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Texture analysis of the transition from slip to grain boundary slidingin a continuously recrystallized superplastic aluminum alloy

M.T. Perez-Prado a,b , T.R. McNelley c, *, D.L. Swisher c , G. Gonzalez-Doncel a ,O.A. Ruano a

a Departamento de Metalurgia F sica, Centro Nacional de In v estigaciones Metalurgicas, C.S.I.C., A v da de Gregorio del Amo 8, 28040 Madrid, Spainb Department of Mechanical and Aerospace Engineering, Uni v ersity of California-San Diego, 9500 Gilman Dri v e, La Jolla, CA 92093-0411, USA

c Department of Mechanical Engineering, Na v al Postgraduate School, 700 Dyer Road, Monterey, CA 93943-5146, USA

Recei ved 15 March 2002; recei ved in re vised form 25 April 2002

Abstract

An in vestigation was conducted into the phenomenon of continuous recrystallization in a superplastic Al /5%Ca /5%Zn alloy.The as-processed microstructure includes adjacent regions that ha ve lattice orientations corresponding to the symmetric variants of the most prominent texture component, {2 2 5} 5 5 4 . This orientation is near the copper, or C, component, {1 1 2} 1 1 1 . Acellular dislocation structure with highly disoriented cell walls was present within these regions. Continuous recrystallization duringstatic annealing resulted in the de velopment of distinct boundaries accompanied by retention and sharpening of the texture and thedevelopment of a bimodal grain boundary disorientation distribution. The high-angle boundaries (50 /62.8 8 ) are the interfacesbetween grains ha ving lattice orientations as symmetric variants of the texture, while the low-angle boundaries (2 /15 8 ) correspondto a cellular structure within the variants. Such a structure persists during superplastic deformation o ver a wide range of temperatureand strain rate conditions. Both dislocation creep and grain boundary sliding operate simultaneously in response to the appliedstress under all testing conditions in vestigated. The relati ve contribution of each of these mechanisms varies depending on the testingconditions. This is a consequence of the presence of the variants in the microstructure and their persistence during deformation.Fiber texture formation was not obser ved during either longitudinal or trans verse deformation.# 2002 Published by Else vier Science B.V.

Keywords: Aluminum alloys; Recrystallization and reco very; Grain boundaries; Creep; Superplasticity

1. Introduction

In pre vious work [1] micro-texture and its e volutionduring ele vated temperature deformation was analyzedfor a superplastic 5083 aluminum alloy. This material isrepresentati ve of alloys for which thermomechanicalprocessing (TMP) includes an o veraging treatmentfollowed by se vere plastic deformation. Such a TMPresults in grain refinement by particle-stimulated nuclea-tion (PSN) of discontinuous, or primary, recrystalliza-tion, leading to grain orientations and grain boundarydisorientations that are both predominantly random incharacter. The ele vated temperature mechanical beha-

vior of the 5083 alloy was consistent with the predictionsof accepted phenomenological models for the indepen-dent, additi ve contributions to the total deformationrate by dislocation creep and grain boundary sliding(GBS) [2 /5]. Deformation in the dislocation creepregime was reflected in the formation of a 1 1 1 fibertexture by slip-induced lattice rotation in grains of initially random orientation. The transition from dis-location creep to GBS took place o ver about an order of magnitude in diffusion-compensated strain rate, andsuperplastic deformation in the GBS regime resulted inrandomizing of texture due to random grain rotations.

Several in vestigations o ver a long period of time ha vepro vided results for certain superplastic metals that donot conform to such a pattern [6 /28]. For example, insome of these alloys deformation texture componentsthat had de veloped during prior TMP were retained

* Corresponding author. Tel.: ' /1-831-656-2589; fax: ' /1-831-656-2238

E-mail address: [email protected] vy.mil (T.R. McNelley).

Materials Science and Engineering A342 (2003) 216 /230www.else vier.com/locate/msea

0921-5093/02/$ - see front matter # 2002 Published by Else vier Science B.V.PII: S 0 9 2 1 - 5 0 9 3 ( 0 2 ) 0 0 2 7 5 - 7
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during superplastic deformation, or other texture com-ponents were obser ved to form. Anisotropy of super-plastic deformation has been obser ved in other materials[6 /25]. Furthermore, transmission electron microscopy(TEM) studies ha ve pro vided e vidence of dislocationacti vity in the form of slip lines that were obser ved insamples following superplastic deformation [26 /28].These obser vations ha ve led some authors to suggestthat dislocation creep and GBS may contribute jointlyand simultaneously to the total strain during super-plastic deformation, and do so o ver a wide range of diffusion-compensated strain rates. This is in distinctcontrast to the beha vior obser ved in the superplastic5083 alloy and to the predictions of phenomenologicalmodels that are based on the independent, additi vecontributions of these mechanisms to the total deforma-tion rate [1].

These obser vations are common to superplastic

aluminum alloys that exhibit continuous recrystalliza-tion, either during static annealing or during super-plastic straining. The term continuous recrystallizationis a phenomenological description for a reco very-domi-nated microstructural transformation that occurs homo-geneously throughout a deformation-induced micro-structure in the absence of long-range high-angleboundary migration [29].

In many discussions of superplastic beha vior inaluminum alloys, the deformation-induced microstruc-ture at the conclusion of TMP has been en visioned toconsist of elongated prior grains that contain cells orsubgrains of small disorientation. Se veral in vestigatorsha ve then suggested that continuous recrystallizationconsists of a reco very-controlled build up of the a veragedisorientation angle for subgrains within such a struc-ture [30 /36]. Howe ver, the mechanism of this increase indisorientation is uncertain. It has been attributed tosubgrain growth [31], to subgrain coalescence [32], tosubgrain rotation [33], to subgrain rotation and switch-ing [34] in a response to the tensile stress, or to theaccumulation of dislocations in grain boundaries duringelevated temperature deformation [35,36].

A more complex picture of deformation-inducedmicrostructures has emerged in recent in vestigations of

large-strain, low-temperature deformation of pure me-tals (e.g. [37]). Grain elongation with cell/subgrainformation at small strains gi ves way as the strainincreases to processes of grain subdi vision. A classifica-tion of resulting boundary types and glossary of termsemployed in description of deformation microstructureshas recently been pro vided [37]. At large strains, highlyelongated, banded or ribbon-like grain structures areseen to de velop. These structures may include largefractions of high-angle boundaries although the initialgrain size, the deformation temperature, the solutecontent and the presence of second-phase particles allstrongly influence the resulting structure.

During annealing of such deformation-induced mi-crostructures, reco very processes in volving local dislo-cation rearrangements and short-range boundarymigration may lead to the de velopment of a fine grainstructure that also comprises a large fraction of high-angle boundaries. In the absence of long-range migra-tion of high-angle grain boundaries these processeswould constitute continuous recrystallization. Recentinvestigations into the beha vior of the Al /Ca /Zn alloy[16] of this research and of Supral 2004, an Al /Cu /Zralloy [38], ha ve examined this perspecti ve on continuousrecrystallization using computer-aided electron back-scatter diffraction (EBSD) pattern analysis methods.These micro-texture studies ha ve shown that theboundary disorientation distribution in as-processedmaterial is that of a fine, deformation-induced cellularstructure. The cell walls likely consist of dislocationarrays of high density due to the se vere cold working

typical of the final processing stages for such materials.The grain boundary disorientation distributions afterannealing corresponded closely to the distribution ob-ser ved in the cellular structure in the as-processedmaterial. Therefore, it has been suggested that contin-uous recrystallization during annealing consists mainlyof the de velopment of boundaries by e volution of thedislocation arrays of the cell walls. Also, many of theresulting grain boundaries were retained during anneal-ing while others were eliminated, altogether in a mannerconsistent with retention of the deformation texture.

In the present work, texture and mechanical propertydata for the Al /5%Ca /5%Zn alloy will be used as anexample of a material that exhibits continuous recrys-tallization. These results suggest a distinctly differentpattern of ele vated temperature deformation beha viorthan obser ved in 5083 aluminum [1]. A model for thedeformation-induced microstructure will be introducedand employed to explain this new pattern of beha vior.

2. Experimental procedure

The Al /5%Ca /5%Zn alloy was prepared by Alcan,Inc. using aluminum of 99.99% purity. Details of the

composition are pro vided in Table 1 . Cast ingots werehot rolled and subsequently cold rolled to a 3.2-mmthick sheet [39].

Tensile tests were performed at various strain ratesranging from 10

( 5 to 10( 1 s

( 1 at temperatures rangingfrom 300 to 550 8 C (thus including both superplastic

Table 1Alloy composition (wt.%)

Ca Zn Fe Si Mg Al

5.0 4.95 0.18 0.1 0.042 Bal

M.T. Perez-Prado et al. / Materials Science and Engineering A342 (2003) 216 / 230 217


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and non-superplastic conditions). Test coupons wereprepared with tensile axes aligned either with the rollingdirection (RD) or the trans verse direction (TD) of theas-processed sheet. Details of the sample geometry andtesting procedure ha ve been gi ven in an earlier report[15]. Tests were also performed to various intermediatestrains smaller than the fracture strain. This allowed theevolution of texture with deformation to be followed atall the testing temperatures. Macro- and micro-texturemeasurements as well as microstructural examinationwere performed in the mid-layer of the sheet alloyfollowing the procedures gi ven in Ref. [1].

Microstructural obser vation by TEM was performedin a Phillips EM 400 operating at 120 kV. The Al /5%Ca /5%Zn material was sectioned so that the result-ing foil normal would be parallel to the TD of the rolledsheet. Thin foils were prepared in a Struers twin-jetelectropolishing apparatus using a solution of nitric acid

(20%) and methanol (80%).Orientation imaging microscopy (OIM) was alsoemployed in this in vestigation. A thorough introductionto EBSD and OIM has been gi ven by Randle [40]. Theelectron beam of a scanning electron microscope (SEM),operating in the spot mode, is used as a local orientationprobe in OIM on samples of bulk material. Systemsoftware and hardware (EDAX/TSL) was installed on aTopcon S-510 SEM. In the present work the sampleswere electropolished with the same nitric acid (20%) andmethanol (80%) solution employed for TEM samplepreparation. Electron interactions within approximately50 nm of the sample surface produce Kikuchi patternson a phosphor screen in the SEM sample chamber. Alow-light camera allows these patterns to be captured,analyzed and unambiguously indexed in terms of theEuler angles f 1 , F and f 2 that describe the local latticeorientation relati ve to the sample axes. The electronbeam is deflected, point-by-point, in raster pattern onthe sample surface and the orientation data are acquiredand stored along with the location of each point on thesample surface. The point-to-point step size was basedon the expected microstructure and size of the regionbeing examined. Data clean-up procedures were em-ployed to ensure that data points with a probability ! /

95% of correct indexing were retained in the analysis.Indi vidual points ha ving lower probability of correctindexing were re-assigned to neighboring regions of similar orientation. This method was chosen to reducethe effects of pattern o verlap in the vicinity of grainboundaries and second-phase particles. The productionof grain maps based on the orientation measurementswas accomplished by assigning points (pixels) to a grainin regions with orientations differing by less than 2 8 . Theorientation data may also be represented by assigninggray tones to pixels based on quality (sharpness) of theKikuchi pattern image. Finally, the orientations mayalso be plotted as discrete pole figures as representations

of the micro-texture in the regions of the maps. Varioushighlighting functions in the software were employed tocorrelate local lattice orientation as reflected in polefigures to the location of the orientation in the micro-structure.

3. Results

Macro- and micro-texture measurements ha ve beenpre viously performed on this Al /5%Ca /5%Zn alloy inthe as-recei ved condition as well as after annealing orelevated temperature deformation. [15,16,41] . The X-raymacro-texture results indicated that the as-recei vedmaterial has a weak but definite deformation texture.The most prominent orientation was {2 2 5} 5 5 4 ,which is located just 5 8 away from the copper, or C,

component, {1 1 2} 1 1 1 [40,41]. The {2 2 5} 5 5 4component lies close to the b-fiber, which connects the Cand the brass, or B, component ({0 1 1} 2 1 1 ) inEuler space, and therefore is typical of a deformed FCCmetal [42]. The micro-texture data were obtained by aninteracti ve EBSD method [16] and also showed thepresence of this component in the deformation textureof the as-recei ved material, although a random compo-nent was clearly predominant in the texture. Thedistribution of the grain-to-grain disorientations exhib-ited a maximum near 45 8 [16] and appeared to be similarto the Mackenzie distribution for randomly orientedcubes [43]. The OIM data of the present work areconsistent with these pre vious results. Fig. 1 includesOIM results for the as-recei ved microstructure of theAl /5%Ca /5%Zn alloy. Fig. 1 a shows a grain color mapin which successi ve orientations were obtained with astep size of 0.2 mm. This map has been plotted to re vealorientation contrast by randomly assigning differentcolors to (sub)grains ha ving disorientations E /28 ; withthis resolution the a verage (sub)grain size is about 0.5mm. Fig. 1 b shows discrete (2 0 0), (2 2 0), and (1 1 1)pole figures, which illustrate a deformation texture aswell as a random component. The two symmetricvariants of the C-type texture component, ((2 2 5) /

[5 5 4] and (2 2 5) /[5 5 4]); can be separately distin-guished in the orientation measurements and thesevariants ha ve been highlighted in either red or blue,respecti vely, in the discrete pole figures. The indi vidualorientation measurements may also be correlated withtheir corresponding locations in the (sub)grain structureas shown in Fig. 1 c. In this representation the datareveal that the microstructure consists of clusters of (sub)grains that belong to each texture variant, as wellas inter vening regions that correspond to the randomcomponent in the pole figures. The latter regions arerepresented by gray tones based on image quality of theKikuchi patterns.

M.T. Perez-Prado et al. / Materials Science and Engineering A342 (2003) 216 / 230218
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The effect of annealing of this alloy at 520 8 C hasbeen described in detail pre viously [16]. It was shownthat the weak C-type component obser ved in the as-recei ved material is retained and progressi vely strength-ened, while the random component is diminished, forannealing times up to 90 h in duration. Simultaneously,the grain size increased. The retention of a deformationtexture component during annealing is commonlyassociated with the phenomenon of continuous recrys-tallization [30]. A bimodal distribution of the grain-to-grain disorientation angles became apparent after ashort annealing time (7 min), with a predominance of either low-angle boundaries, of 2 /15 8 disorientation, orhigh-angle boundaries, of 50 /62.8 8 disorientation. Thebimodal character of the disorientation distributionbecame increasingly pronounced as the annealing timeincreased.

The variants of the main texture component, (2 2 5) /

[5 5 4] and (2 2 5) /[5 5 4]); are related by a rotation of 528

about a 1 1 0 and so it was suggested [16] that thehigh-angle boundaries in the disorientation distributionseparated grains belonging to these variants. Then, itwas proposed that the moderately disoriented bound-aries separated (sub)grains within each texture variant.Fig. 2 illustrates direct e vidence for such a microstruc-ture. The TEM and OIM data presented in this figurewere obtained on the RD /ND plane of sample of theAl /5%Ca /5%Zn alloy after 15 min of annealing at520 8 C. Fig. 2 a is a TEM micrograph showing astructure with an a verage (sub)grain size of 2 mm afterthis short annealing treatment. Distinct, clearly definedboundaries are e vident in this TEM image but manypoorly-defined, fragmented boundaries can also beobser ved as well. Fig. 2 b is a corresponding OIM graincolor map in which (sub)grains disoriented more than 2 8

or more ha ve been randomly assigned different colors;the apparent (sub)grain size in this grain map isconsistent with that obser ved by TEM. The effecti vemagnification in the grain maps of Fig. 1 a and Fig. 2 bdiffer by a factor of fi ve. Thus, microstructural coarsen-ing is rapid in the early stages of annealing at thistemperature. Fig. 2 c shows the discrete (2 0 0), (2 2 0),and (1 1 1) pole figures, in which orientations located

within 158

of the two variants of the C-type texture areagain highlighted in either red or blue. The highlightingwas accomplished by locating the highest concentration

of poles in, for example, the discrete (1 1 1) pole figureand then including all orientations ha ving a {1 1 1}within 15 8 of the selected location on the pole figure.The number of orientations represented in the polefigures of Fig. 2 c is four times that in Fig. 1 c and sothese discrete pole figures cannot be compared directly.Ne vertheless, the texture appears to be somewhat moresharply defined after a 15 min anneal and this isconsistent with results obtained in pre vious studies[16]. Fig. 2 d and e are OIM maps of the same regionas in Fig. 2 b and in which the orientations ha ve beencolor coded to correspond to the discrete pole figures. Inthis form these maps illustrate the spatial distributionwithin the microstructure of these two variant orienta-tions. In contrast to Fig. 1 c, it can be seen now, that,after a brief anneal, the microstructure consists almostentirely of clusters of (sub)grains ha ving lattice orienta-tions that correspond to the two variants of the main C-

type texture component. Comparison among Fig. 2 b, cand d re veals that the clusters of (sub)grains belongingto either of the two variants are irregularly shaped andgenerally intermingled but also tend to be somewhatelongated and aligned weakly with the RD. Pre viousinvestigation of this material [16] had demonstrated thepredominance of boundaries disoriented either in therange of 2 /15 8 or 50 /62.8 8 in the annealed microstruc-ture of this material. Highlighting has also beenemployed in Fig. 2 d and e to show the location of thehigh-angle ( Fig. 2 d) and low-angle ( Fig. 2 e) boundaries,respecti vely. These data document for the first time thatthe high-angle boundaries (green in Fig. 2 d) within sucha microstructure separate grains belonging to the twovariant orientations, while moderately disorientedboundaries (yellow in Fig. 2 e) separate (sub)grainswithin each variant.

Creep data for this alloy are plotted in Fig. 3 ondouble logarithmic coordinates as the deformation rateversus the steady state flow stress for tests conductedwith the tensile axis parallel to or trans verse to the finalRD. Separate lines show data for each testing tempera-ture. The slopes of these cur ves correspond to the stressexponent n , and n values close to 3 were obser ved whenthe flow stress was below about 25 MPa, while n values

of about 5 were obtained for flow stresses abo ve 25MPa. Data for the elongation to failure as a function of temperature for two strain rates are plotted in Fig. 4 .

Fig. 2. OIM data for the Al /5%Ca /5%Zn alloy after annealing at 520 8 C for 15 min: (a), a TEM micrograph showing the (sub)grain structure; (b),a random grain color map for (sub)grains disoriented more than 2 8 ; (c), discrete (2 0 0), (2 2 0), and (1 1 1) pole gures in which the two symmetricvariants of the main C-type texture component, ((2 2 5) /[5 5 4] and (2 2 5)/[5 5 4]); ha ve been colored in blue or red, respecti vely, using a tolerance of 9 /15 8 around the ideal orientations; (d and e), OIM maps showing the spatial distributions of (sub)grains oriented as the two symmetric variants of the main texture component, as well as the location of the high-angle (d) and low-angle boundaries (e), which are highlighted in green or yellow,respecti vely.

Fig. 1. OIM data for the Al /5%Ca /5%Zn alloy in the as-recei ved condition: (a), a random grain color map for (sub)grains disoriented more than 2 8 ;(b), discrete (2 0 0), (2 2 0), and (1 1 1) pole gures in which the two symmetric variants of the main C-type texture component, (2 2 5) /[5 5 4] and(2 2 5)/[5 5 4]; ha ve been color coded in either blue or red, respecti vely, using a tolerance of 9 /15 8 around the ideal orientations. In (c), the OIM dataare re-plotted to show the spatial distribution of (sub)grains oriented as the two symmetric variants of the main texture component.

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The elongation to failure increased with increasingtemperature, and reached a maximum of 600% at550 8 C. High values of the elongation to failure wereobtained e ven at strain rates of 10

( 2 s( 1 , in contrast to

the beha vior of the 5083 alloy wherein the elongation tofailure decreased rapidly with increasing strain rate [1].

No significant texture changes were detected whendeforming the Al /5%Ca /5%Zn alloy outside the super-plastic regime, at strain rates of 10

( 2 s( 1 and tempera-

tures lower than 3008

C. The stress exponents then were5 or higher, and the corresponding elongation to failurevalues were smaller than 100%. The formation of a fibertexture, which was detected when deforming a discon-

tinuously recrystallized 5083 alloy under dislocationcreep conditions [1], was not obser ved for this Al /5%Ca /5%Zn alloy.

The e volution of the macro-texture of the Al /5%Ca /5%Zn alloy after deformation at high temperatures (400and 550 8 C) is illustrated in Fig. 5 a /e. The texture isrepresented by means of specific f 1 0 /constant sectionsof the orientation distribution function (ODF). Fig. 5 acorresponds to the as-recei ved material. The{2 2 5} 5 5 4 component is the main texture compo-nent and is close to the C orientation, {1 1 2} 1 1 1 .Again, it can be seen that the texture is weak (maximumintensity : /3). The change in the texture of this alloyafter tensile deformation at 400 8 C and 10

( 2 s( 1 along

either the rolling (RD) or the trans verse (TD) directionis illustrated in Fig. 5 b or c, respecti vely. It is importantto note that the elongation to failure values achie vedunder these testing conditions were 200 /300%, while the

stress exponent n , was close to 5. It can be seen in Fig.5b that a small lattice rotation during longitudinaltensile extension (parallel to RD) has resulted in achange in the main texture component, from the{2 2 5} 5 5 4 C-type orientation, to {1 1 2} 1 1 1 ,which is the exact C orientation. Howe ver, as shown inFig. 5 c, a large rotation during trans verse tensileextension (parallel to TD) has resulted in a change inthe main texture component from the initial,{2 2 5} 5 5 4 (C-type) to the {0 1 1} 2 1 1 B-typetexture component [15]. Evidence of fiber textureformation was not seen in the ODF data for these

conditions [15]. Ne vertheless, the lattice rotations as wellas the sharpening of the texture after deformation(maximum intensities of the ODF increase to /7 and10 for the longitudinal and trans verse tests, respec-tively), are consistent with the predominance of crystal-lographic slip during deformation for these conditions.

A corresponding study of the texture e volution for theAl /5%Ca /5%Zn alloy deformed under optimum super-plastic conditions, at 550 8 C and at 10

( 2 s( 1 , with

tensile axis parallel to either the RD or the TD, isdepicted in Fig. 5 d and e, respecti vely. The elongation tofailure values attained for these conditions were ap-

proximately 600% while the stress exponent n , was closeto 3. As re vealed by comparison of the X-ray results inFig. 5 d and e to those in Fig. 5 a there is little apparentchange in the {2 2 5} 5 5 4 C-type texture componentfollowing longitudinal extension. A weak B-type com-ponent is apparent in the data of Fig. 5 e for a sampledeformed by trans verse tensile deformation. Altogether,the reduction in texture intensity e vident in these data isconsistent with a large contribution of GBS to the totaldeformation rate for these testing conditions. Still, theretention of the initial C-type component after long-itudinal deformation and the formation of a weak Btexture component after trans verse deformation suggest

Fig. 3. Creep data for the Al /5%Ca /5%Zn alloy plotted as the

logarithm of the steady-state creep rate versus the logarithm of theapplied stress for tests conducted with the tensile axes parallel andtrans verse to the nal RD.

Fig. 4. Elongation to failure data for the Al /5%Ca /5%Zn alloy as afunction of temperature for samples deformed at a strain rate of either10

( 2 or 10( 1 s

( 1 .



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Fig. 5. Macro-texture data for the Al /5%Ca /5%Zn alloy, in the form of specic 8 1 0 /constant sections of the ODF, illustrating texture e volutionduring high-temperature deformation. Data in (a), are for the as-recei ved material; (b), corresponds to material deformed at 400 8 C/10

( 2 s( 1 along

the rolling direction while (c), is for material deformed at 400 8 C/10( 2 s

( 1 along the TD. In (d), data are shown for material deformed at 550 8 C/10

( 2 s( 1 along the rolling direction while in (e), data are for material deformed at 400 8 C/10

( 2 s( 1 along the TD.



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that crystallographic slip is also contributing to defor-mation well into the superplastic regime.

Fig. 6 pro vides OIM data for this alloy followinglongitudinal tensile deformation at 400 8 C and 10 2 s

( 1 ,which correspond to the ODF data in Fig. 5 b. The OIMgrain color map in Fig. 6 a illustrates an equiaxed(sub)grain structure. The corresponding micro-texturedata is represented in Fig. 6 b by means of discrete(2 0 0), (2 2 0), and (1 1 1) pole figures in which the twovariants of the main C-type texture component ha vebeen highlighted in either red or blue. The grain map in

Fig. 6 c is for the same region as that in Fig. 6 a but now,shows the spatial location of these two symmetrictexture variants (in red and blue) as well as the locationsof the high-angle boundaries (disorientation of 50 /62.8 8 ) in green. Adjacent clusters of (sub)grains belongto the different variants and the clusters now, exhibitelongation along the tensile axis, which is the RD. Thismap again demonstrates that the high-angle boundariesseparate grains belonging to different variants. Fig. 6 d isa map of the same region as in Fig. 6 a and c now,showing the location in the microstructure of the low-

Fig. 6. OIM data for the Al /5%Ca /5%Zn alloy following deformation at 400 8 C and 10( 2 s

( 1 along the rolling direction. In (a), a random graincolor map is shown to illustrate the (sub)grain structure; in (b), discrete (2 0 0), (2 2 0), and (1 1 1) pole gures ha ve been color coded in either blueor red to highlight the two symmetric variants of the C texture component; (c), shows the same OIM data in the form of map illustrating the spatialdistribution of the two symmetric texture variants (also in blue or red) as well as the high-angle boundaries (50 /62.8 8 , in green); (d), is for the sameOIM data but now, highlights the low-angle boundaries (2 /15 8 , in yellow).



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angle boundaries (disorientation of 2 /15 8 ) in yellow. Itcan be clearly seen here that the low-angle boundariesseparate (sub)grains within a cluster.

Fig. 7 pro vides OIM data for deformation of this Al /5%Ca /5%Zn alloy at 400 8 C and 10

( 2 s( 1 along the

TD; these results correspond to the ODF data in Fig. 5 c.The grain color map in Fig. 7 a illustrates an equiaxed(sub)grain structure following trans verse deformation of this material; the structure is similar in appearance tothat following longitudinal deformation. The micro-texture after trans verse deformation is shown in Fig. 7 bby means of discrete (2 0 0), (2 2 0), and (1 1 1) polefigures, which now, indicate the de velopment of a B-

type texture component. This change in texture asso-ciated with the trans verse deformation may be seen mostreadily by comparing the (1 1 1) pole figure in Fig. 7 b tothe corresponding (1 1 1) pole figure in Fig. 6 b, whichhad been obtained after longitudinal deformation. TheC-type texture in Fig. 6 b is marked by a concentrationof poles along the RD, while the B-type texture in Fig.7b is indicated by the de velopment of a concentration of poles along the TD. The B-type texture also has twodistinct variants and these ha ve been highlighted ineither red or blue. Fig. 7 c is OIM map of the sameregion as in Fig. 7 a but which now, shows the spatiallocation of these two symmetric texture variants (in red

Fig. 7. OIM data for the Al /5%Ca /5%Zn alloy after deformation at 400 8 C and 10( 2 s

( 1 along the TD. In (a), a random grain color mapillustrates the (sub)grain structure; in (b), discrete (2 0 0), (2 2 0), and (1 1 1) pole gures ha ve been color coded to highlight the two variants of themain B texture component (compare these data to the pole gures in Fig. 6 , wherein a C texture component de veloped during deformation); (c),shows the same OIM data in the form of a map illustrating the spatial distribution of the two symmetric texture variants (also in blue and red) as wellas the high-angle boundaries (50 /62.8 8 , in green); (d), is for the same OIM data but now, the low-angle boundaries are highlighted (2 /15 8 , in yellow).



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and blue), as well as the high-angle boundaries (disor-iented by 50 /62.8 8 ) in green. Again, adjacent clusters of (sub)grains belong to the two variants. These clustersare now, elongated along the TD, which is the tensileaxis. Also, the high-angle boundaries separate(sub)grains belonging to different variants. The grainmap in Fig. 7 d shows the locations of the low-angleboundaries (disoriented by 2 /15 8 ) in yellow within thesame region as represented in Fig. 7 a /c. It can be clearlyseen that the low-angle boundaries separate (sub)grainswithin a cluster belonging to the same texture variant.

4. Discussion

The macro- and micro-texture data and the mechan-ical response of the Al /5%Ca /5%Zn alloy of this studycorrelate well with the recognized characteristics of

aluminum alloys that transform by a continuous recrys-tallization reaction. A model for the microstructuremust be capable of explaining the de velopment andevolution of the grain boundaries, as well as the grainsize and the macro- and micro-texture, during bothannealing and ele vated temperature deformation. Such amodel will be discussed and employed to describe,firstly, the annealing beha vior and, subsequently, theelevated temperature deformation characteristics of thisalloy.

4.1. E v olution of microstructure during annealing of Al / 5%Ca / 5%Zn

Altogether, pre vious studies [15,16] of this Al /5%Ca /5%Zn alloy ha ve clearly shown that the two-phasemicrostructure of the as-processed material is veryfine. The Al 3CaZn second-phase particles are homo-geneously distributed, slightly elongated in the RD of the sheet, and about 0.5 mm in length and 0.2 mm indiameter. A cellular substructure, finer than 1 mm insize, is also present. The most prominent component inthe texture of the as-processed material is{2 2 5} 5 5 4 , which is very close to the C orientation,a common component of deformation textures of FCC

metals. The OIM data obtained for as-processed mate-rial in the present study are consistent with thesepre vious results.

The current understanding of the e volution of defor-mation-induced microstructures is based mainly onstudies of se verely deformed pure metals [29,37]. Thus,in the initial stages of deformation, subgrains de velopand grain subdi vision takes place. This is followed bythe formation, within the prior grains, of blocks orregions in which lattice rotation takes place in oppositesenses. At large strains, a banded, ribbon-like structuremay de velop in which the prior grain boundaries are nolonger readily distinguishable.

Texture de velopment during large-strain deformationby rolling reflects lattice rotation toward stable endorientations. The crystallography of the two C-texturevariants is depicted in Fig. 8 ; the C component is morereadily illustrated than {2 2 5} 5 5 4 . Each variant in aC-type texture component has four slip systems withequi valent Schmid factors during plane strain deforma-tion under a Tucker-type stress state ( s RD,RD 0 /( /s ND,ND ) [42]. The Schmid factors for all slip systemsin both variants are summarized in Table A1 inAppendix A ; the four slip systems ha ving equi valentSchmid factors ( 9 /0.544) for this stress state are inconjugate pairs. The incremental strain may be calcu-lated separately for each of the variants in tensor formassuming an identical incremental shear d g on each of these slip systems [1]:

do C 2

0 dg

1:088 0 ( 0:962

0 0 0( 0:962 0 ( 1:088

0@

1A

do C 2 0 dg1:088 0 0:962

0 0 00:962 0 ( 1:088

0@

1A

where d o is the incremental strain corresponding to d g ,and C 1 and C 2 refer to the variants (Table A1 inAppendix A ). Indi vidually, each variant experiencesplane strain deformation with an additional shear

term, o RD,ND in the strain. Fig. 8 also includes aperspecti ve representation, adapted from Hirsch andLu cke [42], showing an alternating arrangement of elongated bands which ha ve lattice orientation corre-sponding to the C 1 and C 2 variants. For such anarrangement, a veraging of the incremental strains o vera region comprising equal volumes of each orientation,as depicted in Fig. 8 , would gi ve

Fig. 8. An idealization of a microstructure formed by alternatingbands of lattice orientation corresponding to the symmetric variants of the C texture component, {1 1 2} 1 1 1 , developed during planestrain deformation. The lattice orientations of the variants areillustrated at the right in this diagram.



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do ave 0 dg1:088 0 0

0 0 00 0 ( 1:088

0@

1A

i.e. plane strain deformation. Such an arrangement isessentially that predicted by deformation banding mod-els. The potential importance of deformation bandinghas long been recognized [44,45]. Due to the relaxationof constraints in indi vidual bands, a banded structure isable to deform compatibly with the acti vation of lessthan fi ve slip systems in each band [46 /48].

Accommodation of the Al 3CaZn second-phase parti-cles during se vere plastic deformation would disrupt atendency to form well-defined bands in the material of this in vestigation. The presence of such particles, as wellas the need to accommodate the additional shears thatarise in each band, would be reflected in the de velop-ment of a cellular structure within the indi vidual bands.

In the initial stages of deformation processing theinterfaces between adjacent bands may be thick, transi-tional regions of high dislocation density and latticecur vature, reflecting gradual lattice reorientation fromthe orientation of one band to that of the next. Aftermore se vere deformation such interfaces may becomemore sharply defined (e.g. [49]). Lattice cur vatureassociated with the interfaces between the bands, withthe cellular structure inside of the bands, and withaccommodation of the Al 3CaZn particles would accountfor a large spread of orientations about the main texturecomponent and the appearance of random orientations.This was e vident in Fig. 1 .

Annealing, particularly at temperatures abo ve500 8 C, has been shown to result in coarsening of thematrix grains, accompanied by coarsening and spher-oidization of the Al 3CaZn second-phase particles [16].Three additional obser vations lead to the conclusionthat a continuous recrystallization reaction occurs dur-ing such post-TMP annealing. These were: (a) retentionand progressi ve sharpening of the initial deformationtexture; (b), absence of formation of new texturecomponents; and (c), de velopment of a bimodal bound-ary disorientation distribution, with a high-angle bound-ary peak at 50 /62.8 8 and a lower-angle peak between 2

and 158

[16]. Coarsening of the matrix grain structureand sharpening of the initial deformation texture duringannealing are also e vident when Fig. 1 and Fig. 2 arecompared. The texture sharpening is consistent with areduction in lattice cur vature, and thus orientationspread about the {2 2 5} 5 5 4 texture component,due to reco very during the annealing. Following anneal-ing, the microstructure therefore consists mainly of grains of lattice orientations distributed near one orthe other of the two distinct variants of this C-typetexture component. The highlighting in Fig. 2 d clearlyshows that the high-angle boundaries (50 /62.8 8 ) are theinterfaces between regions of lattice orientation near one

or the other of the symmetric variants of the{2 2 5} 5 5 4 texture component, while lower-angleboundaries (2 /15 8 ) separate cells within such grains.

Processes of grain subdi vision during the prior rollingof this material ha ve resulted in the de velopment of grain clusters of lattice orientation corresponding to thetwo variants of the {2 2 5} 5 5 4 texture component.According to the deformation banding model for texturedevelopment [44 /48], the microstructure would com-prise elongated, ribbon-like grains that alternate inlattice orientation. Substructure within such grainswould reflect the need for accommodation of the o RD,NDshear term and of the Al 3CaZn particles, although the

presence of these particles would also disrupt thetendency to form well-defined bands. Thus, the disor-ientation of the high-angle boundaries in this materialbecame established during the prior deformation pro-cessing as a result of grain subdi vision and lattice

rotation toward the end orientations of the texturevariants. The disorientation of the high-angle bound-aries is the lattice rotation that relates the variants of thetexture (nominally 52 8 in this material). Cell andsubstructure formation within the bands during defor-mation processing then accounts for the disorientationof the lower-angle boundaries. Continuous recrystalliza-tion during ele vated temperature static annealing of thisalloy reflects the reco very-controlled de velopment of theboundaries within the deformation-induced microstruc-ture. These processes would include climb-controlledrearrangement of dense dislocation arrays that separatethe adjacent grain clusters, or the cells within clusters,resulting in the e volution of well-defined boundaries inplace of the arrays. Grain growth during annealingresults in the elimination of many boundaries de velopedduring the prior deformation, but in a manner thatmaintains the texture in the material. Thus, grains orcells of initial lattice orientation near that of eithervariant of the texture apparently grow at the expense of nearby regions ha ving lattice orientations in the randompopulation due to lattice cur vature associated with ahigh dislocation density. Such a description of thecontinuous recrystallization process is consistent withmicrostructural and microtextural data obtained in an

investigation of the annealing response of this alloy [16].

4.2. Ele v ated temperature mechanical beha v ior

At the onset of ele vated temperature deformation of the superplastic 5083 alloy [1] the microstructure con-sisted of fine, randomly oriented grains with random,high-angle boundaries. This microstructure had beenproduced through PSN of discontinuous recrystalliza-tion during heating and annealing prior to tensilestraining. In contrast, the microstructure of the Al /5%Ca /5%Zn alloy of this study consists of adjacentgrain clusters ha ving lattice orientations corresponding

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to the symmetric variants of the main texture compo-nent. The interfaces that separate the grain clusters aswell as those that separate cells within the clusters aredeformation-induced boundaries that e volve from densedislocation arrays by reco very.

An acti vation energy near that for self-diffusion maybe inferred from the data of Fig. 3 and this suggests thatlattice self-diffusion controls deformation at the strainrates and temperatures in vestigated. Constituti ve equa-tions for self-diffusion controlled slip creep and GBSprocesses were presented in Ref. [1] as equations 1 /4.Accordingly, the data of Fig. 3 were re-plotted innormalized form as diffusion-compensated strain rate,o =DL ; versus modulus-compensated stress, s /E . Latticeself-diffusion [50] and dynamic Youngs modulus data[51] for pure aluminum were used and the results arepresented in Fig. 9 . Many pure metals and alloys exhibitpower law beha vior characterized by a constant n value

for o =DL/ 0 /1015 m(

2 . Here, the data fall on a singlecur ve but there is a progressi ve transition from n 0 /5 ton 0 /3 as diffusion-compensated strain rate, o =D L ; de-creases, and superplastic ductility is obser ved o ver sixorders of magnitude, from o =D L/ 0 /10

14 m( 2 downward

to 10 8 m( 2 . Examination of these data re veals that the

transition from n 0 /5 to n 0 /3 occurs progressi v ely over amuch wider o =DL range than for the 5083 alloy.Howe ver, n values for this Al /5%Ca /5%Zn alloy atthe extreme values of o =DL (10

8 and 10 14 ) are similar tothose obtained for the 5083 material [1].

A contribution of dislocation creep to the superplastic

response during tensile deformation at o =DL/ 0 /5 ) /1013

m( 2 (400 8 C and 10

( 2 s( 1) is evident in the macro-

texture data of Fig. 5 . Elongation to failure values of : /300% were accompanied by the de velopment of adistinct C-type deformation texture (Fig. 5 a and b) bya small lattice rotation from the initial {2 2 5} 5 5 4component, and the absence of fiber texture formation .

This is in distinct contrast to the de velopment of apredominant 1 1 1 fiber texture that was obser ved inthe 5083 alloy when it was deformed under similarconditions in volving predominance of dislocation creep.In addition, grain elongation during deformation of theAl /5%Ca /5%Zn alloy [15] was notably less than thatobser ved in 5083 [1]. This is consistent with thesimultaneous operation of dislocation creep and GBSmechanisms under these testing conditions.

The C texture component is also apparent in themicro-texture data of Fig. 6 b. A 1 1 1 becomesaligned with the tensile axis as lattice rotation to theexact C orientation takes place during tensile extensionparallel to the RD. Grains with such a lattice orientationcan deform compatibly with their neighbors duringdislocation creep and without further lattice rotation.Thus, the C component is a stable end orientation in thetexture for uniaxial tension parallel to the RD. The

absence of fiber texture formation may be furtherunderstood by considering deformation of a FCCcrystal along an axis that lays near a 1 1 1 direction,e.g. 5 8 from such an orientation. It is straightforward toshow by means of a stereographic projection that thelattice rotations needed to bring the tensile axis for sucha crystal into alignment with the 1 1 1 in question willtake place about an axis that is perpendicular to that

1 1 1 and not parallel to it. Thus, such small rotationswill ha ve the effect of stabilizing the pre-existing Ccomponent but will not produce a fiber texture. Thelimited extent of grain elongation apparent in the grainmap of Fig. 6 a is consistent with a contribution of GBSto the total strain, but the high-angle boundaries are stillpredominantly the interfaces between variant grains.

Deformation at high o =DL values of samples withtensile axes parallel to the TD resulted in the de velop-ment of a distinct B-type texture component (idealorientation is {1 1 0} 1 1 2 ) and, again, the absenceof fiber texture formation . This is e vident in the macro-texture data of Fig. 5 c and may also be seen in Fig. 7 a /d. The apparent instability of the C component andsubsequent lattice rotation resulting in the de velopmentof a B texture component during trans verse tensiledeformation requires further assessment. Calculation

of the incremental strains corresponding to incrementalshears on the acti ve slip systems in the C componentduring tensile deformation in the TD may pro videfurther insight into the de velopment of the B texturecomponent. For uniaxial deformation in the TD, thetensile axis tends to align with a 1 1 0 in C-orientedgrains ( Fig. 8 ). The Schmid factors for the slip systemsin the C component under such a uniaxial stress state arelisted in Table A2 of Appendix A , wherein it can be seenthat both variants ha ve four slip systems with thehighest Schmid factors ( 9 /0.408). The incremental strainfor equal shears, d a , on each of these four systemswould be:

Fig. 9. Diffusion-compensated strain rate as a function of modulus-compensated stress for ele vated temperature tension testing of the Al /5%Ca /5%Zn alloy.



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do C 1 0 da( 0:544 0 0:769

0 1:633 00:769 0 ( 1:088

0@

1A

do C 2 0 da( 0:544 0 ( 0:769

0 1:633 0( 0:769 0 ( 1:088

0@

1A

Averaging o ver equal volumes of two adjacentvariants gi ves:

do ave 0 da( 0:544 0 0

0 1:633 00 0 ( 1:088

0@

1A

which corresponds to uniaxial extension along the TD.Howe ver, the R -value, which may be defined as theratio of the width strain (along RD) to the through-thickness strain (along ND), [52] is not predicted to beunity. This differs from the result for the 5083 alloy and,as well, the result for tensile deformation along the RDof the Al /5%Ca /5%Zn alloy.

The experimental data in Fig. 5 c and Fig. 7 a /d showthat the C component is not stable during trans versedeformation, and that lattice rotation results in forma-tion of a B texture component. Detailed analysis of thistexture change in pre vious work [15,16] has shown thatthe tensile axis rotates along the (0 1 1) /(1 1 1) symme-try boundary of the unit triangle during trans versetensile deformation. It was proposed that this latticerotation is initiated by slip on two of the four mosthighly stressed slip systems for the C orientation under

trans verse tension. As lattice rotation brings a 1 1 1direction into alignment with the tensile axis (the TD inthe B component is a 1 1 1 ) no further rotation needoccur; this is therefore a stable orientation. For uniaxialtension along the TD, the incremental strains for the Corientation when only these two coplanar slip systemsoperate are:

do C 1 0 db( 0:272 0:334 ( 0:769

0:334 0:816 0:471( 0:769 0:471 ( 0:544

0@

1A

do C 2 0 db( 0:272 0:334 0:769

0:334 0:816 ( 0:4710:769 ( 0:471 ( 0:5440@ 1A

The a verage strain tensor o ver two adjacent variantsthen becomes:

do ave 0 db( 0:272 0:334 0

0:334 0:816 00 0 ( 0:544

0@

1A

This would again correspond to a uniaxial tensiledeformation along the TD for which the R -value isdifferent from unity. Howe ver, there is now, an addi-tional shear term, o 12 , the presence of which is reflected

in the obser ved lattice rotation. When the tensile axisreaches the (1 1 1) pole, the resulting B componentbecomes stable, the shear terms disappear, and the R -value becomes unity.

The exact C orientation with four equally stressed slipsystems may reflect a metastable condition when thematerial is strained in uniaxial tension along the TD.Orientations initially located slightly away from C alongthe symmetry boundary already ha ve higher Schmidfactors for the two coplanar systems abo ve, and there-fore would tend to rotate along the symmetry boundarytoward B rather than back toward the C orientation.

The large tensile elongations obtained after deforma-tion at high values of o =DL (280% at 400

8 C/10( 2 s

( 1)and retention of an equiaxed grain shape indicates aprominent contribution of GBS in addition to disloca-tion creep. Grain switching in the absence of grainrotation during GBS along the boundaries between

adjacent variants (i.e. the high-angle boundaries) mayalso allow the retention and stabilization of a texturecomponent.

At low values of o =DL ; where very high tensileelongations (up to 600%) are achie ved the stressexponent n , was about 3 for the Al /5%Ca /5%Zn alloy,a value greater than that for the 5083 alloy under GBS-controlled conditions. The maximum tensile ductilitywas obtained for the sample deformed at o =D L/ 0 /10

9

m( 2 (550 8 C 10

( 2 s( 1) and GBS should be the

predominant deformation mechanism. In a polycrystal-line material, GBS must be accommodated by deforma-tion within the grains; otherwise, voids will form, whichmay lead to premature failure. Accommodation of GBSby slip in volves the generation and short-range motionof dislocations that do not contribute to the total strain[53,54] and, apparently, do not contribute to thedevelopment of preferred orientation [1]. Ne vertheless,the texture data pro vide clear indication of slip con-tributions to the total strain for these conditions. This isespecially notable in the texture data for the samplestrained in the trans verse orientation ( Fig. 5 e) for whichlattice rotation from the initial C orientation to a final Borientation occurred during test. Such a lattice rotationimplies that intragranular slip, in volving long-range

motion of dislocations, is contributing to the total strainfor deformation under these conditions in addition todislocation accommodated GBS. The de velopment of aweak C orientation in the sample deformed parallel toRD is also consistent with this obser vation.

As the deformation temperature is increased (i.e. o =DLdecreases), the e volution of the deformation microstruc-ture and de velopment of distinct boundaries should takeplace more and more rapidly. Unless boundaries areable to support GBS upon initiation of the tension test,dislocation creep processes will predominate and willinitiate the same processes of lattice rotation obser ved inmaterial deformed at high o =D

L/values. This will result in



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lattice rotation to the C orientation for testing with thetensile axis parallel to RD, and lattice rotation towardthe B orientation for a test with tensile axis parallel tothe TD. Concurrent de velopment of distinct boundarieswill eventually allow GBS to begin pro vided that thedisorientation distribution includes a sufficient popula-tion of boundaries capable of sliding and the grain sizeremains sufficiently fine for the deformation conditions.Indeed, prior in vestigation [16] revealed that more than90% of the boundaries had disorientation angles ! /10 8

after only 7 min of annealing at 520 8 C, and more than85% ! /10 8 after 6 h of annealing at this temperature. Inthis material the grain size remained B /10 mm after 6 h.This emphasizes the need to retard boundary migration;otherwise, excessi ve grain growth will suppress super-plastic response.

Following the onset of GBS, random grain rotationwill tend to randomize the texture. The persistence of

deformation texture components seen e ven in samplesdeformed to failure (with elongation close to 600%)indicates that some grains still remain in a stableorientation while surrounding grains rotate during GBS.

5. Conclusions

Microstructure and texture data corresponding to theAl /5%Ca /5%Zn alloy ha ve been used to exemplify thethermal and mechanical beha vior of superplastic alloysin which the microstructure e volves by continuousrecrystallization. There are significant differences be-tween the beha vior of alloys that transform by contin-uous recrystallization and those which transform bydiscontinuous recrystallization.

Grain subdi vision during the se vere prior rollingdeformation leads to the de velopment of adjacent grainclusters ha ving lattice orientations corresponding to thevariants of the deformation texture. This may reflectdeformation banding during straining, although accom-modation of precipitate particles and shears within thebands may preclude the formation of well-definedribbon-like grains. These accommodation processesapparently lead to the de velopment of a cellular

structure within the grain clusters.Upon annealing the grain clusters retain their identity

in the structure. The interfaces between the grainclusters e volve and become the high-angle boundariesin the disorientation distribution. The cell walls withinthe clusters become the low-angle and moderatelydisoriented boundaries. Reco very occurs in a mannerthat preser ves the orientation of grain clusters.

This microstructure allows the simultaneous occur-rence of dislocation creep and GBS under all the testingconditions in vestigated. Dislocation creep predominatesat small strains because the boundaries are not capableof supporting GBS despite ha ving sufficient disorienta-

tion. The e volution of boundary structure occurs morerapidly at lower values of o =D L and so the transitionfrom dislocation creep to GBS takes place more readilyand GBS predominates o ver a greater strain inter val,leading to greater superplastic ductility. Such alloys arecapable of undergoing superplastic deformation athigher strain rates than those that transform bydiscontinuous recrystallization. This reflects the greaterdegree of refinement in the former due to retention of the fine scale of the deformation-induced microstructureproduced during prior processing and, perhaps, thesimultaneous contributions of dislocation creep andGBS to the strain during ele vated temperature deforma-tion of such microstructures.

Acknowledgements

This work was supported in part by the SpanishCommission of Science and Technology (CICYT) undergrant MAT 97/0700. MPT acknowledges nancialsupport from the Ramony Cajal program of the SpanishMinistry of Science and Technology.

Appendix A

Table A1. Schmid factors corresponding to a Tuckerstress state ( sxx 0 /( /szz ) for each of the 12 slip systems in

variants

C 1 ((1

12

)[1

1 1])

andC 2 ((

1 2

1)[

1 1 1])

/

Slip plane Slip direction Schmid factor

C 1 C 2

(1 1 1) /[0 1 1]/ 0.408 0/[1 0 1]/ 0.136 0/[1 1 0]/ ( /0.544 0

/(1 1 1)/ /[0 1 1]/ ( /0.136 0.136[1 0 1] ( /0.408 ( /0.544

/[1 1 0]/ 0.544 0.408

/(1 1 1)/ /[0 1 1]/ 0 ( /0.408[1 0 1] 0 0.544

/[1 1 1]/ 0 ( /0.136

/(1 1 1)/ /[0 1 1]/ 0.544 ( /0.544/[1 0 1]/ ( /0.544 0[1 1 0] 0 0.544

Table A2. Schmid factors corresponding to C 1((1 1 2)[1 1 1]) and C 2 ((1 2 1)[1 1 1]) orientations undera tensile stress state in which the tensile axis is parallel toTD



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Slip plane Slip direction Schmid factor

C 1 C 2

(1 1 1) /[0 1 1]/ 0 0.408/[1 0 1]/ 0 ( /0.408/[1 1 0]/ 0 0

/(1 1 1)/ /[0 1 1]/ ( /0.408 0.408[1 0 1] 0 ( /0.408

/[1 1 0]/ 0.408 0

(1 1 1) /[0 1 1]/ ( /0.408 0[1 0 1] 0 0

/[1 1 0]/ 0.408 0

/(1 1 1)/ /[0 1 1]/ 0 0/[1 0 1]/ 0 0

[1 1 0] 0 0

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