active slip systems evaluated by a crystal rotation axis

Active Slip Systems Evaluated by a Crystal Rotation Axis Method

in Cold-Rolled Cube-Oriented Aluminum Single Crystals

K. Kashihara1 and T. Shibayanagi2

1Wakayama National College of Technology, Gobo 644-0023, Japan2JWRI, Osaka University, Ibaraki 567-0047, Japan

Crystal orientations after cold rolling to a 50% thickness reduction were measured at mid-thickness parallel to the rolling plane for twoaluminum single crystals: one having a {100} h001i orientation and the other having an orientation deviated 5� about the rolling direction axisfrom ideal {100} h001i. The crystal rotation axis orientations calculated from electron backscatter diffraction were compared with h112i latticerotation axis orientations geometrically assigned to individual slip systems. The crystal rotation axis orientations were explained by the resultantlattice rotation axis orientation consisting of the four active slip systems having high Schmid factors. The microstructure in the single crystalhaving {100} h001iwas subdivided by primary active slip systems, whereas the microstructure in the single crystal with deviated orientation wassubdivided by secondary active slip systems, which developed band structure parallel to the rolling direction. The crystal rotation axisorientation method is useful for determination of the type and slip amplitude of active slip systems. [doi:10.2320/matertrans.L-M2009820]

(Received March 2, 2009; Accepted May 28, 2009; Published July 29, 2009)

Keywords: rolling, deformation microstructure, slip system, crystal rotation, aluminum, single crystal

1. Introduction

When a polycrystalline metal is cold rolled, the grains aredivided by slip into fragments with different crystal orien-tations. The behavior of these fragments is called grainsubdivision.1,2) Grain subdivision of a cube-oriented grain(i.e. {100} h001i oriented grain) is especially interesting,because a small fragment (or cell) becomes a nucleus for arecrystallized grain with cube orientation.3–6) To clarify themechanism, cube-oriented single crystals were examinedunder plane-strain compression7–10) and cold rolling.11–16) Itis important to clarify which slip system is activated duringdeformation. Wert and co-workers performed cold-rollingexperiments in pure aluminum single crystals with variousinitial orientations in order to determine slip systemsactivated through the specimen thickness.15,16) They analyzedactive slip systems on a plane normal to the transversedirection (TD plane) by electron backscatter diffraction(EBSD) method. In cube-oriented single crystals, crystalrotation occurred about the TD axis relative to the initialorientation, which was explained by an unbalance in twoco-directional slip pairs of four active slip systems. Bassonand Driver also mentioned crystal rotation about the TD axis,or crystal rotation about TD and rolling direction (RD) axesin cube-oriented aluminum single crystal deformed in plane-strain compression.8)

It seems that observation of deformation microstructure ismainly conducted on the TD plane, however it is well knownthat deformation inhomogeneity also occurs on a planeparallel to the rolling plane. In a previous report,17) purealuminum single crystals having cube orientation or anorientation rotated by 5� about the RD axis from cubeorientation were cold rolled to 30% to 95% thicknessreductions. The former and latter crystals were called JCand 5RD, respectively. The rolling texture at mid-thicknesswas macroscopically measured by X-ray diffraction. In cold-rolled JC crystals, the texture was rotated about the TD axiswith respect to the initial orientation, and this rotation was

maintained up to 70% thickness reduction. The mainorientation was {201} h102i. The texture weakened dramat-ically in the range from 80% to 90% thickness reduction, andfinally the texture at 95% thickness reduction was nearlyrandom. In 5RD crystals, the main component of the textureshowed continuous crystal rotation from the initial orienta-tion, i.e. {100} h001i, to {123} h634i at 95% thicknessreduction. The crystal rotation relative to the initial orienta-tion consisted of not only TD rotation but also RD and NDrotations. Experimentally, we clarified the effect of deviationin initial orientation from ideal cube orientation on thedevelopment of rolling texture, although simulations using arelaxed Taylor model showed that cube orientation rotatestowards {123} h634i during rolling, if a crystal has an initialorientation of 5� away from the ideal cube orientation.14)

In this study, using these two types of single crystals (JCand 5RD), microstructure after rolling to a 50% thicknessreduction was investigated by the crystal rotation axis (CRA)method. This method was applied to inhomogeneous defor-mation in bi-crystal deformed in tension18) and tri-crystaldeformed in compression.19) We discuss the effect ofdeviation in initial orientation from ideal cube orientationon the microscopic crystal rotation relative to the initialorientation, the type and slip amplitude of active slip systems,and the development of microstructure.

2. Experimental Procedures

2.1 Single crystal preparation and rollingTwo different types of single-crystal plates were made

from 99.99% aluminum ingots by the Bridgeman method.The JC single-crystal plate had an initial orientation veryclose to cube orientation, where the deviation from ideal was1�. The 5RD plate had an initial orientation rotated clockwiseby 5� about the RD axis from the cube orientation. A16:0� 18:0� 7:4mm3 specimen was cut from each crystalplate using an electric discharge machine. The specimenswere rolled to reduce their thickness by 50% at room

Materials Transactions, Vol. 50, No. 9 (2009) pp. 2192 to 2200#2009 The Japan Institute of Light Metals

http://dx.doi.org/10.2320/matertrans.L-M2009820

temperature. The cold-rolled specimens were ground usingemery papers to their mid-thickness parallel to the rollingplane (the ND plane). Finally, the mid-thickness plane waselectrolytically polished, and an EBSD measurement wasperformed. The measured area was 550� 250 mm2 at mid-width of specimen. The scan step was 1 mm. The EBSD datawas obtained at about 158,800 points, and was analyzed bycommercial software (OIM analysis ver.4.6) and customsoftware written by one of the authors.

2.2 Slip system and Schmid factorThe designation of slip systems in the present study

followed the notation proposed by Bishop and Hill.20)

Figure 1 shows a view of an octahedron depicting {111}slip planes, showing the relationship between samplecoordinates and crystal coordinates. There are twelve slipsystems, a1 to d3, and their h110i slip directions are indicatedby arrows on the {111} slip planes. The slip planes, slipdirections, and Schmid factors of twelve slip systems in JCand 5RD crystals are shown in Table 1. The Schmid factoris one factor representing the activity of slip system. TheSchmid factor in rolling, Sr, has often been expressed asSr ¼ St� Sc,21) where St and Sc are Schmid factors fortensile stress and compressive stress, respectively. A slipsystem with a high Schmid factor would preferentiallyoperate during rolling. In a JC crystal, a2, b2, c2, and d2 arepreferentially activated. In 5RD crystal, a2 and c2 havehigher Schmid factors than b2 and d2, and thus unbalancedoperation of slip systems may occur during rolling.

2.3 CRA orientationIn the present study, a common rotation axis between

crystal orientations before and after deformation is called acrystal rotation axis (CRA) orientation. Wert represents CRAorientation on a sample coordinate projection.16) In thepresent study, CRA orientations are represented on a crystalcoordinate projection. For example, two CRA orientations (pand q vectors) are represented on the projection in Fig. 2.[100], [010] and [001] are parallel to the x, y, and z axes,respectively, in the crystal coordinates. Since the p vector is

located in z � 0, it is colored red on the projection (p0). Onthe other hand, the q vector is colored blue on the projection(q0), since it is in z < 0. The CRA orientation was obtained ateach EBSD data point by comparing crystal orientationsbefore and after deformation. If the rotation angle at a datapoint was below 3� relative to the initial orientation, theCRA orientation was not represented on the projection.

2.4 CRA mapThe CRA map expression was first proposed by Wert in

order to spatially represent CRA orientation in an areameasured by EBSD.16) CRA orientation is represented on amap, following the color coding shown in Fig. 4(a) andFig. 6(a). For example, if an EBSD data point has crystalrotation about [100] or [�1100] with respect to the initialorientation, this point is colored red on the map. If a datapoint has rotation about [010] or [0�110], it is colored blue. Thisrepresentation offers a good understanding of the spacedistribution of CRA orientation. The data points with crystalrotation angles below 3� relative to the initial orientationare colored white, implying that this point offers no data onCRA orientation.

Fig. 1 An octahedron imaging {111} slip planes showing twelve slip

systems. h110i slip directions of slip systems are indicated as arrows.

Table 1 Slip system and Schmid factor (SF) of JC and 5RD crystal at the

initial orientation.

Slip system Slip plane Slip directionSF, JC

crystal

SF, 5RD

crystal

a1 01�11 0.41 0.40

a2 111 �1101 0.82 0.85

a3 1�110 0.41 0.44

b1 0�11�11 0.41 0.41

b2 �11�111 101 0.82 0.78

b3 �1110 0.41 0.44

c1 01�11 0.41 0.40

c2 �1111 101 0.82 0.85

c3 �11�110 0.41 0.44

d1 0�11�11 0.41 0.41

d2 1�111 �1101 0.82 0.78

d3 110 0.41 0.44

Fig. 2 Expression of CRA orientations in crystal coordinates. [100], [010],

and [001] are parallel to x, y, and z axes, respectively. Two examples, p

and q vectors, are shown. Since p and q vectors have z � 0 and z < 0,

respectively, these are colored red (p0) and blue (q0) on the projection.

Active Slip Systems Evaluated by a Crystal Rotation Axis Method in Cold-Rolled Cube-Oriented Aluminum Single Crystals 2193

2.5 LRA orientationIn FCC single crystals with high stacking fault energy,

such as aluminum, crystal rotation relative to the initialorientation mostly occurs by slip. An active slip systemoperates toward a h110i direction on a {111} plane, so thatpiled-up edge dislocations introduced by active slip systemsgeometrically bend (or rotate) the crystal lattice about theh112i axis. In this study, the geometrical bend axis is calledthe lattice rotation axis (LRA). LRA orientation r isrepresented as r ¼ b� n. Here, b and n denote slip directionvector and slip plane normal vector, respectively. In order todiscuss the relationship between CRA and LRA orientations,the four active slip systems having the highest Schmid factorswere examined.

2.6 Relationship between CRA orientation and LRAorientation

If crystal rotation with respect to initial orientation iscaused by lattice bending which results from accumulation ofdislocations on four active slip systems having the highestSchmid factors, the relationship between CRA and LRAorientations is given as

ng ¼ n1r1 þ n2r2 þ n3r3 þ n4r4 ð1Þg ¼ n01r1 þ n02r2 þ n03r3 þ n04r4 ð2Þ

where g denotes the unit vector of the CRA orientation, andr1, r2, r3, and r4 are unit vectors of the LRA orientations ofthe four slip systems, and n1, n2, n3, and n4 are coefficientsdepending on the slip amplitude introduced by the corre-sponding slip system. Since the coefficient n, which dependson the amplitude of the crystal rotations, is undetermined, thecoefficients of n01, n

02, n

03, and n04 do not yield quantitative

values for slip operation. In this study, only relative slipamplitudes of the active slip systems (n01, n

02, n

03, and n04)

were evaluated by comparing with g being the unit vector ofCRA orientation.

3. Experimental Results

3.1 MicrostructureFigure 3 shows IQ (image quality) maps of 5RD and JC

crystals, using the IQ function included in the OIM analysissoftware. The image indicates the quality of the Kikuchipattern measured at each EBSD data point. The better thepattern quality, the lighter the color painted on the IQ map. Incontrast, when a lower pattern quality is obtained, a darkercolor mapped. Therefore, an IQ image can indirectly revealdislocation density, since dislocation changes the patternquality. As shown in Fig. 3, a band structure developed in the5RD crystal. Bands with high and low dislocation densitiesparallel to RD were alternately formed. This structure wouldcorrespond to the macroscopic band structure observed on aspecimen surface of cube-oriented aluminum single crystaldeformed in plane-strain compression.8) In JC crystal, noband structure was apparently observed, and no higher dis-location density area was distinguished at least on this scale.

3.2 Relationship between active slip system and CRAorientation in 5RD crystal

A color coded projection and CRA map for 5RD crystal

are shown in Fig. 4(a) and (b), respectively. CRA orienta-tions were colored according to the color-coding system.The pattern of the CRA map corresponded well with that ofthe IQ map. This implies that the type and slip amplitudeof active slip systems in the high dislocation density bandwere different from those in the low dislocation densityband. Figures 4(c) and (d) show CRA orientations havingz � 0 and z < 0, respectively. Since 5RD crystal had a largespread of CRA orientation, the CRA orientations wereclassified into three groups. The first group consisted oforientations having x � 0, y < 0, and z < 0, which arerepresented on the CRA map in Fig. 4(e). This colored areawas called area A. The second group contained CRAorientations having x � 0, y � 0, and z � 0. These areshown in Fig. 4(f), and the colored area on the CRA mapwas called area B. Figure 4(g) indicates area C in whichCRA orientations had x � 0, y < 0, and z � 0. Area C waslocated between areas A and B. It was found from Figs. 4(e),(f), and (g) that areas A and B were matrix bands, whichhad different characteristic slip operations, and that area Cwas the transition band between them. The crystal rotationangles and axes relative to the initial orientation were19.4�[15 �22�66 �44], 11.6�[18 16 13], and 10.4�[26 �99 2] in areasA, B, and C, respectively.

The Schmid factors were calculated, based on the averagecrystal orientations in bands at 50% thickness reduction, (7 624) [30 1 �99] in area A, (�11 2 9) [23 �22 3] in area B and(�11 �22�77 7) [20 �11 �11] in area C. Under a compressive stress alongND and tension along RD, if the slip direction of a slip systemin compression is opposite to the slip direction in tension, thisslip system becomes geometrically difficult to operate (nooperation). Therefore, Schmid factors were calculated for slipsystems operating to the same slip direction under bothcompression and tension, and LRA orientation was deter-mined from the slip direction. LRA orientations and Schmidfactors in areas A, B, and C are listed in Table 2,

Fig. 3 Image quality (IQ) maps of (a) 5RD crystal and (b) JC crystal. IQ

image is a function of the commercial software package OIM analysis.

2194 K. Kashihara and T. Shibayanagi

respectively. In this study, the four slip systems with thehighest Schmid factors, in order, were called ‘‘active slipsystems’’. In area A, the active slip systems were a2, c2, c3,and d2, while the active slip systems in areas B and C werea2, b2, c2, and d2.

Figure 5 shows the indices of the major CRA orientationsplotted on the CRA orientation projections (Fig. 4(c) and(d)). The relationship between active slip systems and CRAorientations was examined. In area A, as shown in Fig. 5(a),the CRA orientations were mainly distributed among [2�44�11]-[4�44�11]-[6�44�11]-[5�220]-[1�110]-[1�220]. CRA orientations of [2�44�11],[4�44�11], and [6�44�11] and the relative slip amplitudes of active slipsystems (corresponding to coefficients n01, n

02, n

03, and n04 in

equation (2)) are listed in Table 3. CRA orientations of[2�44�11], [4�44�11], and [6�44�11] were called group I. As shown inTable 2, the LRA orientations a2, c2, and d2 were [1�221],[12�11], and [�11�22�11], respectively. If the ratio of the relative slipamplitudes of active slip systems is a2 : c2 : d2 ¼ 4 : 3 : 3,

then the resultant LRA orientation becomes 4½1�221� þ3½12�11� þ 3½�11�22�11� ¼ ½4�88�22� ¼ ½2�44�11�. Therefore, the CRA ori-entation of [2�44�11] observed in area A was satisfied by theLRA orientations a2, c2, and d2 with different slip ampli-

Fig. 4 The results of CRA analysis performed for 5RD crystal, (a) color coded projection, (b) CRA map, (c) CRA orientations having

z � 0, (d) CRA orientations having z < 0, (e) CRAmap showing CRA orientations having x � 0, y < 0, and z < 0, (f) CRAmap showing

CRA orientations having x � 0, y � 0, and z � 0, and (g) CRAmap showing CRA orientations having x � 0, y < 0, and z � 0. The areas

observed in (e), (f), and (g) are called areas A, B, and C, respectively.

Fig. 5 Crystal orientation indices of major CRA orientations plotted on

CRA orientation projections shown in Fig. 4(c) and (d).

Table 2 Lattice rotation axis (LRA) and Schmid factor (SF) of areas A, B

and C in 5RD crystal at 50% thickness reduction.

Area A Area B Area C

Slip

systemLRA SF LRA SF LRA SF

a1 2�11�11 0.49 no operation no operation

a2 1�221 0.76 1�221 0.86 1�221 0.88

a3 �11�112 0.28 �11�112 0.58 �11�112 0.54

b1 no operation �221�11 0.43 no operation

b2 �1121 0.56 �1121 0.67 �1121 0.66

b3 112 0.49 no operation �11�11�22 0.46

c1 no operation 211 0.45 211 0.38

c2 12�11 0.81 12�11 0.90 12�11 0.90

c3 �111�22 0.69 �111�22 0.45 �111�22 0.51

d1 �22�111 0.53 no operation �22�111 0.36

d2 �11�22�11 0.61 �11�22�11 0.71 �11�22�11 0.71

d3 no operation no operation �1112 0.48


tudes. In other words, crystal rotation about [2�44�11] relative tothe initial orientation occurs by unbalanced operation of a2,c2, and d2. Next, the combination of active slip systems isdiscussed in order to fit the resultant LRA orientation to theCRA orientation of [4�44�11]. If the ratio of the relative slipamplitudes of active slip systems is a2 : c2 : d2 ¼ 6 : 5 : 3,the resultant LRA orientation becomes ½4�44�11�. Furthermore,to obtain the CRA orientation of [6�44�11], the ratio of therelative slip amplitudes has to be a2 : c2 : d2 ¼ 8 : 7 : 3.Stronger operation of the a2 and c2 slip systems was requiredfor the CRA orientation to be [6�44�11]. Thus, crystal rotation inarea A (or group I) was caused by the unbalanced operationof a2, c2, and d2.

In Fig. 5(b), the CRA orientations in area C were classifiedinto two groups: [1�220]-[1�110]-[3�220]-[8�110] and [2�111]-[8�111].The former and latter groups were called groups II and III,respectively. As shown in Table 3, the CRA orientations ofgroup II were obtained by a combination of the three activeslip systems, while four active slip systems were necessaryto find the CRA orientations of group III. In group III, if theratio of the relative slip amplitudes was a2 : b2 : c2 : d2 ¼7 : 2 : 4 : 1, the resultant LRA orientation corresponds withthe CRA orientation of [2�111]. The crystal rotation in area Coccurs by the unbalanced operation of four active slipsystems.

Area B showed a large spread of CRA orientations, whichwere classified as group IV for [101]-[201]-[801], group Vfor [122]-[211]-[811], and group VI for [251]-[661]-[1041].In area B, CRA orientations were obtained by a combinationof the three active slip systems. The CRA orientation of [101]

in group IV corresponds with the resultant LRA orientationof a2, b2, and c2, if the ratio of the relative slip amplitudeswas a2 : b2 : c2 ¼ 2 : 1 : 3. CRA orientations of [122] ingroup V and [251] in group VI were obtained from a2 : b2 :

c2 ¼ 3 : 3 : 2 and a2 : b2 : c2 ¼ 6 : 7 : 9, respectively. Thus,although the CRA orientations in area B were widelydistributed, the slip operation in area B can be explained byunbalanced operation of the three active slip systems a2, b2,and c2. Stronger operation of a2 and c2 was necessary toobtain the CRA orientation near [100].

From the relationship between active slip system and CRAorientation in area A, B and C, it was found that the type andslip amplitude of active slip systems change continuouslyacross the three bands.

3.3 Relationship between active slip system and CRAorientation in JC crystal

Color coded projection and a CRA map of JC crystal areshown in Fig. 6(a) and (b), respectively. The CRA maprevealed an irregular pattern. Areas which had crystalrotation angles below 3� relative to the initial orientationwere observed. CRA orientations having z � 0 and z < 0

were represented in Figs. 6(c) and (d), respectively. Com-pared with the CRA orientations in 5RD crystal shown inFig. 4(c) and (d), JC crystal had a smaller spread of CRAorientations, which were mainly distributed around [010] and[0�110]. We chose the CRA orientation having crystal rotationcomponent about [010] and [0�110] as representative ones to beanalyzed. The data points of CRA orientations with x � 0,y < 0, and z < 0 were colored on the CRA map in Fig. 6(e),and denoted area A. Points with CRA orientations havingx < 0, y < 0, z < 0 and having x � 0, y � 0, z � 0 wererepresented in Fig. 6(f) and (g), respectively. The former andlatter areas were called areas B and C, respectively. Theborder between areas A and B was uncertain, and it appearedthat area A contained area B. Area C was completelyseparated from areas A and B. The misorientation betweenareas A and B was 3�, and between areas A and C was 13�.The crystal rotation angles and axes relative to the initialorientation in areas A, B, and C were 5.8�[2 �11�22 �33],7.2�[�22 �11�33 �22], and 5.3�[4 29 2], respectively.

The Schmid factors of slip systems common to areas A andB at 50% thickness reduction are given in Table 4, since theircrystal orientations were close. Schmid factors in area C arealso shown in Table 4. LRA orientations of slip systems arelisted in the table. Based on Schmid factor, in all areas, slipsystems of a2, b2, c2, and d2 were estimated to be active slipsystems.

Figure 7 shows indices of major CRA orientations plottedon the CRA orientation projections. CRA orientations inarea A were classified into two groups of [1�11�11]-[1�22�11]-[1�44�11]-[1�66�11] and [0�22�11]-[0�44�11]-[0�88�11]. The former and latter groupswere called group I and II, respectively. CRA orientationsand relative slip amplitudes of active slip systems are listedin Table 5. A combination of active slip systems was used tofit the resultant LRA orientation to the CRA orientation of[1�11�11] in group I. If the ratio of the relative slip amplitudesof active slip systems was a2 : c2 : d2 ¼ 3 : 4 : 3, then theresultant LRA orientation was 3½1�221� þ 4½12�11� þ 3½�11�22�11� ¼½4�44�44� ¼ ½1�11�11�. That is, a CRA orientation of [1�11�11] was

Table 3 Relationship between CRA orientation and relative slip amplitude

of slip system in areas A, B and C of 5RD crystal. Group I belongs to

area A. Groups II and III, and Groups IV, V and VI area C and area B,

respectively. N.A. means no active slip system evaluated from Schmid

factor.

CRA Relative slip amplitude of slip system

orientation a2 b2 c2 d2 c3

Group I 2�44�11 4 N.A. 3 3 0

4�44�11 6 N.A. 5 3 0

6�44�11 8 N.A. 7 3 0

Group II 1�220 2 0 1 1 N.A.

1�110 3 0 2 1 N.A.

3�220 4 0 3 1 N.A.

8�110 17 0 16 1 N.A.

Group III 2�111 7 2 4 1 N.A.

8�111 19 2 16 1 N.A.

Group IV 101 2 1 3 0 N.A.

201 4 1 5 0 N.A.

801 16 1 17 0 N.A.

Group V 122 3 3 2 0 N.A.

211 6 3 5 0 N.A.

811 18 3 17 0 N.A.

Group VI 251 6 7 9 0 N.A.

661 7 4 9 0 N.A.

1041 11 3 12 0 N.A.


obtained from the LRA orientations of a2, c2, and d2 withdifferent slip amplitudes. In group II, a CRA orientation of[0�22�11] was obtained from the resultant LRA orientations of a2,c2, and d2, and a ratio of relative slip amplitudes ofa2 : c2 : d2 ¼ 1 : 1 : 2. Thus, in area A, crystal rotationrelative to the initial orientation occurred by unbalancedoperation of three active slip systems. It was noted thatstronger operation of a2 and d2 were necessary to obtainCRA orientations near [0�110], such as [1�66�11] and [0�88�11].

In area B, CRA orientations were distributed among [�22�44�11]-[�22�88�11], labeled group III (Fig. 7(a)). As shown in Table 5.The CRA orientations in group III corresponded with theresultant LRA orientations of four slip systems: a2, b2, d2,and c2. The unbalanced operation of four slip systems wasnecessary to obtain the crystal rotations in area B.

In area C, the CRA orientations were distributed around[281], [161], and [081] (Fig. 7(b)). This was called group IV.For example, the CRA orientation of [081] was obtained

from the resultant LRA orientation of three slip systems, witha ratio of relative slip amplitudes of a2 : b2 : c2 ¼ 1 : 5 : 4.The CRA orientations near [010] were obtained by strongeroperation of b2 and c2.

Fig. 6 The results of CRA analysis performed on JC crystal, (a) color coded projection, (b) CRA map, (c) CRA orientations having z � 0,

(d) CRA orientations having z < 0, (e) CRA map showing CRA orientations having x � 0, y < 0, and z < 0, (f) CRA map showing CRA

orientations having x < 0, y < 0, and z < 0, and (g) CRA map showing CRA orientations having x � 0, y � 0, and z � 0. The areas

observed in (e), (f), and (g) are called areas A, B, and C, respectively.

Fig. 7 Crystal orientation indices of major CRA orientations plotted on

CRA orientation projections shown in Fig. 6(c) and (d).

Table 4 Lattice rotation axis (LRA) and Schmid factor (SF) of areas A and

B, and area C in JC crystal at 50% thickness reduction.

Areas A and B Area C

Slip

systemLRA SF LRA SF

a1 2�11�11 0.49 no operation

a2 1�221 0.81 1�221 0.80

a3 no operation �11�112 0.47

b1 no operation �221�11 0.47

b2 �1121 0.79 �1121 0.81

b3 112 0.49 no operation

c1 no operation 211 0.47

c2 12�11 0.78 12�11 0.81

c3 �111�22 0.50 no operation

d1 �22�111 0.48 no operation

d2 �11�22�11 0.79 �11�22�11 0.81

d3 no operation 1�11�22 0.47


4. Discussion

4.1 Relationship between LRA orientation and CRAorientation

CRA orientations observed in JC and 5RD crystals wereexplained by resultant LRA orientations of active slipsystems. The resultant LRA orientation consisted of LRAorientations of three or four active slip systems havingdifferent slip amplitudes. The type and slip amplitude ofactive slip systems differed depending on the deformed areas,such as area A, B, or C.

Engler et al. conducted rolling experiments using two-phase Al-Cu alloy with a cube orientation.14) The crystalrotations relative to the initial orientation were comparedwith h112i lattice rotations caused by the operation of slipsystems. After cold rolling to 40% thickness reduction, adeformation zone developed around a second-phase particle,being described by a h112i rotation relative to the initialorientation, which was attributed to the operation of an activeslip system. At 60% thickness reduction, crystal rotationobserved in the deformation zone was h012i rotation withrespect to the initial orientation. This rotation was interpretedas the superposition of individual h112i rotations caused bytwo of four active slip systems. Engler et al. showed evidencethat crystal rotations about h112i and h012i axes observed indeformation zones were explained by single-slip operationand double-slip operations, respectively. However, in theirstudy only two patterns of crystal rotation were resolved. Thepresent study demonstrates that various CRA orientations canbe successfully evaluated by the combination of four slipsystems with different slip amplitudes. Further exploration ofthe type and slip amplitude of active slip systems is possibleby comparing crystal rotations relative to the initial orienta-tion with h112i axes assigned to individual active slipsystems.

4.2 Crystal rotation with respect to initial cube orienta-tion

Wert and co-workers established a crystal rotation mech-

anism in cold-rolled pure aluminum single crystals.12,13) Theyrepresented the crystal rotation axis in the sample coordinatesystem, while the present study adopted an expression of thecrystal rotation axis in the crystal coordinate system. Wertinvestigated crystal rotations in aluminum single crystalswith various initial orientations of cube, rotated-cube, andGoss.16) EBSD measurements were carried out on the TDplane after rolling to 30% and 50% thickness reductions, andthe crystal rotation axis relative to the initial orientation wascalculated. These single crystals after rolling showed crystalrotations about the TD axis relative to the initial orientations.The deformation structure in cube-oriented single crystalswas classified into two deformation areas: matrix bands andtransition bands. At 30% thickness reduction, four matrixbands and three transition bands were formed over thespecimen thickness. Slip geometry was related to macro-scopic strain imposed on single crystals. In cube-orientedsingle crystal, a slip system pair of a2 and d2, and anotherpair of b2 and c2 introduced shear strain parallel to RD andND (eRD/ND), if the two slip systems of a pair operateequivalently. Their operation gives rise to clockwise orcounter-clockwise rotation about the TD axis relative to theinitial orientation. The amplitude of crystal rotation about theTD axis observed in the crystal corresponded well with thecalculated crystal rotation resulting from unbalanced oper-ation of two slip system pairs. Although crystal rotation aboutthe TD axis was dominant overall, crystal rotation about anintermediate axis between the RD and ND axes was observedin one of the three transition bands. This implies that shearstrains parallel to RD and TD (eRD/TD), and TD and ND(eTD/ND) were imposed on the transition band. Possible CRAorientations were calculated by changing the increments ofshear strains of the four active slip systems. The CRAorientations were confined to orientations near the planecontaining TD and RD, which did not overlap the inter-mediate axis between the RD and ND axes. This implies thatunpredicted slip systems operate in the transition band togenerate shear strains of eRD/TD and eTD/ND. The reason foroperation of unpredicted slip systems is not yet clear, buttwo possibilities were mentioned. The first possibility was adeparture from ideal rolling conditions, due to eithervariations in lubrication conditions or misalignment whensmall single crystals were introduced into the roll gap. Thesecond possibility was that the crystal chose an internal slippattern of opposing shears, which led to strain incompati-bility between matrix bands. To accommodate this incom-patibility, the unpredicted slip systems operate in thetransition band.

In this study, we carried out EBSD measurement at mid-thickness parallel to the ND plane. CRA orientations in JCand 5RD crystals were explained by the resultant LRAorientation of slip systems predicted to be active. A largespread of CRA orientations were seen, particularly in 5RDcrystal, but CRA orientations in two matrix bands (areas Aand B) and one transition band (area C) corresponded wellwith the resultant LRA orientations calculated by changingthe relative slip amplitudes of three or four active slipsystems. We conclude that the development of deformationstructure at the mid-thickness is characterized by theoperation of three or four predictable slip systems.

Table 5 Relationship between CRA orientation and relative slip amplitude

of slip system in areas A, B and C of JC crystal. Groups I and II belong to

area A. Group III and Group IV area B and area C, respectively.

CRA Relative slip amplitude of slip system

orientation a2 b2 c2 d2

Group I 1�11�11 3 0 4 3

1�22�11 1 0 1 1

1�44�11 3 0 2 3

1�66�11 2 0 1 2

Group II 0�22�11 1 0 1 2

0�44�11 2 0 1 3

0�88�11 4 0 1 5

Group III �22�44�11 2 2 1 5

�22�88�11 4 2 1 7

Group IV 281 3 5 6 0

161 2 4 4 0

081 1 5 4 0


4.3 Effect of deviation in initial orientation on develop-ment of microstructure

The development of deformation structure in 5RD crystalwas different from that of JC crystal. The relationshipbetween active slip systems and deformation structure wasillustrated in Fig. 8. As shown in Fig. 8(a), 5RD crystalshowed a band structure consisting of two areas, labeledareas A and B, with low and high dislocation densities,respectively. The band structure was similar-looking tothat observed in cube-oriented aluminum single crystaldeformed in compression at " ¼ 0:62,8) although the type ofslip systems operating within each band was different fromthat observed in this study. In area A, crystal rotationoccurred by the slip operations a2, c2, and d2. Accordingto Table 3, a2 and c2 were the primary active slip systemsand d2 was a secondary active slip system. In area B, theoperation of a2, c2, and b2 gave rise to a crystal rotationrelative to the initial orientation. The primary active slipsystems were a2 and c2, and the secondary active slipsystem was b2, based on Table 3. Area C was locatedbetween the two matrix bands of areas A and B, and thefour slip systems a2, b2, c2, and d2 were active. a2 and c2were the primary active slip systems, while b2 and d2 weresecondary slip systems (Table 3). Thus in 5RD crystal, theprimary active slip systems (a2 and c2) operated throughthree bands (areas A, B, and C), and the operation of

secondary active slip systems was partially induced, such asd2 in area A and b2 in area B. At the onset of deformation,the cube-oriented single crystal experienced the operation ofprimary active slip systems a2 and c2. And then, the crystalwas subdivided by the operation of secondary active slipsystems d2 in area A and b2 in area B. Area C is atransition region between areas A and B, where secondaryactive slip systems meet, in addition to the primary activeslip systems.

As shown in Fig. 8(b), JC crystal did not develop adistinct band structure, but the type and slip amplitude ofslip systems differed depending on the deformed area. Inarea A, the primary active slip systems were a2 and d2, andthe secondary active slip system was c2. In area C, b2 andc2 were the primary active slip systems and a2 was asecondary active slip system. Area B underwent the oper-ation of four active slip systems a2, b2, c2, and d2. Area Ain JC crystal, where a2 and d2 mainly operate, was clearlyseparated from area C, where b2 and c2 mainly operate.This result corresponds with that reported by Wert.16) JCcrystal was subdivided by the two pairs of primary activeslip systems (the a2-d2 pair and the b2-c2 pair), andsecondary active slip systems of c2 in area A and a2 inarea C may have compensated for microscopic strainincompatibility.

In JC crystal, the rotation angles of areas A, B, and Crelative to the initial orientation were 5.8�, 7.2�, and 5.3�,respectively. Liu and Hansen calculated crystal rotationangles relative to the initial cube orientation in rolling,based on the concept that the crystal rotation about the TDaxis occurs by unbalanced operation between a two slipsystem pairs: a2-d2, and b2-c2.13) If the two pairs operatedequivalently, the crystal rotation relative to the initialorientation would be zero. According to their calculations,when the unbalanced operation of the two pairs is in therange from 23 to 32%, the crystal rotation angle relative tothe initial orientation will be in the range from 5� to 7�.Therefore, in JC crystal, at the onset of rolling, four activeslip systems operate simultaneously and equivalently. Atmoderate thickness reduction, the pair of active slipsystems a2 and d2 operates more strongly in area A thanthe other pair, and in area C, the pair of b2 and c2 operatesmore strongly. In 5RD crystal, however, areas A and B hadrotation angles of 19.4� and 11.6�, respectively. The formerand latter rotation angles were obtained when the unbal-anced operation of slip system pairs (a2-c2 and b2-d2) wasabout 80% and 50%, respectively. Therefore, in 5RDcrystal four active slip systems operate at the onset ofrolling, but immediately the unbalanced operation of fourslip systems occurs. a2 and c2 operate much more stronglythan other slip systems. The unbalanced slip operationstarts earlier in area A than in area B in rolling, becausethe crystal rotation angle relative to the initial orientationis larger in the former area. As shown in Fig. 3(a), thedislocation density in area A was lower than that in area B.The reason for difference in dislocation density is un-known. The development of band structures with high andlow dislocation density might be related with a differencein the start of unbalanced operation of four active slipsystems.

Fig. 8 Schematic illustrations of the development of deformation structure

in (a) 5RD crystal and (b) JC crystal. Primary and secondary active slip

systems evaluated in areas A, B, and C are indicated on octahedrons

imaging {111} planes. Fine and coarse hatching show {111} planes where

primary and secondary active slip systems operate, respectively.


5. Conclusion

(1) CRA (crystal rotation axis) orientation is explained by aresultant LRA (lattice rotation axis) orientation result-ing from four active slip systems having high Schmidfactors.

(2) 5RD crystal had an initial orientation deviating about 5�

from the RD axis of ideal cube orientation. A bandstructure develops after cold rolling to a 50% thicknessreduction. Two matrix bands and one transition bandare formed. The type and slip amplitude of active slipsystems change continuously across the three bands.

(3) In 5RD crystal, two primary active slip systems, a2 andc2, operate in two matrix bands. One secondary activeslip system, d2, is induced in one matrix band having alow dislocation density, while the other secondaryactive slip system, b2, is induced in the other matrixband having a high dislocation density. The transitionband undergoes operation of four active slip systems.5RD crystal is subdivided by secondary active slipsystems.

(4) In JC crystal having cube orientation, there is no bandstructure formed. The deformation area where theprimary active slip systems, a2 and d2, operate isseparated from the deformation area where the otherprimary active slip systems, b2 and c2, operate. Theformer deformation area activates the secondary activeslip system, c2, whereas the latter deformation areaactivates the secondary active slip system, a2. JC crystalis subdivided by primary active slip systems, althoughfour active slip systems operate equivalently at theonset of rolling.

Acknowledgements

This paper is dedicated to the memory of Dr. HirosukeInagaki who passed away in August 2008. One of the authors(KK) would like to acknowledge financial support by theLight Metal Educational Foundation Inc. and Joining andWelding Research Institute, Osaka University.

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active slip systems evaluated by a crystal rotation axis

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