Recrystallization Behavior and Formation of {411}<148> Grain from α-fiber Grains in Heavily Cold-rolled Fe-3%Si Alloy

Abstract

Recrystallization texture is essential to control the mechanical and magnetic properties of steels. Both γ-fiber (ND//<111>) and α-fiber (RD//<011>) textures are known to develop during the rolling process of bcc iron. Recrystallization behavior from γ-fiber has been extensively studied. On the other hand, recrystallization behavior from α-fiber, in particular after heavy cold rolling reduction, has not been sufficiently clarified. In this study, recrystallization behavior from α-fiber, focusing on the formation of {411}<148> recrystallized grain, was investigated by means of EBSD and TEM. {411}<148> region already existed in the vicinity of deformed grains having upper α-fiber orientation({100}<011>~{211}<011>). TEM observation revealed the existence of the lamellar structure with {411}<148> relatively fine dislocation cells in the {211}<011> deformed grains. With the progress of the recovery, {411}<148> subgrains (dislocation cells) are postulated to easily form and are surrounded by the deformed matrix grains with high angle interface. Thus, it is easy to form the recrystallization nuclei having the potential to grow with the sake of both high driving force and high interface mobility. At the early stage of recrystallization, {411}<148> recrystallized grains developed in {211}<011> deformed grains. At the later stage, {411}<148> recrystallized grains from {211}<011> deformed grains encroach {100}<011> deformed grains and new {411}<148> recrystallized grains developed in {100}<011> deformed grains.

1. Introduction

Texture in ferritic steel via the rolling process is characterized by two kinds of fiber texture. One isγ-fiber (ND//<111>), the other is α-fiber (RD//<011>), where ND denotes the normal direction and RD denotes the rolling direction. Development of γ-fiber texture contributes to superior deep drawability, which is preferred for automobile applications.^1,2) Although the suppression of α-fiber texture is required from the viewpoint of formability, it is necessary to understand the mechanism of α-fiber texture formation because it is inevitably formed in the rolling and recrystallization process. The formation of recrystallization texture has been explained by the hypothesis of oriented nucleation (ON) theory and/or oriented growth (OG) theory, but there is no unified consensus yet. Regarding the recrystallization of γ-fiber orientated grains in Interstitial Free (IF) steel, it has been reported from the viewpoint of ON theory^3,4,5,6,7,8) that local inhomogeneous deformation occurred near the grain boundary during cold-rolling, where ND//<111> recrystallized grains preferentially formed. Thus, {111} recrystallization texture developed.³⁾ However, a few studies have been conducted from the viewpoint of OG theory.^9,10) According to OG theory, the recrystallized nuclei have no preferred orientation, but the recrystallized nucleus with {554}<225> (near {111}<112>) has a rotational relationship with a main cold rolling texture {211}<011> of about 27° around the <110> axis. As the interface between two orientations has high mobility, the {111} recrystallized texture could preferentially developed.⁹⁾

Regarding recrystallization from α-fiber, {h,1,1}<1/h,1,2> recrystallized grain has been generally presumed to recrystallize from α-fiber. Among them, research on {411}<148> (φ1=~19.5°, Φ=~19.5°, and φ2=45° at Euler angle notation of Bunge) has been actively conducted. Homma et al.¹¹⁾ researched heavily cold-rolled bcc Fe and proposed that {411}<148> recrystallized grains formed in α-fiber grains such as {100}<011> ~ {211}<011> especially in the vicinity of the grain boundary. Similarly, Gobernado et al.¹²⁾ studied cross-rolled IF steel and reported that {311}<136> (φ1=~20°, Φ=~25°, and φ2=45° at Euler angle notation of Bunge, deviation angle 5.6 from {411}<148>) recrystallized in the grain boundary of {100}<011> and the deformation band. Quadir and Duggan¹³⁾ confirmed {411}<148> recrystallized in the deformation band within grain having {100}<011> in IF steel cold-rolled with 95% reduction. These reports could support the theory of ON. On the other hand, Verbeken et al.¹⁴⁾ proposed the mechanism for the development of {411}<148> based on OG theory using IF steel cold-rolled with 95% reduction. The {211}<011> deformed grains, which are one of the stable cold rolling texture, have a rotational relationship with {311}<147> (φ1=~17°, Φ=~26°, and φ2=45° at Euler angle notation of Bunge, deviation angle 7.0 from {411}<148>). Consequently, recrystallized grains with {311}<147> preferentially grow into the {211}<011> deformed grains because the interface having a rotational relationship of 26.5° around the <110> axis easily moves. The recrystallization behavior from α-fiber and the origin of {411}<148> recrystallized grains still remain unclear because of the differences in steel compositions and cold rolling reduction.

In our previous study,¹⁵⁾ we focused on the formation of {411}<148> recrystallization texture in heavily cold-rolled Fe-3wt%Si alloy (hereinafter referred to as%) and consistently investigated texture changes from recrystallization to grain growth. It was reported that during recrystallization, most of {411}<148> recrystallized grains nucleated at the grain boundary and they consumed neighboring deformed grains, resulting in large grain size. Moreover it was clarified that during normal grain growth, {411}<148> grains consumed the neighboring small recrystallized grains due to its size advantage, resulting in the further increase in the main orientation {411}<148>. Therefore, in this study, to clarify the origin of {411}<148> recrystallized grains in heavily cold-rolled Fe- 3%Si alloy, recrystallization behavior from α-fiber was intensively investigated. First, we investigated texture in annealed hot band prior to cold-rolling to clarify the origin of {411}<148> orientation in cold-rolled structure . Next, in order to clarify recrystallization behavior of {411}<148> recrystallized grain, the texture and structure changes with annealing temperature were macro/mesoscopically examined in detail using XRD (X-ray diffraction) and EBSD (electron back scattering diffraction). Furthermore, dislocation substructures in these specimens were microscopically observed using a TEM (transmission electron microscopy) and EBSD. The recrystallization behavior was discussed based on the observation results of cell structures, subgrains structures, and recrystallized grains.

2. Experimental Procedure

An annealed hot band with a thickness of 2.8 mm was used as the starting material. It had the following chemical composition: Fe-3.25%Si-0.06%C. The material was cold-rolled to a thickness of 0.3 mm with 89% reduction. The cold-rolled sheet was heated at the rate of 15°C/s to 580°C, 620°C, 640°C, 680°C, 690°C, 700°C, 720°C, 750°C and then quenched without holding. Thus, partially recrystallized specimens were prepared.

The TD (transverse direction) cross section of the annealed hot band was nitaletched and observed by an optical microscope. The specimen was electro-polished to measure crystal orientation by SEM-EBSD (JEOL: JSM-7800, EDAX OIM DATE COLLECTION), and the orientation distribution function (ODF) was obtained. In this paper, the texture was represented by the φ₂=0, 45° ODF section in Euler space.

The cold-rolled sheet and partially recrystallized sheet were reduced to a 1/10 layer by mechanical polishing and measured to obtain the {200}, {220}, and {222} pole figures by XRD (Rigaku RINT 2500HF). The experimental data were processed to obtain the ODFs. The specimen was electro-polished to measure local crystal orientation by SEM-EBSD. Detailed measurement conditions for EBSD are listed in Table 1.

Table 1. Measurement condition of EBSD for each sample.

Sample	Step size	Figure No.
Hot annealed band	4 μm	Fig. 2
Cold rolled sheet	0.15 μm	Fig. 3
	0.015 μm	Fig. 4
	0.15 μm	Fig. 15
Recovered specimen annealed at 580°C	0.15 μm	Fig. 6
	0.015 μm	Fig. 7
Partially recrystallized specimen annealed at 580–750°C	0.015 μm	Fig. 18

The specimen cold-rolled and annealed at 580°C was cut out as a thin film by FIB (Hitachi High-Tech: NB5000) for TEM observation so as to have the same field as that observed by SEM-EBSD. Bright field images were taken with an accelerated voltage of 200 kV by FE-TEM (Field Emission-Transmission Electron Microscopy) (JEOL JEM-2100F), and crystal orientation was identified by electron diffraction.

3. Result

Figure 1 shows the optical microstructure of the TD cross section in the annealed hot band. Recrystallized grains are recognized from the surface layer to the center layer. In this study, texture in the surface layer, especially the 1/10 layer, was focused. Therefore, the texture of the annealed hot band was also characterized in the surface layer (280 μm). The outermost surface layer in the specimen was decarburized, whereas carbides precipitated along the grain boundary in the innermost layer. Moreover, {110}<001> and weak α-fiber orientation were developed in the surface layer (Fig. 2). The microstructure in the surface layer had a block shape slightly elongated structure to RD, and the average grain size was about 50 μm in RD and about 30 μm in ND.

Fig. 1.

Optical micrograph of annealed hot band observed from TD cross section.

Fig. 2.

(a) ND IPF map, (b) TD IPF map and (c) ODFs in φ2=0, 45° section in surface layer of annealed hot band.

Figure 3 shows a typical microstructure having α-fiber orientation in the surface region of the cold-rolled specimen. It had a lamellar structure mostly with α-fiber orientation and some of them with γ-fiber orientation. The α-fiber orientation in Fig. 3 was mainly {211}<011>, but many areas with α-fiber having {100}<011> were also observed. The thickness of deformed grains was about 3–5 μm. Considering no width strain by rolling deformation and 89% cold-rolling reduction, the thickness of deformed grains 3–5 μm after cold-rolling matches well with the expected thickness assuming 30 μm ND thickness of the recrystallized grains in the annealed hot band. The individual deformed grains in the cold-rolled sheet can be presumed to originate from individual recrystallized grains in the annealed hot band. It is well known that a single crystal with {110}<001> rotates to {111}<112>.^{16,17,18,19,20)} Whereas, in the case of polycrystalline with {110}<001> as the main initial orientation, the following crystal rotation was reported.²¹⁾ First, {110}<001> rotated to {554}<225>, close to {111}<112>, in the range of 30% to 50% reduction and then rotated to {211}<011> at a further increase in reduction, and finally rotated to {111}<011>. Thus, in this way, what is called γ-fiber, was formed. The rolling texture of the cold-rolled specimen after 89% reduction in this study could be explained by the similar crystal rotation.

Fig. 3.

Typical area of α-fiber orientation (a) ND IPF map, (b) orientation map of {411}<148>, {100}<011> and {211}<011> and (c) ODFs in φ2=0, 45° section in surface layer of cold rolled sheet.

The enlarged microstructure of the rectangular area shown in Fig. 3 exhibited the existence of the {411}<148> region both in the vicinity of the grain boundary and grain interior of the deformed grains having {211}<011> (Fig. 4). At the boundary between the {211}<011> deformed grains and the {411}<148> region, there was a cell wall whose crystal orientation was difficult to identify by EBSD. Moreover, {411}<148> region was situated along the cell wall. Therefore, a thin film sample with a TD cross section was cut out at exactly the same location of the rectangular area shown in Fig. 4 by FIB, and was subjected to TEM observation to investigate the dislocation substructure. Special attention was payed to focus on the {411} <148> region in the {211} <011> deformed grains (Fig. 5). Here, the confirmation that the areas observed were the same for both TEM and SEM-EBSD was made by identifying the {211}<011> and the {411}<148> regions by the electron diffraction pattern. The {211}<011> deformed grains had a lamellar structure composed of a dislocation cell with a thickness of 300 nm, which was inclined 18° in the rolling direction. Whereas, the {411}<148> region was composed of a dislocation cell with a finer thickness of 100 nm (Fig. 5(a)). The boundary of dislocation cells was depicted as schematically shown in Fig. 5(b) by the repetition of taking bright field image and determining crystal orientation using electron diffraction pattern for each dislocation cell by tilting the sample in TEM. The dislocation cell with {411}<148> ((411)[$1\overline{8}4$]) in the {211}<011> ((211)[$0\overline{1}1$]) deformed grains had a misorientation angle of 24.2°from (211)[$0\overline{1}1$]. Thus, the boundary between them was considered a large angle boundary. The dislocation cell with {411}<148> also neighbored to another dislocation cell with the locally modulated thickness of 30 nm having other orientation. This orientation was close to {221}<122> (($1\overline{2}2$)[$\overline{2}12$]). Thus, the misorientation angle from {411}<148> was 58.1° and the boundary was considered a high angle one. This high angle grain boundary (bold red line in Fig. 5(b)) between {411}<148> and neighboring grains is inferred to be originated from the grain boundary in the annealed hot band specimen. In this study, we measured the Euler angle by EBSD to obtain the misorientation angle.

Fig. 4.

(a) IQ map and (b) superimposed orientation map of {411}<148> and {211}<011> in IQ map in surface layer in cold-rolled sheet.

Fig. 5.

(a) TEM bright-field image showing the embedded {411}<148> region in the vicinity of {211}<011> grain boundary of cold-rolled sheet specimen, (b) sketch of (a) and (c) electron diffraction pattern in TEM image (a) (The diffraction patterns were taken with the incident electron beam parallel to the [111]_α-Fe or [113]_α-Fe).

Figure 6 shows a typical area with α-fiber orientation in the surface of the recovered specimen annealed at 580°C. A lamellar structure consisting of α-fiber orientation and γ-fiber orientation was again confirmed. The α-fiber orientation in Fig. 6 was mainly {100}<011> ~ {211} <011>. The thickness of deformed grains was about 3–5 μm. The magnified microstructure of the rectangular area shown in Fig. 6(b) exhibited the existence of {411}<148> oriented region in the deformed α-fiber grains, especially in the vicinity of the grain boundary (Fig. 7). This feature was similar to the cold-rolled specimen (Figs. 3 and 4). A thin film sample with a TD cross section was cut out at the same location of the rectangular area shown in Fig. 7 by FIB, and the dislocation substructure was observed by TEM (Fig. 8). The dislocation cells with {411}<148>, or subgrains after the progress of recovery, pre-existed in the vicinity of the deformed grains having {211}<011> and the thickness was almost the same as that of the dislocation cells observed in the cold-rolled specimen, about 100 nm (Fig. 8(a)). The dislocation cells (subgrains) with {411}<148> ((411)[$1\overline{8}4$]) in the {211}<011> ((211)[$0\overline{1}1$]) deformed grains were situated along the dislocation cells with (211)[$0\overline{1}1$] which is relatively larger as schematically shown in Fig. 8(b). The misorientation angle between them was 28.5° and the boundary was considered a high angle one. The dislocation cell (subgrain) with {411}<148> also neighbored another dislocation cell with different orientation (Fig. 8(a)). The orientation was close to {211}<120> ((211)[$1\overline{2}0$]). The misorientation angle from {411}<148> was 42.4° and the boundary was considered a high angle one. This high angle grain boundary is also inferred to be originated from the grain boundary in the annealed hot band specimen.

Fig. 6.

Typical area of α-fiber orientation (a) ND IPF map, (b) orientation map, and (c) ODFs at φ2=0°, 45° section in surface layer of the specimens annealed at 580°C.

Fig. 7.

(a) IQ map and (b) superimposed orientation map of {411}<148> and {211}<011> in IQ map in surface layer of the specimen annealed at 580°C.

Fig. 8.

(a)TEM bright-field image showing the embedded region of {411}<148> in the vicinity of grain boundary of {211}<011> deformed matrix in the specimen recovery annealed at 580°C, (b) sketch of (a) and (c) electron diffraction patterns in TEM image (a) (The diffraction patterns were taken with the incident electron beam parallel to the [111]_α-Fe or [113]_α-Fe).

The distinction between “dislocation cell” and “subgrain” should be made precisely based on the dislocation wall thickness and the amount of dislocation in the cell. In this paper, the structure surrounded by low angle grain boundaries and having many dislocations was defined as a dislocation cell or a subgrain, and no clear differentiationent was made by TEM observation. However, considering the transition from dislocation cell to a subgrain during the recovery process, the dislocation cell recovered by annealing at 580°C might be called the subgrain.

Fraction recrystallized of specimens annealed at 620, 640, and 680°C were 17, 27, and 53% respectively. At each recrystallization stage, {411}<148> recrystallized grains were observed by SEM-EBSD. Furthermore, the number of {411}<148> recrystallized grains was 190, 214, and 254 for each specimen. The nucleation sites of {411}<148> recrystallized grains were classified into the following three groups: (i) between deformed grains (Fig. 9(a)); (ii)between recrystallized grains and deformed grains (Fig. 9(b)); and (iii) between recrystallized grains (Fig. 9(c)). Since most of deformed grains had upper α-fiber orientation ({100}<011>~{211}<011> is called upper α-fiber in the present paper) , upper α-fiber orientation was further classified into {100}<011> and {211}<011>. The grains that do not belong to any type were removed from the parameters, and their frequency was evaluated (Table 2). At each recrystallized stage, the most of {411}<148> recrystallized grains belonged to type (ii). One of the sides of them was often in contact with the deformed α-fiber and the other side was in contact with the recrystallized grains. In particular, in the early stage of recrystallization, they appeared to have a high contact frequency with the α-fiber orientated {211}<011>. And then, in the later stage of recrystallization, they appeared to have a high contact frequency with {100} <011> (Table 2, Fig. 10). Furthermore, as shown in Table 2, for type (i), they often contacted with {211} <011> deformed grain in the early stage of recrystallization. The transition from type (i) to type (ii) is suggested to occurr with the progress of recrystallization.

Fig. 9.

Classification of {411}<148> recrystallized grain and {100} pole figures in partially recrystallized specimens: (a) between deformed grains, (b) between deformed grains and recrystallized grains and (c) between recrystallized grains.

Table 2. Classification of {411}<148> recrystallized grains and change in their types with fraction recrystallized.

Fraction recrystallized		17%	27%	53%
Annealing temperature		620°C	640°C	680°C
(i) Between deformed grains	{100}<011>/{100}<011>	1	2	3
	{211}<011>/{100}<011>	10	5	9
	{211}<011>/{211}<011>	8	4	4
(ii) Between deformed grain and recrystallized grains	{100} <011>/recrystallized grains	13	17	19
	{211} <011>/recrystallized grains	47	41	26
(iii) Between recrystallized grains		21	31	39
Inside deformed grain	{100}<011>	0	0	0
	{211}<011>	0	0	0
total		100	100	100
(%)

Fig. 10.

Change in frequency of {411}<148> recrystallized grains formed along {100}<011> and {211}<011> deformed grains with fraction recrystallized.

Textures were measured by XRD as a function of annealing temperature. Figure 11 shows the changes in both the microstructures on the ND section and the textures as a function of fraction recrystallized. The difference ODFs are also shown to clearly indicate the change in texture with the progress of recrystallization. The specimen annealed at 580°C did not recrystallize and the specimen annealed at 620°C partially recrystallized. Deformed grains mainly had α-fiber orientation and slightly had γ-fiber orientation of {111}<011>. Concerning γ-fiber orientation, {111}<011> decreased and {111}<112> increased with the progress of recrystallization. For α-fiber orientation, at the early stage of recrystallization - from 580°C to 620°C - {111}<011>~{211}<011> decreased. In the later stage of recrystallization - from 680°C to 720°C - {211}<011>~{100}<011> decreased. Figure 12 shows the changes in ODF intensity with annealing temperature, where {111}<011>, {211}<011>, and {411}<148> are chosen as important orientations. It can be seen that the {411}<148> increased, whereas the {211}<011> decreased in the early stage of recrystallization. It is suggested that {411}<148> recrystallized grains nucleate from {211}<011> deformed grains in α-fiber and simultaneously {111}<112> recrystallized grains nucleate from {111}<011>deformed grains in γ-fiber. It can also be seen that the {100}<011> decreased significantly, while the {411}<148> increased further in the later stage of recrystallization. The decrease of {211}<011> and {100} <011> in the later stage of recrystallization is considered to be due to the fact that the nucleation and growth of {411} <148> recrystallized grains simultaneously occurred at a expense of {211}<011> and {100}<011> deformed grains. The fact that the change of these orientations confirmed by XRD (global) has the same tendency as the EBSD results (local) (Fig. 10 and Table 2) supports the validity of the experimental data regardless of scale.

Fig. 11.

(a) IQ maps in ND section, (b) ODFs at φ2=45deg. (c) difference ODFs at φ₂=45deg showing texture change with increase in fraction recrystallized in surface layer of partially recrystallized specimens.

Fig. 12.

Change in intensities of orientations in ODF with annealing temperature: (a)upper α-fiber textures such as {100}<011> and {211}<011>, (b){411}<148>.

4. Discussion

4.1. Recrystallization of {100}<011>~{211}<011> Deformed Grains

It is presumed that the {411}<148> recrystallized grains is originated from the deformed grains having upper α-fiber orientation ({100}<011>~{211}<011>) which was rotated from Goss orientation in the surface of the annealed hot band. From the detailed observation of nucleation and growth behavior of recrystallized grains (Table 2, Fig. 10) and the change in major orientations during recrystallization (Fig. 12), it is suggested that {211}<011> deformed grains were associated with the formation of {411}<148> recrystallized grains in the early stage of recrystallization, whereas {100}<011> deformed grains were also associated with it in the later stage of recrystallization. Here, the recrystallization behavior of {100}<011>~{211}<011> deformed grains is discussed. The easiness of recrystallization generally depends on the final stable orientation because the stored energy accumulated by rolling deformation depends on orientations of grains. Although the formation mechanism of rolling texture is much more complicated than that of simple uniaxial tensile or compression deformations, a plane strain condition consisting of strains in the normal and rolling directions can be assumed because of almost no width strain during rolling. Moreover, the strain and stress experienced by individual grains constituting a polycrystalline during plastic deformation are also very complex and several models have been proposed.^22,23,24) In this paper, assuming the Taylor model, the stored energy that determines the easiness of recrystallization is expressed by the M value in Eq. (1).   

$$M=\frac{\sigma }{\tau }=\frac{\mathrm{\Sigma }d\gamma }{d\epsilon }$$(1)

where σ is the principal stress, τ is the shear stress, dε is the increment of principal strain, and Σdγ is the sum of the shear strains on the crystallographically defined slip systems. Therefore, M value means the sum of shear strains to bear the principal strain. Because the orientation with a large M value indicates many movable dislocations, dislocation density in the deformed structure may be judged high. From the viewpoint of the high-energy block theory, the grain with the high M value could be easy to recrystallize. Dillamore²⁴⁾ calculated the M value assuming that the rolling deformation satisfies the plane strain condition. The following relation was reported to hold in the typical RD//<011> orientations.   

$$M_{\left\{111\right\}<011>}>M_{\left\{211\right\}<011>}>M_{\left\{100\right\}<011>}$$(2)

The M value in Eq. (2) indicates that {211}<011> deformed grain is easier to recrystallize than {100}<011> because it has higher stored energy. In this study about the recrystallization behavior of the {100}<011>~{211}<011> deformed grains, in the early stage of recrystallization the {211}<011> deformed grains could first recrystallize, and then the {100}<011> deformed grains recrystallize in the later stage of recrystallization. Furthermore, these deformed α-fiber regions could be consumed by the nucleation and growth process of newly recrystallized grains. On the other hand, as described in the previous report,¹⁴⁾ ND//<111> grains also have high stored energy and are expected to recrystallize early.

4.2. The Formation of {411}<148> Orientation

In this section, the formation of {411}<148> orientation is discussed. There are 24 crystallographically equivalent orientations (variants) in cubic crystal and these variants decrease with symmetry. The {411}<148> orientations have four types of variants, whereas {211}<011> orientations have two types of variants (Fig. 13). Figure 14(a) shows the orientation map using variant color coding shown in Fig. 13, while Fig. 14(b) shows the {100}, {110} and {211} pole figures of the {211}<011> deformed grain and {411}<148> region in the interior of this deformed grain. Although the {411}<148> and {211}<011> have four and two types of different variants respectively as shown in Fig. 13, only one of each variant appeared in the actual observation as shown in Fig. 14. This combination of these variants is characterized by a smaller difference in misorientation than other variant combinations. If the slip system is not taken into account, the orientation can be reached with less crystal rotation. In the case of bcc iron, 24 slip systems of the {110}<111> type and the {211}<111> type could be activated. If the {123}<111> type is included, there are 48 slip systems. Assuming a single slip system, the rotation axis is parallel to the slip plane and perpendicular to the slip direction. From the pole figures shown in Fig. 14(b), it is suggested that {211}<011> and {411}<148> have a common <110> axis as the rotation axis and the slip plane is {211}. In the vicinity of the grain boundary, inhomogeneous deformation likely occurs due to the restriction from the grain boundary and adjacent grains. Thus, {211}<011>, which is the stable orientation, could rotate locally. For this reason, it is presumed that {411}<148> oriented region pre-existed near the grain boundary. Gobernado et al.¹²⁾ also claimed that {100}<011> in the vicinity of the grain boundary locally rotates to {311}<136> by inhomogeneous deformation. Moreover, Takenaka et al.²⁶⁾ claimed that the carbides or solute carbons by the addition of carbon would lead to the inhomogeneous deformations during cold-rolling, because multiple slip systems could be activated locally after cold-rolling Fe-3%Si -C alloy with 90% reduction.

Fig. 13.

{100} pole figures showing (a) two symmetrically equivalent {211}<011> orientations (b) four symmetrically equivalent {411}<148>orientations.

Fig. 14.

(a) Orientation map of {211}<011> and {411}<148> in TD cross sectional surface layer in cold-rolled sheet, where the color coding corresponds to that in Fig. 13, and (b) pole figures showing (211)[011] in blue color and (411)[184] in red color. A green circle indicates the common rotational axis.

4.3. The Formation of {411}<148> Recrystallized Grain

Here, the formation of the {411}<148> recrystallized grains is discussed taking into account the locally embedded {411}<148> region in the vicinity of the grain boundary in the {211}<011> deformed grains. Figure 15 shows the orientation map and {100} pole figure of both deformed grains close to {211}<011> and the partially recrystallized grains with {411}<148> observed from ND. Similar to the result shown in Fig. 14, only limited variants appeared with a small misorientation angle between the four types of {411}<148> and two types of {211}<011> in the partially recrystallized specimen. Regarding {411}<148> and {211}<011>, variants with a small misorientation angle among the four variants and the two variants, respectively, pre-exist as dislocation cells in the same deformed grain. After the transition from dislocation cell to subgrain with the progress of recovery, recrystallized nuclei surrounded by the high angle grain boundaries is speculated to form.

Fig. 15.

(a) Orientation map of {211}<011> deformed grains and {411}<148> recrystallized grains which was color-coded by each variants in partially recrystallized specimen annealed at 650°C. (b) {100} pole figure corresponding to color map in (a).

Regarding the mechanism of the formation of the {411}<148> recrystallized grains, the orientation distribution of {211}<011> and {411}<148> are considered. Although the orientation {211}<011>, which is the stable orientation in rolling, fluctuates locally between dislocation cells (subgrains in the case of the recovered specimen), only a slight orientation change is expected in the entire {211}<011> deformed grain. Because each orientations of dislocation cells could cancel out in the short range. On the other hand, in the vicinity of the grain boundary in the {211}<011> deformed grain, local crystal rotation from {211}<011> to {411}<148> is assumed to occur by inhomogeneous deformations due to the restriction from the grain boundary and adjacent grains, resulting in the large misorientation. The conceptual diagram is illustrated in Figs. 16(a), 16(b). Figures 16(c), 16(d) show the measured value of the misorientation change in the location indicated by arrows in Fig. 4. Line A shows misorientation between neighboring points, while Line B shows misorientation from the origin to the point. The {211}<011> deformed grain, which is presumed to have high uniformity because of stable orientation, was compared with the {411}<148> region, which is presumed to have high inhomogeneity. Compared with the {211}<011> deformed grain, the {411}<148> region actually had a large misorientation change.

Fig. 16.

Schematic diagrams showing change in misorientation with distance in (a) stable orientation area, and (b) inhomogeneous orientation area. Experimetally determined change in misorientation with distance in (c){211}<011> orientation area and (d) {411}<148> orientation area.

The formation of the {411}<148> recrystallized grain is schematically shown in Fig. 17. The dislocation cells having {411}<148>, which was locally formed by inhomogeneous deformation, could transform from dislocation cell structure to the subgrain structure through annihilation and rearrangement of dislocations (Fig. 17(a)). Slight migration of the sub-boundary (subgrain-growth) could occur because of large misorientation between adjacent subgrains having {411}<148> (Fig. 17(b)). Since subgrain boundaries with a relatively large misorientation are easy to migrate, large subgrains are likely to be formed. Furthermore, these subgrains had a high angle boundary with the adjacent {211}<011> deformed grain. Therefore this boundary could relatively migrate rapidly (Fig. 17(c)). As a result, the {411}<148> region is assumed to become a recrystallized grain surrounded by the high angle grain boundaries (Fig. 17(d)). Thus, the {411} <148> recrystallized grain, surrounded by {211} <011> deformed grain and adjacent deformed grain having other orientation, is formed.

Fig. 17.

Schematic diagrams showing {411}<148> recrystallization behavior together with misorientation change with distance in {411}<148> region. (a) Transition from cells to subgrains through annihilation and rearangement of dislocations. (b) Acquisition of large misorientation with adjacent subgrains through subgrain-growth. (c) Migration of low angle boundary of subgrains as well as high angle interface between recrystallized and deformed grains. (d) Acquisition of recrystallized grain surrounded by high angle grain boundaries.

Based on the experimental data that variants with a small misorientation between {411}<148> and {211}<011> were selected in the cold-rolled specimen (Figs. 14 and 15), the mechanism of the formation of {411}<148> recrystallized grains seems to support the orientation nucleation theory. However, as Verbeken¹⁴⁾ pointed out, the interface between {311}<147> recrystallized grain and deformed grain has a high mobility and may preferential migrate because it has a rotational relationship of 27° against {211}<011> deformed grains around the <110> axis. Therefore, the oriented growth theory cannot be categorically refused. Concerning the origin of {411}<148>, the present study focused on the recrystallization of {411}<148> from the {211}<011> deformed grains. Separately from that, in the later stage of recrystallization, the intensity of {411}<148> increased with the decrease in the intensity of {100}<011> as shown in Fig. 12. Moreover, {411}<148> was reported to recrystallize in the vicinity of the grain boundary of deformed grains having {100}<011>¹²⁾ and in the inhomogeneous deformation band within grain having {100}<011>.^13,27) The investigation into the recrystallization of {411}<148> from the {100}<011> deformed grains is a topic for future study.

5. Conclusions

For heavily cold-rolled Fe-3%Si alloy, the recrystallization behavior from deformed α-fiber grains, in particular {211}<011> deformed grains, was investigated to clarify the origin of {411}<148> recrystallized grains. The following conclusions were obtained.

• The deformed α-fiber orientation of {211}<011> at the surface layer in cold-rolled sheet was derived from Goss orientation in the surface layer of annealed hot band.

• In cold-rolled sheet, {411}<148> orientated region pre-existed in deformed upper α-fiber {100}<011> ~{211}<011> grain, especially in the vicinity of the grain boundary.

• {411}<148> and {211}<011> have four and two variants, respectively. In the same deformed grain, the variants with a small misorientation existed. Similarly, during recrystallization the variants with a small misorientation were selected.

• Considering the characteristics of the combination of variants, {411}<148> recrystallized grain was assumed to form by the local crystal rotation of stable {211}<011> grain in the vicinity of grain boundary.

• Based on the observation of the dislocation substructure, the {411}<148> region in the deformed grains with {211}<011> has a lamellar structure composed of relatively fine dislocation cells. In the {411}<148> regions, subgrains were formed by annihilation and rearrangement of dislocation, and misorientation between subgrains became relatively large. Consequently, the subgrains have a high angle boundary against the {211}<011> and neighboring other oriented deformed grains. Therefore, it is easy for the subgrains with {411}<148> to grow to form recrystallized nuclei surrounded by the high angle boundary.

• In the early stage of recrystallization, {411}<148> is assumed to recrystallize from {211}<011> deformed grains, while in the later stage of recrystallization {411}<148> is assumed to recrystallize from {100}<011> deformed grain. The {411}<148> nucleated recrystallized grains grow easily to consume the deformed grains withe {211}<011> and {100}<011> orientation.

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