The evolution of cube ({001}<100>) texture in non-oriented electrical steel

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The Evolution of Cube ({001}¡100¿) Texture in Non-oriented Electrical Steel Mehdi Mehdi , Youliang He , Erik J. Hilinski , Leo A.I. Kestens , Afsaneh Edrisy PII: DOI: Reference:

S1359-6454(19)30853-5 https://doi.org/10.1016/j.actamat.2019.12.024 AM 15720

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Acta Materialia

Received date: Accepted date:

29 November 2019 12 December 2019

Please cite this article as: Mehdi Mehdi , Youliang He , Erik J. Hilinski , Leo A.I. Kestens , Afsaneh Edrisy , The Evolution of Cube ({001}¡100¿) Texture in Non-oriented Electrical Steel, Acta Materialia (2019), doi: https://doi.org/10.1016/j.actamat.2019.12.024

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The Evolution of Cube ({001}<100>) Texture in Non-oriented Electrical Steel Mehdi Mehdi1, 2, Youliang He1*, Erik J. Hilinski3, Leo A. I. Kestens4, Afsaneh Edrisy2 1

2

CanmetMATERIALS, Natural Resources Canada, Hamilton, ON, Canada L8P 0A5

Department of Mechanical, Automotive, and Materials Engineering, University of Windsor, Windsor, ON, Canada N9B 3P4 3

4

Tempel Steel Co., Chicago, IL, USA 60640-1020

EEMMeCS Department, Metals Science and Technology Group, Ghent University, Ghent B9052, Belgium

*Corresponding author: [email protected]

Abstract Due to the alignment of two easy <100> axes in the sheet plane, the cube orientation ({001}<100>) is an ideal texture for non-oriented electrical steel sheets used as core lamination for electric motors. However, this magnetically favorable texture was rarely able to be produced using conventional rolling and annealing routes in non-oriented electrical steels. In this research, inclined cold rolling  a simple rolling scheme to alter the initial texture before cold rolling  was applied to a 2.8 wt% Si non-oriented electrical steel, in order to intentionally ―create‖ a rotated Goss ({110}<110>) texture before cold rolling, which was not commonly observed in hot-rolled electrical steels. Plane-strain compression (rolling) of the rotated Goss was able to produce cube crystallites within the matrix, at the grain boundaries and within the shear bands of the deformed rotated Goss grains. The cube crystallites within the shear bands had lower stored energy than their surroundings, and served as the initial seeds for nucleation. Upon annealing,

the cube crystallites preferentially nucleated from the shear bands and competitively grew out of the surrounding substructure, forming a strong cube texture in the final sheet. The formation of the initial cube crystallites within the shear bands of the deformed microstructure was believed to be necessary for the development of a final cube texture in the annealed electrical steel sheet. Although inclined rolling may be difficult to be implemented in industrial production, its unique capability to produce uncommon initial texture before cold rolling provides an interesting technique for the study of texture involution during thermomechanical processing.

Keyword: Cube texture, non-oriented electrical steel, inclined rolling, shear bands, recrystallization, EBSD.

1. Introduction Ferromagnetic cores used in electric motors are normally made of non-oriented electrical steel (NOES) laminates containing 0 to 3.5% (wt) of silicon. Although it is called ―non-oriented‖ electrical steel, the fact that the motor core is magnetized in all the directions of the laminate plane requires that the crystals’ easy <100> axes lie in the sheet plane [1-7], i.e. a <100>//ND (normal direction, -fibre) texture is desired. The cube texture ({001}<100>), which has two easy <100> axes lying in the rolling and transverse directions, respectively, is one of such orientations, and is thus highly demanded. However, after conventional rolling and annealing, it is rarely able to develop a cube texture in the non-oriented electrical steel sheets. This is partially because all the thermomechanical processing steps utilized to produce the final thin sheets, e.g. hot rolling, cold rolling and annealing, will alter the initial crystallographic texture formed during the solidification process, and metallurgical mechanisms that govern the formation of texture during these processes tend to favor a -fibre (<111>//ND) and an -fibre (<110>//RD,

rolling direction), not the cube texture, in the final sheets [7]. On the other hand, the formation mechanisms of specific textures during thermomechanical processing are still not completely understood, especially those during recrystallization and grain growth. It is thus very difficult to control the operational parameters during material processing to obtain the desired final texture. Many studies have been conducted trying to understand the formation mechanisms of specific textures during the processing of electrical steels. An example was the Goss ({011}<100>) texture in grain-oriented electrical steels (GOES) [8-11]. It was accepted that the formation of shear bands in the deformed matrix played an important role in the nucleation and growth of the Goss grains during recrystallization. Dillamore et al. [12] attributed the formation of shear bands to the geometric softening of grains with high Taylor factors. It was believed that these grains had high resistance to deformation, and were more susceptible to plastic instability, which resulted in geometric softening through the formation of localized shear bands. The retention of Goss grains in the microstructure after cold rolling [8-11] resulted in the formation of the final Goss texture after annealing. It was also shown [8, 13] that a sharp lattice curvature on the Goss component, and a low local dislocation density inside the shear bands promoted the formation of this texture [14]. A few papers [15-19] have also reported the formation of cube texture after recrystallization in body-centred-cubic (bcc) alloys (including non-oriented electrical steels), and it was pointed out that the recrystallized cube grains originated from the deformation/transition bands within the deformed <100>//ND grains (including the cube), or the shear bands of the {111}<110> grains. It was proposed that a strong initial cube texture, e.g. the columnar structure obtained from twin-roll casting [15], was needed to obtain a final recrystallization cube texture. More recently, cube texture was reported to form from fragments of deformed {114}<481>

grains in 3 wt% Si steel with a large grain size before cold rolling [20]. Although the cube texture was frequently observed in cast bcc alloys, cold rolling of these alloys would eventually eliminate this texture and result in the - and -fibre textures. The cube texture was also occasionally found in hot-rolled low carbon steels, and the formation of the cube texture after hot rolling was attributed to the inheritance of this texture from the phase transformation process [15], which, however, was not applicable to high silicon electrical steels (Si > ~2.5%), since these steels did not undergo an austenite-to-ferrite transformation. Thus, there was still controversy about the origin of the initial cube texture in high silicon steels. A study by Nguyen-Minh et al. [21] revealed that crystal volumes (or crystallites) with the cube orientation could be formed in the shear bands of deformed rotated Goss ({110}<110>) grains in a 1.2 wt% Si steel, which might have served as the cube nuclei during recrystallization. The formation of the rotated Goss texture in the cold-rolled structure was attributed to the phase transformation process, in which the rotated Goss grains (inherited from the parent phase) were retained during plane-strain compression, due to its high Taylor factor. Although the occurrence of rotated Goss in cold-rolled electrical steel was rare, their findings did provide an interesting route for the investigation of cube recrystallization texture, i.e. through the formation of the rotated Goss texture in the cold-rolled steel. Previous investigations have proven that it was very difficult to form the rotated Goss texture in high silicon steels (>2.5% Si) since the addition of silicon suppressed the austenite-to-ferrite transformation. Thus, in this study, a special rolling scheme, i.e. inclined rolling [22, 23], was utilized to intentionally ―create‖ the rotated Goss texture from a hot-rolled and annealed high silicon (2.8 wt% Si) electrical steel, through a simple rotation of the steel plate around the ND before cold rolling. In this way, the required rotated Goss texture could be obtained from the

rotation of the brass texture, which was commonly observed in hot-rolled and annealed high silicon steels. The rotation resulted in an inclination angle between the cold rolling direction (CRD) and the hot rolling direction (HRD), which rendered the name of ―inclined rolling‖. Both moderate and high thickness reductions (50% and 80%) were applied to the steel plates, which were able to produce shear bands in the rotated Goss grains. The cold-rolled steel sheets were then annealed to form the cube crystals (from the shear bands of the rotated Goss grains) during both partial and complete recrystallization. The formation of the cube orientation during planestrain compression of rotated Goss was also simulated using a full-constraint Taylor crystal plasticity model, which confirmed the development of a cube texture within the matrix (in addition to the shear bands) of rotated Goss grains during rolling, as observed in the experiments. Although it may not be feasible to implement the inclined rolling scheme in mass production, it does provide a viable method to investigate the effect of initial texture on the cold rolling and final annealing textures, since in this rolling scheme the chemistry, microstructure and processing history of the material were kept the same, and the only parameter altered was the initial texture prior to cold rolling. This rolling scheme was initially used by He et al. [22] to process a 0.88 wt% Si electrical steel, which produced a strong cube texture when the inclination angle was 60°. However, that paper did not reveal the origin of the cube texture, nor did it explain the formation mechanisms that had led to the final cube texture. The current investigation was intended to exploit the mechanisms associated with the formation of the cube texture during thermomechanical processing. It was also intended to examine if this rolling scheme had a similar effect on the formation of the cube texture in high silicon (2.8 wt%) electrical steel that did not show phase transformation.

2. Formation of Cube from Rotated Goss Numerous experiments and simulations [6, 7, 24-26] have shown that, after plane-strain compression (rolling) of bcc iron or low carbon steel, the final textures are usually very similar regardless of the composition and processing parameters, i.e. typically - and - fibres will form in the deformed steel. This is because the initial textures obtained from hot rolling are usually very similar, and the rolling deformation will result in the stabilization of certain orientations including those in the - and - fibres, e.g. {001}<110>, {112}<110>, {111}<110>, and {111}<112>. Since rotated Goss is a rare texture in hot-rolled high silicon electrical steel, its deformation during cold rolling is rarely studied or simulated. Thus, in this research, plane-strain compression of the rotated Goss is simulated using a full-constraint Taylor crystal plasticity model [27] implying {110}<111>, {112}<111> and {123}<111> slip systems, and the results are shown in Fig. 1. It is seen that with the increase of the strain, the rotated Goss gradually rotates to the stable {111}<110> orientation, and finally forms a -fibre. In the meantime, when the strain   0.4, a cube texture starts to appear, and when  0.5, an uncommon {335}<053> texture (1 = 50°,  = 40°, 2 = 45°) begins to form. With the increase of strain, the cube intensity essentially does not change, but the {335}<053> orientation gradually extends to {111}<110> and {111}<112>, and finally forms the -fibre. When the strain is  0.9, a weak -fibre starts to appear (including the rotated cube, {001}<110>). From the simulation, it is seen that the deformation of the rotated Goss is indeed expected to produce the desired cube texture. However, it should be noted that, the formation of the cube texture from the plane-strain compression of the rotated Goss is different from the formation of the cube crystallites within the shear bands of the rotated Goss, since the full-constraint Taylor model used in the simulations

does not consider the formation of shear bands within the material. Nevertheless, simulations by Nguyen-Minh et al. [28] have shown that cube-oriented crystals were the most stable orientation in the shear bands of the rotated Goss grains (with the increase of the strain), which were observed in Fe-1.2 wt% Si steel as well. The experiments in this study were mainly focused on the formation of the cube crystallites within the shear bands of the deformed material, since these played the most important role in the annealing process.

Fig. 1. The evolution of the rotated Goss ({110}<110>) texture under plane-strain compression as simulated using the full-constraints Taylor model. 2 = 45 sections of the ODFs (Bunge notation). 3. Experimental The material used in this investigation was a 2.8 wt% Si non-oriented electrical steel, and the chemical composition (wt%) was: 2.8 Si, 0.003 C, 0.3 Mn, 0.52 Al, 0.01 P. The steel was melted in a vacuum induction furnace and cast into an ingot with a cross-section area of 200  200 mm2. The ingot was heated up to a nominal temperature of ~1040 °C and hot rolled to a thickness of 25 mm (~88% reduction) in six passes in a reversing rolling mill. The surface oxides were then removed (~3 mm on each side), and a second hot rolling process was applied, in which the steel plates were heated again to a temperature of ~1040 °C (held for 1.5 hours) and further rolled to a

thickness of 2.5 mm (~87% reduction) in four passes (70, 50, 10 and 5 percent thickness reduction, respectively), also in a reversing rolling mill. The measured entry-exit temperatures of the four passes were (°C): 943-897, 886-853, 828-766, and 726-666. The steel plates were pickled in a HCl solution to remove the surface oxides, and were then annealed at 840 °C for 60 hours in a 100% dry hydrogen atmosphere. The extended annealing time was intended to produce large recrystallized grains in the microstructure before cold rolling, since it has been shown [29, 30] that large initial grains were beneficial to the formation of shear bands in the cold-rolled structure, which would promote the <100>//ND texture (including cube) during final annealing. In order to obtain the rotated Goss as a starting texture for cold rolling and examine the formation of the cube texture in rotated Goss, inclined rolling [22, 23] was employed in this study to ―create‖ the rotated Goss from the annealed hot band. As shown in previous investigations [24, 31, 32], the brass ({110}<112>), Goss ({110}<001>) and copper ({112}<111>) textures were normally produced at the surface/subsurface of the plate after hot rolling of high silicon steel due to the shear induced by the friction between the material and the rolls. In order to create a strong rotated Goss texture in the steel, the top ~1 mm of the electrical steel plate was machined (Fig. 2a) from the hot band (after annealing), since the surface/subsurface contained a strong brass texture. A small rectangular strip (90 mm  30 mm  1 mm) was cut at a 55° angle from the hot rolling direction (HRD), and cold rolled in the longitudinal direction (i.e. along the longest axis of the sample) as in conventional rolling (Fig. 2b). A rotation of the brass orientation (1 = 55°,  = 90°, 2 = 45°) by 55° around the ND (inclined rolling) will bring it to the rotated Goss (1 = 0°,  = 90°, 2 = 45°). However, it should be noted that the brass texture consists of two twin-related components: (110)[1 ̅ 2] (1 =

55°,  = 90°, 2 = 45°) and (110)[ ̅

] (1 = 125°,  = 90°, 2 = 45°). While a rotation of 55°

around [110] (ND) will bring the (110)[1 ̅ 2] to the rotated Goss, the same rotation will transfer the other component to (110)[1 ̅ 4] (1 = 70°,  = 90°, 2 = 45°). In this study, focus will be placed on the rotated Goss orientation (after rotation). The 90 mm  30 mm  1 mm plate was cold rolled to a thickness of 0.5 mm (50% reduction) in five passes. During the cold rolling, the rolling direction was kept the same in all the passes (not reversing).

Fig. 2. Schematic illustration of the inclined rolling process: (a) sectioning the top 1 mm layer from the annealed hot band for inclined rolling, (b) cutting a smaller plate with the longitudinal axis at 55 to the hot rolling direction, (c) rolling the plate conventionally. It should be noted that, although the initial texture was rotated by 55° around the plate normal direction, the cold rolling process itself was the same as conventional rolling (Fig. 2c), i.e. the orthotropic symmetry was maintained and the deformation was also plane-strain compression. Although the initial texture (after rotation) does not exhibit the orthotropic symmetry in the new reference system of the inclined rolling operation, the rolling reduction of 50% or 80% will restore the orthotropic sample symmetry. The textures after inclined rolling

were measured with respect to the (new) cold rolling reference frame, not the hot rolling reference frame. The cold-rolled steel strip was then annealed at 750 °C for 5 minutes to create a partially recrystallized microstructure so that the relationship between the recrystallized grains and the deformed matrix (with shear bands) could be examined. Inclined cold rolling with a 60° inclination angle (not 55 because of a slight deviation of the texture from brass) was also conducted on a full 2.5-mm-thick hot-rolled and annealed plate (the same 2.8 wt% Si steel) to a thickness of 0.5 mm (80% reduction) to verify if the same inclined rolling scheme can also produce a final cube texture in high silicon steel, like in the low silicon steel shown in [22]. In this case, the material was annealed at 750 °C for 60 minutes to obtain a completely recrystallized microstructure and examine if the cube texture could be finally retained after the completion of recrystallization. EBSD scans were performed on samples after all the thermomechanical processing stages under a field emission gun (FEG) scanning electron microscope (Nova NanoSEM, FEI) equipped with an EDAX Orientation Imaging Microscopy system (OIM 6.2). The samples were prepared by conventional metallographic grinding/polishing procedures plus a final polishing step using a colloidal silica solution (0.05 µm). The EBSD scans were performed on the cross sections (RD-ND planes) of the plates/sheets, which covered essentially the entire thickness of the plates or sheets. Orientation distribution functions (ODFs) were calculated from the measured Euler angles (Bunge notation) using a harmonic series expansion method with a maximum series rank of 22. The textures were plotted on the

sections of the Euler

space. For isolation of specific crystallographic orientations from the EBSD scans, e.g. cube, Goss, copper, brass, rotated Goss, etc., a tolerance of 15° was allowed from the exact orientation.

4. Results 4.1 Hot rolling The microstructure and microtexture of the 2.8 wt% Si electrical steel after hot rolling are shown in Fig. 3. It is seen that the microstructure is very heterogeneous across the thickness of the plate, i.e. essentially three different regions can be distinguished. At the surface (about 0.5 mm) the microstructure is composed of very small equiaxed grains, which is the result of recrystallization of the top layer that has been subjected to heavy shear deformation (induced by the friction between the rolls and the plate). These crystals have a variety of orientations, as illustrated by the various colors in the inverse pole figure (IPF) map. Immediately below the surface layer is a relatively thin layer (~0.3 mm) of elongated grains (the transition region) with mostly green and purple colors, which are <110>//ND and <112>//ND crystals, respectively. This layer has also been subjected to shear deformation, but the strain is relatively small as compared to the surface layer, and it may not undergo recrystallization during hot rolling. The central layer, which is about 1/3 of the entire thickness, has been subjected to plane-strain compression, and thus consists of elongated grains with essentially the <001>//ND (red) and <111>//ND (blue) orientations. The unique color map shown in Fig. 3b indicates that, although some sparsely distributed small rotated Goss grains can be found in the microstructure, the area fraction is very small and they are mostly located in the surface and subsurface regions. Some cube grains are also noticed in the microstructure. The calculated ODFs shown in Fig. 3c confirmed that the overall texture of the entire cross section is composed of the typical orientations observed in each region, i.e. rotated cube, Goss, brass, copper and -fibre. The rotated cube shows the strongest intensity

(12.0), and the brass and Goss are relatively strong. There are a weak copper texture and some minor -fibre components, but there is no rotated Goss texture component.

Fig. 3. Cross-section (RD-ND) microstructure and microtexture of the hot-rolled 2.8 wt% Si electrical steel: (a) EBSD inverse pole figure (IPF) map of the cross section, (b) image quality (IQ) map highlighting the cube and rotated Goss crystallites, (c) 2 = 45 section of the ODF (Bunge notation) showing the major texture components, (d) texture index. 4.2 Hot band annealing After hot band annealing, both the microstructure and microtexture of the steel have been significantly altered. As shown in Fig. 4a, the cross-section microstructure consists of equiaxed grains with various sizes (25~700 µm in diameter). The entire thickness can be divided into three layers based on the grain orientations (different colors in IPF map). The transition region in the

hot-rolled state is not obvious here. The top and bottom surfaces are again composed of grains mainly with the {110} orientations (green), and the major texture is <110>//ND with peaks at {110}<665>, {110}<112> and {110}<115>. A copper texture is also noted (Fig. 4c). The central layer is dominated by red ({001}), purple ({112}) and blue ({111}) grains, and the texture is mainly composed of a {001}<570> on the -fibre and a {112}<110> on the -fibre (Fig. 4d). Compared to the hot rolling texture (Fig. 3c), the overall texture (Fig. 4e) is considerably randomized, but the <110>//ND fibre is strengthened. The copper and Goss textures are essentially retained. The cube grains observed in the hot-rolled steel (Fig. 3) have been mostly eliminated, i.e. no cube texture is seen on the ODF, although a couple of cube grains are still seen on the grain unique color map (Fig. 4b). No rotated Goss is seen in the microstructure or texture.

Fig. 4. Microstructure and microtexture after hot band annealing: (a) EBSD inverse pole figure map, (b) image quality map, (c) texture of the surfaces, (d) texture of the central layer, (e) overall texture of the entire thickness, (f) texture index. 2 = 45 section of the ODF (Bunge notation).

4.3 Inclined cold rolling As mentioned before, inclined rolling is a rolling process where the cold rolling direction (CRD) is rotated from the hot rolling direction (HRD) around the ND by a certain angle, which is able to conveniently alter the initial texture before cold rolling while maintaining the same material chemistry, processing history and microstructural features (e.g. grain size). As shown in Fig. 5, the initial texture of the top 1 mm layer of the plate (RD-TD plane) after hot band annealing consists of a strong near-brass component and a relatively strong copper orientation. There is no rotated Goss texture. By rotating the rolling direction around the ND by 55° (Fig. 2b), the brass is brought to the rotated Goss, as shown in Fig. 5d. It should be noted that the orthotropic symmetry of the texture is lost due to the rotation, thus the texture after rotation is plotted with 1 = 0-360. The starting texture for cold rolling now contains a relatively strong rotated Goss texture. Since the maximum intensity of the original texture is at about 55° from the Goss, a rotation of this orientation by 55° results in a strong Goss texture. The original copper component ({112}<111>) is rotated to an orientation close to {112}<3 11 4>, which has Euler angles: 1 = 35°,  = 35°, 2 = 45°.

Fig. 5. Initial texture of the top 1-mm layer before inclined cold rolling: (a) EBSD inverse pole figure map showing the original crystal orientations on the plane RD-TD plane, (b) the original texture, (c) the IPF map after 55 rotation around the ND, (d) the texture after 55 rotation (without orthotropic symmetry). 2 = 45 sections, Bunge notation. The microstructure and microtexture after inclined cold rolling (from 1 mm to 0.5 mm, with 50% reduction) are shown in Fig. 6. The elongated grains show various colors (orientations) within the grains, indicating grain fragmentation (subdivision) during deformation (Fig. 6a). The texture (Fig. 6c) consists of rotated cube, two uncommon components: {114}<10 14 1> and {557}<7 14 5>, the {111}<112> on the -fiber, and a component close to the rotated Goss. Compared to the texture after conventional cold rolling (not shown here), the main differences are the appearance of the rotated Goss texture and the shift of the -fibre towards the *-fibre ({11h}<1 2 1/h>).

Fig. 6. Microstructure and microtexture after inclined cold rolling (50% reduction from 1 mm to 0.5 mm): (a) EBSD inverse pole figure map, (b) image quality map showing rotated Goss, {335}<053> and cube crystals within the deformed matrix, (c) texture (2 = 45 section, Bunge notation). From the grain unique color map (Fig. 6b) it is seen that a relatively large fraction of the rotated Goss grains is retained after inclined cold rolling. The {335}<053> orientation, as predicted by crystal plasticity simulation (Fig. 1), is also produced in the microstructure. Traces of cube crystallites in the microstructure are also noticed. Two regions that show apparent rotated Goss orientations, marked as Regions B and C in Figs. 6a and 6b, are further scanned using a smaller step size (0.5 µm) to examine the crystal orientations within the shear bands, and the results are shown in Fig. 7 and Fig. 8, respectively.

Fig. 7. The first example showing the formation of shear bands in a deformed rotated Goss grain (50% reduction from 1 mm to 0.5 mm), and the formation of cube crystallites within the shear bands, at the grain boundary, and within the matrix: (a) EBSD inverse pole figure map, (b) grain unique color map highlighting the rotated Goss, cube and {335}<053> grains, (c) 2 = 45 ODF section showing the orientations of the highlighted grains, (d) texture predicted from plane-strain compression of rotated Goss grains (reproduced from Fig. 1), (e) {001} pole figure showing the orientations. As illustrated in Figs. 7a and 7b, the crystal orientations of Region B are mainly the rotated Goss, {335}<053> and cube. The calculated ODFs agree well with the simulation results shown in Fig. 1 (partially reproduced here as Fig. 7d), where it was illustrated that the deformation of the rotated Goss gradually moves it up along the -fibre, and in the meantime produces the {335}<053> and cube components. However, it should be noted that the ODFs calculated from these small scanned areas are not representative of the bulk texture because the number of grains covered is too small. Thus, in the following discussion, pole figures (Fig. 7e), instead of ODFs, will be used to represent the orientations from such small scans.

Under this magnification, numerous shear bands are visible within the deformed rotated Goss grain and they are inclined approximately 20° to the RD, forming a fishbone like structure [3335]. Cube crystallites are observed in three locations (Fig. 7b), i.e. at the shear bands, at the grain boundaries, and within the deformed matrix. The ones within the deformed matrix (deformation bands) have much larger sizes than those at the shear bands and grain boundaries. About 50% (area fraction) of the rotated Goss grain has been changed to other orientations, thus the pole figure (Fig. 7e) exhibits a strong scattering around the rotated Goss, especially a stretch in the rolling direction. Fig. 8 (Region C) shows another deformed rotated Goss grain, within which numerous shear bands (inclined ~20° to RD) and cube crystallites are also visible. Again, the {335}<053> grains are seen in the deformed microstructure. However, in this case, the cube crystallites are essentially observed at the shear bands only, not at the grain boundaries or within the deformed matrix (Fig. 8b). The rotated Goss orientation is mostly retained (i.e. ~90%) after deformation, although the pole figure shows a strong stretch in the transverse direction.

Fig. 8. The second example of deformed rotated Goss grain (50% reduction from 1 mm to 0.5 mm), with the cube crystallites formed within the shear bands only: (a) EBSD inverse pole figure map, (b) grain unique color map highlighting the rotated Goss, cube and {335}<053> grains, (c) {001} pole figure showing the orientations of the highlighted grains. To further determine the orientation relationship between the cube crystallites and the shear bands formed in the deformed rotated Goss grain, even finer scans (step size 0.05 µm) were carried out on some shear bands, and one example is shown in Fig. 9. It is seen that, the shear band is inclined at ~25° to the RD, and within the shear band exact cube crystallites are observed, which fill most of the shear bands. The width of the shear bands is around 0.4~0.5 µm. However, it should be noted that (as will be shown later), in many other shear bands observed in the same sample, the orientations of the crystallites within the shear bands may show other orientations. This is because the formation of shear bands is the results of localized deformation,

which normally leads to the formation of very fine and highly misoriented dislocation cells [35], thus crystallites with different orientations may form. In fact, as predicted by Nguyen-Minh et al. [21], the rotated Goss gradually rotates to the cube when shear bands form within the rotated Goss grain. Thus, within the shear bands of the rotated Goss, cube is not the only orientation that can be formed.

Fig. 9. An example showing the formation of cube crystallites within the shear bands of deformed rotated Goss grain (50% reduction from 1 mm to 0.5 mm): (a) IPF map, (b) grain unique color map, (c) {001} pole figure showing the orientations of the crystals.

4.4 Partial recrystallization of the incline-rolled top 1 mm plate The steel sheet after inclined cold rolling (with 50% thickness reduction of the top 1 mm plate) was annealed at 750 °C for 5 minutes (partial recrystallization) to investigate the nucleation and recrystallization of the steel. As shown in Fig. 10, the steel clearly illustrates the nucleation and growth of cube grains within the shear bands of rotated Goss grains. The recrystallization starts at the shear bands that have higher stored energy than the matrix. The nuclei show various crystallographic orientations (including the cube and the {335}<053>), and the cube only occupies a small area fraction of all the nuclei. It is also noted that, due to the heterogeneity in deformation, the shear bands in the lower left part of the grain, which show larger recrystallized grains within the bands, recrystallize faster than those in the upper right part. The newly formed grains usually start to grow right after nucleation, and the new grains are essentially aligned along the original shear bands.

Fig. 10. Nucleation of cube crystals from the shear bands of deformed rotated Goss grains after inclined cold rolling (50% reduction from 1 mm to 0.5 mm): (a) inverse pole figure map, (b) image quality map.

Very fine scans (step size 0.05 µm) were also performed on recrystallizing shear bands to closely examine the orientation relationships of the nuclei with respect to their neighbours. An example is shown in Fig. 11, where it is seen that a number of grains with different orientations nucleate within the shear bands of rotated Goss, and the grains mostly have an elliptical shape with major axes parallel to the shear band direction, i.e. about 25° to the RD. It is noticed that, in addition to cube crystals, other orientations, e.g. {114}<151>, {012}<23 4 2>, may also form within the shear bands, but the cube grains show a much larger area fraction and grain size than other grains.

Fig. 11. A close-up view of the crystals nucleated from a shear band within the deformed rotated Goss grain (50% reduction from 1 mm to 0.5 mm): (a) IPF map showing the crystal orientations of the nuclei, (b) the corresponding {001} pole figure. 4.5 Formation of the final cube texture in incline-rolled 2.5 mm plate As an application of the inclined rolling scheme to produce final cube texture in high silicon non-oriented electrical steel sheets, a plate of the hot-rolled and annealed 2.8 wt% Si steel (2.5 mm thickness) was incline cold rolled to a thickness of 0.5 mm (80% reduction). The original cross-section (RD-ND) microstructure and microtexture of the steel was shown in Fig. 12a. Again, the microstructure can be divided into three layers according to the orientations (colors of the grains): top, centre and bottom. The surfaces (Fig. 12b) are mainly composed of copper, near-brass and {110}<665> components, together with a weak {112}<110> on the -fibre. The central layer (Fig. 12c) consists of a strong {112}<110>, a relatively strong -fiber (peaks at {001}<110> and {001}<160>), a weak -fiber, and a minor brass. In order to create the required rotated Goss texture, the rolling direction of the hot band was rotated around the ND for 60° to bring the near-brass texture on the surfaces to {110}<110>. The resulted IPF map and the related textures are shown in Figs. 12d-f. It is seen that a strong rotated Goss texture is created on the surfaces, together with a Goss texture (Fig. 12e). The same

rotation brings the {001}<110> and {001}<160> in the central region to the {001}<130> component on the -fibre, while the minor brass texture in the central region is also transformed into the rotated Goss (Fig. 12f). Thus, both the surface and central layers contain a rotated Goss texture after the rotation.

Fig. 12. Initial texture before inclined cold rolling (2.5-mm thick plate): (a) EBSD IPF map showing the original crystal orientations on the RD-ND plane, (b) the texture in the surfaces, (c)

the texture in the central layer, (d) the IPF map after 60 rotation around the ND, (e) the surface texture after 60 rotation, (f) the central layer texture after 60 rotation. 2 = 45 sections, Bunge notation. Note that (e) and (f) are plotted with 1 = 0-360 because of the loss of the orthotropic symmetry due to the rotation.

After inclined cold rolling (with an inclination angle of 60° as described above), similar microstructure and microtextures to those shown in Figs. 6-9 were observed, i.e. cube crystallites within the shear bands of the deformed rotated Goss grains were formed (not shown here). The cold-rolled sheet was then annealed at 750 °C for 60 minutes to obtain a completely recrystallized microstructure. As shown in Fig. 13, a strong cube texture was formed in the final annealed steel, and the -fibre is essentially eliminated (Fig. 13c). It is also noted that the cube grains are distributed across the entire thickness (Fig. 13b), which are due to the original rotated Goss texture in both the surface and central layers as caused by inclined rolling. Thus, through inclined rolling it is possible to produce a strong cube texture in the 2.8 wt% Si non-oriented electrical steel, which was rarely able to be produced through conventional rolling. As comparison, the same steel was also conventionally cold rolled (along the HRD) to the same thickness (0.5 mm), and annealed under the same conditions (750 °C for 60 minutes), but the resulted texture is mainly composed of a -fibre and a near *-fibre (Fig. 13d), typical of nonoriented electrical steel after conventional rolling and annealing. No cube texture is observed.

Fig. 13. The formation of a strong cube texture in the 2.8 wt% Si non-oriented electrical steel after inclined cold rolling (80% reduction from 2.5 mm to 0.5 mm) and annealing: (a) IPF map, (b) grain unique color map, (c) the texture after inclined rolling and annealing, (d) the texture after conventional rolling and annealing. 2 = 45 ODF sections, Bunge notation. 5. Discussion It is well known that the cube texture is very difficult to be produced in electrical steels using conventional rolling and annealing routes, especially in steels with silicon content more than ~2.5 wt% (no phase transformation in the steel). Inclined rolling has been used in a previous research to produce a strong cube texture in a 0.88 wt% Si electrical steel [22], but the formation mechanism was not known, and detailed microstructure characterization was not conducted. The above analysis indicates that, inclined rolling can also produce the cube texture in high silicon steel that does not have phase transformation. It has been shown that, in order to produce a certain amount of cube crystallites in the deformed microstructure (e.g. shear bands) so that they can serve as the initial seeds for

nucleation during annealing, some uncommon initial textures, e.g. the rotated Goss, should be created, e.g. using special rolling schemes (like inclined rolling in this study), since conventional hot rolling almost always leads to the formation of the -fibre and -fibre textures, not the rotated Goss or cube texture. The preferential recrystallization from the substructures (e.g. shear bands) of the deformed -fibre grains normally results in a final -fibre texture in the annealed steel. This has already been shown in many investigations [6, 7, 24-26]. The current work showed that the rolling (plane-strain compression) of the rotated Goss grains was able to produce the cube crystallites, which were observed within the shear bands of the rotated Goss, in the deformed matrix (deformation bands), or at the grain boundaries (Fig. 7). It was also shown that during recrystallization (Fig. 10), it was the shear bands (and the cube crystallites within which) that played the most important roles in the nucleation process, which led to the cube nuclei and the final cube texture. Shear banding is the result of local plastic instability induced by inhomogeneous deformation [12]. Although the fundamental theory regarding the formation of shear bands is still under debate, it can be generally accepted that shear banding is caused by shear deformation on specific shear systems, be it crystallographic [36] or non-crystallographic [37]. Thus, shear band formation is dependent on the initial crystal orientations with respect to the local stress distribution. Both the non-uniformity of the initial state of the material and the non-uniform distribution of local stresses contribute to shear banding [38]. From Fig. 6b, it is seen that the densities of shear bands in some grains are higher than in other grains, which is because the activation of shear banding also requires a critical resolved shear stress be reached [37], and the resolved shear stress and the mechanical properties of individual crystals are dependent on the crystal orientation. It is also noted that shear bands may

or may not cross the initial grain boundaries, which is orientation dependent as well. The local lattice re-orientation in the shear banding regions may cause the shear bands to cross the grain boundaries if the conditions for shear banding are satisfied by the re-orientation on both sides of the boundary [39]. The constraints imposed by the neighbouring grains across the grain boundaries inevitably cause the non-uniform rotation of the lattice, leading to lattice curvature and accumulation of dislocations. Thus, large shear is noticed in the grain boundaries of Figs. 7 and 8 where shear bands cross the initial grain boundaries. The origin of plastic instability (i.e. been attributed to geometric softening, i.e.

), and thus the formation of shear bands, has , where M is the Taylor factor of a given

orientation [12]. The concentration of strain on local shear bands changes the local deformation geometry of the crystal, which results in a smaller deformation resistance in the shear bands than that in homogeneous conditions. The Taylor factor is a dimensionless but orientation dependent measure of the plastic power dissipation for a given plastic strain mode. It has been shown that the resistance to plane strain compression and thus the potential to shear banding is high in grains with high Taylor factors [28]. Fig. 14a illustrates the Taylor factors (under plane-strain compression) of the common texture components for bcc metals calculated using a fullconstraint Taylor model by considering the {110}<111>, {112}<111> and {123}<111> slip systems with equal critical resolved shear stresses on each of the slip systems. It is seen that the Taylor factor of the rotated Goss (4.24) is the highest among all the bcc texture components, thus it exhibits the most prominent potential for shear banding. The observation of extensive shear banding in the rotated Goss grains confirmed this.

Fig. 14. Calculated Taylor factors of typical texture components in electrical steels: (a) Taylor factor map under plane strain compression (rolling), (b) Taylor factor map under simple shear. 2 = 45 sections of the Euler space (Bunge notation).

On the other hand, if shear banding is considered as a local simple shear on conventional crystallographic slip systems, the Taylor factors of the bcc texture components can also be calculated. As shown in Fig. 14b, in this case, the cube orientation has the largest Taylor factor, and thus exhibits the largest resistance to shear deformation. As a result, the cube orientation tends to be retained from shear banding. Crystal plasticity simulations by Nguyen-Minh et al. [28] also showed that cube-oriented crystals are the most stable orientation in the shear bands of rotated Goss grains. The results shown above have confirmed that cube crystallites can indeed be produced within the shear bands of the rotated Goss grains. The inclined rolling applied in this study is intended to create a rotated Goss orientation in the initial microstructure so that shear bands with the desired cube crystallites can be produced. It should be noted that, rotated Goss can be generated by rotating a brass or near-brass orientation by 55° or 60° around the ND (inclined rolling), or by rotating a Goss orientation by 90° around

the ND (cross rolling). Although all these rotations will create a rotated Goss texture in the material, the overall textures of the samples created by different rotations will be different since the rotations of the other crystal orientations in the material are different. On the other hand, these rotations will not affect the total dislocation density in the specimen, but the dislocation configuration in the material will be changed [40]. Apparently, a rotation of 55° or 60° will lead to significantly different overall texture (with respect to the new reference axes) from those rotated by 90°. For example, the rotated cube orientation will not change by a 90° rotation around the ND (due to crystal symmetry), while it will be transformed into {001}<130> if a rotation of 60° around ND is applied. Thus, with different rotations, the obtained rotated Goss grains may be surrounded by different neighbouring grains and exhibit different deformation behaviors during rolling. When the rotated Goss grains are deformed, the local stress distributions may be different because the constraints imposed by the neighbouring grains are different. This may explain why inclined rolling (55° or 60° rotation) can produce the desired shear bands (with cube crystallites) in the rotated Goss and give rise to the final cube texture, while cross rolling (although it can generate rotated Goss as well) may not lead to the same results. The apparent differences (e.g. the different amounts of rotated Goss retained after deformation) between the two rotated Goss grains shown in Fig. 7 and Fig. 8 may be explained by this as well, since the neighbouring grains of these two rotated Goss grains are different (one was bounded by all {111} grains, and the other was bounded by one {100} grain and one {111} grain). Similarly, the deviation of the real crystal orientation from the exact rotated Goss orientation may lead to different activated slip systems or shear banding systems and thus different deformation behaviours.

Shear banding is usually a high strain phenomenon [35] and it is closely related to the amount of deformation applied. For bcc Fe-3.0% Si alloy, a 20% thickness reduction can lead to shear band formation, and the number of shear bands increases with increasing deformation [36]. It has been shown that the 50% and 80% thickness reductions applied in this study are large enough to create a certain amount of shear bands in the microstructure, which lead to the formation of the final cube texture. The large grain size in the studied steel before cold rolling also contributed to the formation of shear bands since the tendency for shear banding increases with increasing grain size [41, 42]. If the starting grain size before rolling is reduced, shear bands may become fewer or cease to exist [35]. It has been well accepted that recrystallization preferentially starts at sites that contain high stored energy, e.g. shear bands, grain boundaries, deformation/transition bands, microbands, etc. [6, 8, 19, 43, 44]. The driving force for nucleation and growth is the reduction of the overall energy through the formation of new grains. Thus, within the high-stored-energy sites, there should be some regions having lower stored energy than their adjacent areas, which serve as the initial seeds for nucleation, and the orientations of these crystallites are very close to those of the nuclei that they form [43-45]. Both simulations [37] and experiments [39] have shown that there are high local orientation changes at the borders between the shear bands and the matrix, and there is a release of stress inside the shear bands. The fact that the cube orientation within the shear bands has a high resistance to further shear (Fig. 14b) and that there is a stress release inside the shear band [37] may have led to a lower stored strain energy in these cube crystallites than their neighbours. Another possibility is that the cube orientation, because of its high Taylor factor in simple shear (Fig. 14b), is more susceptible to dynamic recovery, and therefore has a high potency to nucleation.

The EBSD work conducted in this study confirmed this. As shown in Fig. 15, the cube crystallites within the shear bands of the rotated Goss grain have lower stored energy than the surrounding areas, as indicated by the higher image quality indices shown in the EBSD image quality maps. It is known that the higher the image quality index, the lower the strain and thus the lower the stored energy [45-48]. As a result, when the recrystallization starts, these crystallites preferentially form the initial nuclei and grow by consuming their neighbouring domains that have higher stored energy. The results shown in Figs. 10 confirmed that cube could indeed be nucleated within the shear bands of the rotated Goss grain, due to the formation of the cube crystallites with locally lower stored energy than their neighbouring domains.

Fig. 15. Two examples showing the cube crystallites with low stored energy (high image quality index) within the shear bands of deformed rotated Goss (50% reduction from 1 mm to 0.5 mm): (a) IPF map, (b) IQ map, (c) orientations of all the crystals within the shear band, (d) orientations of the circled regions in (b) of the first example, (e) IPF map, (f) IQ map, (g) orientations of all the crystals within the shear band, (h) orientations of the circled regions in (f) of the second example.

It has also been noted in Fig. 10 that, in the initial recrystallization stage, the nuclei formed in the shear bands only grow within the shear band regions, due to the local energy difference between the nuclei and the surrounding domains. Once these new grains cross the band-matrix borders, they will continue to grow, driven by the difference in stored energy between the newly formed grains bulging out of the shear bands and the deformed matrix grains. It is noted that the misorientations between the cube crystals and the neighbouring deformed matrix (mainly {110}<110> and {335}<053>) are 45° and 41°, respectively, which are all high angle boundaries, and are believed to have high mobility. As a result, these new cube crystals will keep growing until the matrix is consumed, or until they meet other growing grains. It should also be noted that, crystals with orientations other than cube have nucleated within the shear bands as well. Thus, the creation of the initial cube nuclei within the shear bands is only the first step for the cube to form. The subsequent growth of the new grains (after the deformed matrix is consumed) will finally determine the texture, and the grain growth process is quite different from the nucleation process since now the grains are all free of strain energy. Although the mechanisms governing the grain growth process are still not completely understood, it is generally believed that the mobility of the grain boundaries and the relative grain size across a boundary play an important role in determining the growth of the crystals [32, 49]. However, it should be noted that grain growth itself is a dynamic process, which changes the grain boundary character both globally and locally while the grains grow. Thus, elaborated insitu experiments [20] will be needed to dynamically track the growth of individual grains surrounded by other grains during the growth process, which will help understand more comprehensively the formation of the final texture after grain growth.

6. Conclusions In order to produce the magnetically favorable cube texture in non-oriented electrical steel, and investigate the formation mechanism of the cube texture, inclined cold rolling was applied to a 2.8 wt% Si electrical steel to create a rotated Goss texture which was not commonly observed in steels after hot rolling. Plane-strain compression of the rotated Goss could produce the desired cube crystallites in the deformed microstructure, i.e. within the matrix (deformation bands), at the grain boundaries, and within the shear bands of the deformed rotated Goss. The cube crystallites within the shear bands provide original nucleation seeds for the formation of the cube grains during the subsequent recrystallization. During early stage of annealing, the crystallites at the shear bands, which include cube and other orientations, preferentially nucleate, and the orientations of these nuclei are close to those of the original crystallites existing within the shear bands after cold rolling, due to lower stored energies than the adjacent areas within the shear bands. The cube grains can survive during the grain growth process and form a strong cube texture in the final steel sheets. Although inclined rolling may not be feasible for industrial implementation, the formation mechanisms scrutinized in this research do provide some insights into the evolution of cube texture in non-oriented electrical steels. It is seen that, by controlling the initial texture before cold rolling (i.e. creating the rotated Goss texture), it is possible to produce the desired final cube texture in the steel.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements Funding of this research was provided by the Program of Energy Research and Development (PERD), Natural Resources Canada, and by Natural Sciences and Engineering Research Council of Canada (NSERC). Michael Attard and Mason Thomas are thanked for cold rolling of the steel. Renata Zavadil and Jian Li are gratefully acknowledged for their assistance in EBSD measurements. LK acknowledges Tuan Nguyen Minh for many inspiring discussions on the subject of shear bands.

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Graphical abstract