Effect of processing route on microstructure and texture development in equal channel angular extrusion of interstitial-free steel

Acta Materialia 54 (2006) 1087–1100 www.actamat-journals.com

Effect of processing route on microstructure and texture development in equal channel angular extrusion of interstitial-free steel Saiyi Li a,*, Azdiar A. Gazder b, Irene J. Beyerlein c, Elena V. Pereloma b, Christopher H.J. Davies b a

Materials Science and Technology Division, Los Alamos National Laboratory, Mail Stop H805, Los Alamos, NM 87545, USA b Department of Materials Engineering, Monash University, Clayton, Vic. 3800, Australia c Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Received 18 April 2005; received in revised form 4 September 2005; accepted 21 October 2005 Available online 20 December 2005

Abstract Microstructure and texture evolution in equal channel angular extrusion (ECAE) of interstitial-free (IF) steel is investigated for up to 4 passes via routes A, BA, BC and C. Observations by transmission electron microscopy reveal that the efficacy of grain refinement depends on both processing route and pass number. The preferred route is found to be route C after 2 passes but route BC after 4 passes. Quantitative analysis of the experimental textures shows the development of {1 1 0}Æu v wæh and {h k l}Æ1 1 1æh partial fiber textures in all routes, but the orientation distribution along these fibers is more uniform in routes A and C than BA and BC. The experimental textures are well predicted using a visco-plastic self-consistent model based on the simple shear assumption of ECAE deformation. Finite element (FE) analysis and further texture simulations using the FE-predicted deformation history suggest that imperfect strain reversal is a main factor for the prevalence of shear-type textures and elongated lamellar substructure observed after the even-numbered passes of route C. Published by Elsevier Ltd on behalf of Acta Materialia Inc. Keywords: Microstructure; Texture; Severe plastic deformation; Strain path change; Slip mode

1. Introduction Equal channel angular extrusion (ECAE) is one of the major forming techniques to produce ultra-fine grained bulk materials [1]. It features severe plastic deformation (SPD) in each passage of extrusion and significant strain path changes (SPCs) during multiple passes. Among the several variables in ECAE processing, the rotation of billet about its longitudinal axis between successive passes (ÔrouteÕ) and the die angle control the SPCs [2]. The influence of such SPCs on microstructural development and ultimately, the efficiency of grain refinement, are of great concern in ECAE; however, the concomitant texture development is also important. For instance, it is known from large strain cold rolling [3] that an increase in high angle *

Corresponding author. Tel.: +1 505 6656054; fax: +1 505 6652676. E-mail address: [email protected] (S. Li).

1359-6454/$30.00 Published by Elsevier Ltd on behalf of Acta Materialia Inc. doi:10.1016/j.actamat.2005.10.042

boundaries resulting from grain subdivision is usually accompanied by strong texture evolution. Considering the SPD associated with ECAE, we can also expect a strong coupling between microstructure and texture evolution. Therefore, simultaneous investigation of microstructure and texture development is important in developing optimal ECAE processing routes. In this regard, much work has been dedicated to face-centered cubic (fcc) materials, and comparatively less work to body-centered cubic (bcc) materials [4]. For bcc metals, a number of studies have reported on the microstructural development. ECAE processing has been able to produce equiaxed or nearly equiaxed grains with an average grain size down to
0.2 lm in pure Fe, low-carbon steels and interstitial-free (IF) steels [5–12]. On the effects of processing route on the microstructural development and subsequent mechanical properties, Fukuda et al. [5] found that route BC is preferable to routes

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A and C in producing a more homogeneous and equiaxed microstructure and thus improved mechanical properties in low-carbon steel. This conclusion was supported by comparing microstructural observations and mechanical data between a 0.08% C low-carbon steel (processed at 298 K via route BC) with those in a 0.0015% C ultralow-carbon steel (processed at 298 K via route A) [6], and a 0.15% C low-carbon steel (processed at 623 K via route C) [7]. However, such comparisons across different studies neglect the possible interference caused by differences in pre-processing, ECAE temperatures and carbon contents in these materials. A more comprehensive study on the effect of processing route would require deforming the same material under similar conditions (such as die geometry, temperature and friction). A recent study in this category was conducted by Kim et al. [12] on an IF-steel, who drew an alternative conclusion suggesting that grain refinement is more rapid in route A than route C. Compared to microstructural studies, even fewer reports have investigated texture evolution in bcc materials [4,13– 16]. Noticeably, Gibbs et al. [13] measured textures in pure Fe after 1, 2 (routes A and BA or BC) and 4 (route C) passes and discussed the effects of processing route on texture development. The results obtained in Ref. [13] were compared to simulations by Agnew [14] and Baik et al. [15] after 1 and 2 passes of route A, but not the other routes. Recently, Li and Beyerlein [16] performed a systematic modeling investigation on the effects of processing route and initial texture on the ECAE texture evolution in bcc materials for the four standard ECAE routes. The simulated textures showed good agreement with the route A experimental data in Ref. [13]. However, simulations of the 2-pass route BA or BC sample in Ref. [16] showed no indication of a fiber texture found in the measurements by Gibbs et al. The present experimental and theoretical investigation was undertaken to concurrently study the microstructural and texture evolution in the four standard ECAE routes for a common bcc metal, IF-steel. Transmission electron microscopy (TEM) observations, texture analysis, polycrystal modeling and finite element (FE) simulations were used to achieve three main objectives: (i) to systematically examine the effect of processing route on microstructural development and efficiency in grain refinement, (ii) to quantify the textures after different routes and pass number and (iii) to evaluate the effects of microstructure and theoretical deformation history on texture evolution.

temperature for 1–4 passes (N) via routes A, BA, BC and C, respectively. The 90
-rotation about the billet long axis in route BC (or prior to the even-numbered passes of route BA) was clockwise when the billet was re-inserted in the inlet channel. As illustrated in Fig. 1(a), the die-set had sharp inner and outer corners with U = 90
. The billet was pressed using a main ram at 5 mm/s, with an almost constant back pressure of 60 MPa applied at the leading end using a back ram. Both the sample and tooling were lubricated using MoS2 mineral oil to reduce friction. Due to the strong resistance the billet received at the die corner, an L-shaped chip was sheared off from its leading end at the beginning of each pass. This chip remained in the outer corner until the end of each pass. To illustrate this, Fig. 1(b) shows a photograph of an as-processed billet together with its Lshaped chip. Because the surface of the L-shaped chip that is in contact with the billet forms an arc, the billet was subsequently deformed as if the die had an ÔeffectiveÕ non-zero rounded outer corner. The corresponding outer corner angle (W) was estimated to be 26
(Fig. 1(b)). For the first pass, the billet was inserted into the inlet channel with the rolling, transverse and normal directions of the plate parallel to the x, y and z axes of the ECAE reference system, which lie parallel to the ED (exit direction), ND (normal direction) and TD (transverse direction) of the die channel, respectively. Fig. 1(a) also indicates a local reference system x 0 y 0 z, which shares a common z-axis as the xyz system but is counter clockwise (CCW) rotated about the z-axis by h = U/2 = 45
. According to the analysis first carried out by Segal [1], under ideal conditions, the billet is

2. Material and ECAE processing A commercially available rolled IF-steel plate (Fe–0.003C– 0.15Mn–0.03Al–0.08Ti–0.007Si–0.01P–0.005S–0.001N wt.%) was machined into 20 · 20 · 80 mm3 billets with the longitudinal direction parallel to the transverse direction of the plate. The billets were annealed at 1023 K for 1 h in an inert atmosphere, resulting in equiaxed grains of approximately 140 ± 10 lm, and then processed by ECAE at room

Fig. 1. (a) Schematic of the ECAE tooling; (b) as-processed 1-pass billet and the L-shaped chip after opening the die.

S. Li et al. / Acta Materialia 54 (2006) 1087–1100

deformed by simple shear on the intersection plane (y 0 -plane) of the die. 3. Microstructure and texture evolution: experimental procedure and results 3.1. Microstructures It is known that heterogeneity in deformation exists both along the length and cross-section of the billet; consequently, differences in microstructure and texture development may arise in each pass, depending on the processing route and the position from the billet where subsequent analysis was undertaken [17]. To allow for a reasonable comparison of different samples, TEM foils were prepared using slices cut from the center of the cross-section (normal to the ED) in the middle portion of each billet. They were electro-polished at 30
C in a solution of 5% perchloric acid and 95% methanol, and at 300 mA and 50 V. TEM was conducted on a Phillips CM-20 operating at 200 kV. Bright field micrographs and top and bottom inset selected area diffraction (SAD) patterns with an aperture diameter of 5.8 and 1.1 lm, respectively, were taken along the Æ1 1 1æ zone axis. The former SAD patterns were representative of the entire micrograph while the latter were taken from the micrograph center. Representative TEM microstructures for the samples after 1 and 2 passes via routes A, BA or BC and C, and 4 passes via routes A, BA, BC and C are shown in Figs. 2 and 3, respectively. The TEM observation of the 1-pass sample (Fig. 2(a)) show the formation of an ultra-fine microstructure com-

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prising high dislocation density, extended and parallel, lamellar boundaries (LBs). The LB substructure typically consisted of long thin plate-like features that were confined to single grains. Detailed examination revealed that the interior of the lamellae consisted of dislocation cells (DCs), which were arranged in one to four elements, normal or inclined to the LBs. While the cell walls were diffused and consisted of tangled arrays of dislocations, the dislocation density within the cell interiors was low. Concentrated diffraction spots in the SAD pattern indicate that the LBs were low angle boundaries (<15
). After 2 passes (Fig. 2(b)–(d)), strongly elongated lamellae were typically observed for all routes. In some local areas of the routes A and C samples (Fig. 2(b) and (d)), nearly equiaxed substructures were also present. In such areas where LBs were no longer clearly distinguishable, the deformation substructure is hereafter referred to as a subgrain. Compared to the 1-pass sample, the SAD patterns of the second pass samples suggest a slight increase in misorientation angles; however, most of the LBs still exhibited low-angled character. In all 4-pass samples (Fig. 3), strongly elongated lamellae co-exist with nearly equiaxed subgrains having more clearly defined boundaries. Concurrent with previous reports [5,8], the SAD patterns (Fig. 3, top insets) confirm the trend of increasing subgrain/grain misorientation with increasing strain. The misorientation between substructures was slightly higher for routes BA and BC than routes A and C. However, in contrast to Ref. [8], our 4-pass route C samples still retain lamellar substructures. In order to identify the family of operative slip systems, grains with the Æ1 1 1æ zone axis parallel to the beam were

Fig. 2. Selected bright field TEM micrographs and SAD patterns measured from the ED-plane of ECAE processed IF-steel samples: (a) 1 pass; 2 passes via routes (b) A, (c) BA or BC and (d) C.

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Fig. 3. Selected bright field TEM micrographs and SAD patterns measured from the ED-plane of the IF-steel billets after 4 passes of ECAE via routes (a) A, (b) BA, (c) BC and (d) C.

0.4

BA

Average LB spacing and DC width (µm)

analyzed, in a way similar to the method adopted by Shin et al. [8]. In the bright field images, the direction of an LB is considered to be parallel to the intersecting line between the slip plane and the viewing plane normal to the selected zone axis (in this case, Æ1 1 1æ). Thus, the direction of the LB corresponds to that of the projection of the slip plane on the viewing plane. Under such conditions, the projections of both {1 1 0} and {1 1 2} slip planes can contain the Æ1 1 0æ LB direction. To resolve such ambiguities, further tilting was allowed to distinguish more precisely between the traces of the {1 1 0} and {1 1 2} planes during TEM analysis. Inspection of the SAD patterns (Figs. 2 and 3, bottom insets) shows that the LBs remain primarily parallel to Æ1 1 0æ directions. In some localized areas, LBs parallel to Æ1 1 2æ directions were also observed (Fig. 3(c)). This indicates that the deformation under the present conditions is accommodated through the activation of {1 1 0}Æ1 1 1æ and {1 1 2}Æ1 1 1æ slip systems which are typical of bcc materials and is in agreement with those reported previously for ECAE of low-carbon steel [5,8]. Fig. 4 shows the average spacing between LBs and the average DC widths in the samples processed via the four routes. The measurements were conducted manually using an eyepiece with a scale bar on the lens. To obtain reasonable statistics, three to five micrographs were used (a single micrograph provides approximately 30 measurements each for the LB spacing and DC width). From the LB spacing, the formation of ultra-fine substructures to the size of
0.35–0.4 lm is evident after 1 pass. The lamellae/subgrains were further refined during the second pass, more in route C than route A followed by route BA or BC. After

0.3

C A LB spacing

BC

0.2 DC width

BA C

0.1

A BC

0 1

2

3

4

Number of passes Fig. 4. Average lamellar boundary (LB) spacing and dislocation cell (DC) width as a function of pass number in the four ECAE routes.

4 passes, a similar level of lamellae/subgrain refinement (
0.3 lm) was achieved for routes A, BA and C, while a relatively finer substructure was attained for route BC (
0.23 lm). Concurrently, the variation of the average DC width with increasing N indicates considerable struc-

S. Li et al. / Acta Materialia 54 (2006) 1087–1100

tural changes within the lamellae. After 3 and 4 passes, the DC widths were relatively smaller in route BC and larger in route BA, while routes A and C returned values in-between these extremes. Considering the broad statistical spread of data points (as indicated by the error bars) due to microstructural inhomogeneity at the TEM length scale, it can be concluded that the present results signify a mild dependency of grain refinement efficiency on the processing route.

Levels:

1.0

1.3

1091 1.6

2.0

2.5

3.2

4.0

5.0

6.4

8.0

N=1

N=2

3.2. Textures N=3

Textures of the initial and ECAE processed billets were measured by X-ray diffraction on a GBC Mini-Materials Analyzer texture goniometer equipped with a Cu Ka anode. Samples for texture measurements, typically
20 mm · 20 mm in size, were sliced from the middle portion of the billets normal to the ED. From experimental (1 1 0), (2 0 0) and (2 1 1) incomplete pole figures, orientation distribution functions (ODFs) f(g), with g = (u1, /, u2) in BungeÕs notation, were calculated using the spherical harmonics method [18]. To indicate the texture strength, the so-called texture index (T) was calculated from the integral of ODF [18] using the MTM-FHM software [19]. The initial texture measured for the IF-steel, as shown in Fig. 5, is very weak (with T = 1.2) and featured by {0 0 1}Æ1 1 0æ and {1 1 0}Æ0 0 1æ components (in the rolling convention). The experimental textures after 1–4 passes via the four routes are shown in Fig. 6 using the recalculated (1 1 0) pole figures projected onto the TD-plane. The corresponding texture indices are given in Table 1. Fig. 6 shows that, as expected from the deformation history, monoclinic sample symmetry with the TD as a dyad axis is evident in the textures developed in routes A and C, but no obvious symmetry can be seen for routes BA and BC. The lower symmetry in the latter cases can be attributed to the 90
rotations about the billet longitudinal axis, which result in the texture developed during a previous pass not aligned at a symmetric position with respect to the deformation in the next pass. To quantitatively describe these ECAE textures, ideal orientations after a single pass of ECAE with U = 90
die are used. A list of Euler angles of these ideal orientations

TD

RD

Fig. 5. (1 1 0) pole figure of the experimental initial texture of the IF-steel. TD and RD indicate the transverse and rolling directions of the billet in the rolling convention, which are parallel to the ECAE ND and ED respectively when the billet is inserted in the inlet channel. Contours: 1/1.3/1.6/2.

N=4

ND ED

a

b

c

d

Fig. 6. (1 1 0) pole figures of experimental textures in the IF-steel after 1 to 4 passes (N) of ECAE via routes (a) A, (b) BA, (c) BC and (d) C.

is given in Table 2. Their locations on the (1 1 0) pole figure are illustrated in Fig. 7. As demonstrated by Li et al. [20], these orientations can be derived from those in simple shear deformation by a TD-rotation of h. For bcc metals [16,20], they are distributed along fibers that can be designated as {1 1 0}Æu v wæh and {h k l}Æ1 1 1æh (abbreviated to {1 1 0}h and Æ1 1 1æh, respectively), while the subscript h indicates the TD-rotation. Note that, in the context of ECAE textures, the Miller index {h k l}Æu v wæ denotes an orientation that has an {h k l} plane parallel to the ND-plane and an Æu v wæ direction parallel to the ED. Accordingly, an orientation along the {1 1 0}h fiber has a {1 1 0}-plane CCW-rotated about the TD from the ND-plane by h, whereas an orientation along the Æ1 1 1æh fiber has a Æ1 1 1æ-direction CCW-rotated about the TD from the ED by h. The formation of these orientation fibers reflects the tendency of the crystallographic slip planes and directions to rotate to the macroscopic shear plane (i.e., y 0 -plane in Fig. 1(a)) and shear direction (i.e., x 0 in Fig. 1(a)), respectively. Fig. 8 presents the ODFs of some representative textures. As shown in Fig. 8(a), the 1-pass texture is characterized by orientations along the b1 (D2h–Eh–D1h), b2 (Fh–Jh–Eh–D2h)
h –J
h –F h Þ fibers, indicated by solid lines across and b3 ðD1h –E the u2 sections in the figure. The b1 fiber only contains orientations belonging to the Æ1 1 1æh fiber, whereas the b2 and b3 fibers consist of both the {1 1 0}h and Æ1 1 1æh fibers. The primary components in this texture are near Jh and J
h . In route A (Fig. 6(a)), the texture changes gradually with N in terms of orientation characteristics and texture

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Table 1 d Texture indices (T) of the experimental or simulated textures and normalized texture indices of DODF ðT^ Þ for the simulated textures after 1 to 4 passes of ECAE via four processing routes d T^

T N=1

N=2

N=3

N=4

N=1

N=2

N=3

N=4

Route A Experiment VPSC {1 1 0} VPSC {1 1 0} + {1 1 2} VPSC {1 1 2} Taylor {1 1 0} + {1 1 2}

1.4 1.6 1.7 1.7 5.1

1.5 2.3 2.2 2.2 8.3

1.9 2.4 2.3 2.1 10.9

1.8 2.5 2.4 2.2 14.5

– 0.33 0.31 0.34 2.42

– 0.32 0.29 0.36 3.60

– 0.18 0.19 0.21 4.02

–

Route BA Experiment VPSC {1 1 0} VPSC {1 1 0} + {1 1 2} VPSC {1 1 2} Taylor {1 1 0} + {1 1 2}

1.4 1.6 1.7 1.7 5.1

1.7 1.9 2.0 2.1 11.8

1.6 2.5 2.4 2.5 28.3

1.5 2.7 2.6 2.6 45.7

– 0.33 0.31 0.34 2.75

– 0.42 0.43 0.49 6.11

– 0.77 0.74 0.80 16.79

–

Route BC Experiment VPSC {1 1 0} VPSC {1 1 0} + {1 1 2} VPSC {1 1 2} Taylor {1 1 0} + {1 1 2}

1.4 1.6 1.7 1.7 5.1

1.7 1.9 2.0 2.1 11.8

2.6 2.1 2.1 2.4 12.0

1.6 2.0 2.2 2.4 10.5

– 0.33 0.31 0.34 2.75

– 0.42 0.43 0.49 5.57

– 0.27 0.33 0.39 4.62

–

Route C Experiment VPSC {1 1 0} VPSC {1 1 0} + {1 1 2} VPSC {1 1 2} Taylor {1 1 0} + {1 1 2}

1.4 1.6 1.7 1.7 5.1

1.4 1.2 1.2 1.2 1.2

1.4 1.6 1.6 1.7 5.0

1.4 1.2 1.2 1.2 1.4

– 0.33 0.31 0.34 2.75

– 0.37 0.37 0.38 0.44

– 0.29 0.28 0.33 2.27

–

0.66 0.62 0.58 6.67

0.61 0.57 0.61 27.15

0.30 0.36 0.51 5.63

0.34 0.36 0.37 0.35

Table 2 Ideal orientations and fibers in a single pass of ECAE deformation (U = 90
) of bcc materials (modified from [16]) Notation

D1h D2h Eh
h E Jh
Jh Fh a b

Euler angles (
)a

Miller indicesb

Equivalent representation with TD-rotation by h

Fibers it belongs to

ð
1
1 2Þ½1 1 1h

Æ1 1 1æh

½
1 1 0

ð1 1
2Þ½1 1 1h

Æ1 1 1æh

½
1 1 2 ½
1 1 2 ½
1 1 1 ½
1 1 1 ½
1 1 0

ð1 1 0Þ½1
1 1h ð1

1 0Þ½
1 1
1h ð1 1 0Þ½1
1 2h ð
1
1 0Þ½
1 1
2h {1 1 0}Æ0 0 1æh

Æ1 1 1æh, {1 1 0}h Æ1 1 1æh, {1 1 0}h {1 1 0}h {1 1 0}h {1 1 0}h

u1

/

u2

ND

ED

99.74/279.74 9.74/189.74 170.26/350.26 80.26/260.26 135 315 15/135/255 75/195/315 45/225 135/315

45 90 45 90 35.26 35.26 54.74 54.74 45 90

0 45 0 45 45 45 45 45 0 45

[1 1 8]

½4 4
1

TD ½1
1 0

½4 4
1

[1 1 8]

[9 1 4] ½
9
1
4 [15 4 11] ½15
4 11 [3 3 4]

½
1 11 5 ½1 11
5 ½
7 26 19 ½7 26 19 ½22 3

Given in the u2 = 0
and 45
sections only. Only one variant is given; the Miller indices for the ND and ED are approximate.

strength. The textures appear to CCW-rotate about the TD with increasing N. The 4-pass texture (Fig. 8(b)) shows a
h ) than for much stronger Æ1 1 1æh fiber (from D1h to Eh =E N = 1. For route BA (Fig. 6(b)), the developed textures can be divided into two groups that are associated with the oddand even-numbered passes, respectively. While a gradual change of texture with N is evident in each group, the overall evolutionary tendency is cyclic. Inspection of the ODFs suggests that the preferred orientations in these textures are also distributed along the b1, b2 and b3 fibers. However, the orientation distributions along these fibers vary notably

with N. In particular, the {1 1 0}h partial fiber becomes less apparent than the Æ1 1 1æh fiber, and even more so at higher N. As shown in Fig. 8(c), the texture after 4 passes exhibits no obvious component near the Fh orientation along the {1 1 0}h fiber. The most complete fiber in this case is seen
h –D1h , to be the b1 (or Æ1 1 1æh) fiber passing through D2h –E
h . Interestwith the maximum orientation density near E ingly, as seen in the pole figures (Fig. 6(b)), the 3-pass texture is approximately the same as the 2 or 4-pass texture, but rotated by 180
about the TD. A previous modeling investigation [16] has indicated this relation between any two successive passes in this route, which is more apparent

S. Li et al. / Acta Materialia 54 (2006) 1087–1100

Fig. 7. (1 1 0) pole figure showing the ideal orientations and partial fibers (solid lines) in a single pass of ECAE deformation of bcc materials with a U = 90
die [16].

at high N. This relation may be attributed to the plus and minus 90
rotations about the billet longitudinal axis during each two successive passes. In route BC (Fig. 6(c)), a gradual texture development (similar to route A) is observed instead of a cyclic development (as is the case of route BA). Evidently, the textures after the even-numbered passes are very similar to those in route BA, though the route BC textures develop a stronger D1h and, concurrently, the primary texture component is
h towards D1h (compare Fig. 8(c) slightly shifted from E and (d)). This rotation of texture component is more apparent at higher N. The textures for the odd-numbered passes can be related to those in route BA by a 180
-rotation about the TD.

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In route C (Fig. 6(d)), the textures do not seem to evolve as would be expected from macroscopic shear and shearreversal deformation during two successive passes associated with the 180
billet rotation. One may expect that a reverse deformation would recover the initial texture (Fig. 5) after an even-number of passes. However a qualitatively shear-type texture is observed for all passes. Inspection of ODFs indicates nearly complete {1 1 0}h and Æ1 1 1æh fiber textures for all passes (see Fig. 8(e) for N = 4), although the primary components vary with N (they are Fh and D2h for N = 2, J h =J
h and Fh for N = 3, and Fh and D1h for N = 4). As shown by the T values (Table 1), the strengths of these textures do not change with N. A similar trend was observed during the ECAE of pure copper [21]. It is also interesting to note that the 2 and 4-pass texture results are consistent with the TEM observation of a persistent elongated substructure (Figs. 2(d) and 3(d)). Both texture and microstructure observations suggest incomplete reversal deformation during the even-numbered passes. 4. Modeling of texture evolution 4.1. Polycrystal models The texture evolution in the different routes was simulated using a visco-plastic self-consistent (VPSC) model [22] and for comparison, the Taylor model [23]. In the Taylor model, the externally imposed deformation is entirely transferred to each grain. Therefore, the change of a grain

Fig. 8. u2 = constant (0–90
in steps of 15
) ODF sections of textures in the IF-steel measured after (a) 1 pass, (b) 4 passes via route A, (c) 4 passes via route BA, (d) 4 passes via route BC and (e) 4 passes via route C. The ODFs in (a, b, e) were plotted after applying the monoclinic symmetry visible from the pole figures in Fig. 6. Contours: 1.4/2/2.8/4/5.6/8.

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orientation is solely determined by the macroscopically applied deformation and the mechanisms available to accommodate that deformation. In the VPSC model, each grain is treated as an ellipsoidal visco-plastic inclusion embedded in and interacting with an anisotropic homogeneous effective medium, which represents the ÔaverageÕ environment seen by each grain. Grains are paired at random at the beginning of a simulation and made to co-rotate to improve strain compatibility at grain boundaries using the so-called grain co-rotation scheme [22]. It has been shown in ECAE of fcc metals [21] that the VPSC modeling coupled with grain co-rotation can lead to far better texture predictions than the Taylor model. A detailed description of the approach used to model the rotations between passes associated with the various routes can be found in Ref. [24]. The present texture simulations for multiple passes were carried out continuously, starting from 3000 single orientations obtained by discretizing the ODF of the experimental initial texture using the ÔstatisticalÕ method in Ref. [19]. In accordance with the TEM observations, dislocation glide along Æ1 1 1æ on the {1 1 0} and {1 1 2} planes were considered to be the deformation mechanisms. During the texture simulations, the evolution of the discrete orientation set was recorded after each pass and then each orientation set was converted into an ODF by placing a Gaussian distribution upon each orientation with a scatter width of 5
. A normalized texture index of difference ODF (DODF) was calculated to quantify the difference of a simulated texture fs(g) with respect to an experimental texture fe(g), by R 2 d ½fs ðgÞ  fe ðgÞ dg T d T^ ¼ ¼ ; ð1Þ R 2 T ½fe ðgÞ dg where T is the texture index [18,19] calculated from the reference texture fe(g) and Td is the texture index of the DODF, i.e., fs(g)  fe(g). Td indicates the magnitude of difference between the two textures. Compared to Td, the nord malized parameter T^ has the advantage of allowing direct comparisons of the texture differences associated with different reference textures. In the following sections, we present texture simulations using two types of deformation history for the ECAE process based on: (i) the simple shear assumption and (ii) FE simulations. For either case, the deformation history was imported into the polycrystal model in an incremental form. 4.2. Simulations based on the simple shear assumption of ECAE deformation 4.2.1. The simple shear assumption According to Segal [1], the deformation imposed on the billet during each pass can be estimated to be simple shear (SS) deformation occurring at the intersectional plane of the channels. This SS deformation can be represented by the following displacement gradient tensor when it is transformed into the ECAE reference system [20]:

0 B G ¼ c@

 sin h cos h

cos2 h

 sin2 h

sin h cos h

0

0

0

1

C 0 A;

ð2Þ

0

where c is the SS strain and h = U/2 = 45
(Fig. 1(a)). This model was proposed for ideal ECAE conditions involving a non-strain-hardening material, frictionless processing conditions and a die with sharp inner and outer corners. Due to the round ÔeffectiveÕ outer corner caused by L-chip formation (see Section 2), the deformation of the billet is unlikely to be restricted only to the intersection plane as assumed in Eq. (2). Nonetheless, c = 1.78, as calculated from the formula in Ref. [25] using U = 90
and W = 26
, was used in Eq. (2) to evaluate G. Such an approach is expected to approximate the deformation at the midthickness of the ECAE samples [17,26]. To evaluate the effect of the variation of slip modes on texture development, three types of simulations were carried out using the VPSC model, engaging either the (i) {1 1 0}Æ1 1 1æ, (ii) {1 1 0} + {1 1 2}Æ1 1 1æ, or (iii) {1 1 2}Æ1 1 1æ families of slip systems. Meanwhile, Taylor simulations were carried out assuming {1 1 0} + {1 1 2}Æ1 1 1æ slip to compare with the VPSC simulations. It is noted that, given the choice of potential slip systems, their relative contributions to plastic deformation are influenced by the critical resolved shear stress (CRSS) and its evolution for each slip system. As a first attempt, the present simulations were carried out assuming identical and constant CRSS values for all slip systems. Differences among the three cases should expose the effect of slip systems on the texture evolution. 4.2.2. Comparison of simulated and experimental textures An overview of the texture predictions can be seen from d Table 1. As indicated by the T^ values, the textures simulated by the VPSC model from the three cases of slip systems achieve similar agreement with the experimental textures. The {1 1 0} + {1 1 2} case, as a compromise between the two extreme cases (i.e., only {1 1 0} slip or only {1 1 2} slip), is preferable when all routes and N are considered. Fig. 9 compares the (1 1 0) pole figures of the experimental textures after 4 passes for the different routes with those obtained from the VPSC and Taylor simulations. For all routes, the differences between the VPSC-predicted textures for the three cases of potential slip systems (Fig. 9(b)–(d)) d are small and consistent with the T^ values in Table 1. Further inspection of ODFs for all routes and passes reveals that, with the change of using slip planes from {1 1 0} to {1 1 2},1 the Æ1 1 1æh fiber strengthens (most obviously at

1

The average number of active slip systems per grain predicted in the VPSC simulations varies with the strain in each pass, the pass number and processing routes. Overall, it is smaller in the cases of only {1 1 0} slip or only {1 1 2} slip than for the case of combined {1 1 0} + {1 1 2} slip. In the latter case, the contribution of slip on {1 1 0} planes is slightly higher than that of {1 1 2} and is similar to that found in simulations initiated from a random texture in Ref. [16].

S. Li et al. / Acta Materialia 54 (2006) 1087–1100 Levels:

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Route A

Route BA

Route BC

Route C

ND ED

a

b

c

d

e

Fig. 9. (1 1 0) pole figures of textures in the IF-steel after 4 passes via routes A, BA, BC and C: (a) measured; (b–d) VPSC predictions from {1 1 0}, {1 1 0} + {1 1 2} and {1 1 2} slip, respectively; (e) Taylor predictions from {1 1 0} + {1 1 2} slip.

the D1h orientation) and the {1 1 0}h fiber weakens (occurring mainly at Fh). This change brings the predictions in better agreement with the texture measurements, which generally show relatively strong D1h component and weak Fh component (see Figs. 6 and 8). Moreover, because the D1h ðð
1
1 2Þ ½1 1 1h Þ orientation also belongs to the {1 1 2}Æu v wæh (abbreviated to {1 1 2}h) fiber, these variations in texture features along with the change of slip planes suggest that an increased amount of grains aligns with their ð
1
1 2Þ, instead of {1 1 0}, planes parallel to the simple shear plane. However, no other obvious orientation distributions can be seen at other locations (e.g. f
1
1 2gh1
1 0ih at (u1 = 45
, / = 54.74
, u2 = 45
)) of the {1 1 2}h fiber in both the simulated and experimental textures. This predilection of D1h against other orientations along the {1 1 2}h fiber might be due to the fact that D1h is also located on the preferable Æ1 1 1æh fiber. It is obvious that the Taylor model performs much worse than the VPSC model in all cases, except for the d even-numbered passes in route C (see the T^ values in Table 1), in which they perform similarly. Inspection of pole figures indicates that, in addition to the significant overestimation of texture strengths, the Taylor predictions lead to components that are not evident in the experimental textures. For example, for the case of 4-pass route A, the Taylor model (Fig. 9(e)) overestimates significantly the J h =J
h components, indicating an unrealistically high stability of these orientations. For the even-numbered passes of route C, the Taylor model leads to similar predictions as

the VPSC model. Apparently, the effects of grain shape and grain interactions on the texture evolution, which are accounted for in the VPSC model, become insignificant in the case of reverse deformation. Overall, the performance of the Taylor in these cases is very similar to that found in ECAE of copper [17,21]. Fig. 10 shows the (1 1 0) pole figures of the textures after 1 to 4 passes via the different routes simulated by the VPSC model using {1 1 0} + {1 1 2} slip systems. Good agreement with the experimental textures is evident for routes A, BA and BC (compare Fig. 10(a)–(c) with Fig. 6(a)–(c)). The simulated textures are in general stronger than their experimental equivalent (see also the T values in Table 1). For route C, as expected from the SS deformation used in the simulations, the predicted textures are similar after the first and third passes and also similar after the second and fourth passes (Fig. 10(d)). Good agreement with the experimental textures (Fig. 6(d)), in terms of both texture feature and texture strength, is evident for the simulations of the odd-numbered passes of route C. For the even-numbered passes of route C, the simulations provide a reasonable prediction of texture strengths, but are less satisfactory in reproducing the shear-type texture components. Instead, the simulated textures for the even-numbered passes are very similar to the initial texture (Fig. 5), though they are slightly rotated about the TD. The underestimation of the shear-type texture components for the even-numbered passes of route C for both polycrystal models can be partly attributed to the perfect

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strategy was not meant to simulate the chip formation, but to account for the existence of a chip at the dieÕs outer corner when the subsequent (major) part of the billet passes through the die corner. The main and back rams were modeled with analytical rigid surfaces and the billet was represented by 3596 4-node plane strain elements. The billet was assumed to have the typical elastic properties of steel. Strain hardening of the material was approximated by an analytical equation in the form of 0:29

r ¼ 465ð
e þ 0:002Þ

N=3

N=4

ND ED

a

b

c

d

Fig. 10. (1 1 0) pole figures of textures in the IF-steel after 1 to 4 passes via routes (a) A, (b) BA, (c) BC and (d) C, simulated by the VPSC model using the {1 1 0} + {1 1 2} slip systems.

shear-reversal at the polycrystal level when a uniform SS deformation is assumed, as discussed in Refs. [16,17,21]. In reality, a certain degree of heterogeneity across the billet thickness is expected in each pass and deformation characteristics can differ between passes. Therefore the billet may not deform in perfect reversal for two consecutive passes of route C, even at the billet center. The postulation of incomplete strain-reversal at the polycrystal level is consistent with the TEM observation of elongated grains (Figs. 2(d) and 3(d)). To better understand the texture or microstructure formation in such cases, it is of interest to use a more realistic description of the ECAE deformation. This reasoning is examined in the following section with the aid of FE analysis.

ð3Þ

;

where is the flow stress (in MPa) and
e denotes the equivalent plastic strain. The parameters in this equation were determined by fitting it to the experimental true stress– strain curve obtained from a uniaxial tensile test conducted on the material prior to ECAE. While the experimental curve was determined to the maximum uniform elongation (
0.33), the fitted curve (Eq. (3)) was extended to a true strain of 1.5 and thereafter, perfectly plastic was assumed. The friction condition between the tooling and the billet was modeled using the CoulombÕs friction law. To determine an appropriate friction coefficient (l), simulations were carried out using different l values from 0.05 to 0.2 in increments of 0.025. As shown in Fig. 11, the simulation with l = 0.125 provides the best agreement with the experimental load–displacement curve. It is emphasized that the initial stage in the experimental curve was associated with the formation of the L-shaped chip, which was not simulated in the FE analysis. Thus, the comparison here is only meant for the stage after the shearing-off of the L-shaped chip. As discussed in similar studies of ECAE copper [17,21], inhomogeneous deformation is one reason for the sheartype texture formation after the even-numbered passes of route C. Under the SS assumption, deformation is homogeneous; however, as our FE simulation shows, the current processing conditions lead to inhomogeneous deformation.

500

4.3. Simulations based on FE-predicted ECAE deformation Load (kN)

400

4.3.1. FE modeling Two-dimensional FE simulations of a single ECAE pass were carried out using ABAQUS [27], assuming plane strain condition. It must be recalled that although the experimental set-up consisted of sharp inner and outer die angles (Fig. 1(a)), an L-shaped chip was sheared off the leading end of the billet during each pass. Consequently the billet underwent subsequent deformation with an effective rounded outer corner defined by W = 26
(Fig. 1(b)). Thus, the FE model was set up using the real die geometry (with the exception of rounding-off the dieÕs outer corner with W = 26
) and actual values of processing variables (such as back pressure and main ram speed). This modeling

300

200

exp. µ = 0.1 µ = 0.125

100

µ = 0.15 0 0

10

20

30

40

50

60

Displacement (mm) Fig. 11. Comparison of experimental (main ram) load–displacement curve with those calculated from FE simulations using different friction coefficients.

S. Li et al. / Acta Materialia 54 (2006) 1087–1100

1097

Fig. 12. FE-predicted deformation behavior in a single pass of ECAE (l = 0.125): (a) distribution of equivalent plastic strain in the billet near the end of one pass; (b) through-thickness variation in accumulated deformation, in comparison with analytical solution from Eq. (2) and (c) distribution of equivalent plastic strain-rate (in s1) at an intermediate stage.

Fig. 12(a) shows the distribution of the von Mises equivalent plastic strain (
e) accumulated in the billet towards the end of the ECAE simulation. It indicates that the two ends of the billets undergo less plastic deformation than the middle portion of the billet. In the middle portion, about 30 mm long, the deformation is more or less uniform along the longitudinal direction. However, the variation along the billet thickness in this region is significant. To illustrate this, Fig. 12(b) presents the distributions of
e and rigid body rotation angle (x) from top (s = 0) to bottom (s = 1) along the ND and in the middle portion of the billet. The parameter s stands for the relative distance of the material point from the top surface of the billet normalized by the cross-section of the outlet channel. As shown, the distributions of
e and x are reasonably uniform in the upper region from s =
0.1 to
0.75, but vary significantly in the bottom region for s > 0.75 showing a much larger x and smaller
e than the upper region.2 The analytical values estimated from the SS model (Eq. (2)) are comparable to the FE-predictions in the middle region, but indicate less 2

The local variations near the top surface might be partly an artifact due to the limited accuracy of the FE code in handling the contact between a rigid body with a very sharp corner and a deformable material.

plastic deformation and rigid body rotation. To illustrate the region where plastic deformation occurs, Fig. 12(c) plots the distribution of equivalent plastic strain-rate
e_ in the billet around the die corner at an intermediate stage. Evidently, the distribution of
e_ in the corner region is neither uniform nor symmetrical about the intersection plane. It decreases significantly from the inner corner to the outer corner. A detailed examination of the FE data indicates that the deformation history and inhomogeneity of deformation across the billet thickness in the present IF-steel billet are similar to that of pure copper also processed by a U = 90
die but with a slightly larger outer corner angle (W = 37
) [17]. As discussed therein, the through-thickness heterogeneity can be mainly attributed to the rounded outer corner of the die and the strain hardening of the material. 4.3.2. Refined predictions of texture after two passes via route C To inspect the effect of deviations in the FE calculated ECAE deformation from the SS model on the texture predictions, the FE-obtained deformation histories per ECAE pass at three thickness positions with s = 0.1, 0.5 and 0.9 were imported into the VPSC model to simulate the texture

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evolution at these locations after 2 passes in route C.3 In these simulations, {1 1 0} + {1 1 2}Æ1 1 1æ slip systems had equal and constant CRSS values were considered. Fig. 13 shows the textures simulated at the three locations as well as the corresponding average texture calculated from them using the same weight for all positions. First of all, the predictions at the different s positions all show shear-type textures, which are distinct from that simulated from the SS deformation. Secondly, there is an obvious texture gradient across the billet thickness. The shear-type texture at s = 0.1 (Fig. 13(a)) is better developed and stronger than those at s = 0.5 and 0.9. From top to bottom or with the increase of s, the textures rotate clockwise about the TD. The texture at s = 0.5 (Fig. 13(b)) is in much better agreement with the experimental texture (Fig. 6(d), N = 2) than that simulated from the SS deformation (Fig. 10(d), N = 2). This result proves that the experimental shear-type texture is at least partly attributed to incomplete strain reversal.4 A further, albeit minor, improvement can be seen in the simulated average texture (Fig. 13(d)). A detailed comparison of the ODFs indicates that the simulated average texture still depicts overestimated components, such as
h and J h =J
h , and underestimated components, such as Fh. E It is anticipated that further improvement in the predictions by averaging textures at more positions across the billet thickness will be minor since some components in the experimental texture (such as Fh) are not apparent in any of the textures simulated at different s. In this regard, a more advanced polycrystal model that accounts for the complex microstructural development, such as the formation of lamellar structures, would be necessary. A more realistic description of the evolution of CRSS with strain based on a physically sound estimation is also needed. 5. Discussion 5.1. Effect of processing route on microstructural development The current TEM observations reveal that the process of simple shear during the first pass results in the initially equiaxed grains deforming into a lamellar substructure divided by parallel, low-angled boundaries. It is also shown that there are more equiaxed subgrains at higher N, although a significant volume fraction of elongated LB substructure remains even after 4 passes. Grain refinement is found to be the greatest during the first pass and diminishes rapidly with increasing N. The SAD patterns also indicate a concurrent increase in subgrain/grain misorientation. While most

3 In principle, a similar approach can also be applied to improve texture predictions for other routes. However, due to space restrictions and the good agreement already obtained in the other cases, the authors do not explore this further in the present paper. 4 The deformation is not a complete strain reversal even though the FEpredicted deformation histories considered for both passes are the same.

Levels:

1.0

1.3

1.6

2.0

2.5

3.2

4.0

5.0

6.4

8.0

ND ED

a

b

c

d

Fig. 13. (1 1 0) pole figures of textures in the IF-steel after 2 passes in route C simulated by the VPSC model with {1 1 0} + {1 1 2} slip using the FEpredicted deformation at (a) s = 0.1, (b) s = 0.5, (c) s = 0.9 and (d) the corresponding averaged texture.

of these observations in substructure development and grain refinement are similar to the results in the literature obtained during ECAE of other bcc materials (e.g. Refs. [5,8,9]), the present investigation is the first that has been conducted for the same material processed under the same ECAE conditions using four different processing routes. This allows for a more comprehensive assessment of the effects of processing on microstructural development. The present results show two notable differences as compared to those in the literature. Firstly, the relative efficiencies of grain refinement between the different routes are found to vary with the pass number. When all passes are considered, no single route shows greater grain refinement compared to other routes. For example, route C is the most efficient route after 2 passes, but route BC becomes most efficient after 4 passes. Similar behavior is not seen in the literature. In particular, the present observation of greater grain refinement in route C than route A after 2 passes (Fig. 4) contrasts with the observation by Kim et al. [12] for an IF-steel. Secondly, the TEM observations reveal the prevalence of strongly elongated LB substructures in the samples after even-numbered passes of route C. This is consistent with the shear-type features observed in the corresponding textures and is partly explained by the incomplete strain-reversal according to the FE analysis. However, this phenomenon is in contradiction to observations in some other studies (e.g. [7,8]) and to the common belief of the recovery of the initial grain shape in such cases based on the SS assumption of ECAE deformation in each pass [1,2]. This variation might be due to the differences in the actual billet deformation, which in turn, is dependent on the particular material and ECAE processing conditions. 5.2. Effect of processing route on texture evolution The present results indicate that textures developed in the studied routes all align closely along the {1 1 0}h and Æ1 1 1æh fibers. This tendency can be attributed to the large plastic strain imposed in each pass, which is sufficient to rotate a majority of the grains to the ideal ECAE orientations along these two fibers. The formation of these orientation fibers also affirms the tendency of the crystallographic slip plane and slip direction rotate to the macroscopic shear plane and shear direction, respectively. Meanwhile, it is also apparent that the preferred orientations along these fibers

S. Li et al. / Acta Materialia 54 (2006) 1087–1100

developed differently in the various routes, which can be mainly attributed to the different entry textures prior to a current ECAE pass caused by different billet rotations. From this point of view, there is a remarkable effect of processing route on texture evolution. The main differences in texture evolution for the four processing routes can be summarized as follows: (i) routes A and BC show a gradual texture evolution in accordance with the continuous unidirectional rotation of the shear plane in the billet, about the TD in the case of route A and the ED in the case of route BC; (ii) route A leads to stronger textures than the other routes at higher N (here N = 4); (iii) routes BA and BC result in less fiber-like textures as compared to routes A and C; (iv) there is a close relation between textures of routes BA and BC, i.e., similar textures after the same even-numbered passes and a 180
TD-rotation between textures after the same odd-numbered passes. These experimental observations are in agreement with the tendencies found in a previous modeling investigation of ECAE textures in hypothetical bcc materials up to 8 passes [16]. For a given processing route, VPSC simulations with different potential slip systems exert only a minor influence on texture formation. Our simulations indicate that the addition of {1 1 2} to {1 1 0} planes in dislocation glide tends to weaken the orientation density along the {1 1 0}h fiber (in particular the Fh component) and enhance the D1h component, which belongs to both the Æ1 1 1æh and {1 1 2}h fibers. Other than the D1h component, there are no significant orientation distributions along the {1 1 2}h fiber. This tendency is in general agreement with the relative intensities for the Fh and D1h components in the experimental textures. Therefore, the D1h orientation appears to be the most stable orientation along the {1 1 2}h fiber due to dislocation glide on {1 1 2} planes. Note that the texture measured after 2 passes in route BA or BC (Fig. 6(b) or (c), N = 2) is quite different to that reported by Gibbs et al. (Fig. 7 in Ref. [13], in the EDview). In particular, the present texture results do not show any indication of a fiber texture with Æ1 1 0æ aligned parallel to the billet longitudinal axis. Although future experiments might help clarify the discrepancy between these two sets of data, our results are corroborated by the excellent agreement with the simulated texture (see Figs. 6(b) and 10(b), N = 2). Moreover, as noted in Ref. [16], an axisymmetric fiber texture should not be expected from the deformation history in this case, i.e., intense simple shear at two intersecting planes during two successive passes. 5.3. Duality in textures between bcc and fcc metals The present experimental results and theoretical analysis both suggest that the textures developed in multi-pass ECAE of bcc metals can be reasonably characterized by orientations along the {1 1 0}h and Æ1 1 1æh fibers. These fibers were originally derived from simple shear torsion experiments, as well as from polycrystal simulations considering deformation to be accommodated by

1099

{1 1 0}Æ1 1 1æ slip [20]. Conversely, in fcc metals, the development of {1 1 1}h and Æ1 1 0æh partial fibers associated with {1 1 1}Æ1 1 0æ slip was suggested by both experiments and simulations [20,21]. This implies a well-preserved duality of ECAE textures between bcc and fcc materials, intrinsically resulting from the dual relation of slip plane and slip direction between the two types of crystal structures. Indeed, after comparing these results with experimental textures in fcc materials, we find that the duality is valid not only for 1-pass textures (as discussed in Ref. [20]), but also for multi-pass textures in different routes. For route BC, for example, the textures developed in pure copper [21] show a primary texture component between
h ðð
1 1
1Þ½
1
1 0 Þ and there is a tenA1h ðð1 1 1Þ½
1
1 2h Þ and A h
h to A with an increase dency of orientation flow from A 1h in N. In the present IF-steel, the primary texture component is located between D1h ðð
1
1 2Þ½1 1 1h Þ and
h ðð
1
1 0Þ½
1 1
1 Þ and there is a tendency of orientation flow E h
h to D1h with an increase in N (see Section 3.2). The from E
h orientations in fcc metals correspond respecA1h and A
h orientations in bcc metals, by tively to the D1h and E exchanging h k l and u v w in the Miller indices. 6. Conclusions The following conclusions can be drawn from the present study on the microstructure and texture evolution in IF-steel which underwent multi-pass ECAE via four different processing routes: 1. The TEM observations indicated only mild dependencies of grain refinement on the ECAE route up to the 4 passes studied. The relative efficiencies of grain refinement between the different routes were found to vary with the pass number: a more rapid grain refinement was found in route C after 2 passes but in route BC after 4 passes. 2. The experimental textures showed the development of {1 1 0}Æu v wæh and {h k l}Æ1 1 1æh partial fibers in all routes, but the orientation distributions along these fibers were more uniform in routes A and C than in routes BA and BC. They were well predicted by the VPSC model assuming simple shear deformation at the dieÕs intersection plane. The Taylor model showed a similar performance as the VPSC model for the even-numbered passes in route C, but was unable to provide quantitatively good texture predictions for the other routes and the oddnumbered passes in route C. 3. The VPSC predictions suggested that slip on {1 1 2} planes in addition to {1 1 0} planes led to more grains aligned with their {1 1 2} planes parallel to the dieÕs intersection plane, and consequently the weakening of the {1 1 0}Æuvwæh fiber (mainly at Fh) and the strengthening of the {hkl}Æ1 1 1æh fiber (mainly at D1h). An overall good agreement of predictions with experimental textures suggested the operation of both {1 1 0}Æ1 1 1æ and {1 1 2}Æ1 1 1æ slip systems, in agreement with the directionality of lamellae substructures observed by TEM.

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4. The FE analysis indicated noticeable deviation from simple shear and heterogeneity across the billet thickness in each pass of ECAE deformation. It implied imperfect strain-reversal in even-numbered passes of route C, which is consistent with the observation of strongly elongated lamellar substructures and supported by the improved texture predictions when the FE-predicted deformation history was used. Acknowledgements This study was supported partly by a Los Alamos Laboratory-Directed Research and Development project (No. 20030216). The authors thank the Monash University Engineering Research Committee Grant, the Monash Graduate Scheme and the Victorian Centre for Advanced Materials Manufacturing for financial support. References [1] Segal VM. Mater Sci Eng A 1995;197:157. [2] Furukawa M, Iwahashi Y, Horita Z, Nemoto M, Langdon TG. Mater Sci Eng A 1998;257:328. [3] Hughes DA, Hansen N. Acta Mater 1997;45:3871. [4] Gazder AA, Davies CHJ, Pereloma EV. In: Zhu et al., editors. Ultrafine grained materials III. Charlotte (NC): TMS; 2004. p. 321. [5] Fukuda Y, Oh-ishi K, Horita Z, Langdon TG. Acta Mater 2002;50:1359. [6] Aoki K, Kimura Y, Azushima A. In: Takaki S, Maki T, editors. Ultrafine grained steels. Tokyo: The Iron and Steel Institute of Japan; 2001. p. 266.

[7] Park KT, Kim YS, Lee JG, Shin DH. Mater Sci Eng A 2000;293:165. [8] Shin DH, Kim I, Kim J, Park KT. Acta Mater 2001;49:1285. [9] Han BQ, Lavernia EJ, Mohamed FA. Metall Mater Trans A 2004;35:1343. [10] Sus-Ryszkowska M, Wejrzanowski T, Pakiela Z, Kurzydlowski KJ. Mater Sci Eng A 2004;369:151. [11] Gazder AA, Timokhina I, Pereloma E. Mater Sci Forum 2003;426– 432:2693. [12] Kim HS, Ryu WS, Janecek M, Baik SC, Estrin Y. Adv Eng Mater 2005;7:43. [13] Gibbs MA, Hartwig KT, Cornwell LR, Goforth RE, Payzant EA. Scripta Mater 1998;39:1699. [14] Agnew SR. In: Szpunar JA, editor. Proceedings of the ICOTOM12. Ottawa: NRC Research Press; 1999. p. 575. [15] Baik SC, Estrin Y, Kim HS, Jeong HT, Hellmig RJ. Mater Sci Forum 2002;408–412:697. [16] Li S, Beyerlein IJ. Model Simul Mater Sci Eng 2005;13:509. [17] Li S, Beyerlein IJ, Necker CT, Alexander DJ, Bourke M. Acta Mater 2004;52:4859. [18] Bunge HJ. Texture analysis in materials science. London: Butterworth; 1982. [19] Van Houtte P. The ‘‘MTM-FHM’’ software system. Belgium: Katholieke Universiteit Leuven; 2000. [20] Li S, Beyerlein IJ, Bourke MAM. Mater Sci Eng A 2005;394:66. [21] Li S, Beyerlein IJ, Alexander DJ, Vogel SC. Acta Mater 2005;53:2111. [22] Tome´ CN, Lebensohn RA, Necker CT. Metall Mater Trans A 2002;33:2635. [23] Taylor GI. J Inst Metals 1938;62:307. [24] Beyerlein IJ, Lebensohn RA, Tome´ CN. Mater Sci Eng A 2003;345:122. [25] Iwahashi Y, Wang J, Horita Z, Nemoto M, Langdon TG. Scripta Mater 1996;35:143. [26] Beyerlein IJ, Li S, Necker CT, Alexander DJ, Tome´ CN. Philos Mag 2005;85:1359. [27] ABAQUS/Standard UserÕs Manual (Version 6.3), Pawtucket (RI): Hibbitt, Karlsson & Sorensen; 2002.