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A crystallographic study of dislocation cell arrangement in aluminium deformed at an elevated temperature
MATERIALS SCIENCE & ENGINEERING ELSEVIER
Materials Science and Engineering A194 (1995) 201-210
A
A crystallographic study of dislocation cell arrangement in aluminium deformed at an elevated temperature P. Cizek a, B.A. Parker a, D.G. M c C u l l o c h b aDepartment of Materials Engineering, Monash University, Clayton, Victoria 3168, Australia bElectron Microscope Unit, The University of Sydney, Sydney, New South Wales 2006, Australia Received 1 June 1994; in revised form 1 August 1994
Abstract The arrangement of dislocation cells in a commercial aluminium alloy 1145 subjected to uniaxial tensile deformation at 150 °C to a true strain of 0.1 has been investigated using transmission electron microscopy and convergent beam electron diffraction. Both misorientations between neighbouring dislocation cells and misorientation gradients across the grain as well as dislocation boundary orientations have been analysed. As an example, illustrating general qualitative features of the deformation microstructure as a whole, results of a detailed crystallographic analysis of a typical cell arrangement are presented. The results obtained in the study are compared to those available for similar deformation conditions at room temperature and the validity of some assumptions from the theory of low-energy dislocation structures is discussed. It is concluded that the observed cell structure has a complex hierarchical character and neither misorientation vector distributions nor dislocation boundary orientations correspond to the simple checkerboard arrangement of cells predicted by the above theory.
Keywords: Dislocation; Aluminium; Deformation
1. Introduction T h e detailed study of the microstructures f o r m e d during plastic d e f o r m a t i o n of metallic materials is important in providing a better understanding of deformation mechanisms, mechanical properties and texture formation. T h e evolution of d e f o r m a t i o n microstructures in aluminium polycrystals has b e e n studied extensively, especially for d e f o r m a t i o n at r o o m temperature [1-7]. T h e r e have been new d e v e l o p m e n t s in the systemization of these microstructures recently and a new m o d e l has b e e n suggested to describe the evolution of microstructure with increasing strain [4,7-9]. According to this model, the subdivision of grains into differently oriented regions occurs during d e f o r m a t i o n of a polycrystal. This process is governed by the requirements for strain a c c o m m o d a t i o n and the principles of energy minimization in developing microstructures [10-12]. During the initial stage of deformation, dislocation cells and later dense dislocation walls (DDWs) develop. L o n g D D W s are the 0921-5093/95/$9.50 © 1995 - Elsevier Science S.A. All rights reserved SSDI 0921-5093(94)09675-9
boundaries between cell blocks (CBs) in which different combinations of slip systems operate. A s a consequence, larger misorientations develop across D D W s than across ordinary cell walls, which leads to the formation of a "hierarchical" cell structure [10]. During deformation at r o o m t e m p e r a t u r e s o m e additional microstructural inhomogeneities (first and second generation microbands) are also observed with increasing strain [4,7] and their role in the deformation process has been described [4,8,9]. T h e detailed analyses of the crystallographic p a r a m e t e r s of d e f o r m a t i o n microstructures in aluminium that are available in the literature deal either with individual estimates of misorientation angles for small isolated regions [1] or the investigation is oriented predominantly towards m i c r o b a n d s [4,6,9]. T h e crystallographic study of regular cell structures created at the initial stages of d e f o r m a t i o n has received less attention and has been limited to r o o m t e m p e r a t u r e [5]. T h e aim of the present work was to investigate the influence of an increased t e m p e r a t u r e on s o m e crystal-
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lographic parameters of the deformed microstructure in aluminium at the initial stage of deformation. For that reason an aluminium alloy 1145 lightly deformed in tension at 150 °C was studied using transmission electron microscopy and microdiffraction. As it is well known that accumulated strain varies from grain to grain during deformation of a polycrystal, the present study is not aimed at a quantitative statistical description of microstructural parameters (such as a mean cell size or a mean misorientation angle), the validity of which remains questionable even after analysing a very large number of dislocation cells in many grains. Instead, most attention is focused on the crystallographic character of dislocation cell arrangement that was found to be qualitatively similar practically in all the grains examined during a preliminary electron microscopic investigation. In this study we used a simplified crystallographic analysis based on the evaluation of Kikuchi line shifts [5]. As an example, a detailed crystallographic study of a dislocation cell arrangement, that reflects typical general features of the studied deformation microstructure, is presented in the following. Misorientations between neighbouring cells as well as misorientation gradients across the grain were analysed including a detailed distribution of misorientation axes. Dislocation boundary orientations with respect to both slip planes {111} and macroscopically imposed deformation geometry were also determined. The results obtained in the study are compared to those available for similar deformation conditions at room temperature and some assumptions of the theory of low-energy dislocation structures (LEDS) [ 13,14] are critically discussed.
2. Experimental procedure The material examined was a commercial aluminium alloy 1145 with the chemical composition given in Table 1. The mean grain size was about 30/~m. The alloy was subjected to uniaxial tensile deformation at 150 °C at a strain rate of 2 × 10 -3 s- l to a true strain of 0.1. Tensile sheet specimens with a cross-section of 1.2 x 12 mm and a gauge length of 80 mm had no pronounced starting texture. Thin foils for transmission electron microscopy were prepared by the standard twin-jet polishing of thin discs in an electrolyte
consisting of 33 ml nitric acid and 67 ml methanol. Optimum polishing conditions were obtained between 10 and 15 V at - 20 °C. The tensile axis direction was marked on each foil and from these marks the relationship between the orientation of electron micrographs and the sample axes was determined within _+2 °. The examination was performed using a Philips CM 20 microscope operating at 200 kV. As the deformation temperature was rather high and the alloy contained some impurities, the dislocation cell structures under investigation could be expected to be rather stable. Nevertheless, a low storage temperature was used to minimize any damage. A mean dislocation cell size was estimated using the modified Johnson method of quantitative metallography [15]. Convergent beam electron diffraction (CBED) was used to study local crystallographic orientations. This technique allows small volumes (less than about 0.5/~m) in diameter to be examined [16]. A computerized method [17] was implemented to process the data measured on Kikuchi patterns. The orientation of each crystallite with respect to the fixed reference (sample) coordinate system was determined first. Then, the misorientation angle and the corresponding misorientation axis (expressed in both the sample and the crystallographic coordinates) were calculated for any two crystallites of interest. This misorientation vector was chosen as the minimum value from 24 possible crystallographically equivalent solutions. Experimental error in the determination of vectors of misorientation was + 0.1 °. Throughout the paper the following conventions are used. If misorientations between any two neighbouring cells are calculated, a misorientation vector describes the rotation bringing crystallographic axes of a lowernumber cell into coincidence with those of a highernumber cell. If cumulative misorientations of any cell with respect to a reference cell are calculated, a misorientation vector represents the rotation bringing crystallographic axes of the reference cell into coincidence with those corresponding to any other cell. A misorientation angle is taken as positive if rotation from one crystallographic cell frame into another is clockwise looking in a misorientation axis direction. In pole figures reflecting the tensile sheet specimen geometry the x axis coincides with the tensile direction, the y axis is parallel to the transverse direction and the z axis coincides with the normal to the sheet plane.
Table 1 Chemical compositionof the studied alloy(mass %) Si
Fe
Cu
Mg
Zn
Ni
Mn
Cr
Ti
AI
0.08
0.36
0.005
0.002
0.007
0.001
0.004
0.004
0.02
99.51
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Results
Fig. l(a) shows a bright-field image of the deformation microstructure in the interior of the grain of interest. The orientations of crystallographic axes of the dislocation ceils inside this grain expressed with respect to the macroscopic sample geometry are presented in a pole figure in Fig. 2. The schematic diagram in Fig. l(b) shows the misorientation angles across all the cell boundaries. From the comparison between the morphological features of the boundaries and the misorientation angles across them it is clear that the cells are not arranged chaotically but that the substructure has a hierarchical character [10]. The most prominent feature is the presence of long continuous boundaries with misorientations of about 1°, and above, which are drawn by the solid line in Fig. l(b). These boundaries, locally combined with those misoriented slightly less than 1°, delineate regions in which the cell misorientation angles are mostly significantly smaller. This indicates that the grain is at the initial stage of its subdivision into mutually rotated cell blocks, delineated by dense dislocation walls, in correspondence with the published model [4,7-9]. A closer examination revealed that the main large CBs tend to be locally subdivided further into smaller fragments which makes the hierarchical structure even more complex. This gives the impression that, with increasing strain, cell hierarchy would tend to become more complicated because larger cell blocks would be gradually subdivided into smaller "second-generation" CBs and these into still fainter "third-generation" ones, and so on [10], the misorientations between these latergeneration CBs being generally smaller than those across the long DDWs formed earlier. The presence of DDWs and the hierarchical character of dislocation cell arrangements described above are typical general features observed practically in all the grains examined during the investigation. Although both the number of DDWs and their length differ from grain to grain, in the majority of cases they are arranged geometrically similar to Fig. 1, along the original grain boundaries. Morphologically, the cells are mostly roughly equiaxed and less rectangular than the majority of those observed during deformation at room temperature [3,4]. The distribution of cell sizes, found in the particular region of interest and represented by the equivalent sphere diameters [15], is shown in Fig. 3. The mean cell size was estimated to be about 2.3/~m with a standard deviation of 0.9 /~m. We tried to find out whether some first-generation microbands are present in the microstructure. They were described in [4] as small pancake-shaped cells often observed along DDWs and characterized by higher misorientation angles across their boundaries compared to ordinary
TA
TA
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+.
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Fig. 1. Dislocation cell structure in the interior of the deformed grain of interest: (a) bright-field image; (b) schematic showing the misorientation angles across the cell boundaries (TA indicates the tensile axis direction).
x
Fig. 2. {100}pole figure representing the orientations of crystallographic axes of the dislocation cells expressed with respect to the macroscopic sample geometry.
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h
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Fig. 3. Distribution of the cell sizes represented by equivalent sphere diameters.
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cells. As far as the grain of interest is concerned, there are several small cells in the microstructure (see Fig. 1) that are morphologically somewhat similar to the above microbands (e.g. 20-21, 5 5 - 5 6 or 6 4 - 6 5 ) but neither their crystallographic parameters nor their size differs significantly from the rest of the cells under investigation. It seems reasonable to suppose that they are small ordinary cells of a particular shape rather than some special kind of inhomogeneity. A n extensive examination of the microstructural features in combination with the simplified crystallographic analysis, mentioned above, shows that the same applies for the rest of the grains under investigation. They contain a statistically roughly equivalent amount of small cells, morphologically similar to those described above, that do not differ crystallographically from the larger ones. No specific and striking morphological features, qualitatively different from those discussed above, have been observed during the present study. The distribution of misorientation angles from Fig. 1 is presented in a histogram in Fig. 4(a). The average misorientation angle is about 0.7 °, with a standard deviation of 0.3 °, the maximum misorientation angle being 1.6 °. Figs. 4(b) and 4(c) show the distribution of corresponding misorientation axes in the pole figure for the sample coordinates and in the standard stereographic triangle respectively. It is clear from Fig. 4(b) that some misorientation axes expressed in the sample coordinate system show a tendency to align themselves parallel to the direction normal to the plane of the tensile sheet specimen but the majority of them are scattered throughout the pole figure. As far as the sense of rotation is concerned, it is necessary to bear in mind that this parameter is influenced by the cell order in which misorientation vectors were calculated (see Section 2). The above misorientation axes expressed in the crystallographic coordinates are distributed almost randomly around the standard stereographic triangle (Fig. 4(c)).
,o
0 00
1
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,~
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001
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cell boundaries: (a) misorientation angles; (b) misorientation axes in the sample coordinates; (c) misorientation axes in the crystal lattice coordinates (filled circles indicate positive rotations while open circles represent negative rotations--the same also applies for Figs. 5-9).
The results of the misorientation gradient analysis performed across the grain at angles of 0 °, 45 °, 90 ° and 135 ° with respect to the tensile direction are presented in Figs. 5-8. From the inspection of the data presented in the above figures it is clear that the maximum misorientation angle of 3.1 ° is observed in a direction parallel to the tensile axis (Fig. 5(a)). It is necessary to note, however, that this value corresponds, at the same time, to the largest number of cells used in the calculation. The lattice curvature developed across the grain is manifested by angles in the range from about 2 °
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3.0
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111
/ 30
/z 001
33 e • 31
e
"~o
•
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0
15
/"
1
001
• 60
e22
011
C C
Fig. 5. Misorientation gradient analysis across the grain along the
tensile axis direction (line A~A* in Fig. l(b)): (a) misorientation angles; (b) misorientation axes in the sample coordinates; (c) misorientation axes in the crystal lattice coordinates (calculation was performed with respect to the reference cell no. 40, e.g. the misorientation vector represented by number 39 corresponds to the misorientation 40/39 and so on--the same convention also applies for Figs. 6-9).
to 3 ° for all four directions under investigation. T h e histograms in Figs. 5 - 8 show that the misorientation angles increase continuously with the distance from one boundary facet towards the opposite one. This means that the misorientations are mutually cumulative and have no tendency to cancel each other effectively. T h e only exception is in the tensile direction where the corresponding histogram has a "wavy" appearance
Fig. 6. Same as in Fig. 5 for an angle of 45 ° to the tensile axis direction (line B ~ B* in Fig. 1(b)) using the reference cell no. 14.
in this particular case (Fig. 5(a)). This observation reminds one of the results presented in [18] where a m o r e turbulent wavy misorientation pattern was observed in the extension direction than in the compression direction during plane strain compression of an aluminium monocrystal at r o o m temperature. However, more experimental evidence would be necessary to decide whether the above p h e n o m e n o n [18] is also applicable, to some extent, to deformed polycrystals. T h e distribution of misorientation axes for the tensile direction expressed in the sample coordinates in Fig. 5(b) is again somewhat different from the rest of the
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~
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Materials Science and Engineering A194 (1995) 201-210
56 57i
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20
25
a
Y
X
b
x 111
111
/ 001
/
10"~. 22
20
01
001
)11
c
Fig. 7. Same as in Fig. 5 for an angle of 90 ° to the tensile axis direction (line C-* C* in Fig. 1(b)) using the reference cell no. 1.
Fig. 8. Same as in Fig. 5 for an angle of 135 ° to the tensile axis direction (line D -,D* in Fig. l(b)) using the reference cell no. 7.
macroscopic directions analysed (Figs. 6(b)-8(b)). Fig. 5(b) shows that in this case the misorientation axes are situated predominantly close to the plane normal to the transverse direction y in the pole figure and are characterized by the largest angular scatter c o m p a r e d to the rest of the macroscopic directions analysed. This observation further suggests a higher turbulence of the misorientation vectors along the tensile direction. T h e above misorientation vectors when expressed in crystallographic coordinates are generally arranged slightly more randomly around the standard stereographic
triangle than is the case for the pole figures reflecting the sample geometry (Figs. 5 - 8 ). T h e detailed analysis of misorientation gradients from the centre of the grain towards its boundary was also made in the same macroscopic directions as the analysis described above. A n example of the results obtained for the tensile direction is shown in Fig. 9. It was generally observed that the misorientation angles increase systematically from the grain centre towards the boundary. T h e maximum misorientation angle of 2.3 ° was observed in the tensile direction (Fig. 9) while
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the rest of the angles lies approximately in the range from 1° to 2 °. The distributions of misorientation axes in both the sample and crystallographic coordinates had a similar character to those in Figs. 5-8, except that a slightly higher scatter was observed (e.g. compare Fig. 9 with Fig. 5). The study of misorientation gradients in a large number of grains, using Kikuchi line shifts, confirms the finding that misorientations across grains are generally strictly cumulative. Slightly oscillating misorientation patterns, similar to that described above for the
o
3.0
31 c 2.0 O
O
.T 1.0 E 5
10 15 distonce [~um]
20
301 z
25
~8J y
×
111
207
tensile direction, are rarely observed and cannot be connected exclusively with this direction. The angles, representing lattice curvatures developed across the grains, are always less than about 5 °. It has also been confirmed that misorientation axis vectors are distributed in a complex way. The results of the trace analysis performed for all dislocation boundaries in the region of interest (i.e. including both ordinary cell boundaries and DDWs) are summarized in Figs. 10-12. It is necessary to note here that for the above analysis traces of the dislocation boundaries in the thin foil instead of their precise crystallographic orientations were used. Fig. 10 shows the distribution of angles between each boundary trace and the nearest l111} slip plane trace. From this figure it is clear that about 40% of the dislocation boundaries lie close (within 10 °) to a slip plane. If only DDWs are taken into account, this value is just slightly lower (about 37%). The relationship between macroscopically imposed deformation geometry and the boundary orientations is illustrated in Fig. 11 showing the distribution of angles between the tensile direction and the individual boundary traces. It is obvious that the observed angles cover essentially the whole angular range from 0 ° to 90 °. The histogram in Fig. 12 represents the distribution of angles between the misorientation axis and boundary normal traces. The angles from the interval 0 °- 10 ° were taken as those corresponding roughly to purely twist boundaries (the boundary normal is parallel to the misorientation axis) and the angular interval 800-90 ° approximates purely tilt boundaries (the boundary normal is perpendicular to the misorientation axis). On the above basis, the fraction of twist and tilt boundaries was about 7.5% and 11% respectively. If just DDWs are taken into account, the fraction of twist boundaries drops to about 3% whereas that of tilt boundaries increases approximately to 13%. From the above analysis it is clear that more than 80% of all the boundaries are of general character. The results of a trace analysis, described above, reflect
5 •
30 ¸ 25 20 ¸
001
0
1
c Fig. 9. Misorientation gradient analysis from the centre of the grain towards its boundary along the tensile axis direction (lines A ~ 0 and 0 ~A* in Fig. l(b)) using the reference cell no. 35: (a) misorientation angles; (b) misorientation axes in the sample coordinates; (c) misorientation axes in the crystal lattice coordinates.
o z
15
UJ
O
10.
UJ
LI-
"
,
0
•
,
5
.
,
10
.
.
.
II I .
,
15 20 25 ANGLE [deg]
IF-] ,
,
30
35
Fig. 10. Distribution of angles measured from each boundary trace to the nearest {111 } slip plane trace.
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10
~8
0
'
'
'
,
10 20
"
,
,
,
"
30 40 50 60 ANGLE [(leg]
,
"
70
'
"
80
'
90
Fig. 11. Distribution of angles between the tensile axis direction and the individualboundary traces.
10 8
0
,
0
-
,
10
•
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20
•
,
•
30
,
40
•
,
50
-
,
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,
60
70
80
•
,
90
ANGLE [deg]
Fig. 12. Distribution of angles between each boundary normal trace and the correspondingmisorientationaxis trace.
general trends observed in the microstructure. The majority of cell boundaries are not parallel to {111 } slip plane traces. There is no pronounced preferred orientation of the boundaries with respect to the macroscopic sample geometry and special (tilt and twist) boundaries do not seem to be observed more frequently than general ones.
4. Discussion
Generally, the results presented here are in a good agreement with the model proposed recently [4,7-9]. Despite the rather low strain, the microstructure has a clear hierarchical character and is composed of both ordinary cells and DDWs (see Fig. 1 ). These DDWs are close to the initial stage of their formation in this case and a gradual increase of their misorientation angles as well as decrease of the mean cell block size could be expected with further straining [4,10]. No pronounced special inhomogeneities (such as microbands) were observed during the present study despite the fact that weakly developed first-generation microbands were often observed in pure aluminium cold rolled to a strain of 0.1 [4]. This suggests that the importance of such inhomogeneities in microstructural evolution
decreases with increasing deformation temperature and decreasing strain rate. A simpler deformation geometry of uniaxial tension compared to rolling may play some role also. To the best of our knowledge, the only available systematic study of misorientations between dislocation cells in aluminium deformed in tension at room temperature to a true strain of 0.1 has been presented by Barker et al. [5]. The mean misorientation angle was reported to be about 1.7 °. The above study, however, was performed on high-purity aluminium with a grain size of 60 /~m at a strain rate of 7× 10 -2 s -1 for an unspecified grain orientation. The comparison with our mean misorientation angle value, that applies just for the particular region of interest and was obtained under somewhat different conditions, may be then only qualitative. Nevertheless, the difference between the mean misorientation angle of 1.7 °, found in [5], and our value of 0.7 ° is so large that the tendency for decrease of misorientation angles with increasing deformation temperature (and decreasing strain rate) may be suggested. This is in correspondence with the results of numerous experiments performed in the hot deformation range [19,20]. As far as the arrangement of dislocation cells is concerned, Barker et al. [5] reported some clustering of weakly and highly misoriented regions and they attributed this phenomenon to probable lack of homogeneity in the starting material. However, e.g. closer examination of the misorientation map in Fig. 4 from [5] indicates that the microstructure may have a hierarchical character somewhat similar to that found in the present study. Nevertheless, it seems reasonable to suppose that the hierarchical character of dislocation cell arrangements tends to be more pronounced with increasing deformation temperature. As far as the orientations of dislocation boundaries are concerned, the results of the present study show that at least 60% of these boundaries definitely do not lie along {111} slip planes (see Fig. 10). This tendency agrees well with published data [3,4]. The explanation of this phenomenon has been proposed in [4] on the basis of the application of Frank's formula to rotation dislocation boundaries created during plastic deformation [21]. According to this concept, a boundary orientation is a function of dislocation content. Even if the boundary begins to be formed on a {111 } plane, it will remain in that orientation only if it receives exactly the right density of dislocations with each contributing Burgers' vector during deformation. Relative shifts in the densities of dislocations with different Burgers' vectors will necessarily rotate the boundary [4,21]. A model of dislocation arrangement that has a particularly low strairL energy per unit length of a dislocation line has been proposed in [13,14,22]. According to this model the dislocations tend to form a three-dimen-
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sional checkerboard pattern of cubic cells with a common axis of relative misorientation. In this arrangement cell walls at right angles to the rotation axis are (essentially) twist boundaries whereas cell walls parallel to this axis represent (essentially) tilt boundaries. The sense of rotation alternates between adjacent cells, across all boundaries. However, dislocation arrangements somewhat similar to those predicted by the above model have been reported just occasionally and a majority of those observations were not tested using a detailed crystallographic analysis. More often cell walls appear to be randomly oriented [5,10]. The above observation was attributed in [10] predominantly to an insufficient mobility of dislocations at lower temperatures accompanied by their restricted ability to rearrange themselves into the checkerboard pattern which would minimize their energy most efficiently. This can be explained using the following argument [4,21]. Provided the dislocations are confined to move on their respective glide planes (at lower temperatures), at least six Burgers' vectors are necessary for the construction of low-energy dislocation boundaries with any arbitrary rotation axis and in any arbitrary orientation. If, however, the dislocations are mobile in three dimensions (at higher temperatures), then three independent Burgers' vectors are sufficient [4,21]. On the basis of the above concept, one may expect that the deformation temperature of 150 °C, used in the present study, should promote the formation of the highly organized checkerboard arrangement of dislocation cells [13,14,22]. The observed microstructural characteristics, however, do not confirm this tendency. Morphologically, neither checkerboard patterns nor parallel banded structures were found in the microstructure. The dislocation cells are characterized by irregular shapes and sizes (see Fig. 1) and their boundaries are oriented in a complex way (see Figs. 10 and 11). The lack of clustering in the distribution of misorientation axes expressed with respect to either macroscopic sample geometry (see Fig. 4(b)) or crystallographic directions (see Fig. 4(c)) indicates that there is no tendency towards arrangements involving rotations about almost parallel axes with alternating sense. This is further confirmed by the analysis of misorientation gradients across the grain showing that the misorientations are strictly cumulative and do not cancel each other (see Figs. 5-9). The fraction of special (tilt plus twist) boundaries is less than about 20% even with a generous allowance of a 10 ° deviation from the exact orientation (see Fig. 12) and, on top of that, the above value derived from the analysis of projected boundary traces always tends to be somewhat higher than a real one. Both the morphological features and the arrangement of misorientation angles (see Fig. 1) show that the cell structure has a hierarchical character.
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From the comparison of the cell structure characteristics described above with those predicted by the checkerboard pattern model [13,14,22] it follows that the model (even if understood as a rough first approximation) does not fit the experimental data. It is worth noting that the validity of the above model has been tested predominantly on banded structures characterized by roughly parallel boundaries with alternating left-right-left misorientation across them [10]. However, these structures may often simply be a manifestation of the presence of one family of parallel "kink" bands [23] or "reorientation" bands [24] in the deformed matrix. The above bands can be modelled as two parallel tilt walls consisting of dislocations with opposite signs and containing the reoriented volume between them [24]. If two such families of bands intersect, a well-organized checkerboard pattern may be formed [24]. Although these arrangements also represent some kind of low-energy dislocation structures, they are of entirely different origin from both ordinary cells and DDWs developed gradually from cell walls which are discussed here [24]. The differencebetween "kink" or "reorientation" bands described above and the banded structures composed of long parallel DDWs is, for instance, clear from the recent study of microstructural evolution in pure iron during hot rolling [25]. It has been shown that the misorientations across the "reorientation" bands (called "microbands" in [25]) were not cumulative, which is a logical consequence of approximately the same matrix orientation on both sides of these bands. On the contrary, the misorientations measured across the bands delineated by DDWs were strictly cumulative, which is also in correspondence with our results. The checkerboard pattern model [13,14,22] described above represents the arrangement in which dislocations screen their stress fields essentially under equilibrium conditions. During deformation, however, dislocations are subjected to gradually evolving stresses that are distributed in a complex and often inhomogeneous way. Dislocation walls seem to form in orientations where they can accommodate the overall strain by deforming a minimum amount themselves [26]. If the stress state changes they tend to rearrange themselves to cope with new accommodation requirements as confirmed by experiments involving a large strain-path change [26,27]. During deformation of polycrystals the above-mentioned accommodation processes lead to the formation of a gradually developing hierarchical cell structure containing dislocation boundaries oriented in a complex way and characterized by a wide range of misorientations. At present, it is not possible to predict quantitatively the parameters of such complex cell structures in general polycrystals but some first attempts have already been made under
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simplified conditions e.g. using samples with a strong cube texture [26].
5. Conclusions T h e cell structure observed in the present study has a hierarchical character being composed of both ordinary cells and DDWs at the initial stage of their formation, which corresponds well to the recently proposed model of deformation microstructures [4,7-9]. It has been d o c u m e n t e d that higher dislocation mobility, accompanying the increase of deformation temperature, does not lead to a tendency towards forming well-organized, simple cell arrangement which could be expected from the theory of low-energy dislocation structures (the checkerboard pattern model) [13,14,22]. Both the dislocation boundary orientations and the corresponding misorientation vectors are distributed in a complicated way that seems to be governed by a c c o m m o d a t i o n processes which are difficult to model at the present time.
[6] D. Juul Jensen and N. Hansen, Acta Metall. Mater., 38 (1990) 1369. [7] B. Bay, N. Hansen and D. Kuhlmann-Wilsdorf, Mater. Sci. Eng., A158(1992) 139. [8] N. Hansen, Mater. Sci. Technol., 6 (1990) 1039. [9] B. Bay, N. Hansen, D.A. Hughes and D. KuhlmannWilsdorf, Acta Metall. Mater., 40 (1992) 205. ]10] N. Hansen and D. Kuhlmann-Wilsdorf, Mater. Sci. Eng., 81 (1986)141. [11] D. Kuhlmann-Wilsdorf, Phys. Stat. Sol. (a), 104(1987) 121. [ 12] D. Kuhlmann-Wilsdoff, Mater. Sci. Eng., A l l 3 (1989) 1. [13] D. Kuhlmann-Wilsdorf and J.H. Van Der Merwe, Mater. Sci. Eng., 55(1982) 79. [14] P.J. Jackson and D. Kuhlmann-Wilsdorf, Scr. Metall., 16 (1982) 105. [15] E Schfickher, in R.T. De Hoff and EN. Rhines (eds.), Quantitative Microscopy, McGraw-Hill, New York, 1968, p. 201. [16] D.B. Williams, Practical Analytical Electron Microscopy in Materials Science, Chapman & Hall, London, 1984. [17] P. Cizek, D.G. McCulloch and B.A. Parker, in D. Allen et al. (eds.), Proc. 13th Biennial Conf. ACEM-13, Gold Coast, Australia, 7-11 February 1994, The Australian Society for Electron Microscopy, 1994, p. 110. [18] H. Weiland and J. Liu, in T.C. Lowe, A.D. Rollet, P.S. Follansbee and G.S. Daehn (eds.), Proc. Int. Symp. on Modelling the Deformation of Crystalline Solids, New Orleans, Louisiana, 17-21 February 1991, The Minerals,
Acknowledgment Financial support from the Australian Research Council is gratefully acknowledged.
References 11] P. Faivre and R.D. Doherty, J. Mater. Sci., 14 ( 1979) 897. [2] N. Hansen, Metall. Trans., 16A (1985) 2167. [3] C.T. Young, T.J. Headly and J.L. Lytton, Mater. Sci. Eng., 81 (1986)391. [4] B. Bay, N. Hansen and D. Kuhlmann-Wilsdoff, Mater. Sci. Eng., A l l 3 (1989) 385, [5] I. Barker, N. Hansen and B. Ralph, Mater. Sci. Eng., A l l 3 (1989) 449.
Metals & Materials Society, 1991, p. 61. [19] H.J. McQueen and J.E. Hockett, Metall. Trans., 1 (1970) 2997. [20] H.J. McQueen, Metall. Trans., 8A (1977) 807. [21] D. Kuhlmann-Wilsdorf, J. Appl. Phys., 33 (1962) 648. [22] M.N. Bassim and D. Kuhlmann-Wilsdorf, Phys. Stat. Sol. (a), 17(1973) 373. [23] J.W. Steeds, Proc. Roy. Soc. London, Ser. A, 292 (1966) 343. [24] A.R. Smirnov and V.A. Moskalenko, Phys. Met. Metall., 66 (1988) 162. [25] Wang Rizhi and T.C, Lei, Mater. Sci. Technol., 9 (1993) 698. [26] P.S. Bate, Metall. Trans., 24A (1993) 2679. [27] B.V.N. Rao and J.V. Laukonis, Mater. Sci. Eng., 60 (1983) 125.
Materials Science and Engineering A194 (1995) 201-210
A
A crystallographic study of dislocation cell arrangement in aluminium deformed at an elevated temperature P. Cizek a, B.A. Parker a, D.G. M c C u l l o c h b aDepartment of Materials Engineering, Monash University, Clayton, Victoria 3168, Australia bElectron Microscope Unit, The University of Sydney, Sydney, New South Wales 2006, Australia Received 1 June 1994; in revised form 1 August 1994
Abstract The arrangement of dislocation cells in a commercial aluminium alloy 1145 subjected to uniaxial tensile deformation at 150 °C to a true strain of 0.1 has been investigated using transmission electron microscopy and convergent beam electron diffraction. Both misorientations between neighbouring dislocation cells and misorientation gradients across the grain as well as dislocation boundary orientations have been analysed. As an example, illustrating general qualitative features of the deformation microstructure as a whole, results of a detailed crystallographic analysis of a typical cell arrangement are presented. The results obtained in the study are compared to those available for similar deformation conditions at room temperature and the validity of some assumptions from the theory of low-energy dislocation structures is discussed. It is concluded that the observed cell structure has a complex hierarchical character and neither misorientation vector distributions nor dislocation boundary orientations correspond to the simple checkerboard arrangement of cells predicted by the above theory.
Keywords: Dislocation; Aluminium; Deformation
1. Introduction T h e detailed study of the microstructures f o r m e d during plastic d e f o r m a t i o n of metallic materials is important in providing a better understanding of deformation mechanisms, mechanical properties and texture formation. T h e evolution of d e f o r m a t i o n microstructures in aluminium polycrystals has b e e n studied extensively, especially for d e f o r m a t i o n at r o o m temperature [1-7]. T h e r e have been new d e v e l o p m e n t s in the systemization of these microstructures recently and a new m o d e l has b e e n suggested to describe the evolution of microstructure with increasing strain [4,7-9]. According to this model, the subdivision of grains into differently oriented regions occurs during d e f o r m a t i o n of a polycrystal. This process is governed by the requirements for strain a c c o m m o d a t i o n and the principles of energy minimization in developing microstructures [10-12]. During the initial stage of deformation, dislocation cells and later dense dislocation walls (DDWs) develop. L o n g D D W s are the 0921-5093/95/$9.50 © 1995 - Elsevier Science S.A. All rights reserved SSDI 0921-5093(94)09675-9
boundaries between cell blocks (CBs) in which different combinations of slip systems operate. A s a consequence, larger misorientations develop across D D W s than across ordinary cell walls, which leads to the formation of a "hierarchical" cell structure [10]. During deformation at r o o m t e m p e r a t u r e s o m e additional microstructural inhomogeneities (first and second generation microbands) are also observed with increasing strain [4,7] and their role in the deformation process has been described [4,8,9]. T h e detailed analyses of the crystallographic p a r a m e t e r s of d e f o r m a t i o n microstructures in aluminium that are available in the literature deal either with individual estimates of misorientation angles for small isolated regions [1] or the investigation is oriented predominantly towards m i c r o b a n d s [4,6,9]. T h e crystallographic study of regular cell structures created at the initial stages of d e f o r m a t i o n has received less attention and has been limited to r o o m t e m p e r a t u r e [5]. T h e aim of the present work was to investigate the influence of an increased t e m p e r a t u r e on s o m e crystal-
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lographic parameters of the deformed microstructure in aluminium at the initial stage of deformation. For that reason an aluminium alloy 1145 lightly deformed in tension at 150 °C was studied using transmission electron microscopy and microdiffraction. As it is well known that accumulated strain varies from grain to grain during deformation of a polycrystal, the present study is not aimed at a quantitative statistical description of microstructural parameters (such as a mean cell size or a mean misorientation angle), the validity of which remains questionable even after analysing a very large number of dislocation cells in many grains. Instead, most attention is focused on the crystallographic character of dislocation cell arrangement that was found to be qualitatively similar practically in all the grains examined during a preliminary electron microscopic investigation. In this study we used a simplified crystallographic analysis based on the evaluation of Kikuchi line shifts [5]. As an example, a detailed crystallographic study of a dislocation cell arrangement, that reflects typical general features of the studied deformation microstructure, is presented in the following. Misorientations between neighbouring cells as well as misorientation gradients across the grain were analysed including a detailed distribution of misorientation axes. Dislocation boundary orientations with respect to both slip planes {111} and macroscopically imposed deformation geometry were also determined. The results obtained in the study are compared to those available for similar deformation conditions at room temperature and some assumptions of the theory of low-energy dislocation structures (LEDS) [ 13,14] are critically discussed.
2. Experimental procedure The material examined was a commercial aluminium alloy 1145 with the chemical composition given in Table 1. The mean grain size was about 30/~m. The alloy was subjected to uniaxial tensile deformation at 150 °C at a strain rate of 2 × 10 -3 s- l to a true strain of 0.1. Tensile sheet specimens with a cross-section of 1.2 x 12 mm and a gauge length of 80 mm had no pronounced starting texture. Thin foils for transmission electron microscopy were prepared by the standard twin-jet polishing of thin discs in an electrolyte
consisting of 33 ml nitric acid and 67 ml methanol. Optimum polishing conditions were obtained between 10 and 15 V at - 20 °C. The tensile axis direction was marked on each foil and from these marks the relationship between the orientation of electron micrographs and the sample axes was determined within _+2 °. The examination was performed using a Philips CM 20 microscope operating at 200 kV. As the deformation temperature was rather high and the alloy contained some impurities, the dislocation cell structures under investigation could be expected to be rather stable. Nevertheless, a low storage temperature was used to minimize any damage. A mean dislocation cell size was estimated using the modified Johnson method of quantitative metallography [15]. Convergent beam electron diffraction (CBED) was used to study local crystallographic orientations. This technique allows small volumes (less than about 0.5/~m) in diameter to be examined [16]. A computerized method [17] was implemented to process the data measured on Kikuchi patterns. The orientation of each crystallite with respect to the fixed reference (sample) coordinate system was determined first. Then, the misorientation angle and the corresponding misorientation axis (expressed in both the sample and the crystallographic coordinates) were calculated for any two crystallites of interest. This misorientation vector was chosen as the minimum value from 24 possible crystallographically equivalent solutions. Experimental error in the determination of vectors of misorientation was + 0.1 °. Throughout the paper the following conventions are used. If misorientations between any two neighbouring cells are calculated, a misorientation vector describes the rotation bringing crystallographic axes of a lowernumber cell into coincidence with those of a highernumber cell. If cumulative misorientations of any cell with respect to a reference cell are calculated, a misorientation vector represents the rotation bringing crystallographic axes of the reference cell into coincidence with those corresponding to any other cell. A misorientation angle is taken as positive if rotation from one crystallographic cell frame into another is clockwise looking in a misorientation axis direction. In pole figures reflecting the tensile sheet specimen geometry the x axis coincides with the tensile direction, the y axis is parallel to the transverse direction and the z axis coincides with the normal to the sheet plane.
Table 1 Chemical compositionof the studied alloy(mass %) Si
Fe
Cu
Mg
Zn
Ni
Mn
Cr
Ti
AI
0.08
0.36
0.005
0.002
0.007
0.001
0.004
0.004
0.02
99.51
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Results
Fig. l(a) shows a bright-field image of the deformation microstructure in the interior of the grain of interest. The orientations of crystallographic axes of the dislocation ceils inside this grain expressed with respect to the macroscopic sample geometry are presented in a pole figure in Fig. 2. The schematic diagram in Fig. l(b) shows the misorientation angles across all the cell boundaries. From the comparison between the morphological features of the boundaries and the misorientation angles across them it is clear that the cells are not arranged chaotically but that the substructure has a hierarchical character [10]. The most prominent feature is the presence of long continuous boundaries with misorientations of about 1°, and above, which are drawn by the solid line in Fig. l(b). These boundaries, locally combined with those misoriented slightly less than 1°, delineate regions in which the cell misorientation angles are mostly significantly smaller. This indicates that the grain is at the initial stage of its subdivision into mutually rotated cell blocks, delineated by dense dislocation walls, in correspondence with the published model [4,7-9]. A closer examination revealed that the main large CBs tend to be locally subdivided further into smaller fragments which makes the hierarchical structure even more complex. This gives the impression that, with increasing strain, cell hierarchy would tend to become more complicated because larger cell blocks would be gradually subdivided into smaller "second-generation" CBs and these into still fainter "third-generation" ones, and so on [10], the misorientations between these latergeneration CBs being generally smaller than those across the long DDWs formed earlier. The presence of DDWs and the hierarchical character of dislocation cell arrangements described above are typical general features observed practically in all the grains examined during the investigation. Although both the number of DDWs and their length differ from grain to grain, in the majority of cases they are arranged geometrically similar to Fig. 1, along the original grain boundaries. Morphologically, the cells are mostly roughly equiaxed and less rectangular than the majority of those observed during deformation at room temperature [3,4]. The distribution of cell sizes, found in the particular region of interest and represented by the equivalent sphere diameters [15], is shown in Fig. 3. The mean cell size was estimated to be about 2.3/~m with a standard deviation of 0.9 /~m. We tried to find out whether some first-generation microbands are present in the microstructure. They were described in [4] as small pancake-shaped cells often observed along DDWs and characterized by higher misorientation angles across their boundaries compared to ordinary
TA
TA
\
+.
,.~.~q~%.?o.~, ~.,,- d, ~ z z x . ~ - . + ~ . 9 , ~
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-.
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59
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Fig. 1. Dislocation cell structure in the interior of the deformed grain of interest: (a) bright-field image; (b) schematic showing the misorientation angles across the cell boundaries (TA indicates the tensile axis direction).
x
Fig. 2. {100}pole figure representing the orientations of crystallographic axes of the dislocation cells expressed with respect to the macroscopic sample geometry.
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h
o~" 20 15
,,z, 10
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.
.
.
.
.
.
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Fig. 3. Distribution of the cell sizes represented by equivalent sphere diameters.
o
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cells. As far as the grain of interest is concerned, there are several small cells in the microstructure (see Fig. 1) that are morphologically somewhat similar to the above microbands (e.g. 20-21, 5 5 - 5 6 or 6 4 - 6 5 ) but neither their crystallographic parameters nor their size differs significantly from the rest of the cells under investigation. It seems reasonable to suppose that they are small ordinary cells of a particular shape rather than some special kind of inhomogeneity. A n extensive examination of the microstructural features in combination with the simplified crystallographic analysis, mentioned above, shows that the same applies for the rest of the grains under investigation. They contain a statistically roughly equivalent amount of small cells, morphologically similar to those described above, that do not differ crystallographically from the larger ones. No specific and striking morphological features, qualitatively different from those discussed above, have been observed during the present study. The distribution of misorientation angles from Fig. 1 is presented in a histogram in Fig. 4(a). The average misorientation angle is about 0.7 °, with a standard deviation of 0.3 °, the maximum misorientation angle being 1.6 °. Figs. 4(b) and 4(c) show the distribution of corresponding misorientation axes in the pole figure for the sample coordinates and in the standard stereographic triangle respectively. It is clear from Fig. 4(b) that some misorientation axes expressed in the sample coordinate system show a tendency to align themselves parallel to the direction normal to the plane of the tensile sheet specimen but the majority of them are scattered throughout the pole figure. As far as the sense of rotation is concerned, it is necessary to bear in mind that this parameter is influenced by the cell order in which misorientation vectors were calculated (see Section 2). The above misorientation axes expressed in the crystallographic coordinates are distributed almost randomly around the standard stereographic triangle (Fig. 4(c)).
,o
0 00
1
\
Oo ~ , , o t . . - . ,
\
, - ~ o o o,,-,.i, ~ .
,~
~o o .,,~o...
i
o
×
111
001
0il
c
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cell boundaries: (a) misorientation angles; (b) misorientation axes in the sample coordinates; (c) misorientation axes in the crystal lattice coordinates (filled circles indicate positive rotations while open circles represent negative rotations--the same also applies for Figs. 5-9).
The results of the misorientation gradient analysis performed across the grain at angles of 0 °, 45 °, 90 ° and 135 ° with respect to the tensile direction are presented in Figs. 5-8. From the inspection of the data presented in the above figures it is clear that the maximum misorientation angle of 3.1 ° is observed in a direction parallel to the tensile axis (Fig. 5(a)). It is necessary to note, however, that this value corresponds, at the same time, to the largest number of cells used in the calculation. The lattice curvature developed across the grain is manifested by angles in the range from about 2 °
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Materials Science and Engineering A 194 (1995) 201-210
3.0
31 ;--'3.0
30
~., 2.0 cO
45
2.o
°0+I
o
Ul
0
-~- 1.0 E
5
0
60 64
o
58
0
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4 0
15 10 distonce [,um]
205
2'0
5
+ti+l 10
15
distance [~um]
2'5
20
Y
Z
X
X
b
111
111
/ 30
/z 001
33 e • 31
e
"~o
•
"~
0
15
/"
1
001
• 60
e22
011
C C
Fig. 5. Misorientation gradient analysis across the grain along the
tensile axis direction (line A~A* in Fig. l(b)): (a) misorientation angles; (b) misorientation axes in the sample coordinates; (c) misorientation axes in the crystal lattice coordinates (calculation was performed with respect to the reference cell no. 40, e.g. the misorientation vector represented by number 39 corresponds to the misorientation 40/39 and so on--the same convention also applies for Figs. 6-9).
to 3 ° for all four directions under investigation. T h e histograms in Figs. 5 - 8 show that the misorientation angles increase continuously with the distance from one boundary facet towards the opposite one. This means that the misorientations are mutually cumulative and have no tendency to cancel each other effectively. T h e only exception is in the tensile direction where the corresponding histogram has a "wavy" appearance
Fig. 6. Same as in Fig. 5 for an angle of 45 ° to the tensile axis direction (line B ~ B* in Fig. 1(b)) using the reference cell no. 14.
in this particular case (Fig. 5(a)). This observation reminds one of the results presented in [18] where a m o r e turbulent wavy misorientation pattern was observed in the extension direction than in the compression direction during plane strain compression of an aluminium monocrystal at r o o m temperature. However, more experimental evidence would be necessary to decide whether the above p h e n o m e n o n [18] is also applicable, to some extent, to deformed polycrystals. T h e distribution of misorientation axes for the tensile direction expressed in the sample coordinates in Fig. 5(b) is again somewhat different from the rest of the
206
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~
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Materials Science and Engineering A194 (1995) 201-210
56 57i
-~2.0
2.0
E o
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.£:
3.0 ?.
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15
10 1'5 distonce [,urn]
20
25
a
Y
X
b
x 111
111
/ 001
/
10"~. 22
20
01
001
)11
c
Fig. 7. Same as in Fig. 5 for an angle of 90 ° to the tensile axis direction (line C-* C* in Fig. 1(b)) using the reference cell no. 1.
Fig. 8. Same as in Fig. 5 for an angle of 135 ° to the tensile axis direction (line D -,D* in Fig. l(b)) using the reference cell no. 7.
macroscopic directions analysed (Figs. 6(b)-8(b)). Fig. 5(b) shows that in this case the misorientation axes are situated predominantly close to the plane normal to the transverse direction y in the pole figure and are characterized by the largest angular scatter c o m p a r e d to the rest of the macroscopic directions analysed. This observation further suggests a higher turbulence of the misorientation vectors along the tensile direction. T h e above misorientation vectors when expressed in crystallographic coordinates are generally arranged slightly more randomly around the standard stereographic
triangle than is the case for the pole figures reflecting the sample geometry (Figs. 5 - 8 ). T h e detailed analysis of misorientation gradients from the centre of the grain towards its boundary was also made in the same macroscopic directions as the analysis described above. A n example of the results obtained for the tensile direction is shown in Fig. 9. It was generally observed that the misorientation angles increase systematically from the grain centre towards the boundary. T h e maximum misorientation angle of 2.3 ° was observed in the tensile direction (Fig. 9) while
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Materials Science and Engineering A194 (1995) 201-210
the rest of the angles lies approximately in the range from 1° to 2 °. The distributions of misorientation axes in both the sample and crystallographic coordinates had a similar character to those in Figs. 5-8, except that a slightly higher scatter was observed (e.g. compare Fig. 9 with Fig. 5). The study of misorientation gradients in a large number of grains, using Kikuchi line shifts, confirms the finding that misorientations across grains are generally strictly cumulative. Slightly oscillating misorientation patterns, similar to that described above for the
o
3.0
31 c 2.0 O
O
.T 1.0 E 5
10 15 distonce [~um]
20
301 z
25
~8J y
×
111
207
tensile direction, are rarely observed and cannot be connected exclusively with this direction. The angles, representing lattice curvatures developed across the grains, are always less than about 5 °. It has also been confirmed that misorientation axis vectors are distributed in a complex way. The results of the trace analysis performed for all dislocation boundaries in the region of interest (i.e. including both ordinary cell boundaries and DDWs) are summarized in Figs. 10-12. It is necessary to note here that for the above analysis traces of the dislocation boundaries in the thin foil instead of their precise crystallographic orientations were used. Fig. 10 shows the distribution of angles between each boundary trace and the nearest l111} slip plane trace. From this figure it is clear that about 40% of the dislocation boundaries lie close (within 10 °) to a slip plane. If only DDWs are taken into account, this value is just slightly lower (about 37%). The relationship between macroscopically imposed deformation geometry and the boundary orientations is illustrated in Fig. 11 showing the distribution of angles between the tensile direction and the individual boundary traces. It is obvious that the observed angles cover essentially the whole angular range from 0 ° to 90 °. The histogram in Fig. 12 represents the distribution of angles between the misorientation axis and boundary normal traces. The angles from the interval 0 °- 10 ° were taken as those corresponding roughly to purely twist boundaries (the boundary normal is parallel to the misorientation axis) and the angular interval 800-90 ° approximates purely tilt boundaries (the boundary normal is perpendicular to the misorientation axis). On the above basis, the fraction of twist and tilt boundaries was about 7.5% and 11% respectively. If just DDWs are taken into account, the fraction of twist boundaries drops to about 3% whereas that of tilt boundaries increases approximately to 13%. From the above analysis it is clear that more than 80% of all the boundaries are of general character. The results of a trace analysis, described above, reflect
5 •
30 ¸ 25 20 ¸
001
0
1
c Fig. 9. Misorientation gradient analysis from the centre of the grain towards its boundary along the tensile axis direction (lines A ~ 0 and 0 ~A* in Fig. l(b)) using the reference cell no. 35: (a) misorientation angles; (b) misorientation axes in the sample coordinates; (c) misorientation axes in the crystal lattice coordinates.
o z
15
UJ
O
10.
UJ
LI-
"
,
0
•
,
5
.
,
10
.
.
.
II I .
,
15 20 25 ANGLE [deg]
IF-] ,
,
30
35
Fig. 10. Distribution of angles measured from each boundary trace to the nearest {111 } slip plane trace.
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10
~8
0
'
'
'
,
10 20
"
,
,
,
"
30 40 50 60 ANGLE [(leg]
,
"
70
'
"
80
'
90
Fig. 11. Distribution of angles between the tensile axis direction and the individualboundary traces.
10 8
0
,
0
-
,
10
•
,
20
•
,
•
30
,
40
•
,
50
-
,
,
,
60
70
80
•
,
90
ANGLE [deg]
Fig. 12. Distribution of angles between each boundary normal trace and the correspondingmisorientationaxis trace.
general trends observed in the microstructure. The majority of cell boundaries are not parallel to {111 } slip plane traces. There is no pronounced preferred orientation of the boundaries with respect to the macroscopic sample geometry and special (tilt and twist) boundaries do not seem to be observed more frequently than general ones.
4. Discussion
Generally, the results presented here are in a good agreement with the model proposed recently [4,7-9]. Despite the rather low strain, the microstructure has a clear hierarchical character and is composed of both ordinary cells and DDWs (see Fig. 1 ). These DDWs are close to the initial stage of their formation in this case and a gradual increase of their misorientation angles as well as decrease of the mean cell block size could be expected with further straining [4,10]. No pronounced special inhomogeneities (such as microbands) were observed during the present study despite the fact that weakly developed first-generation microbands were often observed in pure aluminium cold rolled to a strain of 0.1 [4]. This suggests that the importance of such inhomogeneities in microstructural evolution
decreases with increasing deformation temperature and decreasing strain rate. A simpler deformation geometry of uniaxial tension compared to rolling may play some role also. To the best of our knowledge, the only available systematic study of misorientations between dislocation cells in aluminium deformed in tension at room temperature to a true strain of 0.1 has been presented by Barker et al. [5]. The mean misorientation angle was reported to be about 1.7 °. The above study, however, was performed on high-purity aluminium with a grain size of 60 /~m at a strain rate of 7× 10 -2 s -1 for an unspecified grain orientation. The comparison with our mean misorientation angle value, that applies just for the particular region of interest and was obtained under somewhat different conditions, may be then only qualitative. Nevertheless, the difference between the mean misorientation angle of 1.7 °, found in [5], and our value of 0.7 ° is so large that the tendency for decrease of misorientation angles with increasing deformation temperature (and decreasing strain rate) may be suggested. This is in correspondence with the results of numerous experiments performed in the hot deformation range [19,20]. As far as the arrangement of dislocation cells is concerned, Barker et al. [5] reported some clustering of weakly and highly misoriented regions and they attributed this phenomenon to probable lack of homogeneity in the starting material. However, e.g. closer examination of the misorientation map in Fig. 4 from [5] indicates that the microstructure may have a hierarchical character somewhat similar to that found in the present study. Nevertheless, it seems reasonable to suppose that the hierarchical character of dislocation cell arrangements tends to be more pronounced with increasing deformation temperature. As far as the orientations of dislocation boundaries are concerned, the results of the present study show that at least 60% of these boundaries definitely do not lie along {111} slip planes (see Fig. 10). This tendency agrees well with published data [3,4]. The explanation of this phenomenon has been proposed in [4] on the basis of the application of Frank's formula to rotation dislocation boundaries created during plastic deformation [21]. According to this concept, a boundary orientation is a function of dislocation content. Even if the boundary begins to be formed on a {111 } plane, it will remain in that orientation only if it receives exactly the right density of dislocations with each contributing Burgers' vector during deformation. Relative shifts in the densities of dislocations with different Burgers' vectors will necessarily rotate the boundary [4,21]. A model of dislocation arrangement that has a particularly low strairL energy per unit length of a dislocation line has been proposed in [13,14,22]. According to this model the dislocations tend to form a three-dimen-
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sional checkerboard pattern of cubic cells with a common axis of relative misorientation. In this arrangement cell walls at right angles to the rotation axis are (essentially) twist boundaries whereas cell walls parallel to this axis represent (essentially) tilt boundaries. The sense of rotation alternates between adjacent cells, across all boundaries. However, dislocation arrangements somewhat similar to those predicted by the above model have been reported just occasionally and a majority of those observations were not tested using a detailed crystallographic analysis. More often cell walls appear to be randomly oriented [5,10]. The above observation was attributed in [10] predominantly to an insufficient mobility of dislocations at lower temperatures accompanied by their restricted ability to rearrange themselves into the checkerboard pattern which would minimize their energy most efficiently. This can be explained using the following argument [4,21]. Provided the dislocations are confined to move on their respective glide planes (at lower temperatures), at least six Burgers' vectors are necessary for the construction of low-energy dislocation boundaries with any arbitrary rotation axis and in any arbitrary orientation. If, however, the dislocations are mobile in three dimensions (at higher temperatures), then three independent Burgers' vectors are sufficient [4,21]. On the basis of the above concept, one may expect that the deformation temperature of 150 °C, used in the present study, should promote the formation of the highly organized checkerboard arrangement of dislocation cells [13,14,22]. The observed microstructural characteristics, however, do not confirm this tendency. Morphologically, neither checkerboard patterns nor parallel banded structures were found in the microstructure. The dislocation cells are characterized by irregular shapes and sizes (see Fig. 1) and their boundaries are oriented in a complex way (see Figs. 10 and 11). The lack of clustering in the distribution of misorientation axes expressed with respect to either macroscopic sample geometry (see Fig. 4(b)) or crystallographic directions (see Fig. 4(c)) indicates that there is no tendency towards arrangements involving rotations about almost parallel axes with alternating sense. This is further confirmed by the analysis of misorientation gradients across the grain showing that the misorientations are strictly cumulative and do not cancel each other (see Figs. 5-9). The fraction of special (tilt plus twist) boundaries is less than about 20% even with a generous allowance of a 10 ° deviation from the exact orientation (see Fig. 12) and, on top of that, the above value derived from the analysis of projected boundary traces always tends to be somewhat higher than a real one. Both the morphological features and the arrangement of misorientation angles (see Fig. 1) show that the cell structure has a hierarchical character.
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From the comparison of the cell structure characteristics described above with those predicted by the checkerboard pattern model [13,14,22] it follows that the model (even if understood as a rough first approximation) does not fit the experimental data. It is worth noting that the validity of the above model has been tested predominantly on banded structures characterized by roughly parallel boundaries with alternating left-right-left misorientation across them [10]. However, these structures may often simply be a manifestation of the presence of one family of parallel "kink" bands [23] or "reorientation" bands [24] in the deformed matrix. The above bands can be modelled as two parallel tilt walls consisting of dislocations with opposite signs and containing the reoriented volume between them [24]. If two such families of bands intersect, a well-organized checkerboard pattern may be formed [24]. Although these arrangements also represent some kind of low-energy dislocation structures, they are of entirely different origin from both ordinary cells and DDWs developed gradually from cell walls which are discussed here [24]. The differencebetween "kink" or "reorientation" bands described above and the banded structures composed of long parallel DDWs is, for instance, clear from the recent study of microstructural evolution in pure iron during hot rolling [25]. It has been shown that the misorientations across the "reorientation" bands (called "microbands" in [25]) were not cumulative, which is a logical consequence of approximately the same matrix orientation on both sides of these bands. On the contrary, the misorientations measured across the bands delineated by DDWs were strictly cumulative, which is also in correspondence with our results. The checkerboard pattern model [13,14,22] described above represents the arrangement in which dislocations screen their stress fields essentially under equilibrium conditions. During deformation, however, dislocations are subjected to gradually evolving stresses that are distributed in a complex and often inhomogeneous way. Dislocation walls seem to form in orientations where they can accommodate the overall strain by deforming a minimum amount themselves [26]. If the stress state changes they tend to rearrange themselves to cope with new accommodation requirements as confirmed by experiments involving a large strain-path change [26,27]. During deformation of polycrystals the above-mentioned accommodation processes lead to the formation of a gradually developing hierarchical cell structure containing dislocation boundaries oriented in a complex way and characterized by a wide range of misorientations. At present, it is not possible to predict quantitatively the parameters of such complex cell structures in general polycrystals but some first attempts have already been made under
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simplified conditions e.g. using samples with a strong cube texture [26].
5. Conclusions T h e cell structure observed in the present study has a hierarchical character being composed of both ordinary cells and DDWs at the initial stage of their formation, which corresponds well to the recently proposed model of deformation microstructures [4,7-9]. It has been d o c u m e n t e d that higher dislocation mobility, accompanying the increase of deformation temperature, does not lead to a tendency towards forming well-organized, simple cell arrangement which could be expected from the theory of low-energy dislocation structures (the checkerboard pattern model) [13,14,22]. Both the dislocation boundary orientations and the corresponding misorientation vectors are distributed in a complicated way that seems to be governed by a c c o m m o d a t i o n processes which are difficult to model at the present time.
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Acknowledgment Financial support from the Australian Research Council is gratefully acknowledged.
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