Influence of grain size in the near-micrometre regime on the deformation microstructure in aluminium

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Influence of grain size in the near-micrometre regime on the deformation microstructure in aluminium G.M. Le a, A. Godfrey a,⇑, N. Hansen b, W. Liu a, G. Winther c, X. Huang b a

Key Laboratory of Advanced Materials (MOE), School of Materials Science and Engineering, Tsinghua University, Beijing 100084, People’s Republic of China b Danish-Chinese Center for Nanometals, Section for Materials Science and Advanced Characterization, Department of Wind Energy, Technical University of Denmark, Risø Campus, DK-4000 Roskilde, Denmark c Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark Received 18 June 2013; accepted 23 July 2013 Available online 10 September 2013

Abstract The effect of grain size on deformation microstructure formation in the near-micrometre grain size regime has been studied using samples of aluminium prepared using a spark plasma sintering technique. Samples in a fully recrystallized grain condition with average grain sizes ranging from 5.2 to 0.8 lm have been prepared using this technique. Examination in the transmission electron microscope of these samples after compression at room temperature to approximately 20% reduction reveals that grains larger than 7 lm are subdivided by cell block boundaries similar to those observed in coarse-grained samples, with a similar dependency on the crystallographic orientation of the grains. With decreasing grain size down to approx. 1 lm there is a gradual transition from cell block structures to cell structures. At even smaller grain sizes of down to approx. 0.5 lm the dominant features are dislocation bundles and random dislocations, although at a larger compressive strain of 30% dislocation rotation boundaries may also be found in the interior of grains of this size. A standard h1 1 0i fibre texture is found for all grain sizes, with a decreasing sharpness with decreasing grain size. The structural transitions with decreasing grain size are discussed based on the general principles of grain subdivision by deformation-induced dislocation boundaries and of low-energy dislocation structures as applied to the not hitherto explored near-micrometre grain size regime. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Aluminium; Plastic deformation; Dislocation boundaries; Transmission electron microscopy (TEM); Length scale effects

1. Introduction During plastic deformation of metals grains subdivide by the formation of dislocation and high-angle boundaries, resulting in hierarchical structures on a finer and finer scale as the strain is increased [1]. These structures have been classified as low-energy dislocation structures (LEDS), and it has been found that the morphology and structural parameters describing these structures are strongly influenced by the crystallographic orientation of the grains undergoing plastic deformation [2–13]. Such deformation

⇑ Corresponding author. Tel.: +86 10 62788317; fax: +86 10 62771160.

microstructures are formed when a sufficient number of independent slip systems are operative and when the deformation occurs by dislocation glide [14]. On the grain scale, the process of grain subdivision may take place via formation of deformation/transition bands [15–17]. Such features are typically observed in coarse-grained samples. On a microscopic scale, the grain subdivision takes place via formation of two distinct types of dislocation boundaries, namely incidental dislocation boundaries (IDBs) and geometrically necessary boundaries (GNBs), resulting in the formation of cell blocks and cells/subgrains. The taxonomy describing such features has been discussed extensively and is summarized in Table 1. The difference in origin of the GNBs and IDBs leads to a different evolution of the

E-mail address: [email protected] (A. Godfrey). 1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.07.046

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Table 1 Terminology established for deformation microstructures in coarse-grained face-centred cubic metals [2,8,14]. Abbreviation

Full name

Morphological characteristics

Formation mechanism

IDBs

Incidental dislocation boundaries

Short, sometimes curved dislocation boundaries

Formed by the statistically mutual trapping of glide dislocations within regions (the cell blocks) deforming by the same set of slip systems and slip amplitudes

GNBs

Geometrically necessary boundaries

Extended, planar dislocation boundaries

Formed between regions (cell blocks) deforming with different sets of slip systems and/or slip system amplitudes

CBs

Cell blocks

Parallel extended GNBs connected by IDBs. GNBs subdivide the microstructure into cell blocks, and within these cell blocks IDBs delineate individual dislocation cells

average misorientation angle with strain for the two boundary types, and to different scaling characteristics for the boundary misorientation and spacing distributions of the GNBs and IDBs [18–23]. The strong dependence on the grain orientation of the pattern of grain subdivision at the microscopic length scale reflects an origin in the pattern of slip during deformation. By considering the crystallographic characteristics of the dislocation boundaries, three types of structure are found, referred to as Type 1, Type 2 and Type 3 structures, as described in Table 2. The orientation dependence of these structures with respect to uniaxial deformation (tension or compression) is also summarized in the Table 2. A similar correspondence between grain orientation and deformation microstructure has also been found for other loading modes (e.g. rolling) [24,25], and in each case the observations can be explained by analysis of the underlying slip pattern [26,27]. The above observations and analysis of deformation microstructures have been carried out in nearly all cases on samples with grain sizes of 30 lm or above. It has been shown that deformation bands formed in coarse-grained samples become less prominent with decreasing grain size in the range from 3 mm to 40 lm [15]. The formation of cell blocks may, however, also be affected by grain size, an effect which is of both scientific and technological interest, taking into consideration the strong interest in metals and alloys with high strength obtained through reduction of the microstructural scale to the micrometre/sub-micrometre regime. A few detailed studies have been performed to examine the deformation microstructure in grains of small size. In a study on deformed Ni [28], it was reported that, for a grain size of 18 lm, only cell structures (Type 2 structures) were formed during tension, irrespective of the grain orientation. In contrast, by examining the deformation microstructure in copper after tension deformation, Huang and Hansen [29] found that all three types of microstructure were still formed for grain sizes down to 4 lm during tension. Moreover, the deformed microstructures showed a similar orientation dependence to that seen in coarse-grained copper. This background has led to the present research, where the grain size range over which dislocation patterning is

investigated is extended to the micrometre/sub-micrometre scale. A key challenge in carrying out such a study is the difficulty in obtaining starting material with the desired range of grain sizes, as the limit for grain size refinement by standard thermo-mechanical processing methods (deformation followed by recrystallization) in single-phase materials is around 5 lm [29–31]. Some studies have been carried out previously on samples deformed to high plastic strains followed by a short annealing treatment to promote recovery. In these samples, though, for average grain sizes around 1– 2 lm, the microstructure typically still contains a significant fraction of low-angle dislocation boundaries [32]. These complicate any analysis of deformation microstructure formation, as it is hard to establish which boundaries are formed during deformation. Additionally, such samples usually retain a strong texture and therefore offer only a limited range of possible grain orientations to study. In this work we utilize the spark plasma sintering (SPS) process to prepare suitable starting materials. In the SPS process, powders are consolidated under a relatively low pressure while being heated through application of a pulsed direct current, and it has recently been shown that this method can be used to form metal samples with a fine grain size [33–37]. As a result, we are able to prepare samples with the required range of grain sizes, where the grains are fully recrystallized (with a low dislocation density) and where the samples have a nearly random texture. Using these samples, we examine in this study the grain size and orientation dependence of the deformation microstructure in aluminium for grains in the micrometre/sub-micrometre regime. 2. Experimental SPS was used to produce fully recrystallized and texturefree material with a fine grain size for use in the investigation of deformation microstructure formation. Spherical Al powders with different powder size distributions were used to prepare samples with average grain sizes of 5.2, 1.3 and 0.8 lm. These samples are referred to in this work as Al-5.2 lm, Al-1.3 lm, Al-0.8 lm samples, respectively. The SPS process was carried out using a specially

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Table 2 Terminology established for classification of orientation dependence of deformation microstructure under uniaxial loading [5,6,9]. Name

Morphological characteristics

Physical meaning

Example orientation dependence

Type 1 structure

A CB structure with extended GNBs close to a {1 1 1} plane

A type of CB structure

Uniaxial loading near the centre of the inverse pole figure (IPF) triangle

Type 2 structure

3-D connected dislocation boundary structure

Extended planar boundaries are not formed, instead the microstructure has the appearance of containing only dislocation cells

Uniaxial loading near the [1 0 0] corner of the IPF triangle

Type 3 structure

A CB structure with extended GNBs far away from a {1 1 1} plane, but close to crystal planes with a specific relationship to the active slip systems

A type of CB structure

Uniaxial loading near the [1 1 1] corner of the IPF triangle

developed heating/loading cycle, with a maximum temperature of 600 °C and a maximum sintering pressure of 50 MPa. Further details of the sintering process are given elsewhere [38]. The sintered samples were disc shaped, with a diameter of 20 mm and a height of approximately 4 mm. To allow the investigation up to moderate strains even in the finest grain-size samples, compression testing was used to study the relationship between grain size and deformation microstructure. Samples in the form of rectangular cuboids (dimensions of 3  3  4 mm3) were machined from the sintered samples using spark erosion. Uniaxial compression tests were carried out at room temperature using a Gleeble-1500 apparatus, with the compression direction taken parallel to the loading direction during the SPS process. Graphite lubrication was used to reduce friction between the samples and the compression platens. Samples were compressed to reductions of 20%, with a few additional samples deformed to 30% reduction, at a strain rate of 103 s1. Microstructure and texture investigations of samples using scanning electron microscopy (SEM) were carried out using a Tescan 5136XM instrument and a Zeiss Supra 35 instrument, both equipped with an Oxford Instruments electron backscatter diffraction (EBSD) system. Post-processing of the EBSD data was carried out using both commercially available software package (Channel 5) and using in-house developed software. For more detailed microstructural investigation, thin foils were examined in a JEOL 2000FX transmission electron microscope equipped with a double-tilt holder. Samples were tilted so that each observed grain was oriented with the electron beam nearly parallel to a low-index orientation (preferably a h1 1 0i direction) and adjusted to reveal the dislocation boundaries clearly. The orientation of each grain was also recorded using a semi-automatic Kikuchi diffraction method described elsewhere [39]. Both the EBSD and transmission

electron microscopy (TEM) investigations were carried out in a plane containing the loading direction during sintering (as-SPS samples) or the compression direction during deformation (compressed samples). 3. Results 3.1. Microstructure of as-sintered samples Fig. 1 shows some example images of the samples prepared by the SPS process for use in this study. The presence of a native oxide layer surrounding each particle results in a final microstructure where the grain size is similar to the initial powder size (compare, for example, Fig. 1(a–c)), with each grain surrounded by a thin layer of alumina oxide [40,41]. Under the conditions used in this study, the samples have a density after sintering of 99%. Examination in the transmission electron microscope shows that the grains are fully recrystallized, with a low dislocation density (Fig. 1(c)). Detailed examination at higher magnification (Fig. 1(d)) shows that the grain boundary oxide layers are composed of a large number of small oxide particles, where the powder oxide film has been broken during the SPS process, allowing extrusion and sintering of the Al. The pinning effect of the oxide particles on grain growth results in the final grain size in the SPS samples being similar to the initial powder particle size. Examples of the initial powder size distributions, measured directly from SEM micrographs, are shown in Fig. 2 for the powders used to make the Al-0.8 lm and Al-5.2 lm samples. It is seen that the powder sizes, and hence grain sizes in the samples, cover a wide range, from 14 to 0.2 lm, i.e. from conventional “coarse” grain sizes to the sub-micrometre regime. The textures of the as-sintered samples were studied using EBSD orientation mapping. An example is shown

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in Fig. 3(a) and (b), where both the inverse pole figure colouring (Fig. 3(a)) and the {1 1 1} pole figure (Fig. 3(b)) confirm that the samples have a nearly random texture. The grain size range, microstructure and texture of the starting samples are therefore well suited for an investigation of the grain size and orientation dependence of deformation microstructure formation. 3.2. Overall compression behaviour of as-sintered samples To obtain a general idea of the texture evolution during compression for samples with different grain sizes, EBSD measurements were taken on samples of Al-5.2 lm and Al-0.8 lm deformed to a compression of 30%. The results are shown in Fig. 3(c) and (d). In both samples the EBSD maps show the grains are elongated as expected normal to the compression direction. In the Al-5.2 lm sample the orientation variation in each grain provides some evidence for the presence of a dislocation boundary substructure, whereas in the Al-0.8 lm sample such evidence is only seen for a few large grains. A more detailed study of the deformation microstructure developed during compression based on examination in the transmission electron microscope is given in the next section. Irrespective of the appearance of the microstructure in the two EBSD data sets, the texture evolutions in these two samples are quite similar, with both developing a h1 1 0i fibre texture as expected from dislocation-slip-dominated compression deformation of aluminium, though the texture of the finer grain size sample (Al-0.8 lm) is somewhat weaker than that of the Al-5.2 lm sample. Detailed examination of the microstructure at different locations in the compressed samples showed no evidence for macroscopic strain localization. All thin foils for TEM investigation were nevertheless taken from the centre of the samples. 3.3. Detailed observations of deformation microstructure The EBSD map of the compressed Al-5.2 lm sample shown in Fig. 3(d) shows some evidence of grain subdivision. This is shown more clearly in Fig. 3(e), which shows EBSD data from a sample of Al-5.2 lm compressed to 20% reduction, processed using in-house software to make plots of the rotation axis in the sample reference frame between each pixel and the grain average orientation [4,42]. The figure clearly shows evidence for grain subdivision for grains with average size down to at least 1 lm. However, the detailed deformation microstructure is still not fully resolved using this method. In particular, it is not possible to reveal all the dislocation boundaries formed within each grain, or to identify the local boundary plane, as can be done in TEM investigations. In the remainder of this section we therefore present results from detailed TEM investigations of the as-deformed SPS samples, considering here only the samples deformed to a compression of 20%. The results are analysed based on the observed grain size, collated from examination of TEM foils from the

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compressed samples. In most cases observations of grains of a given size were made from the sample with nearest average grain size, though in a few cases other examples were also included (e.g. data for a 5 lm grain from the Al1.3 lm sample). The grain size is calculated as the root mean square dimension p from observation in the TEM viewing plane (i.e. d = (d1  d2), where d1 and d2 are the lengths measured parallel and perpendicular to the largest observed grain dimension). In total, 121 grains from all three compressed samples were analysed in detail. The studied grains cover a size range from 12 lm down to less than 0.5 lm. Fig. 4 and Table 3 show the size distribution and sample origin of the 121 grains analysed in this study. As shown in the figure, particular attention was paid to grains with size near 1 lm. The observations are summarized in the following, based on a number of size classes. For convenience, the definitions used to identify the different structural features in these grains are summarized in Table 4. 3.3.1. Grains with size greater than 10 lm To allow a comparison of the deformation microstructure in the SPS samples with those reported in previous studies, analysis was first given to the coarsest grains, defined here as those with grain size larger than 10 lm. In total, 11 such grains were studied (all from compressed Al-5.2 lm samples). Two examples are given in Fig. 5(a) and (b), showing well-defined cell block structures of Type 1 and Type 3, respectively. In these figures, and in those following, the traces of the {1 1 1} planes are marked in the lower right corner of each image; the inset in the upper right corner of each image shows the crystal direction parallel to the compression axis for the grain. A similar analysis was applied to all 11 grains in this size class. All of the grains examined showed either a Type 1 or Type 3 structure. A summary of the orientation dependence of the microstructures in these grains is shown in Fig. 5(c). In agreement with previous investigations, grains with a compression direction towards the [1 1 0] corner show a Type 1 structure (indicated by triangle symbols) and grains with orientations near the [1 0 0]–[1 1 1] line, or not far away from the [1 1 1] corner, show a Type 3 structure (indicated by square symbols). Due to the small number of grains of this size class, no examples of grains with orientations near the h1 0 0i corner (where Type 2 structures would be expected) were found. In all of these grains the deformation microstructure followed the pattern expected from previous investigations, with the same dependence of microstructure on grain orientation. Some differences are seen in that, due to the presence of oxide particles, dislocations are also observed to accumulate at grain boundaries, though this takes place on a very fine scale and is localized to the volume just around the particles. 3.3.2. Grains with size from 7 to 10 lm For grains in this size class, all three types of structure (Types 1, 2 and 3) were observed. An example of each is

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Fig. 1. SEM micrographs showing (a) the initial powder and (b) the final sintered grain size for a SPS sample with an average grain size of 0.8 lm. Note the similarity between the powder size and the grain size. (c) TEM micrograph of the same sample showing the fully recrystallized grain structure and (d) oxide particles at the grain boundaries.

of these grains are, however, spread more widely than seen in studies of larger grains [9].

Fig. 2. Particle size distribution for powders used to prepare samples (a) Al-0.8 lm and (b) Al-5.2 lm.

shown in Fig. 6(a–c). In total, 10 grains were studied in detail for this size class. The orientation dependence of the structure type for these grains is summarized in Fig. 6(d). One grain was found showing a Type 2 structure (dislocation cells without the presence of extended planar boundaries), with orientation near the [1 0 0] corner. Three grains with compression directions near the [1 0 0]–[1 1 0] line show a Type 1 structure. For the Type 1 and Type 2 structures, the orientation dependence is comparable to that of the grains with size larger than 10 lm. The other six grains studied show a Type 3 structure. The orientations

3.3.3. Grains with size from 3 to 7 lm With decreasing grain size, the fraction of grains containing well-defined GNBs decreases, as does the number and maximum length of such boundaries in each grain. This makes identification of GNBs, and therefore of cell blocks, more complicated. As indicated in Table 4, in these finer grains we label a boundary as a GNB if it is continuously extended over at least three dislocation cells. Of the 34 grains studied in this size range, only five show a well-defined cell block microstructure over the entire grain. Examples are given in Fig. 7(a) and (c) for Type 1 and Type 3 structures, respectively. Of these grains, four show a Type 3 structure (orientations in the lower half of the unit triangle) and one grain, with an orientation close to the [1 1 0] corner, shows a Type 1 structure (see Fig. 7(d)). A Type 2 microstructure is observed in three other grains, with orientations near the [1 0 0] corner (an example is shown in Fig. 7(b)). For the other 26 grains, it is hard to catalog the structure into any of the established three types. Fig. 8(a–c) shows some examples. In general, boundaries that can be identified as GNBs (based on the definition given in Table 4) are still seen in parts of the grains, but they are often not as straight as those in classic Type 1 and Type 3 structures. Additionally, in most cases only a few GNBs can be identified in each grain. In other parts of these grains a cell structure is seen. This mixture of GNBs and cell structures is thus defined as a mixed type structure. Based on the observation that the structures formed in grains in this size range start to show a transitional behaviour, the alignment of the GNBs has been analysed in more detail in these 26 grains. Specifically, the boundaries identified as GNBs were examined to determine if part of the boundary (over a minimum length of one dislocation cell) was aligned close to a {1 1 1} trace (again within a 10° tolerance). Two examples are shown in Fig. 8(a) and (c). In these mixed structures some GNBs are at least partly nearly parallel to {1 1 1} planes. Note that, for the grain shown in Fig. 8(b), although the GNBs are nearly parallel to a {1 1 1} trace, examination of the boundary plane shows

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Fig. 3. EBSD data for SPS samples: (a) as-sintered Al-5.2 lm sample inverse pole figure colouring, according to the loading direction during sintering, and (b) {1 1 1} pole figure. (c and d) Microstructure (inverse pole figure colouring) and {1 1 0} pole figures (inset) after 30% compression for (c) the Al-0.8 lm sample and (d) the Al-5.2 lm sample. Both show the development of a h1 1 0i fibre (compression) texture. The compression axis is located at the centre of the pole figures. (e) EBSD map constructed by in-house software showing microstructure of Al-5.2 lm sample after 20% compression.

In total, 11 out of the 26 grains that were classified as of mixed structure contained GNBs where at least part of the length was close to a {1 1 1} trace. The orientations of these grains are shown in Fig. 8(d) by a solid red diamond symbol (used to indicate a mixed structure). The hollow symbols show the orientations of the other 15 grains, which are a mixture of cells and Type 3 boundaries. It is seen that all GNBs with a partial {1 1 1}-trace alignment are in grains with orientations in the region associated with Type 1 cell blocks in coarse-grained samples, though not all grains with these orientations contain GNBs with this feature. 3.3.4. Grains with size from 0.8 to 3 lm Grains in this size class were observed to contain either dislocation cells (typical for grains larger than 1 lm) or dislocation bundles and/or random dislocations. A few of the larger grains in this size class contained a near-planar boundary, though not extending over more than three dislocation cells. Such grains were therefore classified as

Fig. 4. Grain size distribution for the 121 grains studied in detail this work.

that these in fact deviate by a large angle from a {1 1 1} plane.

Table 3 Summary of the number of grains in each size class investigated from each SPS sample.

Al-5.2 lm Al-1.3 lm Al-0.8 lm a

>10 lm

7–10 lm

3–7 lm

0.8–3 lm

<0.8 lm

Total

11 – –

10 – –

30 4 –

2 27 30

– – 7a

53 31 37

A larger number of grains were inspected but without recording images or orientations.

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Table 4 Definitions used for identification of structural features observed in the present study. Name

Morphological characteristics

GNB

Continuous dislocation boundary extending smoothly over at a length of at least 3 dislocation cells and approximately straight At least 3 adjacent GNBs approximately parallel to each other Cell block where the deviation of GNBs to the trace of the {1 1 1} slip plane (in a near-edge on condition) is less than 10°

Cell block Type 1 cell block structure Type 3 cell block structure Mixed structure Type 2 structure Dislocation bundle

Cell block as above where the deviation of GNBs to the trace of the {1 1 1} slip plane is more than 10°, in a near-edge on condition Grain with at least one GNB (as defined above), where structure otherwise consists of cells Grain containing only dislocation cells Cluster of individual dislocations that can be mostly resolved but there is no apparent order in the dislocation arrangement and no measurable misorientation across the cluster

Fig. 5. Examples of microstructure and orientations for grains with size larger than 10 lm (a total of 11 grains): (a) Type 1 cell block structure; (b) Type 3 cell block structure; (c) orientation dependence of structure type (Type 1 = triangles; Type 3 = squares).

containing a cell structure. Fig. 9(a–d) shows examples of grains containing cell structures with size down to 0.8 lm. Grains in this size class with only dislocation bundles or random dislocations inside are shown in Fig. 10(a) and (b). It is worth noting that the boundary oxides provide a marker for the grain shape, and confirm that these grains have indeed undergone a plastic deformation similar to the applied nominal reduction. In total, 59 grains were studied in this size class, of which 32 showed a dislocation cell structure and 27 showed bundles or random dislocations. 3.3.5. Grains with size less than 0.8 lm A total of seven grains with size smaller than 0.8 lm were examined in detail. In all of these grains only dislocation bundles or random dislocations are present inside the

grains. Two examples are shown in Fig. 10(c) and (d). The extent of dislocation storage ranges from just a couple of dislocations (one dislocation per 0.8 lm cell corresponds to a dislocation density of approximately 2  1012 m2) to complex bundles, but there is no clear dependence on size for these two cases. It is important to note that a much larger number of grains of this size class were in fact examined by tilting foils of the Al-0.8 lm sample to achieve good imaging conditions, though the images and orientations were not recorded (and hence were not included in the totals counted). These observations confirm that, for grains of size less than 0.8 lm, grain subdivision by boundary formation only occurs very infrequently after a compression of 20%, with most grains containing only dislocation bundles or random dislocations.

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Fig. 6. Examples of microstructure and orientations for grains with sizes between 7 and 10 lm (a total of 10 grains): (a) Type 1 cell block structure; (b) Type 2 cell structure; (c) Type 3 cell block structure; (d) orientation dependence of structure type (Type 1 = triangles; Type 2 = circles; Type 3 = squares).

Fig. 7. Examples of microstructure and orientations for grains with sizes between 3 and 7 lm (a total of eight grains): (a) Type 1 cell block structure; (b) Type 2 cell structure; (c) Type 3 cell block structure; (d) orientation dependence of structure type (Type 1 = triangles; Type 2 = circles; Type 3 = squares).

3.4. Dislocation boundary misorientations One complication in analysis of small grains is that the alignment of extended boundaries is more difficult to

establish, partly because they become less well defined with decreasing grain size, and also as fine grains contain, at most, only a few such boundaries. For a more detailed analysis of the deformation microstructure, misorientation

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Fig. 8. Examples of microstructure and orientations for grains with sizes between 3 and 7 lm (a total of 26 grains): (a and c) mixed structure with partial GNB alignment to a {1 1 1 trace}; (b) mixed structure; (d) orientation dependence of structure type (hollow diamonds indicate mixed structure; solid red diamonds indicate mixed structure with partial GNB alignment to a {1 1 1} trace). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

angles across dislocation boundaries were also measured in the transmission electron microscope. Such measurements were made for more than 25 grains in the compressed Al5.2 lm and Al-1.3 lm samples, in each case taking orientation measurements across all the dislocation boundaries observed in each grain. Fig. 11(a) and (b) shows example maps of the boundary misorientations in three such grains with average sizes of 6.6 lm (a) and 1.5/1.3 lm (b). The grain in Fig. 11(a) contains a mixed structure, showing a number of higher-angle boundaries extending across several cells. The two grains with smaller size in Fig. 11(b) contain a cell structure. Histograms summarizing all the misorientation measurements for the Al-5.2 lm and Al-1.3 lm samples after a compressive deformation of 20% are plotted in Fig. 11(c) and (d), respectively. In total, 203 and 192 boundaries were measured for the Al-5.2 lm and Al1.3 lm samples, respectively. A wide range of angles are seen for both samples, with a low-angle peak at 1–2° and high angles of up to more than 10°. Sample Al-1.3 lm contains more boundary misorientation angles higher than 5°, which results in a higher average misorientation angle of 2.8° compared to the 2.3° for sample Al-5.2 lm. Based on interpolation of data for coarse-grained Al [18,19], the expected average values for GNBs and IDBs at this strain level in coarse grains are 3 and 0.8°, respectively. It is seen, therefore, that, for both SPS samples, and particularly for the Al-1.3 lm sample, the average angle for boundaries is

much closer to the predicted GNB average. The low-angle peak suggests, however, that an IDB-like population may still be present in both samples. 4. Discussion 4.1. Deformation microstructure Extensive studies have revealed the evolution in deformation microstructures in materials with medium to high stacking fault energy deforming by dislocation glide [1,14], and general principles have been established for the grain subdivision by formation of rotational dislocation boundaries in such materials [2–13]. The initial structures in these previous studies have been obtained by plastic deformation followed by a recrystallization heat treatment (or in some cases by the use of single crystal samples), in which the grain sizes range typically from tens of micrometres to a few hundred micrometres, and where the grain boundaries are typically of high-angle character. The objective of the present study is to extend the study of deformation microstructure formation to grains with sizes in the near to sub-micrometre range by using samples prepared by SPS. The material chosen is aluminium, which is covered by a natural thin layer of aluminium oxide, the presence of which hinders structural coarsening during sintering of the aluminium powder. Powders with particle sizes in the range from 0.2 to 14 lm have been used, and

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Fig. 9. Examples of cell structures in grains with sizes between 0.8 and 3 lm (a total of 32 grains).

Fig. 10. Examples of dislocation bundles and random dislocations for grains with sizes smaller than 3 lm: (a and b) 1.4 lm, (c) 0.6 lm, (d) 0.5 lm. Note that the sharp planar boundary in (d) is a twin formed during the SPS process.

as a result samples with equally fine grain sizes can be produced.

These samples differ from typical polycrystal samples in that the grain boundaries contain a dense dispersion of

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very fine aluminium oxide particles. Such a boundary structure is expected to resist dislocation glide more strongly than normal (undecorated) high-angle grain boundaries, and this may have an effect on the slip pattern and on the structural evolution during plastic deformation. This has been investigated by a detailed comparison of large grains (>10 lm) in the SPS sample prepared using the coarsest starting powder, with the typical universal behaviour previously observed in recrystallized polycrystals with larger grain size [5,6,9]. This comparison includes the deformation microstructure and its crystallographic orientation dependence. From this comparison, it is concluded that the behaviour of large grains in the SPS samples can be characterized as typical, with subdivision into cell blocks through formation of GNBs and IDBs, with microstructural characteristics related to the crystallographic orientation of the individual grains. It follows that the structures can be classified as LEDS, where the arrangement of the dislocations in a well-defined boundary structure is preferred over a random arrangement of dislocations due to stress screening [43], thereby resulting in a reduction in free energy per unit line length of dislocation, which is given by the general equation U D ¼ ½Gb2 f ðmÞ=4p lnðR=bÞ where G is the shear modulus, b is the Burgers vector, R is the cut-off radius and f(m) = [(1  m/2)/(1  m)], where m is Poisson’s ratio. By the organization of dislocations into walls or boundaries, UD is reduced through a decrease in R. However, the magnitude of the reduction that can be achieved will depend on the dislocation mobility and the availability of dislocations with different Burgers vectors in order to make the stress screening most effective [44]. 4.2. Grain size and structural transitions A main structural feature of all deformed grains in the SPS samples with size above approx. 1 lm is the formation of rotational dislocation boundaries characterized by an angle/axis pair, which describes the misorientation across each boundary. For the larger grain sizes these boundaries form a cell block structure, whereas in smaller grain sizes either a mixed structure or a cell structure results. However, at the smallest grain sizes, after compression to 20% reduction, subdivision by formation of dislocation boundaries is not observed. The observed dislocation boundary characteristics suggest that the well-defined cell block structures and the mixed structures are LEDS where the cut-off radius (R) can be approximated by b/h, where h is the boundary misorientation angle. The transition into a structure of bundles and random dislocations at very small grain sizes represents a less efficient stress screening and a higher energy per unit length of dislocation line, as for such structure R can be approximated by 1/q0.5, where q is the dislocation density in a random distribution [45]. The lack of dislocation boundaries in the smaller grain size was unexpected, but it is worthwhile to note that, in

addition to the data presented above, some samples were also examined after deformation to a compression of 30%. In these samples the largest grain size in which cell blocks are observed is shifted to a lower value (2.3 lm), and in one case a grain with size of d = 0.4 lm was observed to be subdivided by a well-defined dislocation boundary. A dependence of subdivision on strain is to be expected as the probability of gliding dislocations being stored within the grains increases with increasing strain, leading to enhanced interaction of dislocations and the formation of dislocation boundaries. 4.3. Grain size and orientation dependence A detailed summary of all the observations made on the compressed SPS samples is shown in Fig. 12, where, for each grain investigated, the deformation microstructure is ascribed to one of the classes described previously. With decreasing grain size, the structural transitions show some overlap between the structure types. For the largest grains examined in the SPS samples, the deformation microstructures resemble closely those reported previously for compression (and tension) of conventional grain-sized material [5,6,9]. All three types of characteristic microstructure are observed, namely Type 1 cell blocks (with GNBs close to a {1 1 1} trace), Type 3 cell blocks (with GNBs away from a {1 1 1} trace) and Type 2 cell structures, with a similar relationship between grain orientation and microstructure as seen in coarse grain studies. With decreasing grain size, fewer grains contain boundaries that can be classified based on their appearance as GNBs, and an increasing fraction of grains develop a mixed deformation structure consisting of both partial cell blocks and cells. To analyse the mixed structures, we have used a definition that a boundary is classified as a GNB if it is extended continuously over a distance of at least three dislocation cells. Moreover, for some of these GNBs, at least part of the boundary (over a distance of at least one dislocation cell) is less than 10° from a {1 1 1} trace (marked in Fig. 12 using solid red diamonds1). It is seen, therefore, that, even in deformation structures classified as mixed, parts of some grains still develop boundaries with characteristics similar to GNBs, as seen in deformed coarsegrained samples. The observations suggest that reduction in grain size towards the micrometre level leads to increased difficulty in the formation of well-defined cell block structures rather than to a change in the underlying deformation mechanisms. This is also supported by the observation of rotations towards a standard h1 1 0i fibre texture during compression, even in the 0.8 lm average grain size sample. The data for grains classified as Type 1 or Type 3 show clear evidence for an orientation dependence in the

1 For interpretation of color in Fig. 12, the reader is referred to the web version of this article.

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Fig. 11. Examples maps showing boundary misorientations in grains with size of (a) 6.5 lm, (b) 1.5 and 1.3 lm, with black lines representing grain boundaries, blue lines representing dislocation boundaries (DBs) with misorientations in the range of 0–2°, orange lines representing DBs with misorientations in the range of 2–5° and red dotted lines representing DBs that were not measured; (c and d) histograms of boundary misorientation distributions in SPS-processed samples after 20% compression for (c) Al-5.2 lm and (d) Al-1.3 lm; (e) distribution of misorientation angles across all dislocation boundaries in each investigated grain (all measurements for a single grain are plotted in a single colour) after 20% compression. Large misorientations typical of GNBs are found for grain sizes down to 1.3 lm.

formation of the deformation microstructure in aluminium down to a mean grain size of at least 5 lm. Additionally, in smaller grains with a mixed microstructure, the range of compression directions where GNBs are seen with part of the length aligned close to a {1 1 1} trace (Fig. 8(d)) is similar to the range of orientations found for Type 1 cell block structures in conventional coarse grain size studies, although a wider scatter is observed. Some differences are nevertheless seen between the orientation dependence of microstructure as compared to coarse-grained samples. In particular, the range of compression axes over which Type 3 structures are observed is extended with decreasing grain size (see Figs. 5(c), 6(d) and 7(d)). No data are available

concerning the change with decreasing grain size for grains with compression axis near the [1 0 0] corner of the unit triangle (Type 2), as only a few grains with such orientations were found in the compressed samples. In fine grains with size decreasing down to 0.8 lm, where long extended planar boundaries are not formed due to the limited grain size, the structures formed are defined as cell structures. A further distinction between Type 1 and Type 3 structures is not possible, which leads to a difficulty in the analysis of orientation dependence. There might still, however, be an orientation dependence with respect to which slip systems are activate for grains with different orientations, and to

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differences in misorientation evolution. Further detailed studies, including identification of dislocation slip systems through a g  b analysis, are underway to investigate this question [46]. In the finest grains only dislocation bundles or random dislocations are seen in samples compressed to 20% reduction. It is important to note here that the network of oxide particles along the grain boundaries in the SPS samples provides a useful marker to identify the grain shape. Inspection of the oxide network around fine grains that contain only dislocation bundles or random dislocations confirms that these grains have indeed undergone a plastic strain similar to the nominally applied deformation. It can be concluded, therefore, that the general principle that the characteristics of the deformation structure is related to the crystallographic orientation of the deforming grain is still clearly observed for grain sizes down to less than 7 lm, with a less clear orientation dependence observed in smaller grains where a mixed structure is formed. This may indicate a change in the operating slip systems and may account for the slightly weaker texture seen in the Al-0.8 lm sample (see Fig. 3(c) and (d) and Section 3.2), as a result of the operation of more secondary systems during deformation. 4.4. Grain size and slip pattern The transition in the deformation structure with decreasing grain size indicates a significant change in the slip pattern, which may, for example, be related to a decrease in slip length and an increase in grain–grain interaction effects as the grain size decreases. However, although it may be difficult to identify GNBs by their appearance as extended boundaries forming part of a cell block structure, many dislocation boundaries in grains as small as 1 lm may still have the characteristics of a GNB, especially because the misorientation angle across many boundaries is significantly larger than can be expected for typical cell boundaries (IDBs) formed by statistical trapping (rather than biased trapping, as is the case for GNBs) of glide dislocations. The range of misorientation

angles suggest that both types of boundary are, however, present, and it is worth noting that a similar pattern of dislocation storage has been observed in Type 2 deformation structures, resulting from uniaxial loading along directions near the [1 0 0] corner of the unit triangle. Examination of boundary misorientation angle distributions for such structures shows that a GNB population is still developed [23,47], based on the knowledge that the misorientation angle increases more rapidly with increasing strain for GNBs than for IDBs, and that separate scaling behaviour in the misorientation angle distributions are found for the GNB and IDB distributions [48]. A key question in the study of deformation microstructure is to ask whether the slip pattern within fine grains is similar throughout each grain or whether, as in the case of different cell blocks, different parts of grains experience different sets of slip activity. Some evidence can be seen for this based on the misorientation angle distributions shown in Fig. 11(c) and (d), where a wide range of boundary angles are seen. The observation of many large misorientation angles in particular suggests the presence of boundaries separating regions deforming with different sets of shear amplitudes (and hence a large misorientation angle due to the bias in dislocation trapping during deformation). To examine further the grain size dependence of the spread in boundary misorientation, data from TEM observations are plotted in Fig. 11(e). In this figure, the examined misorientation angles for all dislocation boundaries within each grain are plotted as a function of grain size. It is seen that large misorientations typical of GNB boundaries are indeed found even in grains with size down to 1.3 lm, where only cell structures are observed. Some of these large misorientations come from boundaries separating small volumes near triple junctions, but in many cases they extend continuously across a large fraction of the grains (see Fig. 11(b)). It is seen, therefore, that, in small grains, while well-defined cell blocks may not be formed, subdivision by the formation of boundaries with GNB characteristics still takes place.

Fig. 12. Summary of the effect of grain size effect on deformation microstructure pattern for SPS samples compressed to 20% reduction.

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The presence of many GNBs in grains as small as 1 lm, deforming in accordance with the imposed shape change by compression, may indicate that such GNBs or cell blocks can ensure homologous deformation with four or fewer slip systems, i.e. falling short of the five systems required in accordance with the Taylor criterion [49]. However, the combined deformation over different parts of a grain may, collectively, still fulfil this criterion. For the smallest grain size, the presence of dislocation bundles and random dislocations indicate a slip pattern with a limited dislocation interaction within grains during deformation. This may be a result of a relatively short slip length and efficient storage of dislocations in the grain boundaries instead of in the grain interior regions. The significant change in slip pattern following a reduction in grain size may affect such mechanical properties as the yield stress and the work hardening behaviour [46]. The results therefore are of both scientific and technological interest, and research in progress encompasses an analysis of the strengthening mechanisms and of strength–structure relationships, also including materials other than aluminium with grain sizes in the near-micrometre regime and even lower. 5. Conclusions Samples in a fully recrystallized condition with a random texture have been prepared with a range of grain sizes in the near-micrometre regime by use of a SPS process. Detailed examination of these samples after compression to a strain of 20% reveals the deformation microstructures to be of LEDS type, though with different characteristics as the grain size is decreased. The key observations are as follows:  The microstructure in grains with size of more than 7 lm is subdivided by cell blocks similar to those observed in deformed coarse-grained samples, and with a similar dependence on the crystallographic orientation of each grain.  Structural transitions are observed with decreasing grain size, from well-defined cell blocks to a cell structure down to a size of approx. 1 lm. For smaller grain sizes, the structural features are dislocation bundles and random dislocations, reflecting an increase in the dislocation line energy as a result of less dislocation interaction and reduced stress-screening.  The characteristic process of grain subdivision, either by the formation of cell blocks or by cells, is seen for grains down to a size of approx. 1 lm. For smaller grains, subdivision is observed when the strain is raised to 30% in the form of dislocation rotation boundaries developed in the grain interiors. The texture for all grain sizes is a standard h1 1 0i fibre texture, showing a decrease in sharpness with decreasing grain size.

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 The strong correlation between microstructure, slip pattern and grain size in the near-micrometre regime suggests a significant effect of grain size on the mechanical properties, including yield stress and work-hardening behaviour, which is of both scientific and technological interest.

Acknowledgements The authors gratefully acknowledge support from the Danish National Research Foundation (Grant No. DNRF86-5) and the National Natural Science Foundation of China (Grant Nos. 51261130091 and 50971074) for the Danish–Chinese Center for Nanometals, within which this work was performed. References [1] Hansen N. Metall Mater Trans A 2001;32:2917. [2] Bay B, Hansen N, Hughes DA, Kuhlmann-Wilsdorf D. Acta Metall Mater 1992;40:205. [3] Driver JH, Jensen DJ, Hansen N. Acta Metall Mater 1994;42:3105. [4] Albou A, Driver JH, Maurice C. Acta Mater 2010;58:3022. [5] Huang X, Hansen N. Scripta Mater 1997;37:1. [6] Huang X. Scripta Mater 1998;38:1697. [7] Huang X, Winther G. Philos Mag 2007;87:5189. [8] Hughes DA, Hansen N. Acta Mater 2000;48:2985. [9] Le GM, Godfrey A, Hong CS, Huang X, Winther G. Scripta Mater 2012;66:359. [10] Cizek P. Acta Mater 2010;58:5820. [11] Taylor AS, Cizek P, Hodgson PD. Acta Mater 2012;60:1548. [12] Gutierrez-Urrutia I, Raabe D. Acta Mater 2012;60:5791. [13] Gurtierrez-Urrutia I, Raabe D. Scripta Mater 2013;69:53. [14] Hughes DA, Hansen N. Plastic deformation structures. Materials Park (OH): ASM International; 2004. p. 192. [15] Lee CS, Duggan BJ. Acta Metall Mater 1993;41:2691. [16] Liu Q, Maurice C, Driver J, Hansen N. Metall Mater Trans A 1998;29:2333. [17] Kuhlmann-Wilsdorf D. Acta Mater 1999;47:1697. [18] Liu Q, Hansen N. Scripta Metall Mater 1995;32:1289. [19] Liu Q, Huang X, Lloyd DJ, Hansen N. Acta Mater 2002;50:3789. [20] Hughes DA, Chrzan DC, Liu Q, Hansen N. Phys Rev Lett 1998;81:4664. [21] Hughes DA. Scripta Mater 2002;47:697. [22] Godfrey A, Hughes DA. Acta Mater 2000;48:1897. [23] Pantleon W, Hansen N. Acta Mater 2001;49:1479. [24] Liu Q, Jensen DJ, Hansen N. Acta Mater 1998;46:5819. [25] Lin FX, Godfrey A, Winther G. Scripta Mater 2009;61:237. [26] Winther G, Huang X. Philos Mag 2007;87:5215. [27] Winther G. Acta Mater 2008;56:1919. [28] Feaugas X, Haddou H. Philos Mag 2007;87:989. [29] Huang X, Hansen N. Mater Sci Eng A – Struct 2004;387:186. [30] Thompson AW, Backofen WA. Metall Trans 1971;2:2004. [31] Jensen DJ, Thompson AW, Hansen N. Metall Trans A 1989;20:2803. [32] Kamikawa N, Tsuji N, Huang X, Hansen N. Acta Mater 2006;54:3055. [33] Munir ZA, Anselmi-Tamburini U, Ohyanagi M. J Mater Sci 2006;41:763. [34] Saheb N, Iqbal Z, Khalil A, Hakeem AS, Al Aqeeli N, Laoui T, et al. J Nanomater 2012;2012:13. [35] Fellah F, Schoenstein F, Omrani AD, Cherif SM, Dirras G, Jouini N. Mater Charact 2012;69:1.

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