Microtexture Tracking in Hot-Deformed Polycrystalline Aluminium- Experimental Results

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Acta Materialia 58 (2010) 16291642Microtexture tracking in hot-deformed polycrystallinealuminium: Experimental results

R. Quey *, D. Piot, J.H. Driver

Ecole des Mines de Saint-Etienne, Centre SMS, Laboratoire PECM CNRS UMR 5146, 158 cours Fauriel, 42023 Saint-Etienne, CEDEX 2, France

Received 9 September 2009; received in revised form 4 November 2009; accepted 5 November 2009Available online 16 December 2009Abstract

A split sample of Al0.1%Mn has been deformed by a series of compression tests in a channel-die at 400 C to a final strain of 1.6. Theorientations of 176 grains in a 4 4 mm2 internal surface were followed by high-resolution electron backscatter diffraction at four dif-ferent strains to compare with crystal plasticity models. Typically 3000 orientations per grain were used to quantify the average latticerotations of each grain together with their orientation spreads (termed microtexture tracking). The average orientations tend towards thestandard b-fibre plane-strain compression texture components, albeit with some variations. The in-grain orientation spreads developstrongly at first, then tend to saturate at high strains. Finally, the influence of grain environment on lattice rotation is examined by meansof the rotation variability at constant orientation. On average and at the beginning of the deformation, two grains of the same initialorientation, but different neighbours, would rotate by angles that vary by 25% and axes separated by 37; their orientations at e 1:2would vary by 12. 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Microstructure; Plastic deformation; Deformation structure; Electron backscattering diffraction (EBSD); Aluminium alloys1. Introduction

Accurate deformation texture simulations requireadvanced models of polycrystal deformation for whichthere are now several new variations that go beyond thestandard Taylor model to incorporate grain interactioneffects [14]. These models, although based on the behav-iour of the individual grains in an aggregate, are usuallyevaluated by a comparison of the experimental and simu-lated macrotextures of a large number of grains. Clearly,a comparison of the rotations of individual grains in theirenvironments would be much more instructive. However,there are relatively few such studies, since they require dif-ficult experimental procedures.1359-6454/$36.00 2009 Acta Materialia Inc. Published by Elsevier Ltd. Alldoi:10.1016/j.actamat.2009.11.007

* Corresponding author. Present address: Sibley School of Mechanicaland Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.

E-mail addresses: [email protected] (R. Quey), [email protected] (D. Piot),[email protected] (J.H. Driver).A first approach is to use two-dimensional (2-D) micro-structures, as done by Skalli et al. [5] and later Fortunierand Driver [6] using large-grained aluminium. A similarmethod is to use a columnar grain structure, within the lim-itations of a h100i-fibre texture [7]. These studies are ofinterest, but may not be representative of what occurs ina real polycrystal. Two strategies have been proposed tofollow grains in a 3-D polycrystal. In situ 3-D X-ray dif-fraction characterization of grain average rotations hasbeen used by Poulsen et al. [8], but up to now the techniqueappears limited to a tensile strain less than 0.1. The othermethod is to use a split sample, as first done by Barrettand Levenson [9] for uniaxial compression, then by Pan-chanadeeswaran et al. [10] for hot plane-strain compression(PSC). In the latter case, an AA 1050 sample was split inhalf perpendicular to the transverse direction and grain ori-entations were measured by electron backscatter diffraction(EBSD) on the internal surface before and after a strainof 0.5. In these studies on 3-D polycrystals, the experimen-tal rotations were compared to those predicted by therights reserved.

http://dx.doi.org/10.1016/j.actamat.2009.11.007mailto:[email protected]:[email protected]:[email protected]

RD

TD

ND

Fig. 1. Split sample deformed in channel-die compression.

time

T ( C)PSC to

0.19PSC to

0.42PSC to

0.77PSC to

1.2PSC to

1.6

20

400

Heating ( 60s)

Deformation at 1s 1

Quenching ( 2s)

EBSD (EBSD) EBSD EBSD EBSD (EBSD)

Fig. 2. Cycles of hot plane-strain compression and EBSD analysis.(EBSD) denotes analyses not reported in this paper.

1630 R. Quey et al. / Acta Materialia 58 (2010) 16291642Taylor model. Their conclusions are contradictory: from 3-D X-ray diffraction microscopy, Winther et al. [11] foundthe Taylor model to be successful for 75% of the grains,whereas Panchanadeeswaran et al. [10] concluded that itfails almost completely.

Although Panchanadeeswaran et al. [10] have demon-strated the potential of the split-sample technique to followgrains in a polycrystal during large deformations, theirstudy is not really satisfactory because few orientationmeasurements per grain were made and an accidentalmacroscopic shear strain (as large as 1/3 of the imposedPSC) occurred in the sample during the deformation.

In a recent study by Quey et al. [12], a split sample ofAl0.1 wt.%Mn was deformed in PSC at 400 C to a strainof 0.4. After each of the two passes, the sample wasquenched to avoid recrystallization, and the deformationmicrostructure was analysed by EBSD. In the presentstudy, this experiment has been repeated with another sam-ple, up to a strain of 1.6. The same 176 grains were fol-lowed throughout the deformation with an average of3000 measurements per grain. This paper first discussesthe influence of analysing grain rotations on the internalsurface of a split sample. Then, the rotation properties ofthe 176 grains are described in detail, in terms of averagerotations and in-grain orientation spreads. Finally, amethod is proposed to investigate the possible effects ofgrain interaction on these rotation properties.

A comparison between the experimental results and thepredictions of various polycrystal deformation model isprovided in a second article [13].

2. Experimental

The high-purity binary Al0.1 wt.%Mn alloy was pro-vided by the Alcan Research Centre at Voreppe. After cast-ing, it was cold-rolled 50% then recrystallized at 530 C for5 min. The resulting microstructure showed near-equiaxedgrains of size about 300 lmand a weak crystallographic tex-ture. A split sample of 8 7 10 mm (along the rollingdirection (RD), transverse direction (TD) and normal direc-tion (ND), respectively) was used. It was made of two iden-tical parts assembled along the transverse direction, seeFig. 1. The sample surfaces were machined flat, and bothinternal surfaces were mechanically then electrolyticallypolished. At the centre of one of them, a 4 4 mm2 observa-tion zone was marked with microhardness indentations ofdiameter about 30 lm, located 1 mm apart. The samplewas deformed by successive heating, compression andquenching cycles, as illustrated in Fig. 2. In this way, themicrostructure could be analysed at successive (logarithmic)strains of 0, 0.19, 0.42, 0.77, 1.2, and 1.6. After closing, thetwo parts of the sample were held together through gluedpoints at the corner of the internal surface, and thenwrappedin Teflon films to reduce friction effects. The hot channel-diecompression was imposed at a strain rate of 1 s1 and a tem-perature of 400 C in the equipment described by Mauriceet al. [14]. Typical heating times to temperature stabilizationwere about 1 min. After deformation, the sample was waterquenched within about 2 s to retain the deformation micro-structure (the sample does not recrystallize under these con-ditions due to the strong effect of Mn in solid solutioninhibiting grain boundary movement). After removing theTeflon films the two parts of the sample adhered, but couldbe easily separated for metallographic observation. Beforedeformation and after each pass, the grain structurewas ana-lysed as hot deformed, without any additional polishing(except at the strain of 0.42,where the twoparts of the samplemoved slightly with respect to each other during quenching.A small amount of electropolishing was conducted to cleanup the surface, removing nomore than 35 lmofmaterial.).The analyses were done by EBSD in a JSM6501FFEGSEMequipped with an HKL EBSD system, using a scanning stepof 5 lm. The orientationmaps were studied withHermes, anin-house software development built on Orilib [15]. Thegrainswere detected automatically at e 0 using aminimumdisorientation angle for the grain boundaries of 5 (this valuemay seem small with respect to the usual 15, but wasadopted to obtain near single-crystalline grains). At higherstrains, it was not possible to use this automated proceduredue to the development of in-grain local disorientations, sothe grains were delineated by hand. Only the data at strainsof 0, 0.42, 0.77, and 1.2 are reported here, with the aim ofstudying successive grain rotations for three similar strainincrements of about 0.4. At a strain of 1.6, EBSD analysisbecame impossible in some regions due to a pronounced sur-face rumpling (see Section 3.2).

30 20 10

0102030

alti

tude

[m

]

7 6 5 4 3 2 1 0 1 2 3 4 5 6 7distance [mm]

(a)

30 20 10

0102030

alti

tude

[m

]

7 6 5 4 3 2 1 0 1 2 3 4 5 6 7distance [mm]

(b)

Fig. 4. Internal surface rumpling analysed by rugosimetry profiles along(a) ND and (b) RD. Measurements carried out on a sample deformed ate 0:42. Note that there are two orders of magnitude between thehorizontal and vertical axes, and that the local slopes are morepronounced along ND.

R. Quey et al. / Acta Materialia 58 (2010) 16291642 16313. Validation of the method

The fact that grains are observed on the internal sur-faceof the sample is the main limitation of the methodand could be open to criticism concerning its relevance tothe behaviour of grains in a real polycrystal. The purposeof this section is to ensure, as far as possible, that this doesnot significantly affect grain rotations. This is achievedpartly by following the methodology introduced by Pan-chanadeeswaran et al. [10].

3.1. Deformation mode

The deformation mode experienced at the scale of thesample can be characterized by the array of microhardnessindentation marks on the internal surface. They are repre-sented, at successive strains, on Fig. 3. It appears that thesample undergoes a nearly pure PSC at the beginning ofthe deformation e 00:4, then shows additional shearscaused by the sample/tool friction. At e 1:2, shears arenoticeable, with maximum values of 0.20.3 at the extremi-ties of the zone of observation. The study of lattice rotationspresented in the following, as well as the comparison withsimulations provided separately [13], show that the shearsdo not affect significantly grain rotations, so they areneglected in the presentation of the results.

3.2. Aspect of the internal surface

After deformation, the internal surface appeared rum-pled, as a result of strain heterogeneities at the grain scale.This is illustrated on Fig. 4 by rugosity profiles made alongRD and ND at e 0:42. The maximal out-of-plane dis-placements are of the order of 30 lm (independent of thedirection). The local slopes appear less pronounced alongRD than along ND, which is easily explained by the factthat although the out-of-plane displacements are the samein both directions, the distances over which they occur areproportional to the grain size, and so are higher along RDdue to the sample elongation. At e 0:42, the slopes alongRD are less than 10 and, by grain elongation, were found1 mm

(a)

1 mm

(b

1 mm

(d)1

Fig. 3. Array of microhardness indentations at successive strains: (not to exceed this value at higher strains. On the contrary,the slopes along ND are close to 20 at e 0:42 and werefound to attain values as high as 60 at the higher strains.Usually, for the EBSD analysis of a flat RDND surface,the sample is tilted 70 about RD to avoid major defocus-ing and geometrical constraints in the scanning electronmicroscope. In this configuration, the angle between theelectron beam and ND is equal to 20. In our case, the localslopes along ND can be higher than 20, which wouldcause parts of the surface to be hidden from the beam dur-ing the EBSD analysis (shadowing). To make the wholesurface visible, it was necessary to tilt the sample aboutND.

As found by Panchanadeeswaran et al. [10], no gallingor sliding marks were observed on the internal surface afterdeformation indicating that the two halves of the sampleadhered during deformation. This is attributed to the localfriction stresses, and is almost certainly favoured by thesurface rumpling. This makes the internal surface)

1 mm

(c)

mm

(e)

a) e 0, (b) e 0:19, (c) e 0:42, (d) e 0:77, and (e) e 1:2.

1632 R. Quey et al. / Acta Materialia 58 (2010) 16291642equivalent to a mechanical grain boundary, according tothe terminology proposed by Panchanadeeswaran et al.[10].

3.3. Influence on orientation measurements

The conditions are clearly non-standard for EBSD anal-yses, for which a perfectly flat surface is usually used. Inthis study, the surface rumpling causes defocusing, theinfluence of which on orientation measurements can bequantified. On a standard (flat) sample, the orientation ofa single-crystalline grain was measured in standard condi-tions (perfect focusing), and then with defocusing, whichwas controlled by changing the working distance of themicroscope. The measurement error appeared nearly pro-portional to the defocusing, about 0:025=100 lm over arange of up to 2000 lm. In the deformed sample, themaximum defocusing amplitude is about 200 lm and sothe angular error does not exceed 0.05. This error is verysmall compared to the rotations caused by plastic deforma-tion (see Section 4.2) and so can be neglected.

3.4. Influence on grain rotations

The internal surface has been described above as amechanical grain boundary. The influence of such condi-tions on grain rotations can be characterized by comparingthe orientations on the internal surface to reference orien-tations, which would not suffer from such conditions.Firstly, the macrotexture on the internal surface can be com-pared with the one measured on a cut surface of a standardsample deformed in the same conditions. This is illustratedby the {111}pole figures inFig. 5.Within the statistical errorarising from the limited number of grains, themacrotexturescan be considered similar. Furthermore, the local orienta-tions on the internal surface can be compared with those ofthe same grains just below, in the subsurface regions. The lat-ter can be obtained after removal of 3050 lm of materialfrom the internal surface by electropolishing. As thismethodis destructive, it was not done on the principal sample fol-lowed in this study, but on another sample deformed under(a) (

Fig. 5. The influence of the internal surface on the macrotexture. (a) Macrotexmeasured on a cut surface of a standard sample. Both measured at e 0:77.the same conditions to e 0:5. The orientation maps areillustrated in Fig. 6, where the seven studied grains aremarked. Their orientations in the surface and subsurfacecan be compared quantitatively in terms of average orienta-tion and in-grain orientation spread [16]. The latter is calcu-lated as the average of the disorientation angles with respectto the average orientation. The results are given in Table 1and show that the average orientations differ only by 1and the orientation spreads by 0.5 (relative difference of7%). These values are small compared to those due to plasticdeformation (see Sections 4.2 and 4.3). These two compari-sons show that the rotations on the internal surface are closeto the ones in volume, so that the grains of this study are con-sidered as grains of a real polycrystal.

4. Results

4.1. Microtextures and macrotextures

The microtextures obtained at the successive strains areillustrated by Fig. 7. The 176 grains that were followed dur-ing the deformation are numbered and their contours aremarked. In practice, grains exhibit two different rotationmodes: either a unimodal rotation, composed of an aver-age rotation and an orientation spread, or fragmentation.From e 01.2, it was found that 90% of the grainsundergo a unimodal rotation, confirming the results ofthe previous study by microtexture tracking [12]. Onlythese grains are considered in this study. The specific caseof the grains undergoing fragmentation, usually high-sym-metry orientations, will be reported separately. The exam-ple of a grain undergoing a unimodal rotation is illustratedin Fig. 8. As a large number of orientations are known, it ispossible to accurately calculate an average orientation andan in-grain orientation spread.

The corresponding macrotextures can be characterizedin terms of number of grains in the components of the b-fibre. The fibre runs through the ideal components Copper{112}h111i, S {123}h634i and Brass {110}h112i. Theseare approximate positions, however; their exact orienta-tions in our experiments are, in Euler angles (Bunge con-b)

ture measured on the internal surface of the split sample. (b) Macrotexture

3

45 6 7

21

100 micrometers, step = 5 micrometers

(a)

1 23

4 675

100 micrometers, step = 5 micrometers

(b)

Fig. 6. The influence of the internal surface on the microtexture of a sample deformed at e 0:5. Rodrigues vector maps measured (a) on the internalsurface and (b) in subsurface (after removal of 3050 lm of material). (R being a Rodrigues vector, the RGB colour levels are255 Ri

ffiffiffi2

p 1= 2

ffiffiffi2

p 1

with i 2 f1; 2; 3g, respectively; grey is for non-indexed points). The seven grains considered are marked.

Table 1Influence of the internal surface on the microtexture: difference between the orientations of grains measured in surface and subsurface (after removal of3050 lm of material), as illustrated in Fig. 6. (a) Average orientations and (b) average in-grain disorientations hd .

(a)

n Surface orientation u1; /; u2 () Subsurface orientation u1; /; u2 () disorientation ()1 (164.5, 33.2, 1.7) (163.3, 33.2, 2.6) 0.72 (43.5, 54.3, 16.4) (43.4, 55.4, 15.8) 1.33 (33.7, 78.1, 31.8) (34.4, 77.7, 32.1) 0.94 (69.5, 52.4, 10.3) (69.6, 51.9, 11.1) 1.05 (39.6, 72.2, 10.1) (39.4, 71.6, 10.5) 0.86 (148.5, 34.5, 6.6) (146.8, 34.4, 7.8) 1.07 (33.3, 69.5, 15.5) (33.9, 68.4, 15.1) 1.2

Average = 1.0

(b)n Surface hd () Subsurface hd () Relative difference (%)

1 6.4 6.0 62 5.2 5.7 103 5.8 6.1 54 9.9 10.6 75 11.0 10.6 46 7.7 6.8 127 5.8 6.2 7

Average = 7

R. Quey et al. / Acta Materialia 58 (2010) 16291642 1633vention): (90, 27.5, 45), (57.5, 30, 75) and (35, 35,80), respectively. The grains are characterized in termsof their average orientations, and are assigned to a compo-nent using the standard 15 criterion. The results at the suc-cessive strains are reported in Table 2. It appears that eachb-fibre component systematically increases, while the num-ber of grains outside the fibre continuously decreases.These results are consistent with previous hot-deformationmacrotexture studies (e.g. [17]).

4.2. Average rotations

The average rotations are expressed in the sample coor-dinate system as axis/angle pairs r; h. One can considereither the rotations at the successive strains e measuredfrom the initial orientations, noted re0; h

e0, or the rotations

for the successive strain increments, called incrementalrotations and noted rei ; h

ei . A study of the rotation axis

r requires particular precautions, especially when thereare uncertainties for the rotation angle h. Bate et al. [18]have shown that the angular accuracy b of the axis r isgiven by tan1d=h, where h is the rotation angle and dits absolute accuracy (both expressed in degrees). With atypical value of d 1 attributed to alignment error inthe electron microscope and a maximum angular value ofthe accuracy on the axis of b 20, the rotation angle hmust be greater than 2.7. As a consequence, in the follow-ing only the grains whose incremental rotations are greaterthan 2.7 are taken into consideration for the study of therotation axis.

The use of axis/angle pairs for the rotations is conven-tional, but implies direct, or linear, rotations from one ori-entation to the next. This is unlikely to be correct for largerotations, e.g. those from the initial to the final orientationsr1:20 ; h

1:20 , but not far from real behaviour for the incre-

mental rotations which are preferred here (noting that theincremental rotations should not be too small because ofthe above uncertainty problem for the axes).4.2.1. Rotations with respect to the initial orientations

re0; he0

The frequency distributions of the rotation angles he0 atsuccessive strains are represented in Fig. 9a. As expected,

500 micrometers; step = 5 micrometers; grid 871x806

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Fig. 7. Microtextures at successive strains: (a) e 0, (b) e 0:42, (c) e 0:77 and (d) e 1:2 (Rodrigues vector maps). The 176 grains are numbered andthe black lines represent (a) the boundaries >5, (bd) the contours of the same grains at the subsequent strains.

1634 R. Quey et al. / Acta Materialia 58 (2010) 16291642they vary significantly from one grain to the other, e.g. ate 1:2, they go from 2 to 39. However, it appears that,as deformation increases, the rotation angles increase less:on average, they are 11 at e 0:42, 15 at e 0:77 and 18at e 1:2.

The distributions of the rotation axes re0 are illustrated inFig. 9b by pole figures which are reduced to one-quarterusing the orthotropic symmetry. Each axis is representedby a point and a density function is constructed by associ-ating a Gaussian spread of half-width 7 to each axis. Theaxes appear to be preferentially distributed about TD at thefirst increment (density = 5), and then about an axislocated between TD and ND, more precisely 0:64TD 0:77ND (density = 3). This transition accountsfor irregular rotation paths, which can be better character-ized through the incremental rotations.

4.2.2. Incremental rotations rei ; hei

The frequency distribution of the incremental rotationangles hei are represented in Fig. 10a. To facilitate a com-parison between successive increments, the angles can benormalized to a constant strain increment of 0.4. The nor-malized angles hei are proportional to the angles h

ei and are

defined by hei hei 0:4=De, where De is the increment

deformation (0.42, 0.770.42, or 1.20.77). They takeaverage values of 10 at e 0:42, 7 at e 0:77 and 5 at

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Fig. 7 (continued)

R. Quey et al. / Acta Materialia 58 (2010) 16291642 1635e 1:2, confirming that the rotation rates tend to decreaseas deformation increases.

The equivalent distributions of the incremental rotationaxes are represented in Fig. 10b. During the deformation,these axes tend at first to lie preferentially along TD thenchange closer to NDRD, more precisely 0:9ND0:4RD.

4.2.3. The relations to texture development

The evolution of the incremental rotation angles andaxes can be explained in relation to the texture develop-ment. The tendency of the rotation angles to decrease withstrain is expected since grains, as they rotate, attain morestable orientations and so have smaller rotations.

Concerning the rotation axes, relating their distributionsto texture development can be carried out by partitioningthe set of grains in two subsets: the grains that convergeinto the b-fibre (i.e. which did not belong to the fibre ate 0, but do at e 1:2) and the others. Orientations areconsidered to belong to the fibre if they belong to one ofits components as described in Section 4.1. The distribu-tions of the rotation axes are given in Fig. 11. The grainsthat converge into the b-fibre appear to have the sameproperties as those of all grains: rotations about TD at

RD

TD

{111}stereo. proj.

(a)

1/2-width: 2levels: 1, 5, 10, 20, 50, 100RD

TD

{111}stereo. proj.

(b)

1/2-width: 2levels: 1, 5, 10, 20, 50, 100RD

TD

{111}stereo. proj.

(c)

1/2-width: 2levels: 1, 5, 10, 20, 50, 100RD

TD

{111}stereo. proj.

(d)

Fig. 8. Example of the unimodal rotation of a grain (number 062). (a) e 0, (b) e 0:42, (c) e 0:77, and (d) e 1:2. Note the average rotation and theorientation spread.

Table 2Macrotexture evolution through strain, in terms of number of grainswithin 15 of the b-fibre components (total number of grains = 157).

Component

Copper S Brass Others

e 0 3 7 25 122e 0:42 11 20 40 86e 0:77 14 35 42 66e 1:2 15 44 42 56

1636 R. Quey et al. / Acta Materialia 58 (2010) 16291642the beginning of the deformation, then rotations about0:9ND 0:4RD. On the other hand, the grains whichdo not converge into the b-fibre show distributions of rota-tion axes that are fairly uniform (except, perhaps, at thesecond increment). This indicates that the preferential loca-tions of distributions of rotation axes are related to the tex-ture development. It can be explained by the fact that theb-fibre, running from Copper through S to Brass, has anaxis that can be expressed in the form of: aRDbND, with a 0:97; b 0:24 between Copper and S,and a 0:25; b 0:96 between S and Brass. Thus, TDis a preferential direction for convergence towards theb-fibre. This is particularly true at the beginning of thedeformation. Subsequently, the grains, which are closerto the fibre, rotate more parallel to it in order to reach aparticular component.4.3. In-grain orientation spreads

The in-grain orientation spreads are quantified by theaverage disorientation with respect to the average orienta-tion [16], noted hd . Before deformation, the grains havevery similar orientation spreads of 0.3 on average, whichis typically the error associated with EBSD measurements.Their distributions at successive strains are represented inFig. 12. It appears that the orientation spreads developstrongly at the beginning of the deformation, and thentend to stabilize: their successive average values are 5.1,6.4 then 7.0. These observations confirm those of Glezand Driver [19], made on single crystals of stable orienta-tions (Brass, S and U) deformed under the sameconditions.

4.4. Rotation variability at constant orientation

It is often considered that, in a polycrystal, the active slipsystems and the lattice rotations of a grain do not onlydepend on its orientation, but also on the interaction withits neighbours. This means that two grains of initially thesame orientation can rotate differently according to theirneighbours, known in the widest sense as grain interactions.Here we shall investigate this effect by what we call the rota-

equal-area. proj.1/2-width: 7

levels: 1,2,3,4,5,6,7RD

NDTD

r0.420


levels: 1,2,3,4,5,6,7RD

NDTD

r0.770


levels: 1,2,3,4,5,6,7RD

NDTD

r1.20

(b)

(a)

Fig. 9. Rotations with respect to the initial orientations, at the successive strains: (a) rotation angle h0 and (b) rotation axis r0. Each dot represents a grain;the contour plots highlight their distributions.

R. Quey et al. / Acta Materialia 58 (2010) 16291642 1637tion variability at constant orientation (VCO). To ourknowledge, such an effect of individual grain interaction ongrain rotations has never been quantified (at leastexperimentally).4.4.1. Average rotations

Let r1; h1 and r2; h2 be the rotations of two grains ofthe same orientation, but different neighbours. The differ-ences in rotation can be quantified by the following param-eters for the rotation angles (Drh) and the rotation axes(angle a):

Drh 2 h1 h2h1 h2

; a acos r1 r2 1

the values of which are zero if the rotations are equal.Here, we consider the rotations during the first strain

increment r0:420 ; h0:420 . Ideally, one would wish to quantify

the VCO for every orientation. By definition, this could bedone by comparing the rotations of several grains of thesame orientation, but different neighbours. However, inour sample (and in practice for most other samples), everypair of grains is mutually disoriented by at least a fewdegrees, so that it is impossible to compare the rotations ofgrains having exactly the same orientation. From a theoret-ical point of view, an infinite number of grains would berequired.The alternative approach that we propose is to deter-mine the average of the VCO over all orientations. Thisis done by a comparison of the rotations of grains of differ-ent orientations taking all pairs of grains into consider-ation. This method involves three steps, which lead toFig. 13a and c:

1. For every pair of grains, one calculates (i) the disorien-tation between their initial orientations, allowing forboth the crystal and sample symmetries, and (ii) the dif-ferences between their rotations Drh and a. On the fig-ures, for every pair of grains, Drh and a arerepresented as a function of the disorientation, whichis limited to 20.

2. The average variabilities by disorientation levels are cal-culated using intervals of 4. This value has been chosento obtain a smooth evolution of the average tendency.The averages at zero disorientation obviously cannotbe calculated this way because of the absence of data.

3. The values at zero disorientation are calculated byextrapolating the average tendency from higher disori-entations. By definition, the corresponding value ofDrh or a is the difference between the rotations ofgrains having the same orientation, i.e. the VCO.The values obtained in the present study are:Drh 0:25 (25%) for the rotation angle and a 37for the rotation axis.

(a)


levels: 1,2,3,4,5,6,7RD

NDTD

r0.42i


levels: 1,2,3,4,5,6,7RD

NDTD

r0.77i


levels: 1,2,3,4,5,6,7RD

NDTD

r1.2i

(b)

Fig. 10. Incremental rotations. (a) Rotation angle hi and (b) rotation axis ri. Each dot represents a grain; the contour plots highlight their distributions.

1638 R. Quey et al. / Acta Materialia 58 (2010) 16291642Another quantity of interest is the rotation relative var-iability at constant orientation (RVCO). It is defined bythe VCO divided by the overall variability, the latterbeing obtained by averaging over all pairs of grains. Bydefinition, the RVCO takes values between 0 and 1, andthe higher the value, the lower the effect of the orientationand the stronger the effect of grain interaction. For therotation angle and axis, the overall variabilities areDrh 53% and a 83, respectively, and so the RVCOvalues are 0.50 and 0.45, respectively.

A non-zero (R)VCO is incompatible with the Taylormodel, for which rotations depend only on orientation.To validate the method, it has been applied to the rota-tions provided by the Taylor model for the same set of176 grainssee Fig. 13b and d. The VCO obtained inthis way are 9%/8, i.e. are not strictly zero, which isattributed to the limited number of data. For confirma-tion, the same study was repeated with a more represen-tative set of 2000 random orientations, leading tovariabilities very close to zero. The differences betweenthe two can be associated with the statistical error arisingfrom the limited number of data, and which can there-fore be considered to represent the possible error ofthe experimental values. One can note, however, thatthese errors are small when compared to the experimen-tal VCO, which ensures that the latter can be consideredas valid measurements.The rotation axis/angle VCO acting through deforma-tion leads to a final-orientation VCO. The final orienta-tions are compared by the disorientation angle betweenthem, and the results obtained are illustrated inFig. 14. The final-orientation VCO is 12 (with an errorof 2.4).

4.4.2. In-grain orientation spreads

The same characterization can be applied to the in-grainorientation spreads at e 1:2. The difference in spreads oftwo grains can be quantified as for the rotation angles,

Drhd 2 hd1 hd2

hd1 hd2

2

One can study the relation between the in-grain orienta-tion spreads and the initial orientations (as before) or thecurrent orientations. The results are illustrated in Fig. 15.The VCO obtained are Drhd 31% for the initial orienta-tion and Drhd 24% for the current orientation. The orien-tation spread is therefore more dependent on the currentorientation than on the initial orientation (lower VCO).As for average orientations, these values are to be com-pared to the overall variability, whose value isDrhd 34%. For the current orientation, the RVCO isequal to 0.71. Such a high value means that the dependenceof the in-grain orientation spreads on the grain orientationis small.

equal-area proj.1/2-width: 7

levels: 1,2,3,4,5,6,7RD

NDTD

r0.42i


levels: 1,2,3,4,5,6,7RD

NDTD

r0.77i


levels: 1,2,3,4,5,6,7RD

NDTD

r1.2i

(a)


levels: 1,2,3,4,5,6,7RD

NDTD

r0.42i


levels: 1,2,3,4,5,6,7RD

NDTD

r0.77i


levels: 1,2,3,4,5,6,7RD

NDTD

r1.2i

(b)

Fig. 11. Relation of the incremental rotation axes to the texture development. (a) Case of the grains that converge into the b-fibre. (b) Case of the othergrains. Note that grains in (a) show the same distribution as all grains (see Fig. 10).

0

0.04

0.08

0.12

0.16

0.2

0.24

0.28

Freq

uenc

y

1 3 5 7 9 11 13 15 17 19 21

Disorientation d [degrees]

= 0.42 = 0.77 = 1.20

Fig. 12. In-grain orientation spreads through strain. hd is the averagedisorientation with respect to the mean grain orientation.

R. Quey et al. / Acta Materialia 58 (2010) 16291642 16395. Discussion

5.1. The experiments

This study provides the first statistically sound set ofrotations of grains in a polycrystal undergoing a large plas-tic deformation. The rotations of 176 grains were measuredduring hot PSC applied in several passes up to a strain of1.2. The advantage of high-temperature deformation istwofold: first the ease of EBSD measurements up to highstrains, and secondly the better deformation homogeneityat the grain scale. This type of experiment could be per-formed at room temperature, but the EBSD indexationrate would be lower and greater internal surface rumpling(due to the higher strain heterogeneities) would cause moreproblems. The use of a split sample under the present con-ditions enables one to follow the grains on the internal sur-face. It is shown that EBSD analyses can be carried outdirectly on such a surface without significant measurementerrors. Moreover, the internal surface does not appear tosignificantly affect the grain rotations. As a result, thegrains are considered to be true internal grains of a poly-crystal. The main differences with the experiments of Pan-chanadeeswaran et al. [10] carried out in 1996 are that (i)the sample did not experience any accidental macroscopicshear strain; (ii) the deformation was imposed in severalpasses up to a strain of 1.2; and (iii) the microtexture wasanalysed much more accurately, with typically 3000 mea-surements per grain for each deformation. This enablesone to obtain representative average grain rotations as wellas in-grain orientation spreads, and to study their evolu-tions in a quantitative way during the deformation.

5.2. Average rotations

The average grain rotations were studied in terms ofrotation angles and axes. They can be calculated from

0

20

40

60

80

100

120

140

160

180

[d

egre

es]

Disorientation [degrees]

VCO = 37

V = 83

pair of grainsaverage

(c)

0

20

40

60

80

100

120

140

160

180

[d

egre

es]

0 4 8 12 16 20

0 4 8 12 16 20Disorientation [degrees]

VCO = 8


2000 grains

(d)

0

20

40

60

80

100

120

140

160

180

r

[%]


VCO = 25

V = 53


(a)

0

20

40

60

80

100

120

140

160

180

r

[%]

0 4 8 12 16 20

0 4 8 12 16 20


VCO = 9


2000 grains

(b)

Fig. 13. Variability at constant orientation (VCO) of the grain rotations obtained during the first increment r0:420 ; h0:420 . (a and b) Rotation angle in the

experiments and for the Taylor model, respectively. (c and d) Rotation axis in the experiments and for the Taylor model, respectively. V stands for theoverall variability, which is calculated with no limitation of disorientation (x-axis). For (b) and (d), the VCO does not fall to zero due to the limitednumber of grains in use, but does with a more representative set of 2000 grains.

1640 R. Quey et al. / Acta Materialia 58 (2010) 16291642the initial orientations or for the successive increments,which leads to the incremental rotations. The lattermethod appears to be more interesting because it empha-sizes the evolution of the rotation paths. The incrementalrotation angles tend to decrease as deformation increases.It is shown for the first time that the incremental rotationaxes are initially preferably distributed about TD, thentend to rearrange along a direction situated between RDand ND. These properties are related to the developmentof the standard b-fibre texture. The decrease in rotationangles is due to the obvious fact that, as grain orientationsapproach stable orientations, their rotation rates decrease.Concerning the rotation axes, their initial distributionabout TD can be explained by the fact that it is the direc-tion of preferential convergence to the b-fibre, which is adirection aRD bND (a 0:97; b 0:24 betweenCopper and S, and a 0:25; b 0:96 between S andBrass). Then, when the orientations approach the b-fibre,they tend to rotate along the fibre to reach a particularcomponent and the rotation axes approach a direction0:9RD 0:4ND. An important experimental valida-tion is that this evolution is opposite to the one that wouldhave been caused by a major friction effect: the slight sam-ple barreling that can be seen in Fig. 3 would cause rota-tions about TD that should increase with thedeformation (and not decrease). One can therefore con-clude that the eventual friction-induced rotations can onlybe of second order with respect to the rotations associatedwith plane-strain compression.

These properties, and particularly those of the rotationaxes, as features clearly linked to the texture development,can be used for a comparison between experimental andsimulated rotations at the level of the individual grains.This can be done not only in a qualitative way, by compar-ing the location of the preferential rotation axes, but also ina quantitative way, through the intensities of their distribu-tion functions.

5.3. In-grain orientation spreads

The in-grain orientation spreads strongly develop at thebeginning of the deformation: while they are 0 at e 0,they reach on average 5.1 at e 0:42, then tend to stabi-lize, with values of 6.4 at e 0:77 and 7.0 at e 1:2. Thisconfirms the results by Glez and Driver [19] obtained onsingle crystals of Al1 wt.%Mn with stable orientations(S, Brass and Copper) deformed under the same condi-tions. The orientation spreads develop through the forma-

048

12162024283236404448525660

Fina

ldis

orie

ntat

ion

[deg

rees

]


VCO = 12


(a)

048

12162024283236404448525660

Fina

ldis

orie

ntat

ion

[deg

rees

]

0 4 8 12 16 20

0 4 8 12 16 20


VCO = 2.4


2000 grains

(b)

Fig. 14. Variability at constant orientation (VCO) of the final orientatione 1:2: (a) experimental results and (b) Taylor model.

0

20

40

60

80

100

120

140

r

[%]


VCO = 31

V = 34


(a)

0

20

40

60

80

100

120

140

r

[%]

0 4 8 12 16 20

0 4 8 12 16 20


VCO = 24

V = 34


(b)

dd

Fig. 15. Variability at constant orientation (VCO) of the orientationspread hd at e 1:2. V stands for the overall variability, which iscalculated with no limitation of disorientation (x-axis). (a) Initialorientation and (b) final orientation.

R. Quey et al. / Acta Materialia 58 (2010) 16291642 1641tion of a dislocation sub-boundary structure which hasbeen examined by some EBSD maps over small areas usingsteps of 0:5 lm. This work is not reported here, but one cannote that the sub-structures are very similar to thosereported by Glez and Driver [16] and more recently byHumphreys and Bate [20].

5.4. Rotation variability at constant orientation (VCO)

In a polycrystal, two grains of the same orientation, butpossessing different neighbours, can rotate differently;herein termed rotation VCO. This variability is obviouslyexpected to be smaller than the one between grains of dif-ferent orientations, denoted the overall variability. TheRVCO is defined as the ratio between the two. This param-eter gives an idea of the relative influence of the local grainenvironment on its lattice rotation. The RVCO would be 0if the rotations were only dependent on the orientation,and 1 if there was no such a dependency. A method wasproposed in order to determine the VCO and RVCO. Itis based on a comparison of the rotations of grains of dif-ferent orientations, and the resulting values are the aver-ages of the variabilities over all orientations.

First, this method has been applied to the average grainrotations for the first strain increment, in terms of rotationangle and axis. The rotation angle/axis VCO pair is 25%/37. The rotation angle/axis RVCO pair is 0.50/0.45.Therefore, rotation angle and axis show nearly the samerelative variabilities. These differences in rotation can leadto grains of the same initial orientation developing differentfinal orientations. This can be accounted for by the final-orientation VCO, which, in terms of disorientation angle,is 12. It should be noted that this value is close to the dis-tance between the b-fibre components (typically 1520). Inother words, grain interactions could lead grains of thesame initial orientation having different final texture com-ponents. Consequently, from a qualitative point of view,models for which grain rotations depend only on grain ori-entation cannot exactly predict grain rotations, and theymay even not provide the right final texture component.A quantitative comparison is presented separately [13].

The in-grain orientation spreads were found not todepend greatly on orientation (high RVCO). This is alsoimportant information for texture simulations since themacrotexture would be unchanged by permuting thespreads of the different grains or, equivalently, applyingthe same average spread to all of them. For these single-phase face-centred cubic metals, it is not necessary to knowexactly what the spread of a particular grain is. As a result,the in-grain orientation spread during high-temperaturedeformation does not appear to be an important parameter

1642 R. Quey et al. / Acta Materialia 58 (2010) 16291642to evaluate, and hence models based only on the evolutionof the average orientation, e.g. the Taylor model, do notsuffer from this approximation. This is relevant informa-tion since at the moment only high-resolution finite-ele-ment simulations can provide in-grain orientation spreads.

6. Conclusions

The first statistically sound set of experimental rotationsof grains in a face-centred cubic polycrystal at large strainis provided. A split sample was used, and the orientationswere followed on its internal surface by EBSD throughoutthe deformation; we call this method microtexture track-ing. 176 grains were analysed at successive strains of 0,0.42, 0.77, and 1.2. Typically 3000 orientation measure-ments per grain were obtained, giving access not only tothe average rotations, but also to the in-grain orientationspreads. The results can be used to evaluate models forpolycrystalline deformation. The main results are that:

1. Following grains by EBSD on the internal surface of asplit sample does not affect significantly the orientationmeasurements, or the rotations of the individual grains.

2. 90% of the grains exhibit a unimodal rotation, com-posed of an average rotation and an orientation spread.

3. The average rotations are studied in terms of angle andaxis. The evolution of the incremental rotations is ofmajor interest. The average rotation angles appear todecrease as deformation increases: they are 10, 7,and 5 at the three successive increments of about 0.4.The rotation axes are initially preferentially distributedabout TD, then about 0:9ND 0:4RD. Theseproperties can be related to the convergence of the ori-entations into the b-fibre.

4. The in-grain orientation spreads develop strongly at thebeginning of the deformation, and then stabilize: theiraverage values are 5.1, 6.4, and 7.0, respectively, forthe three strains.

5. A method is proposed to quantify the rotation VCOcaused by grain interactions. It was found that, for thefirst strain increment, two grains of the same orientation,but different neighbours, have rotation angles that differby 25% and rotation axes that differ by 37. At e 1:2,their final orientations differ by 12. Such variabilitiescannot be accounted for by the standard Taylor model.Supplementary data

The microtexture data are available from http://tel.arc-hives-ouvertes.fr/tel-00414120/en/ (file microtexture-tracking-data.tgz).

Acknowledgments

One of the authors (R.Q.) thanks SeverineGirard-Insardifor assistance with the PSC tests and Paul Jouffrey for adviceand assistance with the SEM-EBSD work. The authorsgratefully acknowledge the provision of the alloy by Jean-Marie Feppon of Alcan Research Centre at Voreppe.

References

[1] Sarma GB, Dawson PR. Int J Plasticity 1996;12:1023.[2] Crumbach M, Pomana G, Wagner P, Gottstein G. In: Gottstein G,

Molodov DA, editors. Proceedings of the 1st joint internationalconference on recrystallization and grain growth, vol. 2. Springer-Verlag; 2001. p. 1053.

[3] Van Houtte P, Delannay L, Kalidindi SR. Int J Plasticity2002;18:359.

[4] Quey R, Ringeval S, Piot D, Driver J. Mater Sci Forum2007;539:3371.

[5] Skalli A, Fortunier R, Fillit R, Driver JH. Acta Metall 1985;33:997.[6] Fortunier R, Driver JH. Acta Metall 1987;35:1355.[7] Kalidindi S, Bhattacharyya A, Doherty R. Proc Roy Soc A

2004;460:1935.[8] Poulsen HF, Margulies L, Schmidt S, Winther G. Acta Mater

2003;51:3821.[9] Barrett CS, Levenson LH. AIME 1939;137:112.[10] Panchanadeeswaran S, Doherty RD, Becker R. Acta Mater

1996;44:1233.[11] Winther G, Margulies L, Schmidt S, Poulsen HF. Acta Mater

2004;52:2863.[12] Quey R, Piot D, Driver J. Ceram Trans 2008;210:205.[13] Quey R, Piot D, Driver JH. Acta Mater, accepted for publication.[14] Maurice C, Piot D, Klocker H, Driver J. Metall Mater Trans A

2005;36:1039.[15] Orilib. .[16] Glez J-C, Driver JH. J Appl Crystallogr 2001;34:280.[17] Maurice C, Driver JH. Acta Mater 1997;45:4627.[18] Bate PS, Knutsen RD, Brough I, Humphreys FJ. J Microsc

2005;220:36.[19] Glez J-C, Driver JH. Acta Mater 2003;51:2989.[20] Humphreys FJ, Bate PS. Acta Mater 2007;55:5630.

http://tel.archives-ouvertes.fr/tel-00414120/en/http://tel.archives-ouvertes.fr/tel-00414120/en/http://orilib.sourceforge.net

Microtexture tracking in hot-deformed polycrystalline aluminium: Experimental resultsIntroductionExperimentalValidation of the methodDeformation modeAspect of the internal surfaceInfluence on orientation measurementsInfluence on grain rotations

ResultsMicrotextures and macrotexturesAverage rotationsRotations with respect to the initial orientations ( {r}_{0}^{\varepsilon}, \hskip 0.12em {\theta}_{0}^{\varepsilon})Incremental rotations ( {r}_{i}^{\varepsilon}, \hskip 0.12em {\theta}_{i}^{\varepsilon})The relations to texture development

In-grain orientation spreadsRotation variability at constant orientationAverage rotationsIn-grain orientation spreads

DiscussionThe experimentsAverage rotationsIn-grain orientation spreadsRotation variability at constant orientation (VCO)

ConclusionsSupplementary dataAcknowledgmentsReferences

Documents

Microtexture Tracking in Hot-Deformed Polycrystalline Aluminium- Experimental Results