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Structural and kinetic aspects of continuous grain coarsening in a fine-grained Al–0.3Sc alloy
Acta Materialia 55 (2007) 3479–3491 www.elsevier.com/locate/actamat
Structural and kinetic aspects of continuous grain coarsening in a fine-grained Al–0.3Sc alloy M. Ferry *, N. Burhan School of Materials Science and Engineering, ARC Centre of Excellence for Design in Light Metals, University of New South Wales, UNSW, Sydney, NSW 2052, Australia Received 5 December 2006; received in revised form 30 January 2007; accepted 30 January 2007 Available online 26 March 2007
Abstract A supersaturated Al–0.3 wt.% Sc alloy was produced by equal channel angular pressing to an equivalent von Mises strain of 9.2 then pre-aged at 350 C to generate a starting grain size of 1 lm. The microstructure was highly resistant to grain coarsening at temperatures up to 500 C with discontinuous coarsening only occurring after extended annealing. A detailed statistical analysis showed that the initial grain size distribution was very close to lognormal, and remained lognormal throughout annealing, with the normalized size distribution not affected by time and temperature despite a broadening of the distribution. The homogeneous evolution of the microstructure during annealing, coupled with no appreciable change in texture, is consistent with the advanced stages of continuous recrystallization, and also structurally and kinetically similar to conventional subgrain growth/grain growth in high-stacking fault energy, low-solute alloys. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Aluminium alloys; Annealing; Equal channel angular pressing (ECAP); Electron backscattering diffraction (EBSD)
1. Introduction Severe plastic deformation (SPD) of high-stacking faulty energy, low-solute alloys by processes such as equal channel angular pressing (ECAP) usually generates a microstructure exhibiting an ultra-fine grain (UFG), sometimes referred to as submicron grain (SMG), size [1–4]. The grain structures in these materials are similar to those of recovered and recrystallized metals [2], although they usually contain irregularly shaped boundaries, indicating a nonequilibrium structure. ECAP can also generate a large fraction (>0.7) of high-angle boundaries (HAGBs) after large strains, but the misorientation distribution between adjacent grains usually takes the form of a frequency histogram exhibiting a peak at both low and high misorientations, indicative of a non-random distribution of grain orientations [5]. Furthermore, the low-angle grain boundaries (LAGBs) and HAGBs are not usually distributed uni*
Corresponding author. E-mail address: [email protected] (M. Ferry).
formly, and localized clusters of grains consisting predominantly of either type of boundary may be present [6–9]. Such variability is affected by factors including the deformation path and strain [2,10], as well as the initial microstructure, with either a dispersion of fine particles or a coarse grain size prior to straining making it more difficult to generate a large and uniform HAGB fraction [9]. Similar to the subgrain and grain structures produced during either recovery or after recrystallization, the SPD-UFG microstructure is inherently unstable with coarsening occurring at elevated temperatures to reduce the stored energy associated with the large surface area of grain boundaries in a given volume of material [2,11]. UFG alloys with HAGB fractions greater than 0.6–0.7 may undergo a uniform coarsening process termed continuous recrystallization, as shown in recent theoretical [12,13] and experimental [14] analyses, with discontinuous coarsening only occurring after extended annealing or at elevated temperature [6,15–19]. A characteristic feature of an equiaxed grain structure produced by recovery or recrystallization is a grain size
1359-6454/$30.00 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.01.047
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distribution of a two-dimensional (2-D) section described by probability distributions such as the Hillert, lognormal, Rayleigh and gamma distributions [2]. There is some uncertainty concerning the best fit of experimental data with the various distributions, with some workers arguing that the Rayleigh distribution best describes the grain size distribution in bulk recrystallized metals (see Ref. [2]), whereas, for thin films or foils, the lognormal or gamma distributions show the best fit [20,21]. Regardless of the type of distribution, both subgrain coarsening and grain growth are spatially uniform and the normalized grain size ðD=DÞ is expected to be time invariant [2]. Both coarsening processes are curvature driven with an apparent activation energy comparable to that of either lattice (bulk) or grain boundary diffusion [2]. In comparison, it is not clear if the grain structure of SPD-UFG alloys evolves in a similar manner to these conventional subgrain/grain growth processes. The aim of the present work is to understand the mechanism(s) of grain coarsening in a fine-grained Al–Sc alloy produced by ECAP and to establish if continuous grain coarsening is structurally and kinetically similar to static recovery and normal grain growth. 2. Materials and methods 2.1. Production of starting material and annealing experiments A high-purity Al–0.3 wt.% Sc alloy was chill cast to produce 15 mm diameter ingots, swaged to 10 mm diameter, then solution heat-treated for 48 h at 620 C and cold water quenched. Samples of length 100 mm were deformed at room temperature by ECAP with characteristic angles of U = 90 and w = 0. Deformation was carried out using graphite-based lubricant for a total of eight passes with 90 rotation between each pass to generate an equivalent von Mises strain of 9.2. Following deformation, the alloy was aged for 3 h at 350 C to produce an equiaxed microstructure containing a relatively uniform distribution of
coherent Al3Sc dispersoid particles (see Ref. [6]). The dispersion of fine particles in Al–Sc alloys impede discontinuous recrystallization after rolling [22] and extrusion [23] and grain coarsening after SPD [6] by Zener pinning [24]. The pre-aged samples were annealed for up to 10 h at temperatures of 400, 450 and 500 C, with a limited number of experiments carried out at 550 C. Grain coarsening was investigated using focused ion beam (FIB) microscopy, field emission gun scanning electron microscopy (FEGSEM) and electron backscatter diffraction (EBSD) using an FEI Novalab 200 DualBeam platform. Specimens suitable for imaging by both SEM and FIB were prepared by mechanical grinding and polishing followed by electropolishing at 30 C in a solution of 20% nitric acid in methanol. 2.2. Analysis of microstructure 2.2.1. Grain size distributions For each annealing condition, ion channeling contrast (ICC) imaging was used to determine the grain size distribution. This powerful technique resolves grains below 100 nm in size, which is superior in resolution compared with both EBSD mapping and electron channeling contrast (ECC) imaging and, compared with the latter, generates better-quality orientation contrast images in polycrystalline aluminium [6]. For grain size measurements by EBSD, Humphreys [25] showed that an error in grain size measurement of less than 10% requires at least five steps per grain. While the starting grain size of the Al–Sc alloy is 1 lm, grains as fine as 100 nm were present in the microstructure. Hence, an EBSD step size of <20 nm is required to accurately determine the grain size distribution, which equates to over six million data points for a single 50 · 50 lm area. A further limitation of EBSD is the resolvable misorientation of adjacent grains, which, for a standard system, is at least 0.5 [25]. It is possible to achieve a high-angular resolution using ICC (<0.5) by taking an ICC micrograph of a given area of microstructure
Table 1 Grain size parameters and statistical data after annealing at various times and temperatures Temperature (C)
Time (h)
Mean diameter, D ðlmÞ (Eq. (1))
Dmax =D [31]
Standard deviation, r (lm) (Eq. (2))
r=D
Geometric mean diameter, Dg
Geometric standard deviation, rg
400
0.5 1.0 3.0 5.0 10.0
1.39 1.41 1.51 1.61 1.86
2.3 2.4 2.9 2.6 2.7
0.50 0.49 0.58 0.65 0.72
0.36 0.35 0.38 0.40 0.39
1.39 1.40 1.46 1.57 1.80
0.39 0.38 0.42 0.42 0.39
450
0.5 1.0 3.0 5.0 10.0
1.58 1.83 2.56 2.73 3.15
3.0 3.2 3.1 3.4 3.3
0.69 0.89 1.19 1.49 1.60
0.44 0.49 0.47 0.55 0.51
1.50 1.77 2.46 2.43 2.79
0.43 0.52 0.51 0.50 0.47
500
0.5 1.0 3.0
2.86 3.62 4.17
3.2 3.6 4.3
1.32 1.68 2.24
0.46 0.46 0.54
2.66 3.39 3.54
0.46 0.45 0.48
M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491
with a further micrograph taken after tilting the sample 1–2; this changes the Bragg diffraction conditions and significantly alters the grey level of each grain in the microstructure. By superimposing these ICC micrographs, it is possible to reveal boundaries that may not be apparent in a given micrograph and generates a nearly complete boundary distribution. In the analysis of grain size distributions by ICC imaging, no attempt was made to differentiate areas containing either LAGBs or HAGBs, although the orientation distribution and boundary character of grains were determined by EBSD (Section 2.2.2). ICC imaging was carried out on various random locations on an electropolished sample with over 1000 grains measured for each annealing condition. The grain boundaries of the greyscale images were skeletonized using standard image analysis techniques, with the area of each grain converted to an equivalent circle diameter. The number of grains, Ni, in each ith size interval, Di (=0.2 lm) was computed for each annealing condition and used to generate a frequency histogram for a given population of grains. Without making any assumptions about the form of the grain size histograms (lognormal, Rayleigh, etc.), the arithmetic mean diameter ðDÞ and standard deviation (r) were computed from the data (Table 1): P N i Di D¼ P ; ð1Þ Ni "P # 2 1=2 N i ðDi DÞ P r¼ : ð2Þ Ni
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3. Results 3.1. Initial microstructure The as-deformed alloy was aged for 3 h at 350 C to generate an equiaxed grain structure of average diameter 1 lm (Fig. 1a). As shown in Fig. 1b, the ageing treatment retained a relatively high-dislocation density within grains (circled) and the boundaries are more complex than a conventional recrystallized microstructure although somewhat
For a lognormal grain size distribution, the microstructure can be characterized in terms of the geometric mean (Dg) and geometric standard deviation (rg): P ðN i ln Di Þ P l ¼ ln Dg ¼ ; ð3Þ Ni "P #1=2 N i ðln Di ln Dg Þ2 P ~ ¼ ln rg ¼ r : ð4Þ Ni 2.2.2. Grain orientations and misorientations Using the DualBeam platform in FEGSEM mode, EBSD was carried out using a TSL OIM system operating with an accelerating voltage and working distance of 10 keV and 10 mm, respectively. A suitable area of microstructure was selected by ICC imaging for analysis by EBSD in beam scanning mode at 1000· to 4000· magnification using a step size of 0.1–1 lm, which corresponds to an area ranging from 100 · 100 to 50 · 50 lm. Consistent with previous work [2,6], a LAGB was defined by a misorientation between adjacent grains (hm) of 1.5 < hm < 15, with hm > 15 representing a HAGB. The lower limit of 1.5 was selected due to the resolution limits of EBSD [25]. Transmission electron microscopy (TEM) was carried out on electropolished thin foils using a Philips CM 200 FEGTEM operating at 200 kV.
Fig. 1. ECAP-deformed and pre-aged Al–Sc alloy: (a) EBSD micrograph (section parallel to extrusion axis); (b) bright field TEM micrograph (courtesy N. Hamilton) and (c) grain size distribution.
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similar to a typical subgrain structure. Intragranular dislocations were not observed by Prangnell et al. [13] and Yu et al. [19] in annealed UFG Al–Mg and AA1050 alloys, respectively, and the dislocations seen in Fig. 1b are probably a result of pinning by fine Al3Sc particles that form after 1000 s at 350 C [22]. Fig. 1c shows the grain size distribution after ageing showing a positive skew and low variance. An EBSD micrograph is given in Fig. 2a showing the distribution of the type of grain boundaries in the preaged microstructure: LAGBs and HAGBs are highlighted as white and black, respectively. The total fraction of HAGBs was 0.7 although the boundary misorientation distribution shows two peaks in the histogram (Fig. 2b) at both low (hm 10) and high misorientations (hm 50); this bimodal boundary distribution is in contrast to a random distribution of grain orientations [5] which is superimposed on the data in Fig. 2b. The distribution of the types of grain boundary was not uniform with Fig. 2c and d showing localized clusters of grains consisting predominantly of HAGBs (>70%) or LAGBs (up to 70%). Within the HAGB regions, the misorientation distribution is close to a random distribution of orientations, whereas the LAGB regions show a distribu-
tion characteristic of a conventional recovered substructure [26,27]. The non-random boundary character distribution, together with the bimodal distribution of boundary misorientations, is comparable to several other studies on severely strained Al alloys (see e.g. Refs. [1–4,6,7]). 3.2. General annealing behaviour and evolution of the initial grain size distribution Microstructural evolution of the pre-aged alloy during annealing at 400–500 C is given by the representative ICC micrographs in Fig. 3a, which show gradual and uniform coarsening of the microstructure with discontinuous coarsening occurring after 5 h at 500 C (see Fig. 7). These micrographs also show a persistent curvature of the grain boundaries, which is particularly evident at high-annealing temperatures. Fig. 3b shows the 2-D distribution of dihedral angles at triple junctions after annealing for 1 h at 400–500 C, showing that the distribution is close to normal with an average angle of 120. Fig. 4 gives the mean grain diameter (D3) as a function of time at annealing temperatures of 400–500 C, and shows a moderate rate of grain coarsening at low temperatures and a general broad-
Fig. 2. (a) EBSD micrograph of the pre-aged alloy showing LAGBs as white lines and HAGBs as black lines. Misorientation distribution of adjacent grains of: (b) entire region in (a) with the superimposed theoretical distribution for an aggregate of randomly oriented grains [5]; (c) HAGB-rich region and (d) LAGB-rich region.
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Fig. 4. Arithmetic mean grain size (D3) as a function of time during annealing in the continuous coarsening regime (the significance of D3 vs. t is discussed in Section 4.3).
Fig. 3. (a) Ion-channeling contrast (ICC) micrographs (obtained by FIB) of the pre-aged alloy after annealing for 1 and 3 h at 400–500 C. (b) Distribution of dihedral angles at triple junctions after annealing for 1 h at 400–500 C.
ening of the grain size distribution, as shown in Table 1. The general grain boundary characteristics of the UFG alloy during continuous coarsening are consistent with that observed during subgrain growth and normal grain growth where boundary curvature governs migration [2]. It is per-
tinent to note that the HAGB% remains unchanged (70%) during continuous coarsening, which is consistent with that observed in other SPD-UFG Al alloys [13,14,28]. A better understanding of grain coarsening may be achieved from experimental grain size frequency histograms, with Fig. 5 showing typical results after annealing for 1 h at 400–500 C and for 3 h at 500 C. Superimposed on the frequency histograms are the lognormal and Rayleigh probability distributions; a more detailed comparison is given in Section 4.1. Similar to the pre-aged material, the grain size data are positively skewed but there is a decrease in peak frequency and a moderate broadening of the size distribution during annealing, which is particularly notable after 3 h at 500 C. The general form of the grain size distributions in this alloy are similar to that found by Morris and Munoz-Morris [16] and Yu et al. [19] on annealed, ECAP-deformed Al alloys, although these workers did not comment on the nature of the distributions. The data in Fig. 5 are replotted in Fig. 6 as normalized frequency as a function of logðD=DÞ, showing the invariant nature of size distribution, although some deviation is seen after 3 h at 500 C. The invariant coarsening behaviour shown in Fig. 6 after normalizing the data is interesting since both subgrain growth after deformation [27] and normal grain growth after recrystallization [29,30] are not expected to show a decrease in the peak frequency of the grain size distribution during coarsening. 3.3. Onset of discontinuous grain coarsening The microstructure was highly stable, with discontinuous coarsening occurring only after extended annealing at 500 C. Table 1 includes data of the ratio of the maximum grain diameter to the mean diameter, showing that Dmax =D < 4 for most annealing conditions, but this value increases with increasing grain diameter with
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Fig. 5. Grain size distributions after annealing for 1 h at (a) 400 C, (b) 450 C and (c) 500 C, and (d) 3 h at 500 C. Superimposed on these histograms is the best fit for both the lognormal and Rayleigh probability distribution (see text).
Dmax =D ¼ 4:3 after 3 h at 500 C. Slightly longer times (5 h) result in discontinuous coarsening to a bimodal grain size with Dmax =D > 20 [31]. Fig. 7a shows a typical region after extended annealing (5 h) at 500 C showing both large (>500 lm) and fine (<20 lm) grains coexisting; the latter are often present as individual grains contained completely within the coarse grains (arrowed). It is possible that these island-type grains are a sectioning effect involving protruding segments of an irregularly shaped subsurface grain. However, the fine grains within large grains in Fig. 7a have different orientations and, hence, are likely to be different grains. Using FIB, several of these grains were sectioned
Fig. 6. Normalized grain size distributions of the pre-aged alloy and after annealing for 1 h at 400–500 C and for 3 h at 500 C (advanced stages of continuous coarsening).
perpendicular to the polished face with Fig. 4b and c showing a grain of 20 lm sectioned to reveal no connectivity with other grains, i.e. it is likely to be an island grain. These types of grains have been observed in a range of deformed and annealed Al alloys [32–34], and are thought to form due to differences in the growth rate of recrystallizing grains due to a range of boundary mobilities [35]. 4. Discussion 4.1. Comparison of experimental and theoretical grain size distributions A number of continuous probability distributions have been compared with experimental data in an attempt to gain a more fundamental understanding of normal subgrain/grain growth processes [2]. Hillert [36] proposed a statistical theory of normal grain growth based on the assumption that grain boundary velocity is inversely proportional to its radius of curvature and generated the corresponding grain size distribution during grain growth. However, the grain size distribution derived from theory exhibited both a narrower range of grain sizes and a higher maximum frequency than that observed experimentally. Barmak et al. [20] showed that the empirical gamma probability distribution closely represents the experimental grain size distributions in nanocrystalline aluminium thin films. The general form of this distribution is [37]:
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Fig. 8. Residue of the fitted grain size probability distribution and experimental distribution ð½P ðDÞ f ðDÞDi Þt;T as a function of grain size for: (a) Rayleigh distribution and (b) lognormal distribution.
Fig. 7. (a) EBSD micrograph of the bimodal grain structure after annealing for 5 h at 500 C. (b) ICC micrograph of a potential island grain and (c) ion milled region through a small grain in (a) showing boundary features below the polish surface.
Da1 D exp P ðDÞ ¼ a R 1 a1 ; b b 0 D expðDÞ dD
ð5Þ
where D is the grain size and a and b are independent fitting parameters corresponding to the median and logarithm of the standard deviation, respectively. Barmak et al. [20] also pointed out that this distribution is similar in form to the lognormal distribution; the latter is known to adequately describe the grain size distribution of both subgrains [27] and grains in bulk metals [38], and thin films [20,21], and is given as [37]: " 2 # 1 1 ln D l pffiffiffiffiffiffi exp P ðDÞ ¼ ; ð6Þ ~ 2 r D~ r 2p
~ are the mean and standard deviation of ln D, where l and r respectively. The lognormal distribution does not describe all subgrain/grain growth data, with various studies showing that the grain size distribution in bulk recrystallized metals is better characterized by the Rayleigh distribution [26]. A model of grain growth propounded by Louat [39] actually predicts an invariant Rayleigh grain size distribution, although this model was argued to violate volume conservation [40]. The general form of the Rayleigh distribution is: D D2 ð7Þ P ðDÞ ¼ 2 exp 2 : b 2b The grain size histograms for the annealing conditions given in Table 1 are compared with both the lognormal and Rayleigh distribution using an iterative routine in Origin 6.0 analysis software for calculating the parameters ~ and b. The grain size histograms in Fig. 5 are typexp(l), r ical of all distributions found in the present work and are shown together with the fitted lognormal and Rayleigh distributions. The lognormal distribution appears to be a better fit of the data at both low and high temperatures, with both distributions showing a good fit at 450 C. A more rigorous comparison of Eqs. (6) and (7) with the experimental data was achieved by plotting, for a given grain size class, Di, the residue of the expected and actual frequency, i.e. ð½P ðDÞ f ðDÞDi Þt;T . This parameter is plotted in Fig. 8 for all grain size classes after annealing for 1 h at 400– 500 C (for clarity, data for the other annealing conditions
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are not given). The maximum deviation, ð½P ðDÞ f ðDÞDi Þmax , for the Rayleigh distribution is ±5% at small grain sizes, which is slightly greater than the lognormal distribution (<±3%); this suggests that the grain size data are closer to lognormal throughout annealing. Fig. 9 shows the fitted lognormal grain size distributions during annealing at 400–500 C, showing an increase in the mean diameter, decrease in peak frequency and a broadening of the distribution with increasing annealing time. A comparison of the arithmetic mean grain size ðDÞ and standard deviation (r) of the data with computed values (Dc and rc), derived from the fitted lognormal distributions, allows a rigorous analysis of the entire dataset. Both ~ by the following relations Dc and rc are related to l and r [37,41]: ~2 =2Þ; Dc ¼ expðl þ r pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ~2 Þðexpð~ rc ¼ expð2l þ r r2 Þ 1Þ:
ð8Þ ð9Þ
Fig. 10 shows, for all annealing conditions, the relationship between the experimental and computed values of the mean and standard deviation, respectively. The computed statistical parameters correspond closely to the measured values for a wide range of annealing conditions, although extended annealing (3 h) at 500 C results in rc < r, thereby indicating some variation from lognormality. Indeed, this annealing condition corresponds to the lower limit for the transition from continuous grain coarsening to discontinuous coarsening [31]. Based on the above 2-D microstructural analysis of the Al–Sc alloy, continuous grain coarsening has the following characteristics:
Fig. 9. Fitted lognormal grain size distributions (Eq. (6)) after annealing for various times at 400, 450 and 500 C showing the broadening of the distribution and slight increase in skewness after extended annealing at high temperatures.
Fig. 10. Comparison between measured arithmetic mean grain size and standard deviation with the calculated parameters generated from the fitted lognormal distribution for a given annealing condition.
M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491
1. The starting grain size distribution is close to lognormal (Fig. 1c) and remains lognormal throughout annealing (Figs. 5, 8 and 10). 2. The normalized grain size distribution with respect to frequency is self-similar during coarsening, i.e. f^ ðD=D; t; T Þ ¼ constant (Fig. 6). 3. With increasing grain size, there is a considerable decrease in peak frequency and moderate broadening of the grain size distribution (Fig. 9). 4. Grain boundaries remain characteristically curved with a normal distribution of dihedral angles at triple junctions and a mean value of 120 (Fig. 3). 5. There are no major changes to either the starting texture or HAGB fraction during annealing. 6. Grain coarsening appears to be spatially uniform despite the variation in grain boundary character throughout the microstructure. The evidence suggests that grain coarsening in the UFG alloy is topographically similar to normal subgrain growth or grain growth; the latter processes are known to be driven by the reduction in stored energy by grain boundary migration [2]. However, a notable feature of grain coarsening in the present alloy is the broadening of the grain size distribution with the corresponding normalized distribution remaining time/temperature invariant (Fig. 6). This contrasts the expected behaviour for normal grain growth where the grain size frequency distribution is argued to remain self-similar throughout annealing [29], as found experimentally in some materials [29,30] and predicted in 2-D simulations of normal grain growth [42,43]. However, Huang and Humphreys [27] observed a significant broadening of the subgrain size distribution during subgrain growth in Goss-oriented Al–Si single crystals (see e.g. Fig. 8 in Ref. [27]) with Barmak et al. [20] observing similar behaviour during annealing of 100 nm thick Al films. In general, experimental grain growth data are surprisingly sparse to either confirm or refute the idea that a broadening of the size distribution is characteristic behaviour of normal subgrain/grain growth.
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and discontinuous grain coarsening [31]. With particles present, the local variations in boundary character do not appear to affect the spatial uniformity of grain coarsening, i.e. the grain size distribution of any given region of the microstructure is indistinguishable from other regions. Such uniform coarsening can be explained by a simple analytical model of the effect of fine particles on grain coarsening within an orientation gradient [7]. The rate of grain coarsening (dD/dt) within an orientation gradient (X), defined as the rate of accumulation of orientation, h, over a given distance, x, of microstructure (dh/dx), is given as: dD aMcm Mf cm ¼ ; ½h0 þ XðD D0 dt hm kr
ð10Þ
where a is a constant close to unity, M is the grain boundary mobility, h0 and D0 are the initial values of the average grain misorientation (h) and the diameter, respectively, f is the particle volume fraction, D and r are the grain diameter and particle radius, respectively, and cm is the HAGB energy when the misorientation reaches hm [2]. A typical outcome of the model is shown in Fig. 11, which illustrates the influence of a dispersion of fine particles (given as the dispersion parameter, f/r) on the rate of grain coarsening for a range of orientation gradients. The rate of grain coarsening is given after an arbitrary time (i.e. 200 s) normalized with respect to the rate of coarsening of a uniform, particle-free microstructure (X = 0, f/r = 0). Since most Al alloys contain relatively few fine particles (f/r < 0.1 lm1), values of X typically generated by ECAP (up to 10 lm1) will significantly influence grain coarsening in these regions compared with other, more uniform regions. Hence, particle-free UFG alloys are expected to be unstable against discontinuous grain coarsening, as demonstrated by a number of researchers [1–7,15–19]. In contrast, alloys with a large f/r-value (i.e. >1.0 lm1) tend to
4.2. Spatial uniformity of grain coarsening during annealing Despite the similarities in grain coarsening of the present alloy with the more conventional processes of static recovery and grain growth, ECAP usually generates considerable variation in the spatial distribution of the type of grain boundaries [6]. A recent study on a similar Al–Sc alloy has shown that ECAP generates localized orientation gradients (X) of up to 8 lm1 [6,7]. In single-phase UFG alloys produced by ECAP, such microstructural heterogeneities, in conjunction with the high stored energy associated with the fine grain size, result in favourable conditions for rapid grain coarsening circumvented by recrystallization at low homologous temperatures [15–19]. The present alloy contains a dispersion of extremely fine Al3Sc particles that are known to suppress both continuous
Fig. 11. Rate of grain coarsening as a function of orientation gradient, X. The growth rates are normalized with respect to a particle-free system exhibiting grains with a random distribution of orientations.
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Table 2 Grain-coarsening data for various UFG alloys processed by SPD Alloy
Processing route
True strain
Annealing range (K)
D0 ðlmÞ n Q Q/Qgba (kJ mol1)
Q/Qbb
Notes
Current work
Al–0.3% Sc
9.6
673–773
1.0
3 165
1.92
1.16
Wang et al. [51]
Al–3% Mg
4
443–803
0.2
2 30
0.35
0.21
Park et al. [52]
Al–3% Mg
4
443–803
0.2
5 99
1.15
0.70
Isothermal anneal; ICC-FIB analysis; Pre-aged starting material; nvalue determined from data Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2 Reanalysis of data in Ref. [51] using different n-values
Yu et al. [19]
AA1050 Al
ECAP-Bc @ RT ECAP + rolling @ RT ECAP + rolling @ RT ECAP @ RT
8
573–623
0.35–0.6 2 49
0.57
0.35
4–8
693–963
0.27
5 174–179
1.06–1.09
0.62–0.64
1–3 4 4
437–673
2.5
473–523 523–673 –
2.5
2 34 (1–3) 31 (4) 2 70 25 – 94c
0.37 (1–3) 0.34 (4) 0.78 0.27 0.90
0.2 (1–3) 0.18 (4) 0.52 0.18 0.47
Park and Shin [53] Fe–0.15% C Kim [54]
AZ31 Mg
Kima and Kim [55] AZ31 Mg Jiang et al. [56] a b c
Cu
ECAP-C @ 623 K ECAP-Bc @ RT ECAP-Bc@ 473–523 K High Pressure Torsion
4
0.2
Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2 Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2 Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2 Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2; Three distinct coarsening regimes Anisothermal DSC analysis; TEM analysis; Direct anneal after ECAP
gb, grain boundary diffusion. b, bulk (lattice) diffusion. Calculated using DSC data.
coarsen slowly due to grain boundary pinning, with local orientation gradients produced by SPD not affecting the rate of grain coarsening on a local scale. The shaded zone in Fig. 11 shows the conditions expected for the Al–0.3Sc alloy [31], and demonstrates that local variations in X do not influence the overall process of grain coarsening. Such a tempering effect on the variability of the rate of grain coarsening is supported by recent work on a similar alloy system [6].
4.3. Possible mechanism(s) of grain coarsening in UFG alloys
Coarsening of a polycrystalline aggregate is often analysed using the following relation [2]: Dn D0n Q ¼ c1 exp ; ð11Þ RT t
where D0 and D are the initial and final arithmetic mean grain diameter (at time, t), respectively, n is the grain
Fig. 12. Bright-field TEM micrographs taken from the extrusion direction and corresponding selected area electron diffraction patterns showing microstructural evolution during pre-ageing at 350 C (courtesy N. Hamilton).
M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491
Source
M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491
growth exponent, c1 is a constant, T is absolute temperature and Q is an activation energy term. Q-values computed from Eq. (11) are often used to interpret the mechanism of grain coarsening [2]. Investigations on subgrain growth and normal grain growth have shown that coarsening occurs typically by boundary migration controlled by bulk diffusion [2]. The movement of grain boundary triple junctions to reduce boundary curvature is also a possible mechanism of coarsening, although recent molecular dynamics simulations have shown that this may only be significant for grain sizes considerably less than 100 nm [44]. The grain-coarsening data in Table 1 are analysed using Eq. (11) with n = 3 providing a good fit for all annealing temperatures (r2 > 0.95) (Fig. 4), which is consistent with a similar UFG Al–Sc alloy [6]. The activation energy, calculated to be 165 kJ mol1, is higher than the activation energy for bulk diffusion of aluminium (Qb = 142 kJ mol1) [2] and close to that for volume diffu1 sion of scandium in aluminium ðDSc V ¼ 173 kJ mol Þ [45]. This value is also lower than the activation energy for triple junction migration, where QTJ 2Qb [46]. With reference to the Lifshitz–Slyozov–Wagner (LSW) theory of particle coarsening [47,48], n = 3 is expected in the present alloy if grain growth is controlled by Al3Sc particles that coarsen via volume diffusion of scandium in aluminium [49]. Given the values of n and Q obtained for the present, the following relation is applicable: D3 D30 ¼ c2 DSc V t:
ð12Þ
Such coarsening behaviour is similar to other particle-controlled grain-coarsening processes such as the extended recovery in a fine-grained (D0 1 lm) Al–6 wt.% Ni alloy containing 0.1 volume fraction of 0.3 lm diameter NiAl3 particles [50]. Some notable studies of continuous grain coarsening in SPD-UFG alloys are given in Table 2. Several investigators have argued that the mechanism of coarsening may be significantly different to conventional subgrain/grain growth processes [19,51,53–55]. Using isochronal grain size data (single point per temperature), Q-values up to 5· lower than the present alloy were computed. These Q-values are also considerably lower than either Qgb or Qb, although some workers [52,53,56] report values close to Qgb. Hayes et al. [57] showed that the activation energy of grain coarsening in an ECAP-deformed Al–3% Mg alloy was close to Qb and this was comparable to a coarse-grained alloy of the same composition. It is pertinent to note that Q-values computed for many nanocrystalline materials produced by mechanical alloying, electrodeposition, etc., are also close to that for either bulk diffusion or grain boundary diffusion [58]. The very low Q-values computed for several SPD-UFG alloys do not correspond to any simple diffusion process [2], and this may be a consequence of the nature of the microstructure prior to annealing. For example, Fig. 12 shows the evolution of microstructure during pre-ageing in the present alloy where the moderately aligned deforma-
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tion microstructure rapidly converts to an equiaxed structure that exhibits well-defined boundaries and a lower density of internal dislocations. Beyond the transient stage, this well-defined grain structure coarsens in a similar manner to that occurring at higher annealing temperatures. It is interesting to note that in a study of recovery in lightly strained zone-refined iron [59], the activation energy was found to increase from 91 kJ mol1 ð QFe gb Þ at the initial stages of recovery to 220 kJ mol1 (close to QFe b Þ during the latter stages. In the early stages of recovery, dislocation migration, annihilation and the formation of a subgrain structure were reported. These equilibrating processes are similar to that observed in the present alloy during the transient stage, Fig. 12, and similar to the structural changes observed by Prangnell et al. [13] in UFG Al–Mg, and in the directly annealed alloys given in Table 2. These initial relaxation processes occur by different mechanisms to the curvature-driven process of normal subgrain/grain growth (where Q-values close to bulk diffusion are commonly reported [2]). Unlike a conventional recovering substructure, the UFG alloy initially contains a large fraction of HAGBs (0.7). The subsequent homogeneous evolution of the microstructure during annealing, coupled with no significant appreciable change in texture, is consistent with the later stages of continuous recrystallization involving a gradual increase in grain size by general boundary migration. The experimental investigation of Jazaeri and Humphreys [14] and computer simulations by Prangnell et al. [13] have demonstrated that an aligned deformation microstructure generated in SPD Al alloys rapidly collapses into a more stable, equiaxed configuration, with further coarsening occurring mainly by the migration of grain boundaries. On a final note, solute (Sc) atoms may have an effect on grain coarsening in the present alloy. Various theories of solute-engendered grain growth inhibition have been proposed such as those based on (i) solute drag of boundaries (see e.g. Ref. [1, pp. 159–165]), and (ii) solute segregation at boundaries causing a reduction in driving force for their migration due to a decrease in boundary surface energy [60,61]. For the present alloy, there is substantial evidence that grain coarsening is controlled by the pinning effects of fine Al3Sc particles [6]. However, single-phase (very low solute) Al–Sc SMG alloys also show a slower rate of grain coarsening compared with a Sc-free Al alloy of similar starting microstructure [62]. Work is currently underway using atom probe tomography to investigate Sc segregation to grain boundaries during annealing and its influence on grain coarsening. 5. Concluding summary A supersaturated Al–0.3 wt.% Sc alloy was cold deformed by ECAP to an equivalent von Mises strain of 9.2 then pre-aged at 350 C. This ageing treatment generated an UFG alloy of average grain size 1 lm, together
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with a positively skewed grain size distribution. The grain boundaries in this microstructure were more complex than a conventional recrystallized structure, and individual grains retained a considerable number of internal dislocations. Over distances much greater than the grain size, the microstructure contained a non-uniform distribution of LAGBs and HAGBs inherited from the coarse grain size prior to ECAP. The pre-aged microstructure was highly resistant to grain coarsening at temperatures up to 500 C with discontinuous coarsening occurring only after extended annealing. The non-uniform distribution of boundary character produced by ECAP had no apparent influence on grain coarsening on a local scale, with coarsening occurring uniformly throughout the microstructure. A detailed statistical analysis showed that the initial grain size distribution was very close to lognormal and, throughout annealing, remained lognormal but with a slight broadening of the distribution. An analysis of the kinetics of grain coarsening generated a grain growth exponent and activation energy of n = 3 and Q 165 kJ mol1, respectively; the latter is larger than the activation energy for bulk diffusion (142 kJ mol1) but close to that for volume diffusion of scandium in alumin1 ium ðDSc V ¼ 173 kJ mol Þ. The considerable TEM evidence has shown that grain coarsening is controlled by pinning by fine Al3Sc particles. In conjunction with the kinetic parameters, grain coarsening is likely to be controlled by the rate of particle coarsening, which, in turn is controlled by volume diffusion of scandium in aluminium, i.e. D3 D30 ¼ c2 DSc V t. In contrast to a conventional recovering substructure, the UFG alloy initially contains a large fraction of HAGBs (0.7). The subsequent homogeneous evolution of the microstructure during annealing, coupled with no appreciable change in texture, is consistent with the advanced stages of continuous recrystallization involving a gradual increase in grain size by general boundary migration. Based on the evidence presented herein, the UFG alloy coarsens by continuous recrystallization that is structurally and kinetically similar to conventional subgrain growth/grain growth processes in high-stacking fault energy, low-solute alloys. Acknowledgments The authors acknowledge the Australian Research Council (ARC) for supporting this work by an ARC Discovery Grant (DP0342766) and through the ARC Centre of Excellence for Design in Light Metals (CEO561574). References [1] Humphreys FJ, Hatherly M. Recrystallization and Related Annealing Phenomena. 2nd ed. Oxford: Pergamon Press; 2004. [2] Humphreys FJ, Prangnell PB, Bowen JR, Gholinia A, Harris C. Phil Trans Roy Soc A 1999;357:1663.
[3] Valiev RZ, Islamgaliev RK, Alexandrov IV. Prog Mater Sci 2000;45:103. [4] Valiev RZ, Langdon TG. Prog Mater Sci 2006;51:881. [5] McKenzie JK. Biometrica 1958;45:229. [6] Ferry M, Hamilton NE, Humphreys FJ. Acta Mater 2005;53:1097. [7] Ferry M. Acta Mater 2005;53:773. [8] Apps PJ, Berta M, Prangnell PB. Acta Mater 2005;53:499. [9] Berta M, Apps PJ, Prangnell PB. Mater Sci Eng A 2005;410–411:381. [10] Jazaeri H, Humphreys FJ. Acta Mater 2004;52:3239. [11] Driver JH. Scripta Mater 2004;51:819. [12] Humphreys FJ. Acta Mater 1997;45:4231. [13] Prangnell PB, Hayes JS, Bowen JR, Apps PJ, Bate PS. Acta Mater 2004;52:3193. [14] Jazaeri H, Humphreys FJ. Acta Mater 2004;52:3251. [15] Furukawa M, Horita Z, Nemoto Z, Valiev RZ, Langdon TG. Acta Mater 1996;44:4619. [16] Morris DG, Munoz-Morris MA. Acta Mater 2002;50:4047. [17] Horita Z, Fujinami T, Nemoto M, Langdon TG. J Mater Proc Tech 2001;117:288. [18] Cao WQ, Godfrey A, Liu W, Liu Q. J Mater Lett 2003;57:3767. [19] Yu CY, Sun PL, Kao PL, Chang CP. Mater Sci Eng A 2004;366: 310. [20] Barmak K, Archibald WE, Rollett AD, Ta’asam S, Kinderlehrer D. Interfacial engineering for optimized propertiesm III, vol. 89. USA: MRS; 2004. p. 225. [21] Carpenter DT, Rickman JM, Barmak K. J Appl Phys 1998;84:5843. [22] Jones MJ, Humphreys FJ. Acta Mater 2003;51:2149. [23] Forbord B, Auran L, Lefebvre W, Hallem H, Marthinsen K. Mater Sci Eng A 2006;424:174. [24] Manohar PA, Ferry M, Chandra T. ISIJ Int 1998;38:913. [25] Humphreys FJ. J Mater Sci 2001;36:3833. [26] Ferry M, Humphreys FJ. Acta Mater 1996;44:1293. [27] Huang Y, Humphreys FJ. Acta Mater 2000;48:2017. [28] Oscarsson A, Ekstro¨m E-K, Hutchinson BW. Mater Sci Forum 1993;113–115:177. [29] Detert K. In: Haessner F, editor. Recrystallization of metallic materials. Stuttgart: Dr. Riederer Verlag GmbH; 1978. p. 27. [30] Guo M, Suito H. ISIJ Int 1999;39:1169. [31] Ferry M, Burhan N. Scripta Mater 2007;56:525. [32] Chan HM, Humphreys FJ. Acta Metall 1984;32:235. [33] Ardakani MG, Humphreys FJ. Acta Mater 1994;42:763. [34] Ferry M, Humphreys FJ. Acta Mater 1996;44:3089. [35] Humphreys FJ, Ferry M, Johnson MC, Paillard P. In: Hansen N, Juul Jensen D, Liu YL, Ralph B, editors. Proceedings of the 16th international Risø symposium of microstructural and crystallographic aspects of recrystallization, Roskilde, Denmark; 1995. p. 87. [36] Hillert M. Acta Metall 1965;13:227. [37] Underwood EE. Quantitative stereology. Reading, MA: AddisonWesley; 1970. [38] Saetre TO, Hunderi O, Nes E. Acta Metall 1986;34:981. [39] Louat NP. Acta Metall 1974;22:721. [40] Ryum N, Hunderi O. Acta Metall 1989;37:1375. [41] Anderson RL, Bancroft TA. Statistical theory in research. New York: McGraw-Hill; 1952. [42] Srolovitz DJ, Anderson MP, Sahni PS, Grest GS. Acta Metall 1984;32:793. [43] Marthinsen K, Hunderi O, Ryum N. Acta Mater 1996;44:1681. [44] Upmanyu M, Srolovitz DJ, Shvindlerman LS, Gottstein G. Acta Mater 2002;50:1405. [45] Fujikawa S. Defect Diff Forum 1997;143–147:114. [46] Protasova SG, Gottstein G, Sursaeva VG, Shvindlerman LS. Acta Mater 2001;49:2519. [47] Lifshitz IM, Slyozov VV. Phys Chem Solids 1961;19:35. [48] Wagner CZ. Electrochemistry 1961;65:581. [49] Martin JW, Doherty RD. The stability of microstructures in metals. Cambridge: Cambridge University Press; 1976. [50] Morris LR. In: Proceedings of the 4th international conference on strength of metals and alloys. Nancy. p. 649.
M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491 [51] Wang J, Iwahashi Y, Horita Z, Furukawa M, Nemoto M, Valiev RZ, Langdon TG. Acta Mater 1996;44:2973. [52] Park K-T, Kwon H-J, Shin DH. Metal Mater Trans A 2001;32A:2670. [53] Park K-T, Shin DH. Mater Sci Eng A 2002;334:79. [54] Kim H-K. J Mater Sci 2004;39:7107. [55] Kima HK, Kim WJ. Mater Sci Eng A 2004;385:300. [56] Jiang HY, Zhu T, Butt DP, Alexandrov IV, Lowe TC. Mater Sci Eng A 2000;290:128.
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[57] Hayes JS, Prangnell PB, Bate PS. In: Zhu YT et al., editors. Ultrafine grained materials II. Warrendale, PA: TMS; 2002. p. 495. [58] Gleiter H. Acta Mater 2000;48:1. [59] Michalak JT, Paxton HW. Trans Metall Soc AIME 1961;221: 850. [60] Weissmu¨ller J. J Nanostruct Mater 1993;3:261. [61] Kirchheim R. Acta Mater 2002;50:413. [62] Burhan N. PhD Thesis. University of New South Wales; 2007.
Structural and kinetic aspects of continuous grain coarsening in a fine-grained Al–0.3Sc alloy M. Ferry *, N. Burhan School of Materials Science and Engineering, ARC Centre of Excellence for Design in Light Metals, University of New South Wales, UNSW, Sydney, NSW 2052, Australia Received 5 December 2006; received in revised form 30 January 2007; accepted 30 January 2007 Available online 26 March 2007
Abstract A supersaturated Al–0.3 wt.% Sc alloy was produced by equal channel angular pressing to an equivalent von Mises strain of 9.2 then pre-aged at 350 C to generate a starting grain size of 1 lm. The microstructure was highly resistant to grain coarsening at temperatures up to 500 C with discontinuous coarsening only occurring after extended annealing. A detailed statistical analysis showed that the initial grain size distribution was very close to lognormal, and remained lognormal throughout annealing, with the normalized size distribution not affected by time and temperature despite a broadening of the distribution. The homogeneous evolution of the microstructure during annealing, coupled with no appreciable change in texture, is consistent with the advanced stages of continuous recrystallization, and also structurally and kinetically similar to conventional subgrain growth/grain growth in high-stacking fault energy, low-solute alloys. 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Aluminium alloys; Annealing; Equal channel angular pressing (ECAP); Electron backscattering diffraction (EBSD)
1. Introduction Severe plastic deformation (SPD) of high-stacking faulty energy, low-solute alloys by processes such as equal channel angular pressing (ECAP) usually generates a microstructure exhibiting an ultra-fine grain (UFG), sometimes referred to as submicron grain (SMG), size [1–4]. The grain structures in these materials are similar to those of recovered and recrystallized metals [2], although they usually contain irregularly shaped boundaries, indicating a nonequilibrium structure. ECAP can also generate a large fraction (>0.7) of high-angle boundaries (HAGBs) after large strains, but the misorientation distribution between adjacent grains usually takes the form of a frequency histogram exhibiting a peak at both low and high misorientations, indicative of a non-random distribution of grain orientations [5]. Furthermore, the low-angle grain boundaries (LAGBs) and HAGBs are not usually distributed uni*
Corresponding author. E-mail address: [email protected] (M. Ferry).
formly, and localized clusters of grains consisting predominantly of either type of boundary may be present [6–9]. Such variability is affected by factors including the deformation path and strain [2,10], as well as the initial microstructure, with either a dispersion of fine particles or a coarse grain size prior to straining making it more difficult to generate a large and uniform HAGB fraction [9]. Similar to the subgrain and grain structures produced during either recovery or after recrystallization, the SPD-UFG microstructure is inherently unstable with coarsening occurring at elevated temperatures to reduce the stored energy associated with the large surface area of grain boundaries in a given volume of material [2,11]. UFG alloys with HAGB fractions greater than 0.6–0.7 may undergo a uniform coarsening process termed continuous recrystallization, as shown in recent theoretical [12,13] and experimental [14] analyses, with discontinuous coarsening only occurring after extended annealing or at elevated temperature [6,15–19]. A characteristic feature of an equiaxed grain structure produced by recovery or recrystallization is a grain size
1359-6454/$30.00 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2007.01.047
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distribution of a two-dimensional (2-D) section described by probability distributions such as the Hillert, lognormal, Rayleigh and gamma distributions [2]. There is some uncertainty concerning the best fit of experimental data with the various distributions, with some workers arguing that the Rayleigh distribution best describes the grain size distribution in bulk recrystallized metals (see Ref. [2]), whereas, for thin films or foils, the lognormal or gamma distributions show the best fit [20,21]. Regardless of the type of distribution, both subgrain coarsening and grain growth are spatially uniform and the normalized grain size ðD=DÞ is expected to be time invariant [2]. Both coarsening processes are curvature driven with an apparent activation energy comparable to that of either lattice (bulk) or grain boundary diffusion [2]. In comparison, it is not clear if the grain structure of SPD-UFG alloys evolves in a similar manner to these conventional subgrain/grain growth processes. The aim of the present work is to understand the mechanism(s) of grain coarsening in a fine-grained Al–Sc alloy produced by ECAP and to establish if continuous grain coarsening is structurally and kinetically similar to static recovery and normal grain growth. 2. Materials and methods 2.1. Production of starting material and annealing experiments A high-purity Al–0.3 wt.% Sc alloy was chill cast to produce 15 mm diameter ingots, swaged to 10 mm diameter, then solution heat-treated for 48 h at 620 C and cold water quenched. Samples of length 100 mm were deformed at room temperature by ECAP with characteristic angles of U = 90 and w = 0. Deformation was carried out using graphite-based lubricant for a total of eight passes with 90 rotation between each pass to generate an equivalent von Mises strain of 9.2. Following deformation, the alloy was aged for 3 h at 350 C to produce an equiaxed microstructure containing a relatively uniform distribution of
coherent Al3Sc dispersoid particles (see Ref. [6]). The dispersion of fine particles in Al–Sc alloys impede discontinuous recrystallization after rolling [22] and extrusion [23] and grain coarsening after SPD [6] by Zener pinning [24]. The pre-aged samples were annealed for up to 10 h at temperatures of 400, 450 and 500 C, with a limited number of experiments carried out at 550 C. Grain coarsening was investigated using focused ion beam (FIB) microscopy, field emission gun scanning electron microscopy (FEGSEM) and electron backscatter diffraction (EBSD) using an FEI Novalab 200 DualBeam platform. Specimens suitable for imaging by both SEM and FIB were prepared by mechanical grinding and polishing followed by electropolishing at 30 C in a solution of 20% nitric acid in methanol. 2.2. Analysis of microstructure 2.2.1. Grain size distributions For each annealing condition, ion channeling contrast (ICC) imaging was used to determine the grain size distribution. This powerful technique resolves grains below 100 nm in size, which is superior in resolution compared with both EBSD mapping and electron channeling contrast (ECC) imaging and, compared with the latter, generates better-quality orientation contrast images in polycrystalline aluminium [6]. For grain size measurements by EBSD, Humphreys [25] showed that an error in grain size measurement of less than 10% requires at least five steps per grain. While the starting grain size of the Al–Sc alloy is 1 lm, grains as fine as 100 nm were present in the microstructure. Hence, an EBSD step size of <20 nm is required to accurately determine the grain size distribution, which equates to over six million data points for a single 50 · 50 lm area. A further limitation of EBSD is the resolvable misorientation of adjacent grains, which, for a standard system, is at least 0.5 [25]. It is possible to achieve a high-angular resolution using ICC (<0.5) by taking an ICC micrograph of a given area of microstructure
Table 1 Grain size parameters and statistical data after annealing at various times and temperatures Temperature (C)
Time (h)
Mean diameter, D ðlmÞ (Eq. (1))
Dmax =D [31]
Standard deviation, r (lm) (Eq. (2))
r=D
Geometric mean diameter, Dg
Geometric standard deviation, rg
400
0.5 1.0 3.0 5.0 10.0
1.39 1.41 1.51 1.61 1.86
2.3 2.4 2.9 2.6 2.7
0.50 0.49 0.58 0.65 0.72
0.36 0.35 0.38 0.40 0.39
1.39 1.40 1.46 1.57 1.80
0.39 0.38 0.42 0.42 0.39
450
0.5 1.0 3.0 5.0 10.0
1.58 1.83 2.56 2.73 3.15
3.0 3.2 3.1 3.4 3.3
0.69 0.89 1.19 1.49 1.60
0.44 0.49 0.47 0.55 0.51
1.50 1.77 2.46 2.43 2.79
0.43 0.52 0.51 0.50 0.47
500
0.5 1.0 3.0
2.86 3.62 4.17
3.2 3.6 4.3
1.32 1.68 2.24
0.46 0.46 0.54
2.66 3.39 3.54
0.46 0.45 0.48
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with a further micrograph taken after tilting the sample 1–2; this changes the Bragg diffraction conditions and significantly alters the grey level of each grain in the microstructure. By superimposing these ICC micrographs, it is possible to reveal boundaries that may not be apparent in a given micrograph and generates a nearly complete boundary distribution. In the analysis of grain size distributions by ICC imaging, no attempt was made to differentiate areas containing either LAGBs or HAGBs, although the orientation distribution and boundary character of grains were determined by EBSD (Section 2.2.2). ICC imaging was carried out on various random locations on an electropolished sample with over 1000 grains measured for each annealing condition. The grain boundaries of the greyscale images were skeletonized using standard image analysis techniques, with the area of each grain converted to an equivalent circle diameter. The number of grains, Ni, in each ith size interval, Di (=0.2 lm) was computed for each annealing condition and used to generate a frequency histogram for a given population of grains. Without making any assumptions about the form of the grain size histograms (lognormal, Rayleigh, etc.), the arithmetic mean diameter ðDÞ and standard deviation (r) were computed from the data (Table 1): P N i Di D¼ P ; ð1Þ Ni "P # 2 1=2 N i ðDi DÞ P r¼ : ð2Þ Ni
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3. Results 3.1. Initial microstructure The as-deformed alloy was aged for 3 h at 350 C to generate an equiaxed grain structure of average diameter 1 lm (Fig. 1a). As shown in Fig. 1b, the ageing treatment retained a relatively high-dislocation density within grains (circled) and the boundaries are more complex than a conventional recrystallized microstructure although somewhat
For a lognormal grain size distribution, the microstructure can be characterized in terms of the geometric mean (Dg) and geometric standard deviation (rg): P ðN i ln Di Þ P l ¼ ln Dg ¼ ; ð3Þ Ni "P #1=2 N i ðln Di ln Dg Þ2 P ~ ¼ ln rg ¼ r : ð4Þ Ni 2.2.2. Grain orientations and misorientations Using the DualBeam platform in FEGSEM mode, EBSD was carried out using a TSL OIM system operating with an accelerating voltage and working distance of 10 keV and 10 mm, respectively. A suitable area of microstructure was selected by ICC imaging for analysis by EBSD in beam scanning mode at 1000· to 4000· magnification using a step size of 0.1–1 lm, which corresponds to an area ranging from 100 · 100 to 50 · 50 lm. Consistent with previous work [2,6], a LAGB was defined by a misorientation between adjacent grains (hm) of 1.5 < hm < 15, with hm > 15 representing a HAGB. The lower limit of 1.5 was selected due to the resolution limits of EBSD [25]. Transmission electron microscopy (TEM) was carried out on electropolished thin foils using a Philips CM 200 FEGTEM operating at 200 kV.
Fig. 1. ECAP-deformed and pre-aged Al–Sc alloy: (a) EBSD micrograph (section parallel to extrusion axis); (b) bright field TEM micrograph (courtesy N. Hamilton) and (c) grain size distribution.
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similar to a typical subgrain structure. Intragranular dislocations were not observed by Prangnell et al. [13] and Yu et al. [19] in annealed UFG Al–Mg and AA1050 alloys, respectively, and the dislocations seen in Fig. 1b are probably a result of pinning by fine Al3Sc particles that form after 1000 s at 350 C [22]. Fig. 1c shows the grain size distribution after ageing showing a positive skew and low variance. An EBSD micrograph is given in Fig. 2a showing the distribution of the type of grain boundaries in the preaged microstructure: LAGBs and HAGBs are highlighted as white and black, respectively. The total fraction of HAGBs was 0.7 although the boundary misorientation distribution shows two peaks in the histogram (Fig. 2b) at both low (hm 10) and high misorientations (hm 50); this bimodal boundary distribution is in contrast to a random distribution of grain orientations [5] which is superimposed on the data in Fig. 2b. The distribution of the types of grain boundary was not uniform with Fig. 2c and d showing localized clusters of grains consisting predominantly of HAGBs (>70%) or LAGBs (up to 70%). Within the HAGB regions, the misorientation distribution is close to a random distribution of orientations, whereas the LAGB regions show a distribu-
tion characteristic of a conventional recovered substructure [26,27]. The non-random boundary character distribution, together with the bimodal distribution of boundary misorientations, is comparable to several other studies on severely strained Al alloys (see e.g. Refs. [1–4,6,7]). 3.2. General annealing behaviour and evolution of the initial grain size distribution Microstructural evolution of the pre-aged alloy during annealing at 400–500 C is given by the representative ICC micrographs in Fig. 3a, which show gradual and uniform coarsening of the microstructure with discontinuous coarsening occurring after 5 h at 500 C (see Fig. 7). These micrographs also show a persistent curvature of the grain boundaries, which is particularly evident at high-annealing temperatures. Fig. 3b shows the 2-D distribution of dihedral angles at triple junctions after annealing for 1 h at 400–500 C, showing that the distribution is close to normal with an average angle of 120. Fig. 4 gives the mean grain diameter (D3) as a function of time at annealing temperatures of 400–500 C, and shows a moderate rate of grain coarsening at low temperatures and a general broad-
Fig. 2. (a) EBSD micrograph of the pre-aged alloy showing LAGBs as white lines and HAGBs as black lines. Misorientation distribution of adjacent grains of: (b) entire region in (a) with the superimposed theoretical distribution for an aggregate of randomly oriented grains [5]; (c) HAGB-rich region and (d) LAGB-rich region.
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Fig. 4. Arithmetic mean grain size (D3) as a function of time during annealing in the continuous coarsening regime (the significance of D3 vs. t is discussed in Section 4.3).
Fig. 3. (a) Ion-channeling contrast (ICC) micrographs (obtained by FIB) of the pre-aged alloy after annealing for 1 and 3 h at 400–500 C. (b) Distribution of dihedral angles at triple junctions after annealing for 1 h at 400–500 C.
ening of the grain size distribution, as shown in Table 1. The general grain boundary characteristics of the UFG alloy during continuous coarsening are consistent with that observed during subgrain growth and normal grain growth where boundary curvature governs migration [2]. It is per-
tinent to note that the HAGB% remains unchanged (70%) during continuous coarsening, which is consistent with that observed in other SPD-UFG Al alloys [13,14,28]. A better understanding of grain coarsening may be achieved from experimental grain size frequency histograms, with Fig. 5 showing typical results after annealing for 1 h at 400–500 C and for 3 h at 500 C. Superimposed on the frequency histograms are the lognormal and Rayleigh probability distributions; a more detailed comparison is given in Section 4.1. Similar to the pre-aged material, the grain size data are positively skewed but there is a decrease in peak frequency and a moderate broadening of the size distribution during annealing, which is particularly notable after 3 h at 500 C. The general form of the grain size distributions in this alloy are similar to that found by Morris and Munoz-Morris [16] and Yu et al. [19] on annealed, ECAP-deformed Al alloys, although these workers did not comment on the nature of the distributions. The data in Fig. 5 are replotted in Fig. 6 as normalized frequency as a function of logðD=DÞ, showing the invariant nature of size distribution, although some deviation is seen after 3 h at 500 C. The invariant coarsening behaviour shown in Fig. 6 after normalizing the data is interesting since both subgrain growth after deformation [27] and normal grain growth after recrystallization [29,30] are not expected to show a decrease in the peak frequency of the grain size distribution during coarsening. 3.3. Onset of discontinuous grain coarsening The microstructure was highly stable, with discontinuous coarsening occurring only after extended annealing at 500 C. Table 1 includes data of the ratio of the maximum grain diameter to the mean diameter, showing that Dmax =D < 4 for most annealing conditions, but this value increases with increasing grain diameter with
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Fig. 5. Grain size distributions after annealing for 1 h at (a) 400 C, (b) 450 C and (c) 500 C, and (d) 3 h at 500 C. Superimposed on these histograms is the best fit for both the lognormal and Rayleigh probability distribution (see text).
Dmax =D ¼ 4:3 after 3 h at 500 C. Slightly longer times (5 h) result in discontinuous coarsening to a bimodal grain size with Dmax =D > 20 [31]. Fig. 7a shows a typical region after extended annealing (5 h) at 500 C showing both large (>500 lm) and fine (<20 lm) grains coexisting; the latter are often present as individual grains contained completely within the coarse grains (arrowed). It is possible that these island-type grains are a sectioning effect involving protruding segments of an irregularly shaped subsurface grain. However, the fine grains within large grains in Fig. 7a have different orientations and, hence, are likely to be different grains. Using FIB, several of these grains were sectioned
Fig. 6. Normalized grain size distributions of the pre-aged alloy and after annealing for 1 h at 400–500 C and for 3 h at 500 C (advanced stages of continuous coarsening).
perpendicular to the polished face with Fig. 4b and c showing a grain of 20 lm sectioned to reveal no connectivity with other grains, i.e. it is likely to be an island grain. These types of grains have been observed in a range of deformed and annealed Al alloys [32–34], and are thought to form due to differences in the growth rate of recrystallizing grains due to a range of boundary mobilities [35]. 4. Discussion 4.1. Comparison of experimental and theoretical grain size distributions A number of continuous probability distributions have been compared with experimental data in an attempt to gain a more fundamental understanding of normal subgrain/grain growth processes [2]. Hillert [36] proposed a statistical theory of normal grain growth based on the assumption that grain boundary velocity is inversely proportional to its radius of curvature and generated the corresponding grain size distribution during grain growth. However, the grain size distribution derived from theory exhibited both a narrower range of grain sizes and a higher maximum frequency than that observed experimentally. Barmak et al. [20] showed that the empirical gamma probability distribution closely represents the experimental grain size distributions in nanocrystalline aluminium thin films. The general form of this distribution is [37]:
M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491
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Fig. 8. Residue of the fitted grain size probability distribution and experimental distribution ð½P ðDÞ f ðDÞDi Þt;T as a function of grain size for: (a) Rayleigh distribution and (b) lognormal distribution.
Fig. 7. (a) EBSD micrograph of the bimodal grain structure after annealing for 5 h at 500 C. (b) ICC micrograph of a potential island grain and (c) ion milled region through a small grain in (a) showing boundary features below the polish surface.
Da1 D exp P ðDÞ ¼ a R 1 a1 ; b b 0 D expðDÞ dD
ð5Þ
where D is the grain size and a and b are independent fitting parameters corresponding to the median and logarithm of the standard deviation, respectively. Barmak et al. [20] also pointed out that this distribution is similar in form to the lognormal distribution; the latter is known to adequately describe the grain size distribution of both subgrains [27] and grains in bulk metals [38], and thin films [20,21], and is given as [37]: " 2 # 1 1 ln D l pffiffiffiffiffiffi exp P ðDÞ ¼ ; ð6Þ ~ 2 r D~ r 2p
~ are the mean and standard deviation of ln D, where l and r respectively. The lognormal distribution does not describe all subgrain/grain growth data, with various studies showing that the grain size distribution in bulk recrystallized metals is better characterized by the Rayleigh distribution [26]. A model of grain growth propounded by Louat [39] actually predicts an invariant Rayleigh grain size distribution, although this model was argued to violate volume conservation [40]. The general form of the Rayleigh distribution is: D D2 ð7Þ P ðDÞ ¼ 2 exp 2 : b 2b The grain size histograms for the annealing conditions given in Table 1 are compared with both the lognormal and Rayleigh distribution using an iterative routine in Origin 6.0 analysis software for calculating the parameters ~ and b. The grain size histograms in Fig. 5 are typexp(l), r ical of all distributions found in the present work and are shown together with the fitted lognormal and Rayleigh distributions. The lognormal distribution appears to be a better fit of the data at both low and high temperatures, with both distributions showing a good fit at 450 C. A more rigorous comparison of Eqs. (6) and (7) with the experimental data was achieved by plotting, for a given grain size class, Di, the residue of the expected and actual frequency, i.e. ð½P ðDÞ f ðDÞDi Þt;T . This parameter is plotted in Fig. 8 for all grain size classes after annealing for 1 h at 400– 500 C (for clarity, data for the other annealing conditions
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M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491
are not given). The maximum deviation, ð½P ðDÞ f ðDÞDi Þmax , for the Rayleigh distribution is ±5% at small grain sizes, which is slightly greater than the lognormal distribution (<±3%); this suggests that the grain size data are closer to lognormal throughout annealing. Fig. 9 shows the fitted lognormal grain size distributions during annealing at 400–500 C, showing an increase in the mean diameter, decrease in peak frequency and a broadening of the distribution with increasing annealing time. A comparison of the arithmetic mean grain size ðDÞ and standard deviation (r) of the data with computed values (Dc and rc), derived from the fitted lognormal distributions, allows a rigorous analysis of the entire dataset. Both ~ by the following relations Dc and rc are related to l and r [37,41]: ~2 =2Þ; Dc ¼ expðl þ r pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ~2 Þðexpð~ rc ¼ expð2l þ r r2 Þ 1Þ:
ð8Þ ð9Þ
Fig. 10 shows, for all annealing conditions, the relationship between the experimental and computed values of the mean and standard deviation, respectively. The computed statistical parameters correspond closely to the measured values for a wide range of annealing conditions, although extended annealing (3 h) at 500 C results in rc < r, thereby indicating some variation from lognormality. Indeed, this annealing condition corresponds to the lower limit for the transition from continuous grain coarsening to discontinuous coarsening [31]. Based on the above 2-D microstructural analysis of the Al–Sc alloy, continuous grain coarsening has the following characteristics:
Fig. 9. Fitted lognormal grain size distributions (Eq. (6)) after annealing for various times at 400, 450 and 500 C showing the broadening of the distribution and slight increase in skewness after extended annealing at high temperatures.
Fig. 10. Comparison between measured arithmetic mean grain size and standard deviation with the calculated parameters generated from the fitted lognormal distribution for a given annealing condition.
M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491
1. The starting grain size distribution is close to lognormal (Fig. 1c) and remains lognormal throughout annealing (Figs. 5, 8 and 10). 2. The normalized grain size distribution with respect to frequency is self-similar during coarsening, i.e. f^ ðD=D; t; T Þ ¼ constant (Fig. 6). 3. With increasing grain size, there is a considerable decrease in peak frequency and moderate broadening of the grain size distribution (Fig. 9). 4. Grain boundaries remain characteristically curved with a normal distribution of dihedral angles at triple junctions and a mean value of 120 (Fig. 3). 5. There are no major changes to either the starting texture or HAGB fraction during annealing. 6. Grain coarsening appears to be spatially uniform despite the variation in grain boundary character throughout the microstructure. The evidence suggests that grain coarsening in the UFG alloy is topographically similar to normal subgrain growth or grain growth; the latter processes are known to be driven by the reduction in stored energy by grain boundary migration [2]. However, a notable feature of grain coarsening in the present alloy is the broadening of the grain size distribution with the corresponding normalized distribution remaining time/temperature invariant (Fig. 6). This contrasts the expected behaviour for normal grain growth where the grain size frequency distribution is argued to remain self-similar throughout annealing [29], as found experimentally in some materials [29,30] and predicted in 2-D simulations of normal grain growth [42,43]. However, Huang and Humphreys [27] observed a significant broadening of the subgrain size distribution during subgrain growth in Goss-oriented Al–Si single crystals (see e.g. Fig. 8 in Ref. [27]) with Barmak et al. [20] observing similar behaviour during annealing of 100 nm thick Al films. In general, experimental grain growth data are surprisingly sparse to either confirm or refute the idea that a broadening of the size distribution is characteristic behaviour of normal subgrain/grain growth.
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and discontinuous grain coarsening [31]. With particles present, the local variations in boundary character do not appear to affect the spatial uniformity of grain coarsening, i.e. the grain size distribution of any given region of the microstructure is indistinguishable from other regions. Such uniform coarsening can be explained by a simple analytical model of the effect of fine particles on grain coarsening within an orientation gradient [7]. The rate of grain coarsening (dD/dt) within an orientation gradient (X), defined as the rate of accumulation of orientation, h, over a given distance, x, of microstructure (dh/dx), is given as: dD aMcm Mf cm ¼ ; ½h0 þ XðD D0 dt hm kr
ð10Þ
where a is a constant close to unity, M is the grain boundary mobility, h0 and D0 are the initial values of the average grain misorientation (h) and the diameter, respectively, f is the particle volume fraction, D and r are the grain diameter and particle radius, respectively, and cm is the HAGB energy when the misorientation reaches hm [2]. A typical outcome of the model is shown in Fig. 11, which illustrates the influence of a dispersion of fine particles (given as the dispersion parameter, f/r) on the rate of grain coarsening for a range of orientation gradients. The rate of grain coarsening is given after an arbitrary time (i.e. 200 s) normalized with respect to the rate of coarsening of a uniform, particle-free microstructure (X = 0, f/r = 0). Since most Al alloys contain relatively few fine particles (f/r < 0.1 lm1), values of X typically generated by ECAP (up to 10 lm1) will significantly influence grain coarsening in these regions compared with other, more uniform regions. Hence, particle-free UFG alloys are expected to be unstable against discontinuous grain coarsening, as demonstrated by a number of researchers [1–7,15–19]. In contrast, alloys with a large f/r-value (i.e. >1.0 lm1) tend to
4.2. Spatial uniformity of grain coarsening during annealing Despite the similarities in grain coarsening of the present alloy with the more conventional processes of static recovery and grain growth, ECAP usually generates considerable variation in the spatial distribution of the type of grain boundaries [6]. A recent study on a similar Al–Sc alloy has shown that ECAP generates localized orientation gradients (X) of up to 8 lm1 [6,7]. In single-phase UFG alloys produced by ECAP, such microstructural heterogeneities, in conjunction with the high stored energy associated with the fine grain size, result in favourable conditions for rapid grain coarsening circumvented by recrystallization at low homologous temperatures [15–19]. The present alloy contains a dispersion of extremely fine Al3Sc particles that are known to suppress both continuous
Fig. 11. Rate of grain coarsening as a function of orientation gradient, X. The growth rates are normalized with respect to a particle-free system exhibiting grains with a random distribution of orientations.
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Table 2 Grain-coarsening data for various UFG alloys processed by SPD Alloy
Processing route
True strain
Annealing range (K)
D0 ðlmÞ n Q Q/Qgba (kJ mol1)
Q/Qbb
Notes
Current work
Al–0.3% Sc
9.6
673–773
1.0
3 165
1.92
1.16
Wang et al. [51]
Al–3% Mg
4
443–803
0.2
2 30
0.35
0.21
Park et al. [52]
Al–3% Mg
4
443–803
0.2
5 99
1.15
0.70
Isothermal anneal; ICC-FIB analysis; Pre-aged starting material; nvalue determined from data Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2 Reanalysis of data in Ref. [51] using different n-values
Yu et al. [19]
AA1050 Al
ECAP-Bc @ RT ECAP + rolling @ RT ECAP + rolling @ RT ECAP @ RT
8
573–623
0.35–0.6 2 49
0.57
0.35
4–8
693–963
0.27
5 174–179
1.06–1.09
0.62–0.64
1–3 4 4
437–673
2.5
473–523 523–673 –
2.5
2 34 (1–3) 31 (4) 2 70 25 – 94c
0.37 (1–3) 0.34 (4) 0.78 0.27 0.90
0.2 (1–3) 0.18 (4) 0.52 0.18 0.47
Park and Shin [53] Fe–0.15% C Kim [54]
AZ31 Mg
Kima and Kim [55] AZ31 Mg Jiang et al. [56] a b c
Cu
ECAP-C @ 623 K ECAP-Bc @ RT ECAP-Bc@ 473–523 K High Pressure Torsion
4
0.2
Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2 Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2 Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2 Isochronal anneal; TEM analysis; Direct anneal after ECAP; Assumed n = 2; Three distinct coarsening regimes Anisothermal DSC analysis; TEM analysis; Direct anneal after ECAP
gb, grain boundary diffusion. b, bulk (lattice) diffusion. Calculated using DSC data.
coarsen slowly due to grain boundary pinning, with local orientation gradients produced by SPD not affecting the rate of grain coarsening on a local scale. The shaded zone in Fig. 11 shows the conditions expected for the Al–0.3Sc alloy [31], and demonstrates that local variations in X do not influence the overall process of grain coarsening. Such a tempering effect on the variability of the rate of grain coarsening is supported by recent work on a similar alloy system [6].
4.3. Possible mechanism(s) of grain coarsening in UFG alloys
Coarsening of a polycrystalline aggregate is often analysed using the following relation [2]: Dn D0n Q ¼ c1 exp ; ð11Þ RT t
where D0 and D are the initial and final arithmetic mean grain diameter (at time, t), respectively, n is the grain
Fig. 12. Bright-field TEM micrographs taken from the extrusion direction and corresponding selected area electron diffraction patterns showing microstructural evolution during pre-ageing at 350 C (courtesy N. Hamilton).
M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491
Source
M. Ferry, N. Burhan / Acta Materialia 55 (2007) 3479–3491
growth exponent, c1 is a constant, T is absolute temperature and Q is an activation energy term. Q-values computed from Eq. (11) are often used to interpret the mechanism of grain coarsening [2]. Investigations on subgrain growth and normal grain growth have shown that coarsening occurs typically by boundary migration controlled by bulk diffusion [2]. The movement of grain boundary triple junctions to reduce boundary curvature is also a possible mechanism of coarsening, although recent molecular dynamics simulations have shown that this may only be significant for grain sizes considerably less than 100 nm [44]. The grain-coarsening data in Table 1 are analysed using Eq. (11) with n = 3 providing a good fit for all annealing temperatures (r2 > 0.95) (Fig. 4), which is consistent with a similar UFG Al–Sc alloy [6]. The activation energy, calculated to be 165 kJ mol1, is higher than the activation energy for bulk diffusion of aluminium (Qb = 142 kJ mol1) [2] and close to that for volume diffu1 sion of scandium in aluminium ðDSc V ¼ 173 kJ mol Þ [45]. This value is also lower than the activation energy for triple junction migration, where QTJ 2Qb [46]. With reference to the Lifshitz–Slyozov–Wagner (LSW) theory of particle coarsening [47,48], n = 3 is expected in the present alloy if grain growth is controlled by Al3Sc particles that coarsen via volume diffusion of scandium in aluminium [49]. Given the values of n and Q obtained for the present, the following relation is applicable: D3 D30 ¼ c2 DSc V t:
ð12Þ
Such coarsening behaviour is similar to other particle-controlled grain-coarsening processes such as the extended recovery in a fine-grained (D0 1 lm) Al–6 wt.% Ni alloy containing 0.1 volume fraction of 0.3 lm diameter NiAl3 particles [50]. Some notable studies of continuous grain coarsening in SPD-UFG alloys are given in Table 2. Several investigators have argued that the mechanism of coarsening may be significantly different to conventional subgrain/grain growth processes [19,51,53–55]. Using isochronal grain size data (single point per temperature), Q-values up to 5· lower than the present alloy were computed. These Q-values are also considerably lower than either Qgb or Qb, although some workers [52,53,56] report values close to Qgb. Hayes et al. [57] showed that the activation energy of grain coarsening in an ECAP-deformed Al–3% Mg alloy was close to Qb and this was comparable to a coarse-grained alloy of the same composition. It is pertinent to note that Q-values computed for many nanocrystalline materials produced by mechanical alloying, electrodeposition, etc., are also close to that for either bulk diffusion or grain boundary diffusion [58]. The very low Q-values computed for several SPD-UFG alloys do not correspond to any simple diffusion process [2], and this may be a consequence of the nature of the microstructure prior to annealing. For example, Fig. 12 shows the evolution of microstructure during pre-ageing in the present alloy where the moderately aligned deforma-
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tion microstructure rapidly converts to an equiaxed structure that exhibits well-defined boundaries and a lower density of internal dislocations. Beyond the transient stage, this well-defined grain structure coarsens in a similar manner to that occurring at higher annealing temperatures. It is interesting to note that in a study of recovery in lightly strained zone-refined iron [59], the activation energy was found to increase from 91 kJ mol1 ð QFe gb Þ at the initial stages of recovery to 220 kJ mol1 (close to QFe b Þ during the latter stages. In the early stages of recovery, dislocation migration, annihilation and the formation of a subgrain structure were reported. These equilibrating processes are similar to that observed in the present alloy during the transient stage, Fig. 12, and similar to the structural changes observed by Prangnell et al. [13] in UFG Al–Mg, and in the directly annealed alloys given in Table 2. These initial relaxation processes occur by different mechanisms to the curvature-driven process of normal subgrain/grain growth (where Q-values close to bulk diffusion are commonly reported [2]). Unlike a conventional recovering substructure, the UFG alloy initially contains a large fraction of HAGBs (0.7). The subsequent homogeneous evolution of the microstructure during annealing, coupled with no significant appreciable change in texture, is consistent with the later stages of continuous recrystallization involving a gradual increase in grain size by general boundary migration. The experimental investigation of Jazaeri and Humphreys [14] and computer simulations by Prangnell et al. [13] have demonstrated that an aligned deformation microstructure generated in SPD Al alloys rapidly collapses into a more stable, equiaxed configuration, with further coarsening occurring mainly by the migration of grain boundaries. On a final note, solute (Sc) atoms may have an effect on grain coarsening in the present alloy. Various theories of solute-engendered grain growth inhibition have been proposed such as those based on (i) solute drag of boundaries (see e.g. Ref. [1, pp. 159–165]), and (ii) solute segregation at boundaries causing a reduction in driving force for their migration due to a decrease in boundary surface energy [60,61]. For the present alloy, there is substantial evidence that grain coarsening is controlled by the pinning effects of fine Al3Sc particles [6]. However, single-phase (very low solute) Al–Sc SMG alloys also show a slower rate of grain coarsening compared with a Sc-free Al alloy of similar starting microstructure [62]. Work is currently underway using atom probe tomography to investigate Sc segregation to grain boundaries during annealing and its influence on grain coarsening. 5. Concluding summary A supersaturated Al–0.3 wt.% Sc alloy was cold deformed by ECAP to an equivalent von Mises strain of 9.2 then pre-aged at 350 C. This ageing treatment generated an UFG alloy of average grain size 1 lm, together
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with a positively skewed grain size distribution. The grain boundaries in this microstructure were more complex than a conventional recrystallized structure, and individual grains retained a considerable number of internal dislocations. Over distances much greater than the grain size, the microstructure contained a non-uniform distribution of LAGBs and HAGBs inherited from the coarse grain size prior to ECAP. The pre-aged microstructure was highly resistant to grain coarsening at temperatures up to 500 C with discontinuous coarsening occurring only after extended annealing. The non-uniform distribution of boundary character produced by ECAP had no apparent influence on grain coarsening on a local scale, with coarsening occurring uniformly throughout the microstructure. A detailed statistical analysis showed that the initial grain size distribution was very close to lognormal and, throughout annealing, remained lognormal but with a slight broadening of the distribution. An analysis of the kinetics of grain coarsening generated a grain growth exponent and activation energy of n = 3 and Q 165 kJ mol1, respectively; the latter is larger than the activation energy for bulk diffusion (142 kJ mol1) but close to that for volume diffusion of scandium in alumin1 ium ðDSc V ¼ 173 kJ mol Þ. The considerable TEM evidence has shown that grain coarsening is controlled by pinning by fine Al3Sc particles. In conjunction with the kinetic parameters, grain coarsening is likely to be controlled by the rate of particle coarsening, which, in turn is controlled by volume diffusion of scandium in aluminium, i.e. D3 D30 ¼ c2 DSc V t. In contrast to a conventional recovering substructure, the UFG alloy initially contains a large fraction of HAGBs (0.7). The subsequent homogeneous evolution of the microstructure during annealing, coupled with no appreciable change in texture, is consistent with the advanced stages of continuous recrystallization involving a gradual increase in grain size by general boundary migration. Based on the evidence presented herein, the UFG alloy coarsens by continuous recrystallization that is structurally and kinetically similar to conventional subgrain growth/grain growth processes in high-stacking fault energy, low-solute alloys. Acknowledgments The authors acknowledge the Australian Research Council (ARC) for supporting this work by an ARC Discovery Grant (DP0342766) and through the ARC Centre of Excellence for Design in Light Metals (CEO561574). References [1] Humphreys FJ, Hatherly M. Recrystallization and Related Annealing Phenomena. 2nd ed. Oxford: Pergamon Press; 2004. [2] Humphreys FJ, Prangnell PB, Bowen JR, Gholinia A, Harris C. Phil Trans Roy Soc A 1999;357:1663.
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