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Microstructure and shear band formation in rolled single crystals of AlMg alloy
~cra metall. Vol. 35, No. I, pp. 1747-1755, Printed in Great Britain. All rights reserved
1987 Copyright
0
OOOI-6160/87 $3.00 + 0.00 1987 Pergamon Journals Ltd
MICROSTRUCTURE AND SHEAR BAND FORMATION IN ROLLED SINGLE CRYSTALS OF Al-Mg ALLOY College of ~ngin~~ng,
Y. NAKAYAMA and K. MORE1 University of Osaka Prefecture, Mozu-Umemachi,
Sakai 591, Japan
(Received 7 August 1986; in revised form 8 October 1986)
Abstract-The development of dislocation structures in the (21 I)[fl I] single crystals of AI-3%Mg has been investigated in relation to shear band formation after rolling at room temperature and 473 K. During rolling at RT, the dislocation structures which developed with increasing strain were characterized by homo~eneouslv dist~but~ diffuse cells (t 6 0.35). alianed microbands (6 = 0.50) and shear bands (6 3 OT50).The shear bands nucleated within- the clusters of the microbands. In contrast to this, long dislocations with homogeneous distribution (6 6 0.40) and subboundaries as well as subgrains (c B 0.40) were dominant microstructures at. 473 K rolling. No shear bands were obtained from these microstructures. These results were discussed in terms of the effects of rolling temperature, solute atoms and slip geometry of the Al-Mg alloy. R6sum&-Nous avons Btudii le developpement des structures de dislocations dans les mon~ristaux (211) [Ill] ~~uminium a 3% de magnbsium, en rapport avec ia formation de bandes de cisaiilement apres laminage ti la temperature ordinaire et a 473 K. Au tours du laminage i la temperature ambiante, les structures de dislocations developpies pour des deformations croissantes sont caracteriies par des cellules diffuses r&parties de facon homogene (c: 6 0,35), par des microbandes align&es (c z 0,50), et par des bandes de cisaillement (6 2 0,SO). Les bandes de cisaillement germent a l’interieur des amas de microbandes. Au contraire, les microstructures qui dominent pour les laminages a 473 K sont de longues dislocations distribuies de man&e homogine (6 1<0.40) et des sous-joints ainsi que des sous-grains (f L 0,40). On n’obtient pas de bandes de cisaillement avec ces microstructures. Nous discutons ces resultats en fonction des effets de la temperature de laminage, des atomes solutes et de la geometric du glissement dans l’alliage Al-Mg. Zusammenfussung-Die Ausbilding der Versetzungsstructur in den (21 l)[TJ I] Einkristallen von Al-3%Mg wurde nach der Walzverformung bei Raumtemperatur und 473 K im Zusammenhang mit der Sherbandbiidung untersucht. Wlhrend des Walzens bei R.T. entwickelten sich undeutliche Versetzungszellen mit homogener Verteiling (t 6 0.35), einge~chtete Mikrob~nder (6 = 0.50) und Sherb~nder (6 Z 0.50) mit zunehmendem Ve~o~un~s~ad. Die Sherbgnder wurden sich in den lamellen Mikrob&d&geb$det, die aus schichtformigen-V&setzungswandern bestehten. Im Gegensatz zur Verformung bei R.T. wurden eine homogene Annordnung der langen Versetzungslinien (t. $0.40) und Subkorngrenzen sowie Subkorner (t 3 0.40) nach dem Walzen bei 473 K beobachtet. Keine Sherbander stattfindeten aus diesen Mikrostructuren. Deise Eraibnissen wurden auf dem Effekt von Walztemperature, geldsterm Atomen und Gleitgeometrie betrachtet. 1. I~RODUCT~ON
In the recent paper [l] shear band formation in cold-rolled Al-3%Mg single crystals has been investigated, and correlated with a particular dislocation structure built up during deformation. It has also been suggested that the presence of a lamellar structure such as mechanical twins or microbands consisting of dislocation walls is essential for the shear band formation in f.c.c. material during rolling, and that the shear bands do not form if the development of these lamellar obstacles is suppressed for example by dynamic or static recovery and others. In this regard, the results of recent microstructural studies on low stacking fault energy (SFE) materials [2-l l] are consistent with one another, and indicating that the shear bands are commonly derived from the lamellae of mechanical twins. Whereas in materials with high SFE such as Cu, Al and Al alloys, dislocation structures in which the shear bands nucleated
did not always exhibit an identical pattern for diverse experimental coinditions, e.g. at high temperature deformation [12], ultra high strains [13] and rolling after aging [ 141;at room temperature rolling the shear bands frequently occurred in the microstructure with microbands composed of layered dislocation walls [ 1,6, 10, 15-221. Therefore, the shear band formation of high SFE materials appears to be concerned with various factors. The aim of the present work is to study the interrelation between macroscopic deformation modes and dislocation structures evolved in rolled single crystals of an Al-3%Mg alloy. One part of its results on the orientation dependencies has already been published in elsewhere [l, 211. Then, the effects of rolling temperature and the amounts of strains are treated in this report, because it is known that the dislocation structure after deformation of Al-Mg alloys depends markedly on these factors [23]. In addition, in order to simplify experimental condi1747
1748
NAKAYAMA and MORII: Table
1.
SHEAR BAND FORMATION IN Al-Mg ALLOY
Chemical composition (wt%)
Mg
Fe
Si
CU
Mn
Al
2.95
0.07
0.04
Bal.
la1
(b)
tions, a (211)[ill] orientation is selected, which is believed to be stable during rolling of high SFE materials. 2. EXPERIMENTAL An alloy with the nominal composition of Al-3%Mg was produced from high purity aluminum (99.99%) and magnesium (99.9%) and cold-rolled to 3 mm thick sheets. Single crystal plates with the (211) plane parallel to their wide surfaces were grown in Ar atmosphere by the modified Bridgman method. After homogenization for 2 h at 623 K, specimens with a size 10 mm (W) x 8 mm (L) x 2.5 mm (T) were spark cut to the (211)[Tll] orientation. The chemical composition of the alloy is given in Table 1. Deformation was imposed by rolling at room temperature (RT) and 473 K with a laboratory mill of 53 mm diameter rolls. The rolling speed was about 2.1 mm/min, which corresponded to a strain rate of the order of 10-*/s. In order to maintain the temperature of the specimens as constant as possible during rolling at 473 K, two rolls of the mill were preheated at the temperature by small furnaces, and also the specimens were reheated for 1 min at 473 K between successive rolling passes. The orientation of the specimens was determined before and after rolling by measuring X-ray pole figures with a Ni-filtered CuK, radiation. A slip band pattern was revealed on a polished cross-section of the prerolled specimens by imposing small amounts of rolling strains, and observed by an optical microscope. The microstructure of the rolled specimens was examined with a transmission electron microscope (TEM) operating at 100 kV. Thin foils were prepared from cross-sections by electropolishing in a solution 1 part of perchloric acid and 4 part of ethylalcohol. 3. RESULTS 3.1. Stability of initial orientation An expected slip geometry in a (211) [I 1l] crystal is illustrated in Fig. 1. Asymmetric slip may occur on two co-planar (C/P) and two co-directional (C/D)
Fig. 1. Schematic illustration of slip geometry in a (211) [T11) crystal. C/P: co-planar slip systems, (11 l)[TOl], (11 I)[TlO], C/D: co-directional slip systems, (lTl)[Ol 11, (1 lT)[Oll].
Fig. 2. {Ill} pole figures of (21 I)[11 l] crystals rolled to 6 = 0.80 at (a) RT and (b) 473 K. The initial orientation is given by solid circles.
systems having respectively an identical orientation factor during plane strain rolling deformation. The measurements of X-ray pole figures indicated that though a few orientation spreads occurred about the transverse direction, the (21 l)[Tl l] orientation was maintained almost stably up to high strains at the two rolling temperatures of RT and 473 K. For example, (11 l} pole figures of the specimens rolled to 6 = [In(h,/h)] = 0.8 (54% reduction in thickness) are shown in Fig. 2. 3.2. Slip band observation The slip band patterns were observed as a function of rolling strain. Typical results obtained on the longitudinal section are given ‘in Figs 3 and 4 for the specimens rolled at RT and 473 K, respectively. During rolling at RT (Fig. 3), when imposed strains were low, homogeneous slip occurred on the slip systems indicated in Fig. 1, but as the rolling strain increased to -0.5 (-40% reduction), such a slip pattern was gradually replaced by an inhomogeneous mode of localized deformation, i.e. shear banding. The initial stages of the shear band formation were characterized by the appearance of anomalous slip bands, which ran in the direction deviated slightly (= 15 deg) from the C/P slip planes as indicated by arrows in Fig. 3(b). The anomalous bands were bundled and developed into the shear bands with increasing strain. The direction of the shear bands was inclined by 3&40 deg with respect to the sheet plane, and only a single set of the bands prevailed even at high rolling strains -2.3 (-90% reduction). Similar results have also ben reported in rolled Cu [6] and Al-2%Cu [14,24]. In contrast to the slip behavior at RT, the specimens rolled at 473 K showed a rather homogeneous slip band pattern up to high rolling strains -2.3 (Fig. 4). Although a weak tendency toward the formation of slip band bundles was found, neither the anomalous slip bands nor the shear bands occurred during rolling at this temperature. 3.3. Flow stress The (211)[ill] Al-3%Mg single crystals were deformed by plane strain compression at a strain rate
NAKAYAMA
and MORII:
SHEAR BAND FORMATION
1149
IN Al-Mg ALLOY
Fig. 3. Slip band pattern on longitudinal section of (21 l)[Tl l] crystals rolled at RT to (a) E = 0.45, (b) t = 0.60, (c) c = 0.92, (d) t = 1.30.
Fig. 4. Slip band pattern of longitudinal section of (21 l)[iI l] crystals rolled at 473 K to (a) c = 0.92, (b) 6 = 1.35, (c) c = 2.30.
of 2.5 x 10-‘/s and at RT and 473 K. True stress-true
strain curves are shown in Fig. 5. As expected, work hardening at 473 K was extremely lower than that at RT. 3.4. Observation
of dislocation structure
The TEM microstructure on the longitudinal settion, i.e. on the (Oil) plane, of the rolled specimens is shown in Figs 6-14, while that on the other cross-sections was also used for the characterization of dislocation structures. (i) Rolling at RT. At low rolling strains 6 0.35 ( < 30% reduction), fine equiaxed cells (d = 0.5 pm) with relatively diffuse boundaries were developed (Fig. 6). Misorientation across these cells appeared to be small, but in some regions a band-like structure having a dark or bright contrast formed along the traces of the operative slip planes. Such narrow bands could
be regarded
c2ii)riiii
as the initial form of the micro-
I
300
_ am 5200 E
,” % : r’ 100
(
Fig. 5. Stress strain curves of Al-3%Mg crystals deformed by plane strain compression at RT and 473 K.
Fig. 6. Dislocation structure after rolling at RT to 6 = (
1750
NAKAYAMA
and MORE:
SHEAR BAND FORMATION
IN AI-Mg ALLOY
Fig. 7. Microstructure after rolling at RT to t = 0.48; (a) microband cluster, (b) isolated microbands and fine cells, longitudinal section.
Fig. 8. Layered dislocation walls formed nearly paraliel to the C/P slip planes; diffraction vectors: (a) g = 1II, (b) g = I1 1, longitudinal section after rolling at RT to E = 0.56.
Fig. 9. Inhomogeneities within microband clusters after rolling at RT to t =0.56; (a) misoriented microbands, (b) fragmented microbands (shear bands), longitudinal section.
NAKAYAMA
Fig.
10. Microstructure
and
MORII:
after
rolling
SHEAR
BAND
FORMATION
at RT to t = 0.93; (a) matrix longitudinal section.
Fig. Il. Dislocation structure after rolling at 473 K to L = 0.38: (a) homogeneously distribute dislocations, (b) tangled dislocations, longitudinal section.
IN AI-Mg
region.
ALLOY
(b) intense
shear
bands [25]. Since the contrast of the cell walls did not vanish under various diffraction conditions, the walls were considered to be composed of dislocations belonging to several slip systems. With increasing rolling strain to about 0.5 (~40% reduction), a great number of microbands developed parallel to the C/P slip planes to form a cluster, in which some of the microbands had different contrasts suggesting the presence of a large misorientation between them [Fig. 7(a)]. The microbands were also formed along the C/D slip planes; they were isolated within the microstructure of fine cells with diffuse boundaries [Fig. 7(b)]. As observed in Fig. 7, the microband was composed of aligned dislocation walls, for which contrast experiments were carried out in order to analyze the nature of the walls. It was revealed for the microbands parallel to the C/P slip planes that the contrast of the walls themselves almost disappeared under the diffraction condition g = 711, but appeared clearly when the diffraction vector g = 111 and 200 were used, as shown for example in Fig. 8. According to the usual g-b = 0 criterion for dislocation invisibility, the result implies that many of the dislocations which constitute the microband walls may have the Burgers vectors lying on the (711) plane oriented perpendicular to the rolling direction.
1752
NAKAYAMA
and MORII:
SHEAR BAND FORMATION
IN Al-Mg ALLOY
Fig. 12. Microstructure after rolling at 473 K to c: = 0.56, showing subgrains with alternating contrasts, longitudinal section.
Fig. 13. Microstructure after rolling at 473 K to 6 = 0.92, longitudinal section, showing subgrain structure.
Fig. 14. Microstructure
after rolling at 473 K to L = 1.30, longitudinal section.
Within the microband clusters [Fig. 7(a)], there were some microbands whose configuration and c~stal~ographic orientation were severely distorted (Fig. 9); large orientation spreading was detected in the microbands which inclined by lo-20 deg with respect to the C/P slip planes [Fig. 9(a)]. The direction of their inclination was in accord with that of the anomalous slip bands found in the surface observation [Fig. 3(b)]. Moreover, some of the microbands were fragmented into small blocks with large misorientations [Fig. 9(b)]. These suggest that localized deformation was taking place within the microband cluster so as to nucleate the shear bands. At medium to high rolling strains 0.6-1.2 (50-70% reduction), well defined shear bands of about 10 pm thick occurred in every about IOOpm spacings, as
found in Fig. 3(c). The microstructure in the areas between two neighbouring such shear bands consisted of the microbands or elongated cells having their walls nearly parallel to the C/D slip planes; small clusters of the microbands along the C/P planes were also observed [Fig. IO(a)]. The deformation structure of the intense shear bands at this strain range was composed of fragmented and misoriented microbands [Fig. 10(b)]. (ii) Rolling at 473 K. At low rolling strains g 0.43 (6 35%), homogeneously distributed long dislocations were mainly observed, while in some areas tangled dislocations appeared to build up a wall structure (Fig. 11). With increasing strain, such walls were arranged nearly parallel to the C/D slip planes, and subsequently transformed into well defined sub-
NAKAYAMA
and MORII:
SHEAR
BAND
boundaries with the spacing of 0.5-l.Opm. The resulting microstructure was composed of ellipsoidal subgrains having alternating dark and bright contrasts (Fig. 12). At medium strains =0.6 (-50% reduction), the subgrain structure was further developed (Fig. 13). Although many of the subgrains produced along the C/D slip planes showed a similar contrast under a certain diffraction condition, a close examination indicated that most of the subgrains had rather an equiaxed shape with a size of about 1 pm and were bounded by the two sets of operative slip planes. Such a tendency was also found at high rolling strains 2 1.2 (Fig. 14).
4. DISCUSSION A salient feature obtained in the present experiment is that both the deformation mode and dislocations structure of the (21 l)[Tl I] Al-3%Mg single crystals were strongly dependent on rolling temeperature. Here, it is interesting to note that the initial orientation (21 l)[f 1t J remained stable up to high rolling strains irrespective of the rolling temperature employed, while the operative deformation modes responsible for large plastic strains were quite different at the two different temperatures, i.e. RT and 473 K. Next, the observed deformation behavior will be considered on the basis of the effects of rolling temperature, solute atoms and slip geometry on the evolution of the dislocation structure of alloy. First, it seems to be valuable to examine the general influence of temperature on the deformation behavior of the Al-Mg alloy. During deformation at RT, it is commonly believed that Mg atoms will restrict the mobility of dislocations and prevent dislocation rearrangement and annihilation comparing with those at high temperatures, since they readily interact with and pin the dislocations [26]. It follows that dynamic as well as static recovery, which may occur during rolling and holding time between successive passes, can greatly be suppressed, and that the mean free path of the dislocations is extensively reduced. Although a certain amounts of recovery may inevitably be accompanied with at larger strains due to the increase in the density of dislocations and point defects, these effects of the solute atoms are basically taking place up to high strains, and cont~buting to yield high work hardening. The dislocation structure observed at low strains with the fine diffuse cells and short dislocation segments (Fig. 6) could be ascribed to such effects of Mg atoms. Also the collective jerky motion of dislocations, which is characteristic in particuiar to AI-Mg alloys [27], may play an important role for the onset of unstable serrated flow; its contribution to the shear band formation was estimated to be indirect, influencing the evolution of dislocation structures rather than causing the shear banding itself [I].
FORMATION
IN AI-Mg
ALLOY
1753
In contrast to the behavior at RT, the deformation at 473 K is undoubtedly influenced by dynamic and static recovery, since at this temperature the frequency of cross-slip and climb of dislocations will be enhanced due to the high homologous temperature (T/T,= 0.5). Thereby a little effects on the suppression of recovery processes may be introduced by the presence of Mg atoms. Moreover, Ayres [28] has suggested from stress-relaxation tests that Mg atoms can increase the amounts of dynamic recovery occuring at elevated temperature. Accordingly, it is expected in an early stage of rolling that the mean free path of dislocations increases and then rather smooth and long dislocations are distributed homogeneously in the material (Fig. 11). With increasing rolling strain, however, a great number of dislocations multiplicated are able to rearrange so as to attain stable ~on~gurations because of the enhanced frequency of cross-slip and climb. This process will lead to a microstructure with well defined sub-boundaries and subgrains. The observed subgrain structure having alternating contrasts (Fig. 12) may possibly be interpreted in terms of the arrays of an edge component left after double cross-slip of screw dislocations between the two active C/D slip planes, as suggested by Jackson [29]. As the strain further increased, similar sub-boundaries can also be nucleated along the C/P slip planes, so that nearly equiaxed subgrains bounded by the two active slip planes will be produced (Fig. 13). Since such a subgrain structure is very isotropic and since the more strain increases the more recovery progresses, the deformation at 473 K may suffer low work hardening and yield a homogeneous slip pattern on the active slip systems. Then, the occurrence of unstable flow such as the shear band formation appeared to be prevented during rolhng at the elevated temperature. In the following, attention will be paid to the formation of the microbands and shear bands at RT rolling. A mechanism for the microband nucleation has been proposed by Nes et al. [25], in which dislocation channeling within a cell structure is assumed to cause the local destabiIization or softening of the structure. This seems to be in accord with the present observation: as found in Fig. 6, cleaned channels over several small cells formed separating the cell structure by dislocation walls, which can be regarded as a result of the local softening due to the channeling of successive cells. Here, it is important to note that the development of the microbands was not isotropic but preferred along the C/P slip planes, as indicated in Fig. 7(a). This may partly be correlated with the asymmetry of slip in the (21 I)[11 I] orientation, where the amount of glide strain on the C/P slip pfane is more than twice as large as on the C/D planes in order to achieve orientation stability [30]. Therefore, the channeling of cells to form the microbands may more frequently occur on the C/P slip planes than the others. In addition, the resulting dislocation interaction may partly be responsible for
1754
NAKAYAMA
and MORII:
SHEAR BAND FORMATION
the formation of the dislocation walls on the C/P slip plane. The possibility that the dislocations with the Burgers vectors lying on the (111) plane contributed to the formation of the microband walls was suggested by the contrast experiments (Fig. 8). Since the (Tl 1) plane, which is normal to the rolling direction, is considered to be inactive, these dislocations are supposed to be those produced by the interaction of dislocations on the two active slip planes, e.g. the Lomer dislocations. For the (21 l)[Tl 1] orientation two sets of the Lomer dislocations, a/2[101] and a/2[1 lo], can be nucleated from the dislocations of the C/P and C/D systems on the C/P planes along the [TO11and [TlO] directions, and will act as an effective barrier to dislocation movements on the C/D planes [31]. Hence, the two dimensional dislocation walls are able to develop mostly parallel to the C/P planes. The microbands along the C/P planes did not occupy the whole volume of the material, but appeared as the clusters which were separated from the microstructure consisting of both isolated microbands and diffuse cells (Figs 7 and 8). Within these microband clusters, some irregularities such as the misalignment of their walls and large misorientation occurred, and increased so as to nucleate the shear bands with increasing imposed strain (Fig. 9). This can be interpreted as a result of the localized flow occurring in the clusters. Here, it could be assumed that the local instability in the aligned microband cluster is inherent in the deformation of the layered dislocation walls, and is attributable to the microstructural evolution for the shear band nucleation. As shown by Mughrabi [32], the dislocation wall structure can give rise to substantial long-range internal stresses during deformation, which aid the applied stress in the walls and oppose it between the walls. Therefore, it is possible to imagine that the internal stresses are so highly increased with increasing strain that they will cause cooperative movements of dislocations, which would involve further multiplication, rearrangement and annihilation of the dislocations consisting of the walls [33]. This process is considered to be the local destabilization of the dislocation wall structure. Owing to severely localized strains in the shear band, it can readily grow along its shearing direction as a consequence of strain accommodation at the tips of the band, and the resulting microstructure may be composed of fragmented microbands [Figs 9 and 10(b)]. In contrast to such a deformation mode in the shear bands, in the areas between two intense shear bands, crystallographic slip on the C/D systems was preferred, and then most of the microbands and elongated cells were formed parallel to the C/D slip planes [Fig. 10(a)]. Therefore, the macroscopic deformation as well as the orientation stability of the (211) [Tll] crystal at RT seems to be attained by the balance of the two different deformation modes, i.e. shear banding and slip on the C/D systems.
IN Al-Mg ALLOY 5. SUMMARY
The deformation mode and microstructure were examined in the (21 l)[Tl 1] single crystals of an Al-3%Mg alloy rolled at RT and 473 K. In this particular case, the nucleation of shear bands was correlated with the local destabilization of aligned microband clusters produced at low to medium rolling strains nearly parallel to the C/P slip planes at RT. The microband structure was also related to the transient instability of the diffuse cell structure at low strains [25]. Since the development of these microstructures depends strongly on slip geometry, solute contents and deformation temperature, the shear band formation is naturally dependent on these factors, providing the presence of a particular dislocation structure is prerequisite for the shear banding. Actually, such behavior has been observed in the present work on the effect of deformation temperature, and in the previous work on that of slip geometry and Mg atoms [l, 21,221. As pointed out in [1], the presence of lamellar obstacles to dislocation movements will play a significant role for the shear band formation during rolling of single phase f.c.c. materials.
REFERENCES 1. K. Morii, H. Mecking and Y. Nakayama, Acta merall. 33, 379 (1985). 2. K. Morn, M. Mera and Y. Nakayama, Trans. Japan Inst. Metals 18, 7 (1977).
3. M. Blicharski and S. Gorczyca, Metal. Sci. 12, 303 (1978).
4. B. J. Duggan, M. Hatherly, W. B. Hutchinson and P. T. Wakefield, Metal. Sci. 12, 343 (1978). 5. M. Hatherly and A. S. Malin, Metall. Tech. 6, 308 (1978).
6. K. Morii and Y. Nakayama, Trans. Japan Inst. Metals 22, 857 (1981).
7. B. Plege, T. Noda and H. J. Bunge, 2. Metallk. 72,641 (1981). 8. S. Nourbakhsh and J. Nutting, Metall. Sci. 16, 323 (1982).
9. A. S. Malin, M. Hatherly, P. Welch and J. Huber, 2. Metallk. 73, 489 (1982). 10. Y. Nakayama and K. Morii, Trans. Japan Inst. Metals 23, 422 (1982).
11. J. D. Embury, A. Kobel, V. S. Raghunathan and J. Rys, Acta metall. 32, 1883 (1984).
12. A. Kobel, W. Bochniak, L. Blaz and J. D. Embury, Metall. Sci. 18, 216 (1984). 13. A. Kobel and M. Richert, Acta metall. 33, 1971 (1985). 14. K. Morii and Y. Nakavama, Scriuta metall. 9. 1237 (1986). 15. A. S. Mailn and M. Hatherly, Metall. Sci. 13, 463 (1979).
16. P. T. Wakefield and M. Hatherly, Met&. Sci. 15, 109 (1981). 17. A. A. Ridha and W. B. Hutchinson, Acta metall. 30, 1929 (1982).
18. A. Kobel and M. Szczerba, Acta metall. 30,449 (1984). 19. M. Hatherly and A. S. Malin, Scripta metaff. 18, 449 (1984).
20. F. J. Torrealdea and J. Gill. Seviliano, Proc 6th Int. Conf. on Strength of Metals and Alloys (edited by R. C. Gifkins), p. 547. Pergamon Press, Oxford (1982).
NAKAYAMA
and
MORII:
SHEAR
BAND
21. K. Morii, Y. Nakayama and H. Mecking, Proc. 7th Int. Conf. on Textures of Materials (edited by C. M. Brakmann et al.), p. 117. Netherlands Sot. Mater. Sci. (1984). 22. K. Morii and Y. Nakayama, Scripta metall 19, 185 (1985). 23. M. Raghavan and E. Shapire, MetaH. Trans A IlA, 117 (1980). 24. K. Morii, H. Terada and Y. Nayakama, Trans. Japan Inst. Metals 27, 769 (1986). 25. E. Nes, W. B. Hutchinson and A. A. Ridha, Proc. 7th Int. Conf on Strength qf Metals and Alloys (edited by H. McQueen et a/.), p. 51. Pergamon Press, Oxford (1985).
A.M.
3517-w
FORMATION
IN Al-Mg
ALLOY
1755
26. S. R. MacEwan and B. Ramaswami, Phil. Mag. 22, 1025 (1970). 27. R. A. Ayres, Metall. Trans. A IOA, 849 (1979). 28. T. Tabata, H. Fujita and Y. Nakajima, Acta metall. 28, 795 (1980). 29. P. J. Jackson, Scripta metall. 17, 695 (1982). 30. U. F. Kocks and H. Chandra, Acta metall. 30, 695 (1982). 31. U. F. Kocks, Acfa metall. 8, 345 (1960). 32. H. Mughrabi, Acta metall. 31, 1387 (1983). 33. J. Washburn and G. Murty, Can. J. Phys. 45. 532 (1967).
1987 Copyright
0
OOOI-6160/87 $3.00 + 0.00 1987 Pergamon Journals Ltd
MICROSTRUCTURE AND SHEAR BAND FORMATION IN ROLLED SINGLE CRYSTALS OF Al-Mg ALLOY College of ~ngin~~ng,
Y. NAKAYAMA and K. MORE1 University of Osaka Prefecture, Mozu-Umemachi,
Sakai 591, Japan
(Received 7 August 1986; in revised form 8 October 1986)
Abstract-The development of dislocation structures in the (21 I)[fl I] single crystals of AI-3%Mg has been investigated in relation to shear band formation after rolling at room temperature and 473 K. During rolling at RT, the dislocation structures which developed with increasing strain were characterized by homo~eneouslv dist~but~ diffuse cells (t 6 0.35). alianed microbands (6 = 0.50) and shear bands (6 3 OT50).The shear bands nucleated within- the clusters of the microbands. In contrast to this, long dislocations with homogeneous distribution (6 6 0.40) and subboundaries as well as subgrains (c B 0.40) were dominant microstructures at. 473 K rolling. No shear bands were obtained from these microstructures. These results were discussed in terms of the effects of rolling temperature, solute atoms and slip geometry of the Al-Mg alloy. R6sum&-Nous avons Btudii le developpement des structures de dislocations dans les mon~ristaux (211) [Ill] ~~uminium a 3% de magnbsium, en rapport avec ia formation de bandes de cisaiilement apres laminage ti la temperature ordinaire et a 473 K. Au tours du laminage i la temperature ambiante, les structures de dislocations developpies pour des deformations croissantes sont caracteriies par des cellules diffuses r&parties de facon homogene (c: 6 0,35), par des microbandes align&es (c z 0,50), et par des bandes de cisaillement (6 2 0,SO). Les bandes de cisaillement germent a l’interieur des amas de microbandes. Au contraire, les microstructures qui dominent pour les laminages a 473 K sont de longues dislocations distribuies de man&e homogine (6 1<0.40) et des sous-joints ainsi que des sous-grains (f L 0,40). On n’obtient pas de bandes de cisaillement avec ces microstructures. Nous discutons ces resultats en fonction des effets de la temperature de laminage, des atomes solutes et de la geometric du glissement dans l’alliage Al-Mg. Zusammenfussung-Die Ausbilding der Versetzungsstructur in den (21 l)[TJ I] Einkristallen von Al-3%Mg wurde nach der Walzverformung bei Raumtemperatur und 473 K im Zusammenhang mit der Sherbandbiidung untersucht. Wlhrend des Walzens bei R.T. entwickelten sich undeutliche Versetzungszellen mit homogener Verteiling (t 6 0.35), einge~chtete Mikrob~nder (6 = 0.50) und Sherb~nder (6 Z 0.50) mit zunehmendem Ve~o~un~s~ad. Die Sherbgnder wurden sich in den lamellen Mikrob&d&geb$det, die aus schichtformigen-V&setzungswandern bestehten. Im Gegensatz zur Verformung bei R.T. wurden eine homogene Annordnung der langen Versetzungslinien (t. $0.40) und Subkorngrenzen sowie Subkorner (t 3 0.40) nach dem Walzen bei 473 K beobachtet. Keine Sherbander stattfindeten aus diesen Mikrostructuren. Deise Eraibnissen wurden auf dem Effekt von Walztemperature, geldsterm Atomen und Gleitgeometrie betrachtet. 1. I~RODUCT~ON
In the recent paper [l] shear band formation in cold-rolled Al-3%Mg single crystals has been investigated, and correlated with a particular dislocation structure built up during deformation. It has also been suggested that the presence of a lamellar structure such as mechanical twins or microbands consisting of dislocation walls is essential for the shear band formation in f.c.c. material during rolling, and that the shear bands do not form if the development of these lamellar obstacles is suppressed for example by dynamic or static recovery and others. In this regard, the results of recent microstructural studies on low stacking fault energy (SFE) materials [2-l l] are consistent with one another, and indicating that the shear bands are commonly derived from the lamellae of mechanical twins. Whereas in materials with high SFE such as Cu, Al and Al alloys, dislocation structures in which the shear bands nucleated
did not always exhibit an identical pattern for diverse experimental coinditions, e.g. at high temperature deformation [12], ultra high strains [13] and rolling after aging [ 141;at room temperature rolling the shear bands frequently occurred in the microstructure with microbands composed of layered dislocation walls [ 1,6, 10, 15-221. Therefore, the shear band formation of high SFE materials appears to be concerned with various factors. The aim of the present work is to study the interrelation between macroscopic deformation modes and dislocation structures evolved in rolled single crystals of an Al-3%Mg alloy. One part of its results on the orientation dependencies has already been published in elsewhere [l, 211. Then, the effects of rolling temperature and the amounts of strains are treated in this report, because it is known that the dislocation structure after deformation of Al-Mg alloys depends markedly on these factors [23]. In addition, in order to simplify experimental condi1747
1748
NAKAYAMA and MORII: Table
1.
SHEAR BAND FORMATION IN Al-Mg ALLOY
Chemical composition (wt%)
Mg
Fe
Si
CU
Mn
Al
2.95
0.07
0.04
Bal.
la1
(b)
tions, a (211)[ill] orientation is selected, which is believed to be stable during rolling of high SFE materials. 2. EXPERIMENTAL An alloy with the nominal composition of Al-3%Mg was produced from high purity aluminum (99.99%) and magnesium (99.9%) and cold-rolled to 3 mm thick sheets. Single crystal plates with the (211) plane parallel to their wide surfaces were grown in Ar atmosphere by the modified Bridgman method. After homogenization for 2 h at 623 K, specimens with a size 10 mm (W) x 8 mm (L) x 2.5 mm (T) were spark cut to the (211)[Tll] orientation. The chemical composition of the alloy is given in Table 1. Deformation was imposed by rolling at room temperature (RT) and 473 K with a laboratory mill of 53 mm diameter rolls. The rolling speed was about 2.1 mm/min, which corresponded to a strain rate of the order of 10-*/s. In order to maintain the temperature of the specimens as constant as possible during rolling at 473 K, two rolls of the mill were preheated at the temperature by small furnaces, and also the specimens were reheated for 1 min at 473 K between successive rolling passes. The orientation of the specimens was determined before and after rolling by measuring X-ray pole figures with a Ni-filtered CuK, radiation. A slip band pattern was revealed on a polished cross-section of the prerolled specimens by imposing small amounts of rolling strains, and observed by an optical microscope. The microstructure of the rolled specimens was examined with a transmission electron microscope (TEM) operating at 100 kV. Thin foils were prepared from cross-sections by electropolishing in a solution 1 part of perchloric acid and 4 part of ethylalcohol. 3. RESULTS 3.1. Stability of initial orientation An expected slip geometry in a (211) [I 1l] crystal is illustrated in Fig. 1. Asymmetric slip may occur on two co-planar (C/P) and two co-directional (C/D)
Fig. 1. Schematic illustration of slip geometry in a (211) [T11) crystal. C/P: co-planar slip systems, (11 l)[TOl], (11 I)[TlO], C/D: co-directional slip systems, (lTl)[Ol 11, (1 lT)[Oll].
Fig. 2. {Ill} pole figures of (21 I)[11 l] crystals rolled to 6 = 0.80 at (a) RT and (b) 473 K. The initial orientation is given by solid circles.
systems having respectively an identical orientation factor during plane strain rolling deformation. The measurements of X-ray pole figures indicated that though a few orientation spreads occurred about the transverse direction, the (21 l)[Tl l] orientation was maintained almost stably up to high strains at the two rolling temperatures of RT and 473 K. For example, (11 l} pole figures of the specimens rolled to 6 = [In(h,/h)] = 0.8 (54% reduction in thickness) are shown in Fig. 2. 3.2. Slip band observation The slip band patterns were observed as a function of rolling strain. Typical results obtained on the longitudinal section are given ‘in Figs 3 and 4 for the specimens rolled at RT and 473 K, respectively. During rolling at RT (Fig. 3), when imposed strains were low, homogeneous slip occurred on the slip systems indicated in Fig. 1, but as the rolling strain increased to -0.5 (-40% reduction), such a slip pattern was gradually replaced by an inhomogeneous mode of localized deformation, i.e. shear banding. The initial stages of the shear band formation were characterized by the appearance of anomalous slip bands, which ran in the direction deviated slightly (= 15 deg) from the C/P slip planes as indicated by arrows in Fig. 3(b). The anomalous bands were bundled and developed into the shear bands with increasing strain. The direction of the shear bands was inclined by 3&40 deg with respect to the sheet plane, and only a single set of the bands prevailed even at high rolling strains -2.3 (-90% reduction). Similar results have also ben reported in rolled Cu [6] and Al-2%Cu [14,24]. In contrast to the slip behavior at RT, the specimens rolled at 473 K showed a rather homogeneous slip band pattern up to high rolling strains -2.3 (Fig. 4). Although a weak tendency toward the formation of slip band bundles was found, neither the anomalous slip bands nor the shear bands occurred during rolling at this temperature. 3.3. Flow stress The (211)[ill] Al-3%Mg single crystals were deformed by plane strain compression at a strain rate
NAKAYAMA
and MORII:
SHEAR BAND FORMATION
1149
IN Al-Mg ALLOY
Fig. 3. Slip band pattern on longitudinal section of (21 l)[Tl l] crystals rolled at RT to (a) E = 0.45, (b) t = 0.60, (c) c = 0.92, (d) t = 1.30.
Fig. 4. Slip band pattern of longitudinal section of (21 l)[iI l] crystals rolled at 473 K to (a) c = 0.92, (b) 6 = 1.35, (c) c = 2.30.
of 2.5 x 10-‘/s and at RT and 473 K. True stress-true
strain curves are shown in Fig. 5. As expected, work hardening at 473 K was extremely lower than that at RT. 3.4. Observation
of dislocation structure
The TEM microstructure on the longitudinal settion, i.e. on the (Oil) plane, of the rolled specimens is shown in Figs 6-14, while that on the other cross-sections was also used for the characterization of dislocation structures. (i) Rolling at RT. At low rolling strains 6 0.35 ( < 30% reduction), fine equiaxed cells (d = 0.5 pm) with relatively diffuse boundaries were developed (Fig. 6). Misorientation across these cells appeared to be small, but in some regions a band-like structure having a dark or bright contrast formed along the traces of the operative slip planes. Such narrow bands could
be regarded
c2ii)riiii
as the initial form of the micro-
I
300
_ am 5200 E
,” % : r’ 100
(
Fig. 5. Stress strain curves of Al-3%Mg crystals deformed by plane strain compression at RT and 473 K.
Fig. 6. Dislocation structure after rolling at RT to 6 = (
1750
NAKAYAMA
and MORE:
SHEAR BAND FORMATION
IN AI-Mg ALLOY
Fig. 7. Microstructure after rolling at RT to t = 0.48; (a) microband cluster, (b) isolated microbands and fine cells, longitudinal section.
Fig. 8. Layered dislocation walls formed nearly paraliel to the C/P slip planes; diffraction vectors: (a) g = 1II, (b) g = I1 1, longitudinal section after rolling at RT to E = 0.56.
Fig. 9. Inhomogeneities within microband clusters after rolling at RT to t =0.56; (a) misoriented microbands, (b) fragmented microbands (shear bands), longitudinal section.
NAKAYAMA
Fig.
10. Microstructure
and
MORII:
after
rolling
SHEAR
BAND
FORMATION
at RT to t = 0.93; (a) matrix longitudinal section.
Fig. Il. Dislocation structure after rolling at 473 K to L = 0.38: (a) homogeneously distribute dislocations, (b) tangled dislocations, longitudinal section.
IN AI-Mg
region.
ALLOY
(b) intense
shear
bands [25]. Since the contrast of the cell walls did not vanish under various diffraction conditions, the walls were considered to be composed of dislocations belonging to several slip systems. With increasing rolling strain to about 0.5 (~40% reduction), a great number of microbands developed parallel to the C/P slip planes to form a cluster, in which some of the microbands had different contrasts suggesting the presence of a large misorientation between them [Fig. 7(a)]. The microbands were also formed along the C/D slip planes; they were isolated within the microstructure of fine cells with diffuse boundaries [Fig. 7(b)]. As observed in Fig. 7, the microband was composed of aligned dislocation walls, for which contrast experiments were carried out in order to analyze the nature of the walls. It was revealed for the microbands parallel to the C/P slip planes that the contrast of the walls themselves almost disappeared under the diffraction condition g = 711, but appeared clearly when the diffraction vector g = 111 and 200 were used, as shown for example in Fig. 8. According to the usual g-b = 0 criterion for dislocation invisibility, the result implies that many of the dislocations which constitute the microband walls may have the Burgers vectors lying on the (711) plane oriented perpendicular to the rolling direction.
1752
NAKAYAMA
and MORII:
SHEAR BAND FORMATION
IN Al-Mg ALLOY
Fig. 12. Microstructure after rolling at 473 K to c: = 0.56, showing subgrains with alternating contrasts, longitudinal section.
Fig. 13. Microstructure after rolling at 473 K to 6 = 0.92, longitudinal section, showing subgrain structure.
Fig. 14. Microstructure
after rolling at 473 K to L = 1.30, longitudinal section.
Within the microband clusters [Fig. 7(a)], there were some microbands whose configuration and c~stal~ographic orientation were severely distorted (Fig. 9); large orientation spreading was detected in the microbands which inclined by lo-20 deg with respect to the C/P slip planes [Fig. 9(a)]. The direction of their inclination was in accord with that of the anomalous slip bands found in the surface observation [Fig. 3(b)]. Moreover, some of the microbands were fragmented into small blocks with large misorientations [Fig. 9(b)]. These suggest that localized deformation was taking place within the microband cluster so as to nucleate the shear bands. At medium to high rolling strains 0.6-1.2 (50-70% reduction), well defined shear bands of about 10 pm thick occurred in every about IOOpm spacings, as
found in Fig. 3(c). The microstructure in the areas between two neighbouring such shear bands consisted of the microbands or elongated cells having their walls nearly parallel to the C/D slip planes; small clusters of the microbands along the C/P planes were also observed [Fig. IO(a)]. The deformation structure of the intense shear bands at this strain range was composed of fragmented and misoriented microbands [Fig. 10(b)]. (ii) Rolling at 473 K. At low rolling strains g 0.43 (6 35%), homogeneously distributed long dislocations were mainly observed, while in some areas tangled dislocations appeared to build up a wall structure (Fig. 11). With increasing strain, such walls were arranged nearly parallel to the C/D slip planes, and subsequently transformed into well defined sub-
NAKAYAMA
and MORII:
SHEAR
BAND
boundaries with the spacing of 0.5-l.Opm. The resulting microstructure was composed of ellipsoidal subgrains having alternating dark and bright contrasts (Fig. 12). At medium strains =0.6 (-50% reduction), the subgrain structure was further developed (Fig. 13). Although many of the subgrains produced along the C/D slip planes showed a similar contrast under a certain diffraction condition, a close examination indicated that most of the subgrains had rather an equiaxed shape with a size of about 1 pm and were bounded by the two sets of operative slip planes. Such a tendency was also found at high rolling strains 2 1.2 (Fig. 14).
4. DISCUSSION A salient feature obtained in the present experiment is that both the deformation mode and dislocations structure of the (21 l)[Tl I] Al-3%Mg single crystals were strongly dependent on rolling temeperature. Here, it is interesting to note that the initial orientation (21 l)[f 1t J remained stable up to high rolling strains irrespective of the rolling temperature employed, while the operative deformation modes responsible for large plastic strains were quite different at the two different temperatures, i.e. RT and 473 K. Next, the observed deformation behavior will be considered on the basis of the effects of rolling temperature, solute atoms and slip geometry on the evolution of the dislocation structure of alloy. First, it seems to be valuable to examine the general influence of temperature on the deformation behavior of the Al-Mg alloy. During deformation at RT, it is commonly believed that Mg atoms will restrict the mobility of dislocations and prevent dislocation rearrangement and annihilation comparing with those at high temperatures, since they readily interact with and pin the dislocations [26]. It follows that dynamic as well as static recovery, which may occur during rolling and holding time between successive passes, can greatly be suppressed, and that the mean free path of the dislocations is extensively reduced. Although a certain amounts of recovery may inevitably be accompanied with at larger strains due to the increase in the density of dislocations and point defects, these effects of the solute atoms are basically taking place up to high strains, and cont~buting to yield high work hardening. The dislocation structure observed at low strains with the fine diffuse cells and short dislocation segments (Fig. 6) could be ascribed to such effects of Mg atoms. Also the collective jerky motion of dislocations, which is characteristic in particuiar to AI-Mg alloys [27], may play an important role for the onset of unstable serrated flow; its contribution to the shear band formation was estimated to be indirect, influencing the evolution of dislocation structures rather than causing the shear banding itself [I].
FORMATION
IN AI-Mg
ALLOY
1753
In contrast to the behavior at RT, the deformation at 473 K is undoubtedly influenced by dynamic and static recovery, since at this temperature the frequency of cross-slip and climb of dislocations will be enhanced due to the high homologous temperature (T/T,= 0.5). Thereby a little effects on the suppression of recovery processes may be introduced by the presence of Mg atoms. Moreover, Ayres [28] has suggested from stress-relaxation tests that Mg atoms can increase the amounts of dynamic recovery occuring at elevated temperature. Accordingly, it is expected in an early stage of rolling that the mean free path of dislocations increases and then rather smooth and long dislocations are distributed homogeneously in the material (Fig. 11). With increasing rolling strain, however, a great number of dislocations multiplicated are able to rearrange so as to attain stable ~on~gurations because of the enhanced frequency of cross-slip and climb. This process will lead to a microstructure with well defined sub-boundaries and subgrains. The observed subgrain structure having alternating contrasts (Fig. 12) may possibly be interpreted in terms of the arrays of an edge component left after double cross-slip of screw dislocations between the two active C/D slip planes, as suggested by Jackson [29]. As the strain further increased, similar sub-boundaries can also be nucleated along the C/P slip planes, so that nearly equiaxed subgrains bounded by the two active slip planes will be produced (Fig. 13). Since such a subgrain structure is very isotropic and since the more strain increases the more recovery progresses, the deformation at 473 K may suffer low work hardening and yield a homogeneous slip pattern on the active slip systems. Then, the occurrence of unstable flow such as the shear band formation appeared to be prevented during rolhng at the elevated temperature. In the following, attention will be paid to the formation of the microbands and shear bands at RT rolling. A mechanism for the microband nucleation has been proposed by Nes et al. [25], in which dislocation channeling within a cell structure is assumed to cause the local destabiIization or softening of the structure. This seems to be in accord with the present observation: as found in Fig. 6, cleaned channels over several small cells formed separating the cell structure by dislocation walls, which can be regarded as a result of the local softening due to the channeling of successive cells. Here, it is important to note that the development of the microbands was not isotropic but preferred along the C/P slip planes, as indicated in Fig. 7(a). This may partly be correlated with the asymmetry of slip in the (21 I)[11 I] orientation, where the amount of glide strain on the C/P slip pfane is more than twice as large as on the C/D planes in order to achieve orientation stability [30]. Therefore, the channeling of cells to form the microbands may more frequently occur on the C/P slip planes than the others. In addition, the resulting dislocation interaction may partly be responsible for
1754
NAKAYAMA
and MORII:
SHEAR BAND FORMATION
the formation of the dislocation walls on the C/P slip plane. The possibility that the dislocations with the Burgers vectors lying on the (111) plane contributed to the formation of the microband walls was suggested by the contrast experiments (Fig. 8). Since the (Tl 1) plane, which is normal to the rolling direction, is considered to be inactive, these dislocations are supposed to be those produced by the interaction of dislocations on the two active slip planes, e.g. the Lomer dislocations. For the (21 l)[Tl 1] orientation two sets of the Lomer dislocations, a/2[101] and a/2[1 lo], can be nucleated from the dislocations of the C/P and C/D systems on the C/P planes along the [TO11and [TlO] directions, and will act as an effective barrier to dislocation movements on the C/D planes [31]. Hence, the two dimensional dislocation walls are able to develop mostly parallel to the C/P planes. The microbands along the C/P planes did not occupy the whole volume of the material, but appeared as the clusters which were separated from the microstructure consisting of both isolated microbands and diffuse cells (Figs 7 and 8). Within these microband clusters, some irregularities such as the misalignment of their walls and large misorientation occurred, and increased so as to nucleate the shear bands with increasing imposed strain (Fig. 9). This can be interpreted as a result of the localized flow occurring in the clusters. Here, it could be assumed that the local instability in the aligned microband cluster is inherent in the deformation of the layered dislocation walls, and is attributable to the microstructural evolution for the shear band nucleation. As shown by Mughrabi [32], the dislocation wall structure can give rise to substantial long-range internal stresses during deformation, which aid the applied stress in the walls and oppose it between the walls. Therefore, it is possible to imagine that the internal stresses are so highly increased with increasing strain that they will cause cooperative movements of dislocations, which would involve further multiplication, rearrangement and annihilation of the dislocations consisting of the walls [33]. This process is considered to be the local destabilization of the dislocation wall structure. Owing to severely localized strains in the shear band, it can readily grow along its shearing direction as a consequence of strain accommodation at the tips of the band, and the resulting microstructure may be composed of fragmented microbands [Figs 9 and 10(b)]. In contrast to such a deformation mode in the shear bands, in the areas between two intense shear bands, crystallographic slip on the C/D systems was preferred, and then most of the microbands and elongated cells were formed parallel to the C/D slip planes [Fig. 10(a)]. Therefore, the macroscopic deformation as well as the orientation stability of the (211) [Tll] crystal at RT seems to be attained by the balance of the two different deformation modes, i.e. shear banding and slip on the C/D systems.
IN Al-Mg ALLOY 5. SUMMARY
The deformation mode and microstructure were examined in the (21 l)[Tl 1] single crystals of an Al-3%Mg alloy rolled at RT and 473 K. In this particular case, the nucleation of shear bands was correlated with the local destabilization of aligned microband clusters produced at low to medium rolling strains nearly parallel to the C/P slip planes at RT. The microband structure was also related to the transient instability of the diffuse cell structure at low strains [25]. Since the development of these microstructures depends strongly on slip geometry, solute contents and deformation temperature, the shear band formation is naturally dependent on these factors, providing the presence of a particular dislocation structure is prerequisite for the shear banding. Actually, such behavior has been observed in the present work on the effect of deformation temperature, and in the previous work on that of slip geometry and Mg atoms [l, 21,221. As pointed out in [1], the presence of lamellar obstacles to dislocation movements will play a significant role for the shear band formation during rolling of single phase f.c.c. materials.
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NAKAYAMA
and
MORII:
SHEAR
BAND
21. K. Morii, Y. Nakayama and H. Mecking, Proc. 7th Int. Conf. on Textures of Materials (edited by C. M. Brakmann et al.), p. 117. Netherlands Sot. Mater. Sci. (1984). 22. K. Morii and Y. Nakayama, Scripta metall 19, 185 (1985). 23. M. Raghavan and E. Shapire, MetaH. Trans A IlA, 117 (1980). 24. K. Morii, H. Terada and Y. Nayakama, Trans. Japan Inst. Metals 27, 769 (1986). 25. E. Nes, W. B. Hutchinson and A. A. Ridha, Proc. 7th Int. Conf on Strength qf Metals and Alloys (edited by H. McQueen et a/.), p. 51. Pergamon Press, Oxford (1985).
A.M.
3517-w
FORMATION
IN Al-Mg
ALLOY
1755
26. S. R. MacEwan and B. Ramaswami, Phil. Mag. 22, 1025 (1970). 27. R. A. Ayres, Metall. Trans. A IOA, 849 (1979). 28. T. Tabata, H. Fujita and Y. Nakajima, Acta metall. 28, 795 (1980). 29. P. J. Jackson, Scripta metall. 17, 695 (1982). 30. U. F. Kocks and H. Chandra, Acta metall. 30, 695 (1982). 31. U. F. Kocks, Acfa metall. 8, 345 (1960). 32. H. Mughrabi, Acta metall. 31, 1387 (1983). 33. J. Washburn and G. Murty, Can. J. Phys. 45. 532 (1967).