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Microstructural evolution in a non-cell forming metal: AlMg
Acta metall, mater. Vol. 41, No. 5, pp. 1421 1430, 1993
0956-7151/93 $6.00 + 0.00 Copyright © 1993 Pergamon Press Ltd
Printed in Great Britain. All rights reserved
MICROSTRUCTURAL EVOLUTION IN A NON-CELL FORMING METAL: A1-Mg D. A. HUGHES Materials Department, Sandia National Laboratories, Livermore, CA 94550, U.S.A. (Received 6 April 1992; in revisedform 30 September 1992)
A~tract--Microstructural evolution in AI + 5.5 at.% Mg lightly deformed by rolling was studied using transmission electron microscopy. Observations show that the dislocations are organized into a Taylor lattice containing multiple burgers vectors and having alternating misorientations along {111} slip planes. These observations are in contrast to the usual description of these structures as "random" dislocation tangles. With increasing strain, a grain is subdivided into several domains of differently oriented Taylor lattices. The newly observed boundaries between different domains are long single dislocations walls formed along 'qI l 1}. As a further evolutionary progression, the single walled domain boundaries develop into microbands. The observed grain subdivision parallels that observed in cell forming metals. Subdivision occurs to accommodate strain using fewer slip systems than required by the Taylor criterion.
I. INTRODUCTION During deformation of cell forming polycrystalline metals, grains are subdivided into misoriented regions in which deformation occurs on fewer slip systems than specified by the Taylor criterion for strain accommodation [1]. The selection of active slip systems also differs between these regions. Long dense dislocation walls (DDW) form the boundaries between the misoriented regions of equiaxed cells. For pure nickel and aluminum, microbands are subsequently formed from within these DDWs by a gradual multiple slip process [2, 3]. A schematic drawing of these structures is shown in Fig. 1. With increasing deformation, the regions of equiaxed cells, called cell blocks (CB), are further subdivided by the formation of new DDWs
Fig. 1. Schematic drawing of the deformation microstruction in cell forming metals showing the subdivision into cell blocks (CB) outlined by dense dislocation walls (DDW) and microbands (MB) [3].
and microbands. This evolutionary process and the theoretical interpretation is consistent for cell forming metals. The central idea that grains are subdivided into misoriented regions should also apply to metals which do not form cells [4]. This idea is investigated for lightly rolled A1 +5.5 at.% Mg. In AI +5.5 at.% Mg, solute effects increase the friction stress and thereby inhibit cell formation. Previous TEM studies show that the dislocation substructure of AI + 5.5 at.% Mg following small strain tensile or rolling deformation consists of a uniform distribution of dislocation tangles; no cell structure is formed [5-10]. Some of these studies also show that the dislocation structure at larger strains contains very sharp microbands which cut through these dislocation tangles [9, 11-13]. These microbands are characterized as paired dislocation sheets spaced approximately 0.2/~m apart and reported to be oriented within a few degrees of the trace of a {111} slip plane. Shear offsets, like those created by intersecting deformation twins, are also observed when the microbands in AI +5.5 at.% Mg intersect another microband or grain boundary [9, 11-14]. While dislocation tangles and microbands have been characterized separately, a precursor or intermediate structure to microbands has not been identified in A1 +5.5 at.% Mg. Nor has the possibility that the apparent dislocation tangles are organized into a structure such as a Taylor lattice [4, 15, 16] been considered. In their simplest theoretical form, Taylor lattices consist of uniform arrays of edge dislocations along the primary slip plane which can be stabilized by secondary slip. Although the dislocations in a Taylor lattice are not clustered to minimize their energy as in cell walls, their organization into arrays of alternating sign lowers their energy from that of a random distribution. In the present work, new experimental
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observations of intermediate substructural features and the organization of apparently tangled dislocations in AI +5.5 at.% Mg are presented. These observations are used to describe an evolutionary path for microband formation in A1 +5.5 at.% Mg and relate this evolution to the formation of Taylor lattices and domain boundaries [4] in a fashion parallel to that of substructural evolution in cell forming metals. 2. EXPERIMENT
High purity Ai +5.5 at.% Mg was recrystallized at 773 K for 1 h to a grain size of 0.4 mm. Samples were rolled to cold reductions of 10 and 20% at a von Mises effective strain rate of 0.3 s -I . Standard thin foils were made from longitudinal plane sections of the rolled samples for TEM observation. Misorientations were measured across dislocation boundaries using microdiffraction techniques and the resulting Kikuchi patterns analyzed using a computer program from Heilmann and Clark [17]. 3. RESULTS Following a cold reduction of 10%, the deformation substructure of A1 +5.5 at.% Mg consisted of an apparent net of dislocation tangles with a fairly uniform density (Fig. 2) as expected [5-10]. However, tilting the sample reveals that there is a fine scale organization of this net along {111} planes. This
Fig. 2. A fairly uniform distribution of dislocation tangles is observed following a 10% rolling reduction.
organization is illustrated by the uniform light dark alternating contrast along {111} in Fig. 3. The contrast changes are from 0.3 to 0.5 # m wide and indicate an alternating misorientation along at least one component. Tilting the sample to different diffraction contrast vectors showed that this substructure contains mixed dislocations and multiple Burgers vectors. The organized net of dislocations observed in AI + 5.5 at.% Mg is defined as a multi-Burgers vector Taylor lattice in accordance with Ref. [4]. A Taylor lattice is a uniform distribution of dislocations with planar order about the most highly stressed glide planes. The order of dislocations about the glide planes has an alternating sense and lowers the energy of the distribution from that of a random array [4]. In addition to the fine scale organization, another new dislocation structure, very long single sheetlike dislocation boundaries, was observed on a larger scale subdividing a grain into differently oriented regions from 2-6 #m in width. Examples of this boundary structure and an illustration of its evolution are shown in Fig. 4. Initially these boundaries are so diffuse that the boundary dislocations cannot be distinguished from the surrounding dislocations. Evidence for a boundary is only indicated by a line of contrast change [Fig. 4(a)]. In more developed boundaries, either a few extra dislocations or a resolvable dislocation network was observed delineating the boundary
Fig. 3. The dislocation tangles are not random in AI +5.5 at.% Mg, but form an organized structure called a Taylor lattice. The light and dark contrast in this TEM photomicrograph show that the organization of the dislocations is along {111} slip planes. Dashed lines are the trace {l 11} 90 deg to the plane of the paper.
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Fig. 5. Pairs of parallel dislocation sheets called microbands (MB) form along domain boundaries (DB) during 10% e.r. Dashed and dotted lines show trace of {Ili} planes. B = [112]. from its surroundings [Fig. 4(b)]. Finally at larger cold reductions, 20%, the boundaries are very dense and individual dislocations cannot be resolved [Fig. 4(c)]. This nearly continuous range of dislocation densities observed within these boundaries indicates a gradual formation of the boundary. The uniform contrast change from one side of the boundary to the other in Fig. 4 illustrates the misorientation differenees from one region to another. Misorientation measurements across these boundaries show that a larger change in orientation, 0.5 to 1 deg, occurs across these boundaries than within the net of dislocations forming a Taylor lattice. There is also a plus minus pattern of misorientations across these boundaries. These single dislocation boundaries which separate regions of differently oriented Taylor lattices are defined as domain boundaries (DB) [4]. D o m a i n boundaries were always observed to have a crystallographic orientation in A1 +5.5 at.% Mg. Three families of domain boundaries intersect in a triangle as shown in Fig. 5. By tilting to three zone axes and noting the rotation of these walls with respect to the rotation of the trace of the { 111 } slip planes it was determined that the three families of walls were parallel to a {111} plane within 5 deg. This determination was made in three dimensions, in contrast to the usual practice for polycrystals of noting whether or not the walls are parallel to the "trace" of { 111 } with only a single tilt of the specimen. Fig. 4. Single dislocation boundaries, called domain boundaries (DB), form gradually as indicated by the range of dislocation densities observed within the walls. The domain boundaries are parallel to {111} planes. Dashed lines are the trace of {111}. (a) Initially DB are so diffuse that only a contrast change is observed across the boundary. 10% c.r. (b) A more developed domain boundary in which resolvable dislocations are observed in the boundary. 10% c.r. (c) Dense domain boundaries formed following 20% e.r. AMM 41/5
H
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The same procedures were followed in five grains and three samples. In all cases the boundaries were parallel to { 111 } within 5 deg. Along some sections of single domain boundaries, a second parallel dislocation sheet spaced about 0.3 # m from the DB has formed (Fig. 5). The platellke region defined by the two boundaries has a different orientation from the regions on either side. This platelike region with its own orientation defined by paired dislocation walls is called a first generation microband (MB) [3]. A first generation microband is a platelike region defined by rotation boundaries. The material within the boundaries slips with a different combination of slip systems than the regions on either side of the boundaries [3]. Hereafter the first generation microband will be referred to simply as microband. In Fig. 5, the contrast and the crystal orientation within the volume of the microband changes slightly as the microband traverses a DB into a differently oriented region. Microband walls in Fig. 5 are viewed on edge in Fig. 6, since both the walls and the parallel {111} planes are perpendicular to the B = [11(3] beam direction. When the boundaries are viewed on edge they are very straight, sharp and long. Most of the DBs and microbands observed spanned 50-100% of a grain diameter. A more detailed view of the microband walls under different diffracting conditions is shown in Fig. 7. The dislocation structure of the walls in AI +5.5 at.% Mg is resolvable at this small strain. The walls are composed of a clear dislocation network, Fig. 7(b), which is much more diffuse than the very dense walls in pure aluminum. Note that the dislocations which compose
Fig. 6. Long microband walls along {II I} viewed on edge with B = [lI0]. Dashed lines are the trace of {I II} 90 deg to the plane of the paper. The dotted line is the trace of {I II} 35 deg to the paper.
the microband contain Burgers vectors not represented in the surrounding dislocation net [Fig. 7(b)]. This difference in Burgers vectors was strongly suggested by the appearance of the microband walls compared to the Taylor lattice under several different diffracting conditions.
Fig. 7. High magnification view of two adjacent microbands under different diffracting conditions. (a) Wails perpendicu-
lar to paper with B =[110] beam direction. (b) Clear dislocation network is observed when the walls are tilted.
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Figure 7 also presents some clues as to the formation of parallel walls. In Fig. 7 there are two adjacent microbands sharing a common wall. Only one of these microbands has well formed continuous walls on both sides. In contrast to the first MB, the second MB has one continuous wall and one wall made up of short discontinuous sections [righthand wall in Fig. 7(a)]. These discontinuities provide the impression that one wall was just forming. Only the one well formed microband extends the length of a grain in Fig. 7. While short second walls parallel to the initial domain boundaries and long paired walls (microbands) were frequently observed, no subdivision of the very narrow and diffuse DBs was observed to form microbands at this small strain. Misorientation measurements show that the paired dislocation sheets of the microband delineate a region with a new orientation which differs from the orientations of the regions on either side of the microband. The regions on either side of the microband are also misoriented from each other indicating that a microband bounds different domains of Taylor lattices like the DB from which it was derived. The different orientation of the microband shows that the microband creates a new domain of Taylor lattices within its boundaries. Misoriented regions of domains slip with different sets of operating slip systems [3]. The characteristics of these microbands are identical to those previously reported for AI +5.5 at.% Mg [9, 11-13], except, that at this small strain, no shear offsets were observed. This lack of shear offsets is illustrated in Fig. 8 where a microband intersects a DB without producing any perturbation in the DB. Neither were shear offsets observed at grain boundaries following a 10% cold reduction, as shown in Fig. 9, in which a microband only mildly perturbs a grain boundary where the two meet. The lack of shear offset further shows that these microbands are first generation microbands and not the second generation
Fig. 8. Intersection of microband (MB) with a domain boundary (DB) does not produce shear offsets during a 10% c.r.
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Fig. 9. A microband (MB) intersection with a grain boundary (GB) results in a slight interaction with the boundary but does not produce a shear offset during 10% c.r. microbands defined in Ref. [3]. Second generation microbands are defined as narrow platelike zones formed by localized shear and bounded by rotation boundaries. Following rolling at the larger cold reduction of 20%, shear offsets are produced by some microbandmicroband intersections (Fig. 10) but not all intersections (Fig. 11). These intersections are viewed in the longitudinal rolling plane with the microband walls and the {111 } plane perpendicular to the beam direction to maximize the offset. Note how the walls of the intersected microband [Fig. 10(b)] indicate a smooth progressive shear in the volume within the shearing microband, an observation which differs from the constant shear reported in [9, 14, 18]. While the size of the offset shown in Fig. 10 is of the frequently reported size of 0.3/~m, an entire range of offsets from 0 to 0.4/~m was observed within a single family of microbands along parallel {111 } planes in one grain, indicating that there is no characteristic length scale for these offsets. A single microband produces the same length shear offset at every boundary it intersects. However, one microband does not necessarily produce the same length offset as another parallel microband in the same grain. This range of offsets supports the idea that shear offsets are created after the formation of the microband walls. Thus there are two separate events; the formation of paired dislocation sheets and then the very localized deformation of the volume between the sheets.
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Fig. 11. Microband-microband intersection following 20% c.r. in which no shear offset occurs. Dashed lines are the trace of {111} 90 deg to the plane of the paper. The dotted line is the trace of {111} 35 deg to the paper.
could only be observed by continuously tilting the specimen. The microbands appeared either singly or in clusters with as many as ten adjacent bands. Clustering of bands was also observed at the smaller strain. The density of microbands is higher at the larger strain with a spacing of 2.2 v m following a 20% c.r. compared to 3.8 v m following 10% c.r. The density of background dislocations in the Taylor lattice also appeared higher (compare Figs 2 and 11). 4. DISCUSSION Fig. 10. (a) Shear offset produced at microband-microband intersection during 20% c.r. B near [011]. (b) Higher magnification view of this intersection showing the progressively distributed shear within the shearing microband. The high dislocation density is out of contrast within the bright area of the microband. B near [112]. Many microbands have developed denser walls whose dislocation network cannot be resolved following 20% c.r. (compare Figs 10 and 7). The misorientations across the walls of the MBs and DBs also increased to 1-2 deg at this larger strain. The MB and DB walls still lie parallel to {111} planes. This characteristic orientation was observed in three samples for a total of six grains at 20% c.r. Most of the microbands and the few DB which could be imaged extended across the length of a grain. However since the formation of misoriented regions by both DB and microbands changes the diffraction contrast along a band, the continuity of a particular band
Two new dislocation structures: Taylor lattices and domain boundaries which developed during deformation in AI +5.5 at.% Mg were identified and described together with microbands in the previous section. The following subsections discuss the role of these structures within an evolutionary framework of grain subdivision at two volume levels. The definitions of the levels in noncell forming metals are an extension of the definitions developed in cell forming metals. Central to the two level subdivision in cell forming metals is the idea of incidental dislocation structures at the smallest level and geometrically necessary boundaries at the largest level [19]. Incidental dislocation structures and boundaries are formed as a result of the statistical trapping of glide dislocations together with forest dislocations. Both Taylor lattices and cell structures are incidental structures with small lattice rotations. Geometrically necessary boundaries incorporate the lattice rotations which arise from the geometrical requirements of strain accommodation.
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Fig. 12. Schematic drawing of the subdivision of a grain in Taylor lattice forming metals. The alternating contrast of the Taylor lattice is marked TL. The single domain boundaries (DB) and double walled microbands (MB) subdivide the grain into differently oriented regions along {111} slip planes. As an aid to the discussion, a schematic of this microstructure and the grain subdivision is shown in Fig. 12.
4.1. Taylor lattices (incidental dislocation structures) The dislocation structures in the previous section are consistent with the general trend that the dislocation density increases during deformation through mutual trapping of glide dislocations together with forest dislocations. Although this dislocation trapping occurs in a statistical or incidental fashion, the dislocation structures which arise are not random as was shown in Fig. 3. Rather the structures will rearrange themselves in a manner which minimizes their energy per unit length of dislocation line within the constraints of available slip systems, dislocation mobility, and friction stress [3, 4]. A decrease in energy occurs when the dislocations are arranged to screen their self stresses and to minimize the long range stresses. The dislocation organization observed in AI +5.5 at.% Mg is a notable example of this drive to minimize the energy in the structure. Organization occurs in A1 +5.5 at.% Mg in spite of the very large constraints on rearrangement due to the large solute-dislocation interactions which increase the friction stress. The solute-dislocation interactions are particularly enhanced in A1 +5.5 at.% Mg due to the large atomic mismatch between aluminum and magnesium atoms of 12% and changes in elastic modulus due to magnesium additions [5, 20-22]. The degree of constraint on three-dimensional dislocation mobility affects the structural arrangement of the incidental dislocations. The incidental dislocation structures observed in A1 +5.5 at.% Mg and aluminum represent opposite ends of the spectrum of incidental structures. When there are large constraints, such as in AI +5.5 at.% Mg, a uniform array of dislocations forms a Taylor lattice with the organiz-
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ation of this structure only apparent by the pattern of contrast changes. When there are small constraints and three-dimensional dislocation mobility, as in pure aluminum, a lower energy cell structure forms which has well defined dislocation walls separating spaces cleared of dislocations [23]. Since the level of constraint can vary between these two extremes, a continuous range of incidental dislocation structures from uniform arrays of individual dislocations to well formed cells is possible. For example, the micrographs of deformed aluminum magnesium alloys with less Mg [10, 12] and thus fewer solute~lislocation interactions, show dislocation arrays with dislocation walls formed along {111} planes at locations in which there were only the contrast changes observed in Al + 5.5 at.% Mg. Of the many possible incidental structures observed, however, only the cell structure is consistently labeled in the literature. While Taylor lattice is a general term for non-cell structures, the term is used less frequently. Conseqently, the characteristics of the observed Taylor lattice will be discussed with respect to the definition given in the previous sections. The important features of the Taylor lattice observed in A1 +5.5 at.% Mg include the nearly uniform spacing of dislocations without clear spaces or pile-ups, the multiple Burgers vectors of dislocations within the array, the organization of the dislocations along { 111 } planes with alternating contrast and the alternating plus minus rotations this contrast implies. Although the observed structure is complex, these general features provide the common distinction for a Taylor lattice. Taylor lattice has been introduced as a broad extension of the simple theoretical array of edge dislocations of one Burgers vector suggested by Taylor [15] and the extension of this concept by Kuhlmann-Wilsdorf for real materials [4, 16]. Both the simple theoretical Taylor lattice and the very small strain Taylor lattice in a low stacking fault energy alloy in Ref. [16] have uniform arrays of dislocations with an organization about the slip plane in a plus minus fashion like A1 +5.5 at.% Mg. Those two structures have also been shown to have a much lower energy per line length than a random array of the same dislocations [16, 24]. The fact that the Taylor lattice in AI +5.5 at.% Mg has multiple Burgers vectors and has an alternating pattern of misorientations also implies that it has a lower energy than the simple theoretical Taylor lattice since stress screening is more effective with increasing numbers of Burgers vectors [23]. The introduction of a Taylor lattice as the definition for incidental structures in non-cell forming metals at larger strains is important because it conveys a sense of organization among complex dislocation arrays which are neither random arrays nor cells.
4.2. Domain boundaries and microbands (geometrically necessary boundaries) On a more macroscopic microstructural scale than the Taylor lattice, domain boundaries (DB) form the
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boundaries between misoriented regions of TLs within a grain (Fig. 12). The lattice rotations observed across these DBs, show that these DBs are geometrically necessary boundaries which develop as a consequence of strain accommodation. Each misoriented region delineated by the domain boundaries slips with a different selection of slip systems than its neighbor. Although the misorientations are much smaller across these small strain DBs, the plus minus pattern of misorientations across the DBs in A1 +5.5 at.% Mg has a similar character to the misorientations observed across dense dislocation walls (DDW) and microbands in pure aluminum and nickel [1,25]. Also the misorientations across DB were also found to increase significantly, up to 15 deg, with increasing strain in A1 +5.5 at.% Mg [26]. Thus the single domain boundaries subdividing regions of differently oriented Taylor lattices in non-cell forming metals are the counterparts to dense dislocation walls subdividing cell blocks in cell forming metals as postulated in Ref. [4]. The only difference between the domain boundaries and the dense dislocation walls is that the domain boundaries in AI + 5.5 at. % Mg consistently have a crystallographic orientation parallel to a { 111 } slip plane whereas dense dislocation walls have a macroscopic orientation to the deformation axes and no crystallographic preference. Domain boundaries are initially single dislocation walls that have the same length and orientation as the microbands observed in AI +5.5 at.% Mg. Most of these boundaries do not remain as single walls with increasing strain. Rather, short sections of a second parallel wall, spaced from 0.3 to 0.1/~m from the first forms. As the second wall develops and extends with increasing strain a long microband is formed. The creation of a microband at a single DB provides a new misoriented region and further subdivides a grain. While the formation of a second wall often occurs after the first, in some cases two walls can also develop simultaneously. The mechanism for microband formation by the subdivision of a single geometrically necessary boundary such as a dense dislocation wall in nickel [2, 25] was not observed in A1 +5.5 at.% Mg. Formation of adjacent parallel walls is also favoured energetically, since the stresses associated with the end of a rotation boundary (wall) can be shielded by an adjacent wall [3]. While planar slip is known to promote sheet formation along (111}, end stresses also help explain why the microbands and DB are nearly contiguous across a grain in AI-Mg. Since no cell walls are formed, the only low energy points for these rotation walls to end are at grain boundaries, other microbands or DB's. The creation of a microband at a domain boundary in AI +5.5 at.% Mg is analogous to the formation of a first generation microband at dense dislocation walls in cell forming metals [1-4]. First generation microbands share the same orientation within a grain as the single walled boundary from which they are derived. Thus in A1 +5.5 at.% Mg the microbands
are parallel to {111 } slip planes whereas the microbands in cell forming metals have a macroscopic orientation to the deformation axes like the dense dislocation walls.
4.3. Grain subdivision Grain subdivision was shown to occur for non-cell forming metals in an analogous manner to that in cell forming metals. While a few of the characteristics of the geometrically necessary boundaries (DBs and MBs) for non-cell forming metals differs from those in cell forming metals, the function of the geometrically necessary boundaries is common to both. All of those boundaries arise from the geometrical requirement for strain accommodation [3] within a deforming polycrystal with a finite number of slip planes and directions. A minimum of five slip systems is needed to make any arbitrary shape change, the Taylor criterion [27]. However, activation of so many slip systems raises the flow stress, so that a crystal would prefer to slip on less than five slip systems. To achieve strain accommodation on fewer slip systems, grain subdivision occurs creating regions in which different slip systems operate [3]. These regions act jointly to approximately fulfill the Taylor criterion for strain accommodation. Separately, each region has a different selection of slip systems which are less than the five required by the Taylor criterion. For a material which prefers planar slip such as A1 +5.5 at.% Mg, this subdivision allows for planar slip to continue in separate regions of Taylor lattices at the same time that strain accommodation is achieved. As strain continues the lattice rotations increase across the geometrically necessary boundaries and further subdivision is required for strain accommodation. As in cell forming metals, this further strain accommodation is achieved by creating new geometrically necessary boundaries. New geometrically necessary boundaries are formed by the creation of microbands at the domain boundaries between the differently deforming regions. The microbands provide new misoriented regions which operate with a new selection of slip systems. New domain boundaries can also be formed within a Taylor lattice. The Taylor lattice is organized about the {111} planes along the same orientations as the domain boundaries and microbands. The accumulation of extra dislocations and increased lattice rotations at the contrast boundaries of the Taylor lattice with increasing strain can cause these incidental structures to evolve into geometrically necessary boundaries, i.e. new DBs and MBs. The increased subdivision with increasing strain is illustrated by the decrease in spacing of geometrically necessary boundaries by nearly a factor of two between 10 and 20% cold reductions.
4.4. Comparison of the evolutionary process with avalanche glide theory The present results strongly suggest a very different view of microband formation in AI +5.5 at.% Mg
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MICROSTRUCTURAL EVOLUTION IN A1-Mg
at small to medium strains than that postulated by previous investigators. Previously it was postulated that the paired sheets composing a microband are formed simultaneously by avalanche glide processes [9, 14, 18, 28]. The theory of avalanche glide postulates that paired disclocation sheets are created when large numbers of dislocations on closely spaced parallel slip planes cross slip in a procession [28, 29]. The paired dislocation sheets that are created by this process would be nearly parallel to a slip plane. To promote avalanche glide, a microstructure that is unstable to slip in the current slip direction is required. This type of microstructure is provided by radiation damage [29, 30] or possibly by prior deformation in a different direction than the current deformation mode [31, 32]. While the rate of this process is not indicated by this theory, many authors consider avalanche glide to be a very rapid process for the formation of microbands [28]. The microband walls and the shear offset are considered to form simultaneously. This mechanism was postulated for microband formation in rolled metals because of two experimental observations. Firstly, mtcrobands have been frequently observed nearly parallel to the trace of a {111 } slip plane [9, 14, 18]. Secondly, previous investigators considered substructures formed at large strains where shear offsets were a prominent feature of the microbands they observed [9, 14, 18]. The large shear offsets observed when microbands intersect each other or a grain boundary look similar to the offsets created by deformation twins. Thus, their appearance suggested that they were created in response to a shear instability. The present results, however, provide new substructural observations that change the previous perspective of microband formation. Avalanche glide and narrow glide zones are not the dominant mechanism for microband formation at small to medium strains. Rather, there is an underlying dislocation structure, observed in this work, which is the precursor to microbands at small to medium strains. Observations of this underlying structure describe an evolutionary path for microband formation in A1 +5.5 at.% Mg which parallels that in cell forming metals. Thus the microbands observed in this paper are first generation microbands as defined in Ref. [3]. The second generation microbands defined in Ref. [3] which arise from narrow glide zones were not observed. Furthermore, microband shear offsets were only observed at larger strains, indicating that the shear offsets are a large strain phenomenon separate from the initial microband formation. The range of shear offsets observed indicated that these offsets did not have a characteristic length. While, the cause of shear offsets is not considered in the present paper, geometrical softening could play a role [33, 34]. 5. SUMMARY AND CONCLUSIONS The evolution of the deformation substructure in lightly rolled A1 + 5.5 at.% Mg, which is a non-cell
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forming alloy, was observed using TEM. At small strains, the dislocation substructure of A1 + 5.5 at.% Mg consists of a uniform distribution of dislocations organized along the {111 } slip planes. This organized structure in a non-cell forming metal was defined as a Taylor lattice. Additionally, a new dislocation substructure consisting of long straight domain boundaries (DB) lying nearly parallel to { 111} slip planes was observed. In an analogous manner to dense dislocation walls in cell forming metals, such as pure aluminum and nickel, the domain boundaries in non-cell forming metals are geometrically necessary boundaries which subdivide a grain into misoriented regions. Within these regions, deformation occurs on fewer slip systems than specified by the Taylor criterion for strain accommodation. Microbands consisting of paired dislocation sheets form from the single DBs by gradual glide processes without the initiation of a shear instability. The microbands form new misoriented regions which further strain accommodation. At larger strains, these microbands exhibit the commonly reported shear offsets where they intersect a boundary. This description of substructural evolution provides a general evolutionary framework of grain subdivision for metals and alloys which do not form cells. This framework for continuous grain subdivision in non-cell forming metals is analogous to that observed in cell forming metals. Acknowledgements--Several fruitful discussions with D. K. Wilsdorf and N. Hansen are gratefully acknowledged. This work was supported by U.S. Department of Energy, DOE under contract No. DE-AC04-76DP00789.
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17. P. Heilmann, W. A. T. Clark and D. A. Rigney, Ultramicroscopy 9, 365 (1982). 18. A. S. Malin and M. Hatherly, Metal Sci. 13, 463 (1979). 19. D. Kuhlmann-Wilsdorf and N. Hansen, Scripta metall. mater. 25, 1557 (1991). 20. R. L. Fleischer, Acta metall. 11, 203 (1963). 21. W. Koster and W. Rauscher, Z. Metalk. 39, 111 (1948). 22. G. Thomas and J. Nutting, J. Inst. Metals 85, 1711 (1956). 23. M. N. Bassim and D. Kuhlmann-Wilsdorf, Physica status solidi (a) 16, 241 (1973). 24. N. Hansen and D. Kuhlmann-Wilsdorf, Mater. Sci. Engng 81, 141 (1986). 25. D. A. Hughes and N. Hansen, Mater. Sci. Technol. 7, 544 (1991). 26. D. A. Hughes and Y. L. Liu, Hot Deformation of Aluminum Alloys (edited by T. G. Langdon, H. D.
27. 28. 29. 30. 31. 32. 33. 34.
Merchant, J. G. Morris and M. A. Zaidi), p. 21. The Minerals, Metals and Materials Society, Warrendale, Pa (1991). G. I. Taylor, J. Inst. Metals 62, 307 (1938). P. J. Jackson, Scripta metall. 17, 199 (1983). P. D. K. Nathanson, P. J. Jackson and D. R. Spalding, Acta metall. 28, 823 (1980). M. J. Makin and J, V. Sharp, Physica status solidi 9, 109 (1965). Z. S. Basinski and P. J. Jackson, Physica status solidi 9, 805 (1965). J. V. Sharp and M. J. Makin, Can. J. Phys. 45, 519 (1967). S. V. Harren, H. E. Deve and R. J. Asaro, Acta metall. 36, 2435 (1988). S. V. Harren and R. J. Asaro, J. Mech. Phys. Solids 37, 191 (1989).
0956-7151/93 $6.00 + 0.00 Copyright © 1993 Pergamon Press Ltd
Printed in Great Britain. All rights reserved
MICROSTRUCTURAL EVOLUTION IN A NON-CELL FORMING METAL: A1-Mg D. A. HUGHES Materials Department, Sandia National Laboratories, Livermore, CA 94550, U.S.A. (Received 6 April 1992; in revisedform 30 September 1992)
A~tract--Microstructural evolution in AI + 5.5 at.% Mg lightly deformed by rolling was studied using transmission electron microscopy. Observations show that the dislocations are organized into a Taylor lattice containing multiple burgers vectors and having alternating misorientations along {111} slip planes. These observations are in contrast to the usual description of these structures as "random" dislocation tangles. With increasing strain, a grain is subdivided into several domains of differently oriented Taylor lattices. The newly observed boundaries between different domains are long single dislocations walls formed along 'qI l 1}. As a further evolutionary progression, the single walled domain boundaries develop into microbands. The observed grain subdivision parallels that observed in cell forming metals. Subdivision occurs to accommodate strain using fewer slip systems than required by the Taylor criterion.
I. INTRODUCTION During deformation of cell forming polycrystalline metals, grains are subdivided into misoriented regions in which deformation occurs on fewer slip systems than specified by the Taylor criterion for strain accommodation [1]. The selection of active slip systems also differs between these regions. Long dense dislocation walls (DDW) form the boundaries between the misoriented regions of equiaxed cells. For pure nickel and aluminum, microbands are subsequently formed from within these DDWs by a gradual multiple slip process [2, 3]. A schematic drawing of these structures is shown in Fig. 1. With increasing deformation, the regions of equiaxed cells, called cell blocks (CB), are further subdivided by the formation of new DDWs
Fig. 1. Schematic drawing of the deformation microstruction in cell forming metals showing the subdivision into cell blocks (CB) outlined by dense dislocation walls (DDW) and microbands (MB) [3].
and microbands. This evolutionary process and the theoretical interpretation is consistent for cell forming metals. The central idea that grains are subdivided into misoriented regions should also apply to metals which do not form cells [4]. This idea is investigated for lightly rolled A1 +5.5 at.% Mg. In AI +5.5 at.% Mg, solute effects increase the friction stress and thereby inhibit cell formation. Previous TEM studies show that the dislocation substructure of AI + 5.5 at.% Mg following small strain tensile or rolling deformation consists of a uniform distribution of dislocation tangles; no cell structure is formed [5-10]. Some of these studies also show that the dislocation structure at larger strains contains very sharp microbands which cut through these dislocation tangles [9, 11-13]. These microbands are characterized as paired dislocation sheets spaced approximately 0.2/~m apart and reported to be oriented within a few degrees of the trace of a {111} slip plane. Shear offsets, like those created by intersecting deformation twins, are also observed when the microbands in AI +5.5 at.% Mg intersect another microband or grain boundary [9, 11-14]. While dislocation tangles and microbands have been characterized separately, a precursor or intermediate structure to microbands has not been identified in A1 +5.5 at.% Mg. Nor has the possibility that the apparent dislocation tangles are organized into a structure such as a Taylor lattice [4, 15, 16] been considered. In their simplest theoretical form, Taylor lattices consist of uniform arrays of edge dislocations along the primary slip plane which can be stabilized by secondary slip. Although the dislocations in a Taylor lattice are not clustered to minimize their energy as in cell walls, their organization into arrays of alternating sign lowers their energy from that of a random distribution. In the present work, new experimental
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observations of intermediate substructural features and the organization of apparently tangled dislocations in AI +5.5 at.% Mg are presented. These observations are used to describe an evolutionary path for microband formation in A1 +5.5 at.% Mg and relate this evolution to the formation of Taylor lattices and domain boundaries [4] in a fashion parallel to that of substructural evolution in cell forming metals. 2. EXPERIMENT
High purity Ai +5.5 at.% Mg was recrystallized at 773 K for 1 h to a grain size of 0.4 mm. Samples were rolled to cold reductions of 10 and 20% at a von Mises effective strain rate of 0.3 s -I . Standard thin foils were made from longitudinal plane sections of the rolled samples for TEM observation. Misorientations were measured across dislocation boundaries using microdiffraction techniques and the resulting Kikuchi patterns analyzed using a computer program from Heilmann and Clark [17]. 3. RESULTS Following a cold reduction of 10%, the deformation substructure of A1 +5.5 at.% Mg consisted of an apparent net of dislocation tangles with a fairly uniform density (Fig. 2) as expected [5-10]. However, tilting the sample reveals that there is a fine scale organization of this net along {111} planes. This
Fig. 2. A fairly uniform distribution of dislocation tangles is observed following a 10% rolling reduction.
organization is illustrated by the uniform light dark alternating contrast along {111} in Fig. 3. The contrast changes are from 0.3 to 0.5 # m wide and indicate an alternating misorientation along at least one component. Tilting the sample to different diffraction contrast vectors showed that this substructure contains mixed dislocations and multiple Burgers vectors. The organized net of dislocations observed in AI + 5.5 at.% Mg is defined as a multi-Burgers vector Taylor lattice in accordance with Ref. [4]. A Taylor lattice is a uniform distribution of dislocations with planar order about the most highly stressed glide planes. The order of dislocations about the glide planes has an alternating sense and lowers the energy of the distribution from that of a random array [4]. In addition to the fine scale organization, another new dislocation structure, very long single sheetlike dislocation boundaries, was observed on a larger scale subdividing a grain into differently oriented regions from 2-6 #m in width. Examples of this boundary structure and an illustration of its evolution are shown in Fig. 4. Initially these boundaries are so diffuse that the boundary dislocations cannot be distinguished from the surrounding dislocations. Evidence for a boundary is only indicated by a line of contrast change [Fig. 4(a)]. In more developed boundaries, either a few extra dislocations or a resolvable dislocation network was observed delineating the boundary
Fig. 3. The dislocation tangles are not random in AI +5.5 at.% Mg, but form an organized structure called a Taylor lattice. The light and dark contrast in this TEM photomicrograph show that the organization of the dislocations is along {111} slip planes. Dashed lines are the trace {l 11} 90 deg to the plane of the paper.
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MICROSTRUCTURAL EVOLUTION IN A1-Mg
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Fig. 5. Pairs of parallel dislocation sheets called microbands (MB) form along domain boundaries (DB) during 10% e.r. Dashed and dotted lines show trace of {Ili} planes. B = [112]. from its surroundings [Fig. 4(b)]. Finally at larger cold reductions, 20%, the boundaries are very dense and individual dislocations cannot be resolved [Fig. 4(c)]. This nearly continuous range of dislocation densities observed within these boundaries indicates a gradual formation of the boundary. The uniform contrast change from one side of the boundary to the other in Fig. 4 illustrates the misorientation differenees from one region to another. Misorientation measurements across these boundaries show that a larger change in orientation, 0.5 to 1 deg, occurs across these boundaries than within the net of dislocations forming a Taylor lattice. There is also a plus minus pattern of misorientations across these boundaries. These single dislocation boundaries which separate regions of differently oriented Taylor lattices are defined as domain boundaries (DB) [4]. D o m a i n boundaries were always observed to have a crystallographic orientation in A1 +5.5 at.% Mg. Three families of domain boundaries intersect in a triangle as shown in Fig. 5. By tilting to three zone axes and noting the rotation of these walls with respect to the rotation of the trace of the { 111 } slip planes it was determined that the three families of walls were parallel to a {111} plane within 5 deg. This determination was made in three dimensions, in contrast to the usual practice for polycrystals of noting whether or not the walls are parallel to the "trace" of { 111 } with only a single tilt of the specimen. Fig. 4. Single dislocation boundaries, called domain boundaries (DB), form gradually as indicated by the range of dislocation densities observed within the walls. The domain boundaries are parallel to {111} planes. Dashed lines are the trace of {111}. (a) Initially DB are so diffuse that only a contrast change is observed across the boundary. 10% c.r. (b) A more developed domain boundary in which resolvable dislocations are observed in the boundary. 10% c.r. (c) Dense domain boundaries formed following 20% e.r. AMM 41/5
H
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The same procedures were followed in five grains and three samples. In all cases the boundaries were parallel to { 111 } within 5 deg. Along some sections of single domain boundaries, a second parallel dislocation sheet spaced about 0.3 # m from the DB has formed (Fig. 5). The platellke region defined by the two boundaries has a different orientation from the regions on either side. This platelike region with its own orientation defined by paired dislocation walls is called a first generation microband (MB) [3]. A first generation microband is a platelike region defined by rotation boundaries. The material within the boundaries slips with a different combination of slip systems than the regions on either side of the boundaries [3]. Hereafter the first generation microband will be referred to simply as microband. In Fig. 5, the contrast and the crystal orientation within the volume of the microband changes slightly as the microband traverses a DB into a differently oriented region. Microband walls in Fig. 5 are viewed on edge in Fig. 6, since both the walls and the parallel {111} planes are perpendicular to the B = [11(3] beam direction. When the boundaries are viewed on edge they are very straight, sharp and long. Most of the DBs and microbands observed spanned 50-100% of a grain diameter. A more detailed view of the microband walls under different diffracting conditions is shown in Fig. 7. The dislocation structure of the walls in AI +5.5 at.% Mg is resolvable at this small strain. The walls are composed of a clear dislocation network, Fig. 7(b), which is much more diffuse than the very dense walls in pure aluminum. Note that the dislocations which compose
Fig. 6. Long microband walls along {II I} viewed on edge with B = [lI0]. Dashed lines are the trace of {I II} 90 deg to the plane of the paper. The dotted line is the trace of {I II} 35 deg to the paper.
the microband contain Burgers vectors not represented in the surrounding dislocation net [Fig. 7(b)]. This difference in Burgers vectors was strongly suggested by the appearance of the microband walls compared to the Taylor lattice under several different diffracting conditions.
Fig. 7. High magnification view of two adjacent microbands under different diffracting conditions. (a) Wails perpendicu-
lar to paper with B =[110] beam direction. (b) Clear dislocation network is observed when the walls are tilted.
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MICROSTRUCTURAL EVOLUTION IN AI-Mg
Figure 7 also presents some clues as to the formation of parallel walls. In Fig. 7 there are two adjacent microbands sharing a common wall. Only one of these microbands has well formed continuous walls on both sides. In contrast to the first MB, the second MB has one continuous wall and one wall made up of short discontinuous sections [righthand wall in Fig. 7(a)]. These discontinuities provide the impression that one wall was just forming. Only the one well formed microband extends the length of a grain in Fig. 7. While short second walls parallel to the initial domain boundaries and long paired walls (microbands) were frequently observed, no subdivision of the very narrow and diffuse DBs was observed to form microbands at this small strain. Misorientation measurements show that the paired dislocation sheets of the microband delineate a region with a new orientation which differs from the orientations of the regions on either side of the microband. The regions on either side of the microband are also misoriented from each other indicating that a microband bounds different domains of Taylor lattices like the DB from which it was derived. The different orientation of the microband shows that the microband creates a new domain of Taylor lattices within its boundaries. Misoriented regions of domains slip with different sets of operating slip systems [3]. The characteristics of these microbands are identical to those previously reported for AI +5.5 at.% Mg [9, 11-13], except, that at this small strain, no shear offsets were observed. This lack of shear offsets is illustrated in Fig. 8 where a microband intersects a DB without producing any perturbation in the DB. Neither were shear offsets observed at grain boundaries following a 10% cold reduction, as shown in Fig. 9, in which a microband only mildly perturbs a grain boundary where the two meet. The lack of shear offset further shows that these microbands are first generation microbands and not the second generation
Fig. 8. Intersection of microband (MB) with a domain boundary (DB) does not produce shear offsets during a 10% c.r.
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Fig. 9. A microband (MB) intersection with a grain boundary (GB) results in a slight interaction with the boundary but does not produce a shear offset during 10% c.r. microbands defined in Ref. [3]. Second generation microbands are defined as narrow platelike zones formed by localized shear and bounded by rotation boundaries. Following rolling at the larger cold reduction of 20%, shear offsets are produced by some microbandmicroband intersections (Fig. 10) but not all intersections (Fig. 11). These intersections are viewed in the longitudinal rolling plane with the microband walls and the {111 } plane perpendicular to the beam direction to maximize the offset. Note how the walls of the intersected microband [Fig. 10(b)] indicate a smooth progressive shear in the volume within the shearing microband, an observation which differs from the constant shear reported in [9, 14, 18]. While the size of the offset shown in Fig. 10 is of the frequently reported size of 0.3/~m, an entire range of offsets from 0 to 0.4/~m was observed within a single family of microbands along parallel {111 } planes in one grain, indicating that there is no characteristic length scale for these offsets. A single microband produces the same length shear offset at every boundary it intersects. However, one microband does not necessarily produce the same length offset as another parallel microband in the same grain. This range of offsets supports the idea that shear offsets are created after the formation of the microband walls. Thus there are two separate events; the formation of paired dislocation sheets and then the very localized deformation of the volume between the sheets.
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Fig. 11. Microband-microband intersection following 20% c.r. in which no shear offset occurs. Dashed lines are the trace of {111} 90 deg to the plane of the paper. The dotted line is the trace of {111} 35 deg to the paper.
could only be observed by continuously tilting the specimen. The microbands appeared either singly or in clusters with as many as ten adjacent bands. Clustering of bands was also observed at the smaller strain. The density of microbands is higher at the larger strain with a spacing of 2.2 v m following a 20% c.r. compared to 3.8 v m following 10% c.r. The density of background dislocations in the Taylor lattice also appeared higher (compare Figs 2 and 11). 4. DISCUSSION Fig. 10. (a) Shear offset produced at microband-microband intersection during 20% c.r. B near [011]. (b) Higher magnification view of this intersection showing the progressively distributed shear within the shearing microband. The high dislocation density is out of contrast within the bright area of the microband. B near [112]. Many microbands have developed denser walls whose dislocation network cannot be resolved following 20% c.r. (compare Figs 10 and 7). The misorientations across the walls of the MBs and DBs also increased to 1-2 deg at this larger strain. The MB and DB walls still lie parallel to {111} planes. This characteristic orientation was observed in three samples for a total of six grains at 20% c.r. Most of the microbands and the few DB which could be imaged extended across the length of a grain. However since the formation of misoriented regions by both DB and microbands changes the diffraction contrast along a band, the continuity of a particular band
Two new dislocation structures: Taylor lattices and domain boundaries which developed during deformation in AI +5.5 at.% Mg were identified and described together with microbands in the previous section. The following subsections discuss the role of these structures within an evolutionary framework of grain subdivision at two volume levels. The definitions of the levels in noncell forming metals are an extension of the definitions developed in cell forming metals. Central to the two level subdivision in cell forming metals is the idea of incidental dislocation structures at the smallest level and geometrically necessary boundaries at the largest level [19]. Incidental dislocation structures and boundaries are formed as a result of the statistical trapping of glide dislocations together with forest dislocations. Both Taylor lattices and cell structures are incidental structures with small lattice rotations. Geometrically necessary boundaries incorporate the lattice rotations which arise from the geometrical requirements of strain accommodation.
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MICROSTRUCTURAL EVOLUTION IN A1-Mg
Fig. 12. Schematic drawing of the subdivision of a grain in Taylor lattice forming metals. The alternating contrast of the Taylor lattice is marked TL. The single domain boundaries (DB) and double walled microbands (MB) subdivide the grain into differently oriented regions along {111} slip planes. As an aid to the discussion, a schematic of this microstructure and the grain subdivision is shown in Fig. 12.
4.1. Taylor lattices (incidental dislocation structures) The dislocation structures in the previous section are consistent with the general trend that the dislocation density increases during deformation through mutual trapping of glide dislocations together with forest dislocations. Although this dislocation trapping occurs in a statistical or incidental fashion, the dislocation structures which arise are not random as was shown in Fig. 3. Rather the structures will rearrange themselves in a manner which minimizes their energy per unit length of dislocation line within the constraints of available slip systems, dislocation mobility, and friction stress [3, 4]. A decrease in energy occurs when the dislocations are arranged to screen their self stresses and to minimize the long range stresses. The dislocation organization observed in AI +5.5 at.% Mg is a notable example of this drive to minimize the energy in the structure. Organization occurs in A1 +5.5 at.% Mg in spite of the very large constraints on rearrangement due to the large solute-dislocation interactions which increase the friction stress. The solute-dislocation interactions are particularly enhanced in A1 +5.5 at.% Mg due to the large atomic mismatch between aluminum and magnesium atoms of 12% and changes in elastic modulus due to magnesium additions [5, 20-22]. The degree of constraint on three-dimensional dislocation mobility affects the structural arrangement of the incidental dislocations. The incidental dislocation structures observed in A1 +5.5 at.% Mg and aluminum represent opposite ends of the spectrum of incidental structures. When there are large constraints, such as in AI +5.5 at.% Mg, a uniform array of dislocations forms a Taylor lattice with the organiz-
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ation of this structure only apparent by the pattern of contrast changes. When there are small constraints and three-dimensional dislocation mobility, as in pure aluminum, a lower energy cell structure forms which has well defined dislocation walls separating spaces cleared of dislocations [23]. Since the level of constraint can vary between these two extremes, a continuous range of incidental dislocation structures from uniform arrays of individual dislocations to well formed cells is possible. For example, the micrographs of deformed aluminum magnesium alloys with less Mg [10, 12] and thus fewer solute~lislocation interactions, show dislocation arrays with dislocation walls formed along {111} planes at locations in which there were only the contrast changes observed in Al + 5.5 at.% Mg. Of the many possible incidental structures observed, however, only the cell structure is consistently labeled in the literature. While Taylor lattice is a general term for non-cell structures, the term is used less frequently. Conseqently, the characteristics of the observed Taylor lattice will be discussed with respect to the definition given in the previous sections. The important features of the Taylor lattice observed in A1 +5.5 at.% Mg include the nearly uniform spacing of dislocations without clear spaces or pile-ups, the multiple Burgers vectors of dislocations within the array, the organization of the dislocations along { 111 } planes with alternating contrast and the alternating plus minus rotations this contrast implies. Although the observed structure is complex, these general features provide the common distinction for a Taylor lattice. Taylor lattice has been introduced as a broad extension of the simple theoretical array of edge dislocations of one Burgers vector suggested by Taylor [15] and the extension of this concept by Kuhlmann-Wilsdorf for real materials [4, 16]. Both the simple theoretical Taylor lattice and the very small strain Taylor lattice in a low stacking fault energy alloy in Ref. [16] have uniform arrays of dislocations with an organization about the slip plane in a plus minus fashion like A1 +5.5 at.% Mg. Those two structures have also been shown to have a much lower energy per line length than a random array of the same dislocations [16, 24]. The fact that the Taylor lattice in AI +5.5 at.% Mg has multiple Burgers vectors and has an alternating pattern of misorientations also implies that it has a lower energy than the simple theoretical Taylor lattice since stress screening is more effective with increasing numbers of Burgers vectors [23]. The introduction of a Taylor lattice as the definition for incidental structures in non-cell forming metals at larger strains is important because it conveys a sense of organization among complex dislocation arrays which are neither random arrays nor cells.
4.2. Domain boundaries and microbands (geometrically necessary boundaries) On a more macroscopic microstructural scale than the Taylor lattice, domain boundaries (DB) form the
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HUGHES: MICROSTRUCTURAL EVOLUTION IN AI-Mg
boundaries between misoriented regions of TLs within a grain (Fig. 12). The lattice rotations observed across these DBs, show that these DBs are geometrically necessary boundaries which develop as a consequence of strain accommodation. Each misoriented region delineated by the domain boundaries slips with a different selection of slip systems than its neighbor. Although the misorientations are much smaller across these small strain DBs, the plus minus pattern of misorientations across the DBs in A1 +5.5 at.% Mg has a similar character to the misorientations observed across dense dislocation walls (DDW) and microbands in pure aluminum and nickel [1,25]. Also the misorientations across DB were also found to increase significantly, up to 15 deg, with increasing strain in A1 +5.5 at.% Mg [26]. Thus the single domain boundaries subdividing regions of differently oriented Taylor lattices in non-cell forming metals are the counterparts to dense dislocation walls subdividing cell blocks in cell forming metals as postulated in Ref. [4]. The only difference between the domain boundaries and the dense dislocation walls is that the domain boundaries in AI + 5.5 at. % Mg consistently have a crystallographic orientation parallel to a { 111 } slip plane whereas dense dislocation walls have a macroscopic orientation to the deformation axes and no crystallographic preference. Domain boundaries are initially single dislocation walls that have the same length and orientation as the microbands observed in AI +5.5 at.% Mg. Most of these boundaries do not remain as single walls with increasing strain. Rather, short sections of a second parallel wall, spaced from 0.3 to 0.1/~m from the first forms. As the second wall develops and extends with increasing strain a long microband is formed. The creation of a microband at a single DB provides a new misoriented region and further subdivides a grain. While the formation of a second wall often occurs after the first, in some cases two walls can also develop simultaneously. The mechanism for microband formation by the subdivision of a single geometrically necessary boundary such as a dense dislocation wall in nickel [2, 25] was not observed in A1 +5.5 at.% Mg. Formation of adjacent parallel walls is also favoured energetically, since the stresses associated with the end of a rotation boundary (wall) can be shielded by an adjacent wall [3]. While planar slip is known to promote sheet formation along (111}, end stresses also help explain why the microbands and DB are nearly contiguous across a grain in AI-Mg. Since no cell walls are formed, the only low energy points for these rotation walls to end are at grain boundaries, other microbands or DB's. The creation of a microband at a domain boundary in AI +5.5 at.% Mg is analogous to the formation of a first generation microband at dense dislocation walls in cell forming metals [1-4]. First generation microbands share the same orientation within a grain as the single walled boundary from which they are derived. Thus in A1 +5.5 at.% Mg the microbands
are parallel to {111 } slip planes whereas the microbands in cell forming metals have a macroscopic orientation to the deformation axes like the dense dislocation walls.
4.3. Grain subdivision Grain subdivision was shown to occur for non-cell forming metals in an analogous manner to that in cell forming metals. While a few of the characteristics of the geometrically necessary boundaries (DBs and MBs) for non-cell forming metals differs from those in cell forming metals, the function of the geometrically necessary boundaries is common to both. All of those boundaries arise from the geometrical requirement for strain accommodation [3] within a deforming polycrystal with a finite number of slip planes and directions. A minimum of five slip systems is needed to make any arbitrary shape change, the Taylor criterion [27]. However, activation of so many slip systems raises the flow stress, so that a crystal would prefer to slip on less than five slip systems. To achieve strain accommodation on fewer slip systems, grain subdivision occurs creating regions in which different slip systems operate [3]. These regions act jointly to approximately fulfill the Taylor criterion for strain accommodation. Separately, each region has a different selection of slip systems which are less than the five required by the Taylor criterion. For a material which prefers planar slip such as A1 +5.5 at.% Mg, this subdivision allows for planar slip to continue in separate regions of Taylor lattices at the same time that strain accommodation is achieved. As strain continues the lattice rotations increase across the geometrically necessary boundaries and further subdivision is required for strain accommodation. As in cell forming metals, this further strain accommodation is achieved by creating new geometrically necessary boundaries. New geometrically necessary boundaries are formed by the creation of microbands at the domain boundaries between the differently deforming regions. The microbands provide new misoriented regions which operate with a new selection of slip systems. New domain boundaries can also be formed within a Taylor lattice. The Taylor lattice is organized about the {111} planes along the same orientations as the domain boundaries and microbands. The accumulation of extra dislocations and increased lattice rotations at the contrast boundaries of the Taylor lattice with increasing strain can cause these incidental structures to evolve into geometrically necessary boundaries, i.e. new DBs and MBs. The increased subdivision with increasing strain is illustrated by the decrease in spacing of geometrically necessary boundaries by nearly a factor of two between 10 and 20% cold reductions.
4.4. Comparison of the evolutionary process with avalanche glide theory The present results strongly suggest a very different view of microband formation in AI +5.5 at.% Mg
HUGHES:
MICROSTRUCTURAL EVOLUTION IN A1-Mg
at small to medium strains than that postulated by previous investigators. Previously it was postulated that the paired sheets composing a microband are formed simultaneously by avalanche glide processes [9, 14, 18, 28]. The theory of avalanche glide postulates that paired disclocation sheets are created when large numbers of dislocations on closely spaced parallel slip planes cross slip in a procession [28, 29]. The paired dislocation sheets that are created by this process would be nearly parallel to a slip plane. To promote avalanche glide, a microstructure that is unstable to slip in the current slip direction is required. This type of microstructure is provided by radiation damage [29, 30] or possibly by prior deformation in a different direction than the current deformation mode [31, 32]. While the rate of this process is not indicated by this theory, many authors consider avalanche glide to be a very rapid process for the formation of microbands [28]. The microband walls and the shear offset are considered to form simultaneously. This mechanism was postulated for microband formation in rolled metals because of two experimental observations. Firstly, mtcrobands have been frequently observed nearly parallel to the trace of a {111 } slip plane [9, 14, 18]. Secondly, previous investigators considered substructures formed at large strains where shear offsets were a prominent feature of the microbands they observed [9, 14, 18]. The large shear offsets observed when microbands intersect each other or a grain boundary look similar to the offsets created by deformation twins. Thus, their appearance suggested that they were created in response to a shear instability. The present results, however, provide new substructural observations that change the previous perspective of microband formation. Avalanche glide and narrow glide zones are not the dominant mechanism for microband formation at small to medium strains. Rather, there is an underlying dislocation structure, observed in this work, which is the precursor to microbands at small to medium strains. Observations of this underlying structure describe an evolutionary path for microband formation in A1 +5.5 at.% Mg which parallels that in cell forming metals. Thus the microbands observed in this paper are first generation microbands as defined in Ref. [3]. The second generation microbands defined in Ref. [3] which arise from narrow glide zones were not observed. Furthermore, microband shear offsets were only observed at larger strains, indicating that the shear offsets are a large strain phenomenon separate from the initial microband formation. The range of shear offsets observed indicated that these offsets did not have a characteristic length. While, the cause of shear offsets is not considered in the present paper, geometrical softening could play a role [33, 34]. 5. SUMMARY AND CONCLUSIONS The evolution of the deformation substructure in lightly rolled A1 + 5.5 at.% Mg, which is a non-cell
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forming alloy, was observed using TEM. At small strains, the dislocation substructure of A1 + 5.5 at.% Mg consists of a uniform distribution of dislocations organized along the {111 } slip planes. This organized structure in a non-cell forming metal was defined as a Taylor lattice. Additionally, a new dislocation substructure consisting of long straight domain boundaries (DB) lying nearly parallel to { 111} slip planes was observed. In an analogous manner to dense dislocation walls in cell forming metals, such as pure aluminum and nickel, the domain boundaries in non-cell forming metals are geometrically necessary boundaries which subdivide a grain into misoriented regions. Within these regions, deformation occurs on fewer slip systems than specified by the Taylor criterion for strain accommodation. Microbands consisting of paired dislocation sheets form from the single DBs by gradual glide processes without the initiation of a shear instability. The microbands form new misoriented regions which further strain accommodation. At larger strains, these microbands exhibit the commonly reported shear offsets where they intersect a boundary. This description of substructural evolution provides a general evolutionary framework of grain subdivision for metals and alloys which do not form cells. This framework for continuous grain subdivision in non-cell forming metals is analogous to that observed in cell forming metals. Acknowledgements--Several fruitful discussions with D. K. Wilsdorf and N. Hansen are gratefully acknowledged. This work was supported by U.S. Department of Energy, DOE under contract No. DE-AC04-76DP00789.
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HUGHES:
MICROSTRUCTURAL EVOLUTION IN A1-Mg
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