)exp(DH oG ε−=

Static and Dynamic Grain Growth in Single-phase Aluminium

H. Jazaeri*, F.J. Humphreys and P.S. Bate

The University of Manchester, Materials Science Centre, Grosvenor Street, Manchester M1 7HS, England * Now at Oxford Instruments Analytical, Halifax Road, High Wycombe HP12 3SE, England

hedieh.jazaeri@oxinst.co.uk, john.humphreys@manchester.ac.uk, pete.bate@manchester.ac.uk

Keywords: deformation, large strains, aluminium, static grain growth, dynamic grain growth, EBSD

Abstract. Al-0.1Mg with a 3µm grain size was deformed in channel die plane strain compression

at temperatures up to 200oC. It was found that the reduction in grain thickness was significantly less

than that predicted from geometric considerations, and at larger strains, a minimum high angle grain

spacing, which was equal to the crystallite size was achieved. The velocity of the high angle

boundaries during this process is very many orders of magnitude larger than that predicted for

curvature driven grain growth, and some possible explanations for this are discussed.

Introduction

When aluminium is plastically deformed, the grains (initial diameter Do) generally change shape,

approximately in accord with the overall strain of the sample, with a consequent increase in grain

boundary area [1,2]. During plane strain compression to large strains, the grains become ribbons of

thickness (H), and simple geometric considerations [e.g. 1,3] show that the predicted grain

thickness (HG) is related to Do and the true strain (ε), approximately by:

(1)

In a material of high stacking fault energy and low solute drag, such as a low solute aluminium

alloy, most of the dislocations remaining after deformation are in the form of cell or subgrain

boundaries, and the cells/subgrains are approximately equiaxed. Above strains of ~0.5-1, a steady

state cell or subgrain size (d), which is a function of the deformation temperature and strain rate,

commonly expressed as the Zener-Hollomon parameter (Z), is achieved.

We have previously investigated the effect of initial grain size and cold rolling strain on the

microstructures of various aluminium alloys [4], and reported an unusual correlation between the

spacings of high and low angle boundaries after large strains, particularly in initially fine-grained

material. The present investigation has extended this work to include deformation at higher

temperatures.

Experimental procedures

Cylindrical samples (15 mm diameter by 100 mm long) of a single-phase Al-0.1Mg alloy, supplied

by Alcan International, were pre-processed by ECAE at room temperature, using a 120º die. The

billets were passed 15 times through the die, giving a total strain of ~10 and a resulting grain size of

~1µm. The extruded bars were then annealed at 200oC or 350

oC to coarsen the microstructures by

grain growth, resulting in equiaxed grains of diameter 3µm and 120µm. These provided the starting

materials for the deformation experiments.

Materials Science Forum Vols. 519-521 (2006) pp 153-160Online available since 2006/Jul/15 at www.scientific.net© (2006) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/MSF.519-521.153

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 129.101.79.200, University of Idaho, Moscow, USA-22/08/14,10:06:09)

Specimens of dimensions 15mm×10mm×10mm were machined from the heat-treated ECAE

material for deformation. Samples were deformed in channel die plane strain compression to true

strains of 0.7-2.3 using strain rates of 10-2 s-1 and 10

-4 s-1 at temperatures between 23

oC and 200ºC.

The convention used for the geometry of flat rolling is adopted here, with ND being the

compression direction, RD the extension direction and TD the direction constrained by the channel.

Prior to deformation, samples were lubricated hexagonal boron nitride. The deformed specimens

were quenched in water immediately after deformation.

The deformed materials were sectioned parallel to the ND-RD plane and metallographically

prepared and electropolished. The texture and microstructure of materials were studied by using

high resolution EBSD in various field emission gun SEMs, all equipped with HKL Channel5 EBSD

acquisition systems. EBSD maps of typically 120,000-300,000 pixels with step sizes of 0.05-

0.15µm and 1-2µm were obtained to measure subgrain and grain sizes, respectively. The EBSD

data were subsequently analysed by VMAP, an in-house software package. Boundaries with

misorientations between 0.5º and 15º were defined as low angle grain boundaries (lagb) and those

of misorientation >15º as high angle grain boundaries (hagb). Due to the angular resolution limit,

boundaries of misorientation less than 0.5º were disregarded.

Deformation at room temperature

When a material with a large initial grain size is deformed, the subgrain size is usually very much

smaller than the grain size, but for a material of small initial grain size deformed to large strains, the

grain thickness (H) and the subgrain size become comparable as demonstrated by Jazaeri and

Humphreys [4] on cold rolled aluminium alloys. Because it is difficult to define a meaningful

“subgrain size” in these circumstances, it is preferable to use the “crystallite size” (d), defined as the

mean separation of all boundaries (hagb +lagb).

Figure 1 shows the effect of strain on the high angle boundary (hagb) spacing normal to the rolling

plane (H) and the crystallite size for cold rolled Al-0.1%Mg of initial grain size 3.2µm. Although

the decrease in H follows equation 1 at low strains, it is significant that at strains larger than ~2, the

hagb spacing becomes larger than the predicted value (HG), and at the largest strain of 3.9, H is

some ten times larger than HG. Note also that at the larger strains, the values of H and the crystallite

size (d) remain constant and similar.

Fig. 1. The effect of strain on boundary

spacings in cold rolled Al-0.1%Mg, of initial

grain size 3µm. Also shown is the hagb spacing predicted from equation 1.

(Data from Jazaeri and Humphreys [4])

The effects of temperature and strain rate

Figure 2 shows examples of EBSD maps of the 3µm grained deformed materials, and demonstrates

the effects of deformation temperature and strain on the microstructures. From such maps, a number

of microstructural parameters were determined, and figure 3 shows the crystallite size measured for

samples of different initial grain size and deformed to various strains under different deformation

conditions. It is seen that the crystallite size is a monotonic function of Z, with little effect of initial

154 Aluminium Alloys 2006 - ICAA10

grain size, or strain. The crystallite sizes are consistent with subgrain sizes measured in earlier

work on low solute single phase aluminium alloys, e.g. [5,6].

(a) (b)

(c) (d)

Figure 4 shows the effect of strain on the crystallite size and hagb spacing for 3µm grained samples

deformed at various temperatures at a strain rate of 10-4, and also shows the boundary spacing (HG)

predicted from equation 1. It is seen that, as shown in fig.1, the crystallite size is largely

independent of strain. The hagb spacing (H) decreases with strain, and at the larger strains is larger

than the geometrically predicted spacing (HG), particularly at the higher temperatures. Although the

difference between H and HG at room temperature appears to be rather small at the maximum strain

of 2.3 used in the channel die compression experiments, figure 1 shows that HG falls well below H

at the larger strains of the cold rolled samples from an earlier investigation [4].

Fig. 2. EBSD maps from ND-RD sections of hot-deformed specimens, demonstrating the

effects of deformation temperature (a,b) and strain (c,d). In all cases, RD is approximately

vertical. High and low angle boundaries are shown as black and grey lines respectively.

a) T=150oC, ε=1.2, ε =10-4s-1, b) T=200oC, ε=1.2, ε =10-4s-1,

c) T=150oC, ε=0.7, ε=10-2s-1, d) T=150oC, ε=2.3, ε =10-2s-1.

10µµµµm 10µµµµm

10µµµµm 15µµµµm

Materials Science Forum Vols. 519-521 155

Fig. 3. The effect of deformation conditions (Z) on the crystallite size.

Note that starting grain size and strain have little effect.

Fig. 4. The effect of strain and temperature on boundary spacings

for 3µm grained samples deformed at a strain rate of 10-4s-1.

Figure 5 shows that although the aspect ratio of the grains increases slightly during deformation,

the increase occurs mainly at low strains and is very much less than that predicted from geometric

considerations. If the grain thickness (H) at larger strains (ε=2.3) for a range of conditions is

compared with the crystallite size (d), then, as shown in figure 6, H/d remains constant at ~1, over

the whole range of deformation conditions studied.

156 Aluminium Alloys 2006 - ICAA10

Fig.6. The ratio of grain thickness to that

predicted geometrically, and to the crystallite

size, for3µm grained samples deformed to

ε=2.3, as a function of Z.

(a) (b)

Discussion

The minimum grain thickness (Hmin). The experimental results clearly demonstrate that over a

large range of deformation conditions, there is an equilibrium hagb spacing (Hmin) which is a unique

function of Z, and which is a similar relationship to that found for subgrains. This effect is not

observed in many investigations simply because the initial grain size is large, and the strain is

insufficient to reduce the grain thickness to the minimum value. However, the effect has been noted

in a number of aluminium alloys deformed to large strains at room temperature [4,7,8], and has also

been found during deformation at elevated temperatures [9], and it is clear that it is a general

phenomena. All these investigations have concluded that the Hmin is reached when the boundary

spacing converges with the subgrain or crystallite size. A dispersion of small second-phase particles

tends to reduce the subgrain size at all deformation temperatures, and yet in such alloy it is still

observed that Hmin is equal to the subgrain/crystallite size [9]. It is therefore reasonable to conclude

that it is the scale of the subgrain structure which determines Hmin.

.

Why is Hmin controlled by the subgrain size?. A flattened grain structure is unstable, and will

tend to spheroidise by junction reactions during dynamic recovery, as shown schematically in figure

7, a process which has been substantiated by computer simulation [10]. Normally, this is prevented

by the pinning effects of the substructure (fig.7a), but as H approaches the subgrain size, the

pinning is reduced, and grain coarsening occurs, thus maintaining a dynamic equilibrium at Hmin.

As the subgrain size is a strong function of Z (fig.1), although it should be noted that a good

physical theory for this has still to be given, Hmin will also vary in a similar manner with Z.

Figure 7. Schematic representation of

dynamic recovery during large

strain deformation.

a) At intermediate strains the hagbs are

pinned by the lagbs

b) At large strains a lamellar structure is

formed with a hagb spacing H

c) Collapse of the lamellar structure at

nodes such as A and A1

d) Y-junction movement reduces the

amount of hagb and produces a more

equiaxed structure.

0

1

2

3

4

5

6

7

8

20 30 40 50 60

ln(Z)

Boundary spacing ratio

HAGB spacing/crystallite

HAGB spacing/theory

1

10

100

1000

0 0.5 1 1.5 2 2.5

Strain

Grain aspect ratio

aspect-theory

200

150

100

RT

Fig. 5. The grain aspect ratio as a function of

strain for all deformation conditions in 3µm grained material.

(c) (d)

Materials Science Forum Vols. 519-521 157

R4M

dtdRv γ

==

)RT/Qexp(MM 0 −=

High angle boundary migration during deformation. The process discussed above involves the

migration of high angle boundaries so as to maintain a constant boundary spacing as the grains are

flattened during deformation. The most significant point is that although this is not unreasonable at

high temperatures, high angle boundary migration in aluminium alloys a room temperature is very

slow. We can illustrate this by comparing the hagb velocity during deformation, with that expected

from diffusion controlled boundary migration. Consider a hagb in the deformed microstructure

when H=1µm, which is a typical value from fig.4. At a strain rate of 10-2s-1, the boundary migration

rate required to maintain a spacing of 1µm is 3.2x10-11

m/s, and we can compare this to the

migration rate of a high angle boundary driven by the factors considered in figure 7. For simplicity,

we take the driving pressure as that due to the hagb radius of curvature (R), as in the grain growth

analysis of Hillert [11], taking R as H/2, giving

(2)

where γ, the hagb energy =0.324J/m2, and the mobility (M) is given by

(3)

From static grain growth experiments on our 3µm grained material, at temperatures between 150

and 225oC we determined M0=0.125 m

4J-1s-1 and Q=130 kJ/mol, which is consistent with earlier

experiments on the same alloy [12]. Therefore the boundary migration rate predicted for diffusional

migration when HG~1µm is v=0.16M m/s.

The values of the predicted (Vstatic) and measured (Vmeasured) boundary velocities are given in table

1, where it is seen that the predicted boundary migration rates are lower than the measured values

by factors of between 1014 and 10

5, clearly showing that the dynamic recovery effects leading to the

constant value of HG cannot be ascribed to normal hagb migration.

It is interesting that a rather similar phenomenon to that described in this paper has recently been

reported in ultra-fine grained aluminium produced by deposition [13]. These authors found that

grain growth occurred at room temperature in thin films of high purity aluminium of grain size

~200nm when the sample was nano-indented. However, this did not occur in Al-Mg alloys.

Table 1

Measured and predicted hagb velocities

T(oC) vmeasured vStatic vBreakaway

[m/s]

20 3.2E-11 1.3E-25 1.9E-14

100 3.2E-11 1.2E-20 4.8E-12

150 3.2E-11 1.8E-18 5.3E-11

200 3.2E-11 8.8E-17 3.5E-10

The reasons for rapid dynamic growth. The experimental results clearly indicate that during

deformation of aluminium at low and moderate temperatures, dynamic migration of high angle

boundaries occurs at a rate which is many orders of magnitude faster than that predicted for

boundary migration driven by curvature. This is a very difficult problem to analyse, and there are

several possible causes as outlined below.

Solute breakaway: At low temperatures solute cannot diffuse rapidly and therefore boundaries can

break away from the solute atmosphere under high driving pressures and move with very high

mobility [see e.g. 3]. There are few measurements of the mobility of boundaries under these

158 Aluminium Alloys 2006 - ICAA10

conditions [14,15, 16], but from the results of Gordon and Vandermeer [14], we can estimate the

boundary velocity of a solute-free boundary (Vbreakaway) in aluminium, and this is shown in table 1.

Although these boundary velocities are still less than those required at temperatures below 150oC,

the discrepancy is much smaller, and considering the lack of detailed data on real mobilities and the

approximate nature of our calculations, they may indicate that solute-free boundary migration is an

important factor. It should be noted that room temperature deformation to large strains was carried

out on several different aluminium alloys [4], which all showed similar behaviour, indicating that

solutes did not have a significant effect on the low temperature boundary migration.

Stress induced boundary migration: Low angle symmetrical tilt boundaries are known to migrate

under the influence of stress, by mechanisms involving dislocation glide [3]. Recent work on the

migration at high temperatures of symmetrical tilt boundaries under small stresses [17] has shown

that even high angle boundaries can migrate under the influence of stress. However, in all cases, the

mobilities did not differ substantially for those found for grain growth, and it is difficult to see how

these results could explain the phenomena observed.

Vacancy effects: The dynamic hagb migration is occurring when there is extensive dislocation

motion, and as no significant low angle boundaries are being formed, most of the dislocations are

being annihilated at the hagbs. The resultant vacancy concentration is expected to have a

significant effect both on the free volume at the boundary and on migration, although this is

difficult to quantify.

Mesoscopic elastic strain energy: Although the main issue in the occurrence of a minimum HAGB

spacing is associated with boundary mobility, there could be additional driving pressure

contributions. One of these is due to the different elastic strain energy of different orientations

during deformation. The heavily deformed material approximates to a lamellar composite, with

different orientations having different flow stresses as a result of their different orientations. If the

difference in flow stress is taken to be the same as the difference between the Taylor factors, ∆M, of

two adjoining flat grains, then for an elastically isotropic material the specific strain energy

difference due to this effect is:

∆Eσ ≈ τ2 ∆M

2 /E (4)

-where τ is the slip stress, which is assumed to be uniform, and E is the Youngs modulus. For

aluminium, the elasticity is almost isotropic and M values of 2.5 and 3 with τ = 50 MPa gives ∆Eσ ≈

60 kJ m-3. This effect would be equivalent to a driving pressure due to curvature with R = 2.5 µm,

using a specific boundary energy γ = 0.3 J m-2, i.e. it is of the same order as typical curvature or

substructure difference contributions to growth. Although this contribution should not be ignored, it

is not sufficient to account for the experimental observations.

The observation that there is a minimum HAGB spacing, and that this is closely related to the scale

of substructure, is clear even though there is no simple explanation. It is interesting to note that the

problem might well be of wider interest. The distinction between high and low angle boundaries is

rather arbitrary, and many of the substructural boundaries have relatively large misorientations. The

question could then be: why is there a minimum subgrain size for particular conditions of

deformation in metals which form a well-defined substructure during dynamic recovery? As noted

above, there is no satisfactory theory relating subgrain size with Z and anomalous boundary

migration must be involved.

Materials Science Forum Vols. 519-521 159

Summary and conclusions

1. During deformation in channel die plane strain compression, of a 3µm grained Al-0.1Mg alloy at

temperatures up to 200oC, it was found that the reduction in grain thickness was significantly less

than that predicted from geometric considerations.

2. At larger strains, a minimum high angle grain spacing (Hmin) was reached, which was equal to the

crystallite size, and was a unique function of the Zener-Hollomon parameter.

3. It is shown that this minimum spacing is due to the cessation of substructural pinning of the high

angle boundaries.

4. The velocity of the high angle boundaries during this dynamic recovery is very many orders of

magnitude larger than that predicted for curvature driven grain growth. Various factors which could

cause such rapid boundary migration, including breakaway from solute atmospheres, stress induced

boundary migration and elastic strain energy are discussed, although no firm conclusions can be

drawn at this stage.

Acknowledgements

This research was supported through the University of Manchester EPSRC Light Alloys Portfolio

Partnership (EP/D029201/1). The supply of materials from Alcan International is gratefully

acknowledged.

References

1. J. Gil Sevillano, P. van Houtte, and E. Aernoudt: Prog. Mater. Science. 25, (1980), 69.

2. P.S. Bate and W.B. Hutchinson: Scripta Mater. 52, (2005), 199.

3. F.J. Humphreys and M. Hatherly: Recrystallization and related annealing phenomena. Elsevier,

2nd Edition, (2004).

4. H. Jazaeri and F.J. Humphreys: Acta Mater. 52, (2004), 3239.

5. T. Furu, K.Marthinsen and E. Nes: in Recrystallization'92. ed. Fuentes and Sevillano. San

Sebastian, Spain. (1992), 41.

6. K.D. Vernon-Parry, T. Furu, D.J. Jensen and F.J. Humphreys: Mater, Sci. and Tech. (1996), 12,

889.

7. F.J. Humphreys, P.B. Prangnell, J.R. Bowen, A. Gholinia and C. Harris. Phil. Trans. Royal

Society A. 357, 1663. (1999).

8. P.B.Prangnell, J.R.Bowen and P.J. Apps. Mats Sci. and Eng. A375-377, 178, (2004)

9. A. Gholinia, F.J. Humphreys and P.B. Prangnell. Acta Mater, 50, 4461, (2002).

10. P.B.Prangnell, J.S. Hayes, J.R. Bowen, P.J. Apps and P.S. Bate. Acta Mater. 52, 3193, (2004).

11. M. Hillert. Acta Metall. 13, 227, (1965).

12. Y.Huang and F.J. Humphreys. Proc. 1st Int. Conf. on Recrystallization and Grain Growth. Eds.

Gottstein and Molodov. Springer, 409, (2001).

13. M. Jin, A.M.Minor, E.A. Stach and J.W. Morris. Acta Mater. 52, 5381, (2004).

14. P. Gordon and R.A.Vandermeer. Trans AIME. 224, 917, (1962).

15. F. Haessner and S. Hofmann. (1978), in Recrystallization of Metallic Materials. ed.

Haessner. DR Riederer Verlag, Stuttgart. 63.

16. G. Gottstein and L.S. Shvindlerman. (1992), Scripta Metall. 27, 1521.

17. M. Winning, G. Gottstein and L.S. Shvindlerman. (2002), Acta Mater. 50, 353.

160 Aluminium Alloys 2006 - ICAA10

Aluminium Alloys 2006 - ICAA10 10.4028/www.scientific.net/MSF.519-521 Static and Dynamic Grain Growth in Single-Phase Aluminium 10.4028/www.scientific.net/MSF.519-521.153

DOI References

[1] J. Gil Sevillano, P. van Houtte, and E. Aernoudt: Prog. Mater. Science. 25, (1980), 69.

doi:10.1016/0079-6425(80)90001-8 [2] P.S. Bate and W.B. Hutchinson: Scripta Mater. 52, (2005), 199.

doi:10.1016/j.scriptamat.2004.09.029 [3] F.J. Humphreys and M. Hatherly: Recrystallization and related annealing phenomena. Elsevier, nd

Edition, (2004).

doi:10.1016/B978-008044164-1/50011-6 [4] H. Jazaeri and F.J. Humphreys: Acta Mater. 52, (2004), 3239.

doi:10.1016/j.actamat.2004.03.030 [7] F.J. Humphreys, P.B. Prangnell, J.R. Bowen, A. Gholinia and C. Harris. Phil. Trans. Royal ociety A. 357,

1663. (1999).

doi:10.1098/rsta.1999.0395 [11] M. Hillert. Acta Metall. 13, 227, (1965).

doi:10.1016/0001-6160(65)90200-2 [16] G. Gottstein and L.S. Shvindlerman. (1992), Scripta Metall. 27, 1521.

doi:10.1016/0956-716X(92)90138-5