Chapter 14

CONTINUOUSRECRYSTALLIZATIONDURING AND AFTER LARGESTRAIN DEFORMATION

14.1 INTRODUCTION

A large number of low-angle boundaries are formed when a polycrystalline metal isdeformed (chapter 2) or when the material is subsequently recovered by annealing atlow temperatures (§6.4). On annealing at elevated temperatures, such a microstructurewill usually recrystallize discontinuously as discussed in chapters 7 to 9, this processbeing driven mainly by the energy stored in the low-angle boundaries.

However, after deformation to large strains, particularly at elevated temperatures, amicrostructure consisting predominantly of high-angle grain boundaries may be formed.Minor boundary movements either during the deformation or on subsequent annealingmay then result in a fine-grained microstructure consisting mainly of crystallites whichare surrounded by high-angle boundaries. Such a microstructure is similar to thatresulting from conventional recrystallization, but because no recognisable ‘nucleation’and ‘growth’ of the recrystallized grains occurs, and the microstructure evolvesrelatively homogeneously throughout the material, the process can reasonably beclassified as continuous recrystallization. It is worth emphasising that terminology suchas continuous or discontinuous recrystallization is purely phenomenological, referring

451

only to the spatial and temporal heterogeneity of microstructural evolution, andimplying no specific mechanism of recrystallization.

The occurrence of continuous recrystallization during high temperature deformation,which is known as geometric dynamic recrystallization, has been recognised for sometime. However, recent research has shown that severe cold-working of a metal can alsoresult in a microstructure which consists almost entirely of high-angle grain boundaries,and which, on annealing, may undergo continuous recrystallization. The microstruc-tures which evolve after such low temperature processing, are often sub-micron grain

(SMG) structures, and because such materials may have attractive mechanicalproperties, there has been extensive research recently in this field.

We consider that the phenomena discussed in this chapter can be explained almostentirely in terms of the fundamental processes discussed in earlier chapters, and that nounusual micro-scale mechanisms are involved. Nevertheless, this subject, which wasbriefly alluded to in the first edition of this book, now requires a separate chapter, inwhich the principles underlying the continuous recrystallization of metals deformed ateither ambient or elevated temperatures are considered. In order to simplify discussionand to enable comparison with the conventional deformation processing discussedelsewhere in the book, we will mainly be concerned with microstructures produced byconventional rolling procedures.

There has been considerable research into producing SMG structures using more exoticdeformation routes (see e.g. the reviews of Humphreys et al. 1999, 2001b, Horita et al.2000a, Prangnell et al. 2001), and we will consider the application of these methods tothe production of SMG alloys as a case study in chapter 15.

14.2 MICROSTRUCTURAL STABILITY AFTER LARGE STRAINS

When a polycrystalline metal is deformed, the grain boundary area increases withincreasing strain at a rate which depends on the mode of deformation (§2.2.1). Forexample, during rolling, the grain thickness in the normal direction (H) is related to thestrain (") and the initial grain size D0 (fig. 14.1) by the geometric relationship

H ¼ D0 exp ð�"Þ ð14:1Þ

During the plastic deformation, cells or subgrains are formed, and after a moderatestrain ("� 1) these generally do not change very much. Therefore, with increasingstrain, the percentage of the boundaries which are of high angle (HAGB%) increases(fig. 14.1c). Additionally, new high-angle boundaries may form by grain fragmentationas discussed in chapter 2.

Although it is convenient to discuss the microstructures in terms of the fraction or

percentage of high angle boundaries (HAGB%), it should be recognised that this is only arather crude and arbitrary description, and that it is the overall grain boundarycharacter distribution, e.g. figures 4.2 and A2.1, which is important. Nevertheless, foranalytical purposes, it often convenient to use the simpler descriptions.

452 Recrystallization

The analysis of the stability of cellular microstructures discussed in chapter 10, showedthat microstructures with a large fraction of low angle boundaries are intrinsicallyunstable with respect to discontinuous growth (i.e. discontinuous recrystallization). Ifthe mean low angle boundary misorientation is increased, the boundary propertiesbecome more uniform, and the structure cannot recrystallize discontinuously.

During deformation, the mean boundary misorientation increases, and thus themicrostructure becomes progressively more stable against discontinuous growth asstrain increases. The criteria for the suppression of discontinuous recrystallization,which have been discussed by Humphreys (1997a) and Humphreys et al. (1999), aretherefore the conditions of strain, temperature and initial grain size, which result in asufficient fraction of high angle boundary, (0.6–0.7) to ensure microstructural stability.Alternative criteria for continuous recrystallization can be formulated in terms of theimpingement of corrugated high angle boundaries at large strains as discussed in§14.4.2. However, purely geometric criteria, such as those used to derive equation 14.3are less rigorous, although both approaches give rather similar results.

14.3 DEFORMATION AT AMBIENT TEMPERATURES

Early reports of the deformation of metals which were subjected to true strains in therange 3–7, resulting in grain sizes in the range 0.1–0.5 mm, include copper and nickel(Smirnova et al. 1986), magnesium and titanium alloys (Kaibyshev et al. 1992) andAl–Mg (Wang et al. 1993). Typically, such large strains were produced by a high shearredundant strain method (see §15.6) such as equal channel angular extrusion (ECAE).However, similar fine-scale microstructures can also be produced by conventional coldrolling to large strains. A good example of this phenomenon in aluminium has beengiven by Oscarsson et al. (1992), who found that after very large rolling reductions(>95%), a stable fine-grained microstructure was formed on annealing, whereas atlower strains, normal discontinuous recrystallization occurred. Other examples of theproduction of sub-micron grains in aluminium alloys by low temperature annealingfollowing cold rolling include Ekstrom et al. (1999), Engler and Huh (1999), Humphreyset al. (1999) and Jazaeri and Humphreys (2001, 2002).

14.3.1 The development of stable microstructures by large strain deformation

For simplicity, we consider only the case of deformation by cold rolling or plane straincompression. The size (D) of the cells or subgrains formed on deformation is reducedvery little at strains above �2 (fig. 2.4), and Nes (1998) has shown that the data fromthis figure is consistent with the following relationship for ">2.

D ¼ k"�1 ð14:2Þ

where k is a constant.

The spacing (H) of the high angle boundaries in the normal direction (ND), of amaterial with initial grain size D0, decreases with strain (fig. 14.1a–c) according to

Continuous Recrystallization 453

Fig. 14.2. Schematic diagram of the effect of strain on the cell/subgrainsize (D), HAGB spacing (H) and %HAGB during deformation at ambient

temperatures.

Fig. 14.1. Schematic diagram of the development of microstructure with increasingstrain; (a) initial grain structure, (b) moderate deformation, (c) large deformation,

(d) effect of large second-phase particles on deformation.

454 Recrystallization

equation 14.1. Consequently, as shown in figure 14.2, the HAGB spacing decreasesmore rapidly than the subgrain size with strain, and the fraction of boundaries whichare of high angle therefore increases with strain. At a sufficiently large strain ("cr), thefraction of high angle boundary becomes sufficient (�0.6–0.7) to make the micro-structure stable against discontinuous growth (i.e. recrystallization) as discussed in§14.2. The precise rate of increase in the fraction of HAGB with strain and therefore thecritical strain "cr, is difficult to calculate precisely (Humphreys 1997a, 1999), as itdepends on the shape and planarity of the boundaries, and will be increased by any newhigh angle boundaries created by fragmentation of the old grains (§2.4, §2.7).

14.3.2 The effect of the initial grain size

As shown by equation 14.1, a small initial grain size (D0) will reduce the boundaryspacing H to the critical value at a lower strain than will a larger initial grain size (Harriset al. 1998). The effect of strain and initial grain size on the spacing of high angleboundaries (H) and on the percentage of high angle boundaries in an Al–Fe–Mn alloyare shown in figure 14.3. The HAGB% initially decreases with increasing strain as lowangle boundaries are formed during deformation, but then progressively increases as Hbecomes smaller. If the initial grain size is reduced, it may be seen that the HAGB% athigh strains is larger, and the HAGB spacing (H) at a given strain, is smaller.

It is seen from figure 14.3b that, at the largest strains, the HAGB separations for thematerials of different initial grain size tend to converge. In table 14.1, the measuredHAGB spacing (H) is compared with that predicted (HG) by the geometric reduction ofthe original grain size (equation 14.1) at a true strain of 2.6. The ratio HG/H, which willbe unity if H is determined purely by geometrical factors, is seen to be greatly affectedby the initial grain size. The large value of HG/H for the 260 mm material is consistentwith extensive grain fragmentation in such a large-grained material (§2.7). For the 12 mmmaterial, the value of HG/H implies no grain fragmentation, which is consistent withprevious results for small grain sizes (Humphreys et al. 1999). The 3 mm material is seento have a grain spacing which is considerably larger than the geometric value. There aretwo factors which can contribute to this. At large strains as the deformation texturestrengthens, some grain orientations converge, transforming high angle into lower angleboundaries. Statistical calculations of this effect for the materials of table 14.1, indicate

Table 14.1

The effect of strain and initial grain size on the spacing of high angle boundaries in the

normal direction in Al–Fe–Mn alloy AA8006 cold rolled to a strain of 2.6 (data from

Jazaeri and Humphreys 2002).

Initial grain size(mm)

Measured spacing(H)(mm)

Predicted spacing(HG)(mm)

HG/H

260 1.7 19.3 11.3

12 1.0 0.9 0.9

3 0.6 0.2 0.4

Continuous Recrystallization 455

that the loss of high angle grain boundaries in this way should be no more than �15%,which is insufficient to account for the very small value of HG/H. The second effectwhich can cause this is the local dynamic grain growth (fig. 14.8) which can occur whenhigh angle boundaries approach closely. This effect, which is discussed in §14.4.3, isnormally found only at elevated temperatures, but is clearly able to occur at ambienttemperatures in a low-solute aluminium alloy under these conditions.

Fig. 14.3. The effect of strain and initial grain size on the microstructure of an Al–Fe–Mn alloy (AA8006); (a) The percentage of high angle boundaries, (b) The high angle

boundary spacing (H), (Jazaeri and Humphreys 2002).

456 Recrystallization

14.3.3 The effect of second-phase particles

Large (>1 mm) second-phase particles will increase the rate of formation of high angleboundaries by breaking up the planarity of the boundary structure as shownschematically in figures 2.37 and 14.1d, and also by creating high angle boundariesassociated with the large local lattice rotations close to the particles (§2.9.4). AnEBSD map demonstrating the effect of large particles on the microstructure is shown infigure 14.4. Such particles therefore reduce "cr, although it is difficult to quantify theeffect.

14.3.4 The transition from discontinuous to continuous recrystallization

The transition from discontinuous to continuous recrystallization with increasingrolling reduction, was first reported by Oscarsson et al. (1992), and has been investi-gated in detail by Jazaeri and Humphreys (2001, 2002).

For the larger initial grain sizes and lower strains, normal discontinuous recrystalliza-tion occurred on subsequent annealing (fig. 14.5a), but for larger strains and smallergrain sizes, a predominantly high angle boundary microstructure was formed at compa-ratively low annealing temperatures, with only minor boundary movements (fig. 14.5b),by a process of continuous recrystallization.

The transition between discontinuous and continuous recrystallization is best measuredby monitoring the changes in HAGB content on annealing, and this is shown in figure

Fig. 14.4. EBSD map showing the effect of large (>1 mm) second-phase particles onthe microstructure of Al–Fe–Mn (AA8006) cold-rolled to a strain of 3.9. The particlesare shown as black regions, HAGBs shown as black lines and LAGBs as white lines,

(Jazaeri and Humphreys 2001).

Continuous Recrystallization 457

14.6a,b. When continuous recrystallization occurs, there is a relatively sharp change inthe HAGB% as the deformed substructure is consumed by the recrystallizing grains.However, when continuous recrystallization occurs, there is little change in theHAGB%. During annealing the grains/subgrains gradually become more equiaxed andlarger (fig. 14.6c). These changes are gradual, and quite different to those occurringduring discontinuous recrystallization.

A further difference is that on discontinuous recrystallization, the strong deformationtexture is generally replaced by a different texture, such as a strong cube texture(§12.2.1). However, when continuous recrystallization occurs, the rolling texture is

retained with little change (Engler and Huh 1999, Jazaeri and Humphreys 2001),because there is little microstructural change on annealing following the deformation.

Figure 14.7 summarises the effects of initial grain size and strain on the transition fromdiscontinuous to continuous recrystallization in an AA8006 Al–Fe–Mn alloy.

14.3.5 The mechanism of continuous recrystallization in aluminium

The microstructural changes which occur when a highly deformed material undergoescontinuous recrystallization are rather small, and occur incrementally as the annealingtemperature is increased. As seen from figure 14.6c, there is no significant change in the

Fig. 14.5. EBSDmaps of Al–Fe–Mn (AA8006) annealed after cold rolling; (a) "¼ 0.69,T¼ 250�C, showing discontinuous recrystallization; (b) "¼ 3.9, T¼ 300�C, showing

continuous recrystallization. HAGBs shown as black lines and LAGBs as white lines,(Jazaeri and Humphreys 2001).

458 Recrystallization

Fig. 14.6. Microstructural changes during the annealing of AA8006, as a function ofstrain and initial grain size (D0) (a) % HAGB for D0¼ 3 mm; (b) %HAGB for

D0¼ 12 mm and 260 mm, (Jazaeri and Humphreys 2002); (c) Grain/subgrain size andaspect ratio for D0¼ 12 mm, "¼ 3.9, (data from Jazaeri and Humphreys 2001).

Continuous Recrystallization 459

fraction of high angle boundaries, but the deformed grains/subgrains become moreequiaxed and slightly larger.

In its simplest form, the highly deformed microstructure is similar to that shownschematically in figure 14.1c. It comprises lamellar high angle boundaries alignedparallel to the rolling plane, together with intersecting boundaries which are mainly oflow angle. On annealing such a microstructure, it is thought that the energy is loweredby localised boundary migration as shown in figure 14.8, and this can be considered tooccur in two stages.

� Collapse of the lamellar microstructure

The lamellar structure will tend to collapse due to the surface tension at the nodepoints such as A, where the boundaries (of energy �R) aligned in the rolling plane, arepulled by the boundaries (of energy �N) aligned in the normal direction as shown infigure 14.8b.

The equilibrium configuration of the node A is determined by equation 4.10, and thecritical condition for collapse of the structure is when the nodes A and A0 touch. Thisdepends on the grain length in the rolling direction (L) and the normal direction (N) andon the relative boundary energies. If �R¼ �N then the critical aspect ratio (L/N) forimpingement is �2. However, the boundaries in the normal direction are usually oflower angle, and if for example �R¼ 2�N (corresponding to boundaries in the normaldirection of �3�), the critical aspect ratio is �4. A convincing vertex simulation of thisprocess due to Bate, is seen in figure 16.11, and this has been shown to give goodagreement with the annealing behaviour of a highly deformed Al–3%Mg alloy (Hayes etal. 2002). Additional break-up of the lamellar grain microstructure and production ofhigh angle boundaries during the deformation by large second-phase particles (figs.14.1d and 14.4) will increase �N, and lower the critical grain aspect ratio required forcontinuous recrystallization.

It is interesting that the mechanism of figure 14.8a and b has some geometric similaritiesto that originally proposed by Dillamore et al. (1972) for subgrain growth.

Fig. 14.7. The effects of initial grain size and strain on the transition fromdiscontinuous to continuous recrystallization in AA8006, (Jazaeri and Humphreys

2002).

460 Recrystallization

� Spheroidisation and growth

When the nodes A and A0 touch, node switching (fig. 14.8) will occur, and two newnodes A1 and A2 will form and be pulled apart by the boundary tensions as shown infigure 14.8c. Further spheroidisation and growth will occur due to boundary tensions,as shown in figure 14.8d, leading to a more equiaxed grain structure. Such a fine-grainedmicrostructure will be unstable with respect to normal and perhaps abnormal graingrowth as discussed in §14.5.

14.4 DEFORMATION AT ELEVATED TEMPERATURES

14.4.1 Geometric dynamic recrystallization

As shown in figure 13.3a and 13.5a, grain boundaries develop serrations during dynamicrecovery, and the wavelength of these serrations is similar to the subgrain size. If thematerial is subjected to a large reduction in cross section, for example by hot rolling orhot compression, then the original grains become flattened, as shown schematically infigure 14.9. Because the subgrain size during high temperature deformation is almostindependent of strain (§13.2), the fraction of boundaries which are high angle, increaseswith strain, and eventually the size of the boundary serrations will become comparablewith the grain thickness as shown schematically in figure 14.9b. Interpenetration of thescalloped boundaries will occur, resulting in a microstructure of small equiaxed grainsof a size comparable with the subgrain size (fig. 14.9c), and an example of this process in

Fig. 14.8. Schematic diagram showing the continuous recrystallization of a highlydeformed lamellar microstructure; (a) Initial structure, (b) collapse of the lamellar

boundaries, (c) spheroidisation begins by Y-junction migration, (d) furtherspheroidisation and growth.

Continuous Recrystallization 461

an Al–Mg–Fe alloy is shown in figure 14.10. At lower strains (fig. 14.10a), the flattenedold grains containing subgrains are seen, but at large strains (fig. 14.10b) amicrostructure of almost equiaxed grains has formed.

An equiaxed microstructure with a large number of high angle boundaries thereforeevolves without the operation of any new microscopic recrystallization mechanism andthis process clearly differs from the discontinuous dynamic recrystallization discussed in§13.3. Microstructures of this type are commonly formed in aluminium and its alloysdeformed to large strains (Perdrix et al. 1981). Humphreys (1982) showed that the originof such microstructures was a process of grain impingement as discussed above,and this has been confirmed by later more extensive investigations (McQueen et al.1985, 1989, Humphreys and Drury 1986, Solberg et al. 1989) and the term geometric

dynamic recrystallization has been used to describe the phenomenon. The mechanicalproperties and texture resulting from this process are of interest, and are reviewed byKassner et al. (1992).

One factor which often distinguishes geometric dynamic recrystallization fromconventional discontinuous recrystallization is the crystallographic texture. As discussedin chapter 12, textures resulting from discontinuous recrystallization are often quitedifferent from the deformation textures. However, during geometric dynamicrecrystallization, there is little high angle boundary migration, and the texture remainslargely unchanged (Gholinia et al. 2002b).

It is therefore seen that there is a great deal of similarity between the processes of

continuous recrystallization which occurs on static annealing after very large strains

(§14.3), and that of geometric dynamic recrystallization discussed in this section.

14.4.2 The conditions for geometric dynamic recrystallization

The occurrence of geometric dynamic recrystallization will depend on both the originalgrain size (D0) of the material and on the deformation conditions. If we assume(Humphreys 1982) that the condition for geometric dynamic recrystallization is thatgrain impingement occurs when the subgrain size (D) becomes equal to the grain

Fig. 14.9. Geometric dynamic recrystallization. As deformation progresses, theserrated HAGBs (thick lines) become closer, although the subgrain size remains

approximately constant. Eventually the HAGBs impinge, resulting in amicrostructure of mainly high angle boundaries.

462 Recrystallization

thickness (H), then, using equation 14.1, the critical compressive strain ("cr) for theprocess is

"cr ¼ lnK1D0

D

� �ð14:3Þ

where K1 is a constant of the order of unity.

The relationship between flow stress and subgrain size is given by equation 13.7 andtherefore

"cr ¼ lnð�D0Þ þK2 ð14:4Þ

Fig. 14.10. EBSD maps showing geometric dynamic recrystallization in an Al–3Mg–0.2Fe alloy deformed at 350�C in plane strain compression; (a) "¼ 0.7, (b) "¼ 3.

(HAGBs shown black and LAGBs white), (Gholinia et al. 2002b).

Continuous Recrystallization 463

or, using equations 13.1 and 13.4

"cr ¼ lnðZ1=mD0Þ þK3 ð14:5Þ

When the specimen is deformed at high stresses (large Z), geometric dynamicrecrystallization does not occur until large strains because the subgrain size is small,whereas at low stresses, geometric dynamic recrystallization occurs at smaller strains.The critical strain for geometric dynamic recrystallization is also seen from equation14.3 to be reduced if the original grain size is small.

It should be noted that the condition for geometric dynamic recrystallization may bederived either from geometric conditions as above, or from the theory of the stability ofcellular microstructures as discussed in §10.3.4.

14.4.3 The grain size resulting from geometric dynamic recrystallization

The considerations above predict that geometric dynamic recrystallization should occurwhen the high angle boundary separation is similar to the subgrain size, and that thisshould result in a grain size which is approximately equal to the subgrain size. Thequestion arises as to what happens if deformation is continued to larger strains, so thatthe HAGB spacing might become smaller than the subgrain size. In fact, it has beenshown that this does not happen, even at very large strains, as seen in figure 14.11, inwhich the HAGB separation, the subgrain size and the HAGB spacing given byequation 14.1 are shown.

It is seen that although the HAGB spacing initially decreases more rapidly than thetheoretical value, when it reaches the subgrain size it decreases no further. This isbecause of dynamic grain growth. When the grain spacing is larger than the subgrain

Fig. 14.11. Effect of strain on HAGB spacing and subgrain size in Al–3Mg–0.2Fealloy deformed at 350�C in plane strain compression, (Gholinia et al. 2002b).

464 Recrystallization

size, e.g. figure 14.9a, large scale HAGB migration is prevented by the pinning effects ofthe substructure. However, if the HAGB spacing is smaller than the subgrain size, nosuch pinning is exerted, and the elongated grains will tend to spheroidise as discussed in§14.3.5 and shown schematically in figure 14.8c, under the influence of their boundarytensions by lateral migration of the Y-junctions (A). As the grain spacing becomessimilar to the subgrain size, substructure pinning will reoccur, and in this way a constantHAGB separation is achieved by dynamic equilibrium. A more detailed model ofdynamic grain boundary migration under similar conditions has been proposed byGourdet and Montheillet (2002). It should also be noted that a similar process ofdynamic grain growth under conditions where the grain size is similar to the subgrainsize, is of importance during superplastic deformation, although in this situation thegrain size is stabilised by a dispersion of second-phase particles. Further discussion ofthe effect of second-phase particles on dynamic grain growth is given by Bate (2001b).

14.5 THE STABILITY OF MICRON-GRAINED MICROSTRUCTURES

AGAINST GRAIN GROWTH

Although sub-micron-grained alloys may have impressive mechanical properties(§15.6.3, they cannot be used at elevated temperatures unless the microstructures arestable. Grain growth has been discussed in detail in chapter 11, and here we are onlyconcerned with the behaviour of very fine-grained materials.

14.5.1 Single-phase alloys

Single-phase fine-grain microstructures have a large stored energy, due to the large areaof grain boundary, and during high temperature annealing they are very susceptible tograin growth, as discussed in chapter 11. Hayes et al. (2002) have measured the growthat 250�C of 0.5 mm grains produced in an Al–3%Mg alloy by severe deformation, andfound normal grain growth, with an exponent of 2.6. As may be seen from figure 14.12,the rate of grain growth at this temperature is very rapid.

Fig. 14.12. Annealing of a single-phase 0.5 mm-grained Al–3%Mg alloy at 250�C,showing normal grain growth, (Hayes et al. 2002).

Continuous Recrystallization 465

In contrast, Engler and Huh who obtained continuous recrystallization in high purityaluminium capacitor foil found that the microstructure underwent abnormal grain

growth on further annealing. The difference between the two investigations is due totexture. The material of Hayes et al. (2002) was processed by equal channel angularextrusion (see §15.6.2) which results in a very weak texture. Such a material is notexpected to undergo abnormal grain growth (§11.5). However, the material of Englerand Huh (1999) was heavily cold-rolled and had a strong rolling texture which wasretained on continuous recrystallization. On further annealing, this material underwenttexture-induced abnormal grain growth (§11.5.3).

These limited results show that the high temperature stability of the fine-grainedmicrostructures produced by thermomechanical processing will be very dependent onthe method of deformation, because of the effect that the processing route has on thetexture.

14.5.2 Two-phase alloys

The most effective method of preventing normal or abnormal grain growth of a fine-grained microstructure is with a dispersion of stable second-phase particles as discussedin §11.4 and §11.5. Figure 14.13 shows a version of figure 11.21 which is enlarged toshow the region relevant to micron-grained alloys, and which shows the predictedinfluence of the pinning particles (FV/d) and the grain size (D) on the stability of fine-grain structures. The figure explains the three types of grain growth behaviour discussedin chapter 11. If there are no or few second-phase particles, it is seen that normal graingrowth is predicted to occur during high temperature annealing as discussed above.However, as FV/d increases, normal grain growth will be prevented, but abnormal graingrowth is increasingly likely for smaller grain sizes.

In an alloy such as the Al–Fe–Mn alloy discussed above, in which FV/d�0.1 mm�1, the0.5 mm diameter grains are predicted to undergo abnormal grain growth after a small

Fig. 14.13. The effect of second-phase particles on normal and abnormal grain growthof micron-grained alloys, (Humphreys et al. 1999).

466 Recrystallization

amount of normal grain growth, as is found (Jazaeri and Humphreys 2001). In order tomaintain a very small grain structure at high temperatures, sufficient particles must bepresent to prevent abnormal grain growth, and this requires FV/d>1.5 mm�1 for 0.5 mmdiameter grains. This represents very significant amounts of second-phase particles, e.g.a volume fraction of 0.1 of 60 nm particles, which may be compared with the level ofFV/d� 0.1 mm�1 which is typically required to prevent discontinuous recrystallizationduring conventional processing (§9.2.1), and is rarely achievable in conventionalindustrial alloys (e.g. Hasegawa et al. 1999). However, interest in the superplasticdeformation of micron-grained alloys (e.g. Grimes et al. 2001, Higashi 2001) hasstimulated the development of special alloys containing sufficiently large quantities ofstable intermetallic particles to maintain microstructural stability at elevatedtemperatures.

Continuous Recrystallization 467