**7.1. Thermal stability of Goss orientation formed by shear deformation**

During hot rolling, Rex can take place, thereby the Goss orientation may change to a different orientation. Lee and Lee [64] obtained an IF steel specimen with only the shear texture by a multi- layer warm rolling and discussed the evolution of its Rex texture. The material used was a hot rolled 3.2 mm thick IF steel sheet. The hot-rolled sheet was cold-rolled to 1.1 mm in thickness in several passes. Four of the 1.1mm thick sheet were stacked, heated at 700 o C for 30 min and rolled by 70% in the ferrite region without lubrication. The rolled specimen was quenched into 25 o C water. Each layer was separated from the warm rolled sheet. In order to obtain a uniform shear texture, the surface layer was thinned from the inner surface to a half thickness by chemical polishing. The thinned surface and center layers were annealed at 750 o C for 1 h in Ar atmosphere.

The measured (110) pole figures and ODFs of the outer and inner surfaces of the 75% warmrolled surface layer were similar. The similarity indicates that the texture of the layer is uniform. The texture was approximated by the Goss orientation plus minor {112}<111>. The center layer was similar to the typical texture of cold rolled steel sheet, RD//<110> and ND// {111}(Section 8). The surface texture could also be described as that which is obtained when the center layer texture is rotated through 35o about TD. The measured textures were similar to the calculated textures in Figure 47. The textures of the chemically thinned rolled surface layer and the center layer after annealing at 750 o C for 1 h showed that the texture of the surface layer was almost the same before and after annealing while the center layer underwent a texture change after annealing. Microstructures and hardness tests of the surface layer before and after annealing indicated Rex occurring after annealing [64].

component has the highest density, but has lowest stored energy or the Taylor factor, while the copper component has the lowest density, but has the highest stored energy or the Taylor factor. If grains with the Goss or cube orientation survived during rolling, they must have undergone plane strain compression. They could undergo recovery and act as nuclei for Rex during annealing. This is the reason why the cube Rex texture could be obtained even though the copper component is the least in the deformation texture. When other conditions are the same, the higher relative density component in the deformation texture will give rise to the higher density in the corresponding component in the Rex texture, as shown in the highest relative copper component in the deformation texture yielding the highest cube component in

The Goss orientation {110}<001> in about 3% Si steel has been the subject of speculation due to its scientific and technological points of view. The grain oriented Si steel is made by hot rolling, cold rolling, followed by annealing. The Goss texture is formed near the sheet surface layer rolled in the α phase region at elevated temperatures. The friction between the sheet and rolls tends to increase with increasing temperature, and in turn increases the shear deformation and

During hot rolling, Rex can take place, thereby the Goss orientation may change to a different orientation. Lee and Lee [64] obtained an IF steel specimen with only the shear texture by a multi- layer warm rolling and discussed the evolution of its Rex texture. The material used was a hot rolled 3.2 mm thick IF steel sheet. The hot-rolled sheet was cold-rolled to 1.1 mm in thickness in several passes. Four of the 1.1mm thick sheet were stacked, heated at 700 o

30 min and rolled by 70% in the ferrite region without lubrication. The rolled specimen was

obtain a uniform shear texture, the surface layer was thinned from the inner surface to a half thickness by chemical polishing. The thinned surface and center layers were annealed at 750

The measured (110) pole figures and ODFs of the outer and inner surfaces of the 75% warmrolled surface layer were similar. The similarity indicates that the texture of the layer is uniform. The texture was approximated by the Goss orientation plus minor {112}<111>. The center layer was similar to the typical texture of cold rolled steel sheet, RD//<110> and ND// {111}(Section 8). The surface texture could also be described as that which is obtained when the center layer texture is rotated through 35o about TD. The measured textures were similar to the calculated textures in Figure 47. The textures of the chemically thinned rolled surface

layer was almost the same before and after annealing while the center layer underwent a

C water. Each layer was separated from the warm rolled sheet. In order to

C for 1 h showed that the texture of the surface

C for

the Rex texture in the Cu-4%Mn alloy among the three Cu-Mn alloys.

**7. Plane-strain compressed {110}<001> bcc steel crystal**

**7.1. Thermal stability of Goss orientation formed by shear deformation**

the Goss texture (Figure 47).

38 Recent Developments in the Study of Recrystallization

quenched into 25 o

C for 1 h in Ar atmosphere.

layer and the center layer after annealing at 750 o

o

**Figure 47.** Deformed FEM meshes in rolling and calculated (110) pole figures of layers A and E. In FEM calculation, flow characteristics of IF steel σ = 500ε0.256 MPa, roll diameter of 310 mm, initial sheet thickness of 3.4 mm, and reduc‐ tion of 70% were used [63].

**Figure 48.** Rotation rate dω/dε11about TD//<110> with respect to ε11 for bcc crystal [64].


**Table 4.** Shear strain on each slip system as a function of dε13/dε11 [64].

The unchanged texture in the surface layer after annealing can be explained based on SERM. AMSD is obtained from the slip systems activated during deformation. On the basis of the Taylor-Bishop-Hill theory, the (110)[001] orientation is calculated to be stable at *ε*13/*ε*11=√2 (Figure 48), and active slip systems for the (110)[001] crystal is calculated to be 1 (0-1 1)[111], 2 (-101)[111], 3 (110)[-111], and 4 (110)[1-1 1]. The shear strain on each slip system calculated as a function of *ε*13/*ε*11 is given in Table 4. The shear strains on slip systems 1 and 2 do not change, but those on slip systems 3 and 4 increase with increasing *ε*13/*ε*11. The slip systems 1 and 2 are effectively equivalent to the (-1-1 2)[111] system, and the slip systems 3 and 4 are equivalent to the (110)[002] system. AMSD may be parallel to γ(1,2)[111]+γ(3,4)[002] with γ(1,2) and γ(3,4) being shear strains on slip systems 1 and 2 and slip systems 3 and 4, respectively. Even though the (110)[001] orientation is stable at *ε*13/*ε*11=√2, in real rolling the *ε*13/*ε*11 value is small in the entrance region, increases very rapidly up to a maximum value just ahead of the neutral point, and then decreases in the exit region. The slip systems having the higher shear strain give dominant contribution to AMSD. As shown in Table 4, slip systems 3 and 4 are likely to give dominant contribution to AMSD. Therefore, AMSD is likely to be parallel to the [001] direction, which is also MYMD. Therefore, the Goss orientation is likely to remain unchanged after annealing in agreement with the experimental result (1st priority in Section 2). Another reason for the thermal stability of shear deformation textures is described in [65].

The evolution of the Goss orientation in the (111)[1 1-2] component, a {111}<112>, has been explained by SERM [70]. Slip systems of (-1-1 0)[-1 1-1], (-1-1 0)[1-1-1], (101)[1 1-1], and (011) [1 1-1] are calculated, by the relaxed constraints Taylor model, to be equally active in the (111) [1 1-2] crystal undergoing the plane strain compression. It is noted that the three slip directions are chosen to be at acute angles with RD [1 1-2] of the crystal. Taking the (101)[1 1-1] and (011) [1 1-1] slip systems sharing the same slip direction [1 1-1] into account, AMSD is [-1 1-1] + [1-1-1] + [1 1-1] = [1 1-3]. According to SERM, this AMSD [1 1-3] becomes parallel to MYMD, the <100> directions in bcc iron, in Rexed crystals. Other directional relationships between the matrix and Rexed crystal can be obtained from the 2nd priority in Section 2. Let one of the <100> directions be the [001] direction, then it must be on the (100), (010) or (110) plane, taking the symmetry condition into account. TD of the (111)[1 1-2] crystal is the [1-1 0] direction. These facts give rise to orientation relationship between the deformed and Rexed states (Figure 49). It is noted that the [1-1 0] direction is TD of both the deformed and Rexed states. It follows that the (111)[1 1-2] orientation becomes the (441)[1 1-8] orientation after Rex. The symmetry yields another equivalent orientation, (441)[-1-1 8]. The (110) pole figure of the {441}<118> orientation is shown in Figure 50a along with the Goss orientation {110}<001>. The {441}<118> orientation is deviated from the Goss orientation by 10°. If each {441}<118> orientation is represented by the Gauss type scattering with a half width angle of 12°, the calculated result is as shown in Figure 50b, which is in very good agreement with the measured data in Figure 50c, where the highest intensity poles are the same as those of the Goss orientation, even though it is not real Goss orientation. It is also interesting to note that the rotation angle between (111)[1 1-2] and (441)[1 1-8] about a common pole of [110] is calculated to be 25°and the rotation angle between (111)[1 1-2] and (110)[001] about a common pole of [110] is 35°. Thus the {111}<112> matrix can favor the growth of Goss-oriented crystals or nuclei, which are stable during annealing, if any,

Recrystallization Textures of Metals and Alloys

http://dx.doi.org/10.5772/54123

41

or may generate Goss-oriented nuclei, especially in polycrystalline materials.

*rd* ]110//[]332[

**Figure 49.** Orientation relationship between deformed (*d*) and recrystallized (*r*) states.

*rd* ]001//[MYMD//]311[AMSD// *rd* ]011//[]011[TD//

#### **7.2. Plane-strain compressed {110}<001> bcc metals**

The (110)[001] orientation of bcc metals is calculated to be metastable with respect to plane strain compression (Figure 48), with active slip systems being (-1 0-1)[-1-1 1], (1 0-1)[111], (0-1-1) [-1-1 1], and (0 1-1)[111], on which the shear strain rates are the same. It is noted that the slip directions are chosen to be at acute angles with the [001] direction (Section 2). The two slip directions, [-1-1 1] and [111], are on the (-110) plane, which can be a slip plane in bcc crystals. Therefore, AMSD is [-1-1 1] + [111] = [002] // [001]. This is also MYMD of iron. Since the AMSD is the same as MYMD, if the Goss oriented crystal survives the plane-strain compression, the Goss texture is likely to remain unchanged during annealing according to SERM (1st priority in Section 2).

#### **7.3. Evolution of Goss recrystallization texture from {111}<112> rolling texture**

The Goss orientation, which is not stable with respect to plane strain deformation, rotates toward the {111}<112> orientation forming a strong maximum [66]. The relaxed constraints Tayor model, in which shear strains parallel to RD may occur, causes the formation of the {111}<112> orientation [67]. The {111}<112> rolling component is known to lead to the Goss orientation after Rex [66, 68]. Dorner et al. [68] attributed the transition from the {111}<112> deformation texture to the Goss Rex texture to the fact that the Taylor factor (2.4) of the Goss grains is lower than that (3.7) of the {111}<112> matrix. Dorner et al. [69], in their study with 3.2% Si-steel single crystals, also found two types of Goss crystal volumes in 89 % cold-rolled specimen. Most of the Goss crystal regions are situated inside of shear bands. The Goss crystal volumes are also observed inside of microbands. These Goss crystals may act as nuclei because they are thermally stable (Section 7.2).

The evolution of the Goss orientation in the (111)[1 1-2] component, a {111}<112>, has been explained by SERM [70]. Slip systems of (-1-1 0)[-1 1-1], (-1-1 0)[1-1-1], (101)[1 1-1], and (011) [1 1-1] are calculated, by the relaxed constraints Taylor model, to be equally active in the (111) [1 1-2] crystal undergoing the plane strain compression. It is noted that the three slip directions are chosen to be at acute angles with RD [1 1-2] of the crystal. Taking the (101)[1 1-1] and (011) [1 1-1] slip systems sharing the same slip direction [1 1-1] into account, AMSD is [-1 1-1] + [1-1-1] + [1 1-1] = [1 1-3]. According to SERM, this AMSD [1 1-3] becomes parallel to MYMD, the <100> directions in bcc iron, in Rexed crystals. Other directional relationships between the matrix and Rexed crystal can be obtained from the 2nd priority in Section 2. Let one of the <100> directions be the [001] direction, then it must be on the (100), (010) or (110) plane, taking the symmetry condition into account. TD of the (111)[1 1-2] crystal is the [1-1 0] direction. These facts give rise to orientation relationship between the deformed and Rexed states (Figure 49). It is noted that the [1-1 0] direction is TD of both the deformed and Rexed states. It follows that the (111)[1 1-2] orientation becomes the (441)[1 1-8] orientation after Rex. The symmetry yields another equivalent orientation, (441)[-1-1 8]. The (110) pole figure of the {441}<118> orientation is shown in Figure 50a along with the Goss orientation {110}<001>. The {441}<118> orientation is deviated from the Goss orientation by 10°. If each {441}<118> orientation is represented by the Gauss type scattering with a half width angle of 12°, the calculated result is as shown in Figure 50b, which is in very good agreement with the measured data in Figure 50c, where the highest intensity poles are the same as those of the Goss orientation, even though it is not real Goss orientation. It is also interesting to note that the rotation angle between (111)[1 1-2] and (441)[1 1-8] about a common pole of [110] is calculated to be 25°and the rotation angle between (111)[1 1-2] and (110)[001] about a common pole of [110] is 35°. Thus the {111}<112> matrix can favor the growth of Goss-oriented crystals or nuclei, which are stable during annealing, if any, or may generate Goss-oriented nuclei, especially in polycrystalline materials.

The unchanged texture in the surface layer after annealing can be explained based on SERM. AMSD is obtained from the slip systems activated during deformation. On the basis of the Taylor-Bishop-Hill theory, the (110)[001] orientation is calculated to be stable at *ε*13/*ε*11=√2 (Figure 48), and active slip systems for the (110)[001] crystal is calculated to be 1 (0-1 1)[111], 2 (-101)[111], 3 (110)[-111], and 4 (110)[1-1 1]. The shear strain on each slip system calculated as a function of *ε*13/*ε*11 is given in Table 4. The shear strains on slip systems 1 and 2 do not change, but those on slip systems 3 and 4 increase with increasing *ε*13/*ε*11. The slip systems 1 and 2 are effectively equivalent to the (-1-1 2)[111] system, and the slip systems 3 and 4 are equivalent to the (110)[002] system. AMSD may be parallel to γ(1,2)[111]+γ(3,4)[002] with γ(1,2) and γ(3,4) being shear strains on slip systems 1 and 2 and slip systems 3 and 4, respectively. Even though the (110)[001] orientation is stable at *ε*13/*ε*11=√2, in real rolling the *ε*13/*ε*11 value is small in the entrance region, increases very rapidly up to a maximum value just ahead of the neutral point, and then decreases in the exit region. The slip systems having the higher shear strain give dominant contribution to AMSD. As shown in Table 4, slip systems 3 and 4 are likely to give dominant contribution to AMSD. Therefore, AMSD is likely to be parallel to the [001] direction, which is also MYMD. Therefore, the Goss orientation is likely to remain unchanged after annealing in agreement with the experimental result (1st priority in Section 2). Another

reason for the thermal stability of shear deformation textures is described in [65].

**7.3. Evolution of Goss recrystallization texture from {111}<112> rolling texture**

The (110)[001] orientation of bcc metals is calculated to be metastable with respect to plane strain compression (Figure 48), with active slip systems being (-1 0-1)[-1-1 1], (1 0-1)[111], (0-1-1) [-1-1 1], and (0 1-1)[111], on which the shear strain rates are the same. It is noted that the slip directions are chosen to be at acute angles with the [001] direction (Section 2). The two slip directions, [-1-1 1] and [111], are on the (-110) plane, which can be a slip plane in bcc crystals. Therefore, AMSD is [-1-1 1] + [111] = [002] // [001]. This is also MYMD of iron. Since the AMSD is the same as MYMD, if the Goss oriented crystal survives the plane-strain compression, the Goss texture is likely to remain unchanged during annealing according to SERM (1st priority

The Goss orientation, which is not stable with respect to plane strain deformation, rotates toward the {111}<112> orientation forming a strong maximum [66]. The relaxed constraints Tayor model, in which shear strains parallel to RD may occur, causes the formation of the {111}<112> orientation [67]. The {111}<112> rolling component is known to lead to the Goss orientation after Rex [66, 68]. Dorner et al. [68] attributed the transition from the {111}<112> deformation texture to the Goss Rex texture to the fact that the Taylor factor (2.4) of the Goss grains is lower than that (3.7) of the {111}<112> matrix. Dorner et al. [69], in their study with 3.2% Si-steel single crystals, also found two types of Goss crystal volumes in 89 % cold-rolled specimen. Most of the Goss crystal regions are situated inside of shear bands. The Goss crystal volumes are also observed inside of microbands. These Goss crystals may act as nuclei because

**7.2. Plane-strain compressed {110}<001> bcc metals**

40 Recent Developments in the Study of Recrystallization

in Section 2).

they are thermally stable (Section 7.2).

**Figure 49.** Orientation relationship between deformed (*d*) and recrystallized (*r*) states.

with pancake relaxations (*ε*13 and *ε*23 are relaxed.). The active slip systems of the (111)[1-1 0] crystal are calculated to be (101)[1-1-1], (0-1-1)[1-1 1], (211)[1-1-1], and (-1-2-1)[1-1 1], on which the shear strain rates *dγ*(k) / *dε*<sup>11</sup> with respect to *ε*<sup>11</sup> are 0.0612, 0.0612, 0.107 and 0.107, respec‐ tively. It is noted that the slip directions are chosen to be at acute angles with RD. The four slip systems can be effectively divided into the following two slip systems. 0.0612(101)[1-1-1] + 0.107(211)[1-1-1] // (0.2752 0.107 0.1682)[1-1-1] and 0.0612(0-1-1)[1-1 1] + 0.107(-1-2-1)[1-1 1] //

(111)[011]

(665)[0 63 75] (554)[225]

(665)[110] (665)[11 2.4]

(111)[121] (111)[112] <111>//ND

(665)[0 63 75] (554)[225]

(111)[121] (111)[112] <111>//ND

(110)[110] (110)[001]

(110)[110] (110)[001]

Figure 51. Section of *φ*<sup>2</sup> 2 =45° in Euler space with locations of important orientations and fibers.

Figures 52. ODFs (*φ*2= 45<sup>o</sup> 19 ) of 50, 80, and 95% rolled IF steel sheets (top) before and (bottom) after

0

( ) contour levels: 2, 4, 6, 8,10,15

<sup>1</sup> = 0<sup>o</sup> <sup>2</sup> = 45<sup>o</sup> 

(b)

(111)[1 1 0]

**Figure 52.** ODFs (φ2= 45o) of 50, 80, and 95% rolled IF steel sheets (top) before and (bottom) after annealing at 695 °C

50% 80% 95%

fiber

Max. 12.6

Max. 4.8 Max. 15.5

(111)[011]

(665)[110] (665)[11 2.4]

**8.1. Recrystallization in fiber** 

1

(001)[110] (001)[010]

1

(001)[110] (001)[010]

(334)[483]

0o

<110>//RD

<110>//RD

0o

90o

90o

Max. 6.3

20 annealing at 695 °C for 1000 s [71]

fiber

0 30 60 90

(001)[1 1 0] (112)[1 1 0] (111)[1 1 0] (110)[1 1 0]

<sup>2</sup> = 45o

(334)[483]

**Figure 51.** Section of φ2 =45° in Euler space with locations of important orientations and fibers.

<sup>2</sup> = 45o

(111)[110] (558)[110]

(111)[110] (558)[110]

density along fiber decreases with increasing annealing time.

**8. Cold-rolled polycrystalline bcc metals** 

Figure 50. (110) pole figures for (a) {110}<001> and {441}<118> orientations (●(110)[0 0-1], ■(441)[1 1-8], ▲(4 4-1)[-1-1-8]) [70], (b) Gaussian function

It is well known that the rolling texture of bcc Fe is characterized by the � fiber (<110>//RD) plus the γ-fiber (<111>//ND) and the rolling texture is replaced by the γ-fiber after Rex (Figure 51). This texture transformation will be discussed based on SERM. Figure 52 shows ODFs of 50, 80, and 95% cold-rolled IF steel sheets and their Rex textures, which indicate that the deformation textures are approximated by the and fibers and the Rex texture by the fiber, as well known. As the deformation increases, peak type orientations tend to form. For the 80 and 95% cold rolled specimens, the {665}<110>, {558}<110>, and {001}<110> orientations develop as the main components. The {665}<110> and {558}<110> orientations may be approximated by the {111}<110> and {112}<110> orientations, respectively. The {001}<110> component is the principal component inherited from the hot band. It is stable and its intensity increases with deformation [72,73]. The Rex texture is approximated by the fiber whose main component is

Figure 53 shows the orientation densities along the and fibers for IF steel rolled by 80% and annealed at 695℃. Up to 100 s, little change in the orientation density occurs, although appearance of the {111}<112> component in the fiber is apparent. For the specimen annealed for 200 s, the orientation density along the fiber is almost as high as that of the fully annealed one, while the

http://dx.doi.org/10.5772/54123

43

Recrystallization Textures of Metals and Alloys

We want to know if the {111}<112> Rex texture results from the {111}<110> deformation texture. The (111)[1-1 0] orientation is taken as an orientation representing the {111}<110> deformation texture. The (111)[1-1 0] orientation is calculated to be stable using the rate sensitive model with pancake relaxations (*ε*13 and *ε*23 are relaxed.). The active slip systems of the (111)[1-1 0] crystal are calculated to be (101)[1-1-1], (0-1-1)[1-1 1], (211)[1-1-1], and (-1-2-1)[1-1 1], on which the shear strain rates *dγ*(k) / *dε*11 with respect to *ε*11 are 0.0612, 0.0612, 0.107 and 0.107, respectively. It is noted that the slip directions are chosen to be at acute angles with RD. The four slip systems can be effectively divided into the following two slip systems. 0.0612(101)[1-1-1] + 0.107(211)[1-1-1] // (0.2752 0.107

37

of {441}<118> with half width of 12° and *l*max=11 [70], and (c) Si steel specimen Rexed for 1 min at 980 °C [66].

(a) (b) (c)

approximated by {111}<112>. The density of this orientation increased with increasing cold rolling reduction.

0.1682)[1-1-1] and 0.0612(0-1-1)[1-1 1] + 0.107(-1-2-1)[1-1 1] // (-0.107 -0.2752 -0.1682)[1-1 1]

90o

90o

Figure 51.. Section of *φ*2 =45° in Euler space with locations of important orientations and fibers.

Max. 7.0 Max. 14.4

= 54.74o <sup>2</sup> = 45o 

(111)[121] (111)[1 10] (111)[112]

1

0 30 60 90

(001)[110]

(001)[110]

(-0.107 -0.2752 -0.1682)[1-1 1]

Running Title

1

21 22

for 1000 s [71]

0

**Figure 50.** pole figures for (a) {110}<001> and {441}<118> orientations (●(110)[0 0-1], ■(441)[1 1-8], ▲(4 4-1) [-1-1-8]) [70], (b) Gaussian function of {441}<118> with half width of 12° and *l*max=11 [70], and (c) Si steel specimen Rexed for 1 min at 980 °C [66].
