room temperature, deform with the matrix, so that the critical resolved

zone formation in alloys such as aluminium–copper shear stress is the stress necessary to expand a loop

and aluminium–silver occurs at a rate many orders of dislocation between them. This corresponds to the

of magnitude greater than that calculated from the

Figure 8.11 Cross-slip of (a) edge and (b) screw dislocation over a particle producing prismatic loops in the process .

Strengthening and toughening 269 diffusion coefficient of the solute atoms. In alu-

a decrease in the rate of formation of zones, which minium–copper, for example, the formation of zones

must mean that the dislocations introduced by cold is already apparent after only a few minutes at room

work are more effective as vacancy sinks than as temperature, and is complete after an hour or two,

vacancy sources. Cold working or rapid quenching so that the copper atoms must therefore have moved

therefore have opposing effects on the formation of through several atomic spacings in that time. This cor-

zones. Vacancies are also important in other aspects responds to an apparent diffusion coefficient of copper

of precipitation-hardening. For example, the excess in aluminium of about 10 –10

vacancies, by condensing to form a high density of many orders of magnitude faster than the value of

m 2 s , which is

dislocation loops, can provide nucleation sites for

5 ð 10 m 2 s obtained by extrapolation of high- intermediate precipitates. This leads to the interest- temperature data. Many workers have attributed this

ing observation in aluminium–copper alloys that cold enhanced diffusion to the excess vacancies retained

working or rapid quenching, by producing dislocations during the quenching treatment. Thus, since the expres-

for nucleation sites, have the same effect on the for- sion for the diffusion coefficient at a given temperature

0 phase but, as we have seen above, the contains a factor proportional to the concentration of

opposite effect on zone formation. It is also interesting vacancies at that temperature, if the sample contains an

to note that screw dislocations, which are not normally abnormally large vacancy concentration then the diffu-

favourable sites for nucleation, can also become sites sion coefficient should be increased by the ratio c Q /c o ,

for preferential precipitation when they have climbed where c Q is the quenched-in vacancy concentration and

into helical dislocations by absorbing vacancies, and

c o is the equilibrium concentration. The observed clus- have thus become mainly of edge character. The long tering rate can be accounted for if the concentration of

0 phase observed in aluminium–copper vacancies retained is about 10 –10 .

alloys, shown in Figure 8.4c, have probably formed The observation of loops by transmission electron

on helices in this way. In some of these alloys, defects microscopy allows an estimate of the number of

containing stacking faults are observed, in addition to excess vacancies to be made, and in all cases of

the dislocation loops and helices, and examples have rapid quenching the vacancy concentration in these

been found where such defects nucleate an interme- alloys is somewhat greater than 10 , in agreement

diate precipitate having a hexagonal structure. In alu- with the predictions outlined above. Clearly, as

minium–silver alloys it is also found that the helical the excess vacancies are removed, the amount of

dislocations introduced by quenching absorb silver and enhanced diffusion diminishes, which agrees with the

degenerate into long narrow stacking faults on f1 1 1g observations that the isothermal rate of clustering

planes; these stacking-fault defects then act as nuclei decreases continuously with increasing time. In fact,

for the hexagonal 0 precipitate. it is observed that D decreases rapidly at first and

Many commercial alloys depend critically on then remains at a value well above the equilibrium

the interrelation between vacancies, dislocations and value for months at room temperature; the process is

solute atoms and it is found that trace impurities therefore separated into what is called the fast and

significantly modify the precipitation process. Thus slow reactions. A mechanism proposed to explain the

trace elements which interact strongly with vacancies slow reaction is that some of the vacancies quenched-

inhibit zone formation, e.g. Cd, In, Sn prevent zone in are trapped temporarily and then released slowly.

formation in slowly quenched Al –Cu alloys for up Measurements show that the activation energy in the

C. This delays the age-hardening fast reaction (³0.5 eV) is smaller than in the slow

to 200 days at 30 °

process at room temperature which gives more time for reaction (³1 eV) by an amount which can be attributed

mechanically fabricating the quenched alloy before it to the binding energy between vacancies and trapping

gets too hard, thus avoiding the need for refrigeration. sites. These traps are very likely small dislocation

loops or voids formed by the clustering of vacancies. precipitate by increasing the density of vacancy loops The equilibrium matrix vacancy concentration would

and helices which act as nuclei for precipitation and by then be greater than that for a well-annealed crystal by

0 interfaces thereby reducing

a factor exp [ /rkT], where is the surface energy,

the interfacial energy.

 the atomic volume and r the radius of the defect Since grain boundaries absorb vacancies in many (see Chapter 4). The experimental diffusion rate can

alloys there is a grain boundary zone relatively free

be accounted for if r ³ 2 nm, which is much smaller from precipitation. The Al –Zn–Mg alloy is one com- than the loops and voids usually seen, but they do exist.

mercial alloy which suffers grain boundary weakness The activation energy for the slow reaction would then

but it is found that trace additions of Ag have a ben-

be E D eficial effect in refining the precipitate structure and Other factors known to affect the kinetics of the

removing the precipitate free grain boundary zone. early stages of ageing (e.g. altering the quenching rate,

Here it appears that Ag atoms stabilize vacancy clus- interrupted quenching and cold work) may also be

ters near the grain boundary and also increase the rationalized on the basis that these processes lead to

stability of the GP zone thereby raising the GP zone different concentrations of excess vacancies. In gen-

solvus temperature. Similarly, in the ‘Concorde’ alloy, eral, cold working the alloy prior to ageing causes

RR58 (basically Al –2.5Cu–1.2Mg with additions), Si

270 Modern Physical Metallurgy and Materials Engineering addition (0.25Si) modifies the as-quenched dislocation

character. Thus, for example, the BABAB f1 0 0g plane distribution inhibiting the nucleation and growth of

stacking sequence of the fcc structure can be changed dislocation loops and reducing the diameter of helices.

to BAABA by the propagation of an a/2h1 0 0i shear The S-precipitate ⊲Al 2 CuMg⊳ is homogeneously nucle-

loop in the f1 0 0g plane, or to BAAAB by the propa- ated in the presence of Si rather than heterogeneously

gation of a pair of a/2h1 0 0i partials of opposite sign nucleated at dislocations, and the precipitate grows

on adjacent planes. Again, the AAA stacking resulting directly from zones, giving rise to improved and more

from the double shear is precisely that required for the uniform properties.

embryonic formation of the fluorite structure from the Apart from speeding up the kinetics of ageing,

fcc lattice.

and providing dislocations nucleation sites, vacan- In visualizing the role of lattice defects in the nucle- cies may play a structural role when they precipi-

ation and growth of plate-shaped precipitates, a simple tate cooperatively with solute atoms to facilitate the

analogy with Frank and Shockley partial dislocation basic atomic arrangements required for transforming

loops is useful. In the formation of a Frank loop, a layer the parent crystal structure to that of the product

of hcp material is created from the fcc lattice by the phase. In essence, the process involves the system-

(non-conservative) condensation of a layer of vacan- atic incorporation of excess vacancies, produced by the

cies in f1 1 1g. Exactly the same structure is formed by initial quench or during subsequent dislocation loop

the (conservative) expansion of a Shockley partial loop annealing, in a precipitate zone or plate to change the

on a f1 1 1g plane. In the former case a semi-coherent

‘precipitate’ is produced bounded by an a/3h1 1 1i dis- Al –Cu is shown schematically in Figure 8.12. Ideally,

0 formation in

location, and in the latter a coherent one bounded by

00 phase in Al –Cu consists of an a/6h1 1 2i. Continued growth of precipitate plates layers of copper on f1 0 0g separated by three lay-

occurs by either process or a combination of processes. ers of aluminium atoms. If a next-nearest neighbour

Of course, formation of the final precipitate structure layer of aluminium atoms from the copper layer is

requires, in addition to these structural rearrangements, removed by condensing a vacancy loop, an embryonic

the long-range diffusion of the correct solute atom con-

0 unit cell with Al in the correct AAA . . . stacking centration to the growing interface. sequence is formed (Figure 8.12b). Formation of the

The growth of a second-phase particle with a dis- final CuAl 2 0 fluorite structure requires only shuffling

parate size or crystal structure relative to the matrix half of the copper atoms into the newly created next-

is controlled by two overriding principles–the accom- nearest neighbour space and concurrent relaxation of

modation of the volume and shape change, and the

optimized use of the available deformation mecha- (Figure 8.12c).

0 interplanar distances

nisms. In general, volumetric transformation strains The structural incorporation of vacancies in a pre-

are accommodated by vacancy or interstitial conden- cipitate is a non-conservative process since atomic

sation, or prismatic dislocation loop punching, while sites are eliminated. There exist equivalent conserva-

deviatoric strains are relieved by shear loop prop- tive processes in which the new precipitate structure is

agation. An example is shown in Figure 8.13. The created from the old by the nucleation and expansion

formation of semi-coherent Cu needles in Fe–1%Cu of partial dislocation loops with predominantly shear

is accomplished by the generation of shear loops in

00 0 in Al–Cu by the vacancy mechanism. Vacancies from 00 to form the required AAA Al stacking. 0 fluorite structure then requires only slight redistribution of the copper atom layer and relaxation of the Al

layer spacings (courtesy of K. H. Westmacott) .

Strengthening and toughening 271 which have very good strength/weight ratio applica-

tions, and nickel alloys also develop better properties with multiple ageing treatments.

The basic idea of all heat-treatments is to ‘seed’

a uniform distribution of stable nuclei at the low temperature which can then be grown to optimum size at the higher temperature. In most alloys, there is

a critical temperature T c above which homogeneous nucleation of precipitate does not take place, and in some instances has been identified with the GP

zone solvus. On ageing above T c there is a certain critical zone size above which the zones are able to act as nuclei for precipitates and below which the zones dissolve.

In general, the ageing behaviour of Al –Zn–Mg alloys can be divided into three classes which can be defined by the temperature ranges involved:

0.5 µ m

1. Alloys quenched and aged above the GP zone solvus (i.e. the temperature above which the zones dissolve, which is above ¾155 °

C in a typical Al –Zn–Mg alloy). Then, since no GP zones are

Figure 8.13 The formation of semicoherent Cu needles in ever formed during heat treatment, there are no

Fe–1% Cu (courtesy of K. H. Westacott) . easy nuclei for subsequent precipitation and a very coarse dispersion of precipitates results with nucle- ation principally on dislocations.

2. Alloys quenched and aged below the GP zone into the matrix and incorporation into nearby precipi-

the precipitate/matrix interface. Expansion of the loops

solvus. GP zones form continuously and grow to tate interfaces leads to a complete network of disloca-

a size at which they are able to transform to pre- tions interconnecting the precipitates.

cipitates. The transformation will occur rather more slowly in the grain boundary regions due to the

lower vacancy concentration there but since age- In non-ferrous heat-treatment there is considerable

8.2.5 Duplex ageing

ing will always be below the GP zone solvus, no interest in double (or duplex) ageing treatments to

PFZ is formed other than a very small (¾30 nm) obtain the best microstructure consistent with opti-

solute-denuded zone due to precipitation in the mum properties. It is now realized that it is unlikely

grain boundary.

that the optimum properties will be produced in alloys

3. Alloys quenched below the GP zone solvus and of the precipitation-hardening type by a single quench

aged above it (e.g. quenched to room temperature and ageing treatment. For example, while the interior

C for Al –Zn–Mg). This is the most of grains may develop an acceptable precipitate size

and aged at 180 °

common practical situation. The final dispersion of and density, in the neighbourhood of efficient vacancy

precipitates and the PFZ width are controlled by the sinks, such as grain boundaries, a precipitate-free zone

C where GP zone (PFZ) is formed which is often associated with over-

nucleation treatment below 155 °

size distribution is determined. A long nucleation ageing in the boundary itself. This heterogeneous

treatment gives a fine dispersion of precipitates and structure gives rise to poor properties, particularly

a narrow PFZ.

under stress corrosion conditions. Duplex ageing treatments have been used to over-

It is possible to stabilize GP zones by addition of come this difficulty. In Al –Zn–Mg, for example, it

trace elements. These have the same effect as raising was found that storage at room temperature before

T c , so that alloys are effectively aged below T c . One heating to the ageing temperature leads to the forma-

example is Ag to Al –Zn–Mg which raises T c from tion of finer precipitate structure and better properties.

C, another is Si to Al –Cu–Mg, another This is just one special example of two-step or multiple

C to 185 °

Cu to Al –Mg–Si and yet another Cd or Sn to Al –Cu ageing treatments which have commercial advantages

alloys. It is then possible to get uniform distribution and have been found to be applicable to several alloys.

and optimum properties by single ageing, and is an Duplex ageing gives better competitive mechanical

example of achieving by chemistry what can similarly properties in Al-alloys (e.g. Al –Zn–Mg alloys) with

be done with physics during multiple ageing. Whether much enhanced corrosion resistance since the grain

it is best to alter the chemistry or to change the physics boundary zone is removed. It is possible to obtain

for a given alloy usually depends on other factors (e.g.

strengths of 267–308 MN/m 2 in Mg–Zn–Mn alloys

economics).

272 Modern Physical Metallurgy and Materials Engineering