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

It is well known that the rolling texture of bcc Fe is characterized by the α 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 α and γ fibers and the Rex texture by the γ 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 approxi‐ mated 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 γ fiber whose main compo‐ nent is approximated by {111}<112>. The density of this orientation increased with increasing cold rolling reduction.

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

#### **8.1. Recrystallization in γ fiber**

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

37

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]

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

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)

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] // (-0.107 -0.2752 -0.1682)[1-1 1] **8.1. Recrystallization in fiber**  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

density along fiber decreases with increasing annealing time.

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

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

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

Figure 51.. Section of *φ*2 =45° in Euler space with locations of important orientations and fibers. **Figure 51.** Section of φ2 =45° in Euler space with locations of important orientations and fibers. 90o <sup>2</sup> = 45o

Running Title

1

22

0

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

cold rolling reduction.

Rexed for 1 min at 980 °C [66].

42 Recent Developments in the Study of Recrystallization

**8.1. Recrystallization in γ fiber**

It is well known that the rolling texture of bcc Fe is characterized by the α 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 α and γ fibers and the Rex texture by the γ 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 approxi‐ mated 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 γ fiber whose main compo‐ nent is approximated by {111}<112>. The density of this orientation increased with increasing

(a) (b) (c)

**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

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

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

one, while the density along α fiber decreases with increasing annealing time.

20 annealing at 695 °C for 1000 s [71] 21 (111)[121] (111)[1 10] (111)[112] (111)[1 1 0] (001)[1 1 0] (112)[1 1 0] (111)[1 1 0] (110)[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 for 1000 s [71]

fiber

> 1

0 30 60 90

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

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

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

0

0 30 60 90

fiber

38 Book Title

1.682] 2.752 07.1[

53.70 75.20

16.118 85.86

2]-1 TD//[1

ND, and RD in (111)[2-1-1] crystal.

sensitive pancake model [71]

texture to the {111}<112> Rex texture.

The {111}<112> grains may act as nuclei.


26.35 26.35

1.682]- 1.07- [-2.752

85.86

75.20

ND//[111] 1]//AMSD 1-[1

b a

16.118

0] 1-RD//[1

**Figure 54.** Angular relationships (a) among AMSD, ND, and RD in rolled (111)[1-1 0] crystal and. (b) among MYMD,

Slip plane 101 211 312 0-1-1 -1-2-1 -1-3-2 112 123 213

**Table 5.** Shear strain rates on slip systems in plane strain compressed (665)[1-1 0] crystal calculated based on rate

For the (665)[-1-1 2.4] orientation as an orientation representing the {665}<1 1 2.4> Rex texture, the angles among ND, TD, RD, and [001] are shown in Figure 55b. Comparison of Figures 55a and 55b shows that AMSD in the deformed specimen is almost parallel to [001], MYMD of iron, in the Rexed specimen. This is compatible with SERM. In other words, the transformation from the (665)[1-1 0] deformation orientation to the (665)[1-1 2.4] Rex orientation is compatible with SERM. The deformed matrix and Rexed grains share the [665] ND (2nd priority in Section 2). Taking symmetry into account, the {665}<110> rolling texture is calculated to transform to the {665}<1 1 2.4> Rex texture, in agreement with the experimental result. This transformation relationship may be approximated by the transformation from the {111}<110> deformation

The {111}<112> orientation is not stable with respect to plane-strain compression. However, if the orientation survived during rolling, grains with the orientation must have been planestrain compressed. The plane-strain compressed (111)[1 1-2] crystal is calculated, by the full constrains model, to have slip systems of (110)[1-1-1] and (110) [-1 1-1], whose activities are the same, if we consider slip systems on one side of the rolling plane. It is noted that the slip directions are at acute angles to RD and on the same slip plane. AMSD is calculated to be [1-1-1] + [-1 1-1] = [0 0-2], which is parallel to a MYMD (Figure 56a). Therefore, the {111}<112> deformation texture is likely to remain unchanged during annealing (1st priority in Section 2).

Yoshinaga et al. [74] observed that a {111}<112> nucleation texture was strongly formed in 65% rolled iron electrodeposit with a weak {111}<112> texture, resulting in the {111}<112> Rex

ND//[111]

1] 1-TD//[0

0.0536 0.0086 0.0843 0.0536 0.0086 0.0843 0.0368 0.0148 0.0148

7.54

26.35

)111(

1]-1-RD//[2

[100]//MYMD

Recrystallization Textures of Metals and Alloys

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

45

)111(

1]//AMSD-1-[1

Slip direction 1-1-1 1-1 1 1 1-1

20 subsequently annealed at 695°C for 10 to 1000 s [71]. 21 pancake relaxations (*ε*13 and *ε*23 are relaxed.). The active slip systems of the (111)[1-1 0] crystal are **Figure 53.** Orientation densities along α and γ fibers for IF steel sheets cold-rolled by 80% and subsequently annealed at 695°C for 10 to 1000 s [71].

19 Figure 53. Orientation densities along and γ fibers for IF steel sheets cold-rolled by 80% and

22 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) 23 / *dε*11 with respect to *ε*11 are 0.0612, 0.0612, 0.107 and 0.107, respectively. It is noted 24 that the slip directions are chosen to be at acute angles with RD. The four slip systems can be 25 effectively divided into the following two slip systems. 0.0612(101)[1-1-1] + 0.107(211)[1-1-1] // 26 (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] // (-0.107 -0.2752 - 27 0.1682)[1-1 1] 28 These two slip systems are depicted as locating in the opposite sides of the rolling plane as shown in 29 Figure 54a, and they are physically equivalent. They may not be activated homogeneously, even 30 though they are equally activated macroscopically. In this case, AMSD is [1-1-1] or [1-1 1]. It should 31 be mentioned that all active slip directions are not summed unlike fcc metals in which all slip 32 directions are related to each other through associated slip planes. Figure 54b shows angular 33 relationships among MYMD [100], ND [111], and RD [2-1-1] in the (111)[2-1-1] grains, whose 34 orientation has been supposed to be the Rex texture of the (111)[1-1 0] rolling texture. It can be seen 35 that [1-1 1] in Figure 54a is not parallel to [100] in Figure 54b. According to SERM, the {111}<110> 36 rolling texture is not likely to link with the {111}<112> Rex texture. These two slip systems are depicted as locating in the opposite sides of the rolling plane as shown in Figure 54a, and they are physically equivalent. They may not be activated homoge‐ neously, even though they are equally activated macroscopically. In this case, AMSD is [1-1-1] or [1-1 1]. It should be mentioned that all active slip directions are not summed unlike fcc metals in which all slip directions are related to each other through associated slip planes. Figure 54b shows angular relationships among MYMD [100], ND [111], and RD [2-1-1] in the (111)[2-1-1] grains, whose orientation has been supposed to be the Rex texture of the (111)[1-1 0] rolling texture. It can be seen that [1-1 1] in Figure 54a is not parallel to [100] in Figure 54b. According to SERM, the {111}<110> rolling texture is not likely to link with the {111}<112> Rex texture.

37 Examining the experimental results more closely, the evolution of the {665}<1 1 2.4> Rex texture [(1,,<sup>2</sup> 38 )=(90,59.4,45)] appears to be linked to the {665}<110> deformation texture [(1,,<sup>2</sup> 39 )=(0,59.5,45) or (54.8,58.7,50)]. Let the (665)[1-1 0] orientation be an ideal 40 orientation representing the {665}<110> deformation texture. The (665)[1-1 0] orientation is 41 calculated to be stable using the rate sensitive slip with pancake relaxations. Calculated active slip 42 systems and their activities in the (665)[1-1 0] crystal are given in Table 4. Active slip directions are 43 [1-1-1], [1-1 1], and [1 1-1]. It is noted that the [1-1-1] and [1-1 1] slip directions are chosen to be at 44 acute angles with RD and physically equivalent. The [1 1-1] direction is normal to RD. The 45 relationship between various directions is shown in Figure 55. AMSD is therefore (0.0536 + 0.0086 + 46 0.0843)[1-1-1] + (0.0368 + 0.0148 + 0.0148)[-1-1 1] = [0.0801 -0.2129 -0.0801] // [1 -2.658 -1] or Examining the experimental results more closely, the evolution of the {665}<1 1 2.4> Rex texture [(*φ*1,Φ,*φ*2)=(90o ,59.4o ,45o )] appears to be linked to the {665}<110> deformation texture [(*φ*1,Φ,*φ*2)=(0o ,59.5o ,45o ) or (54.8o ,58.7o ,50o )]. Let the (665)[1-1 0] orientation be an ideal orienta‐ tion representing the {665}<110> deformation texture. The (665)[1-1 0] orientation is calculated to be stable using the rate sensitive slip with pancake relaxations. Calculated active slip systems and their activities in the (665)[1-1 0] crystal are given in Table 5. Active slip directions are [1-1-1], [1-1 1], and [1 1-1]. It is noted that the [1-1-1] and [1-1 1] slip directions are chosen to be at acute angles with RD and physically equivalent. The [1 1-1] direction is normal to RD. The relationship between various directions is shown in Figure 55. AMSD is therefore (0.0536 + 0.0086 + 0.0843)[1-1-1] + (0.0368 + 0.0148 + 0.0148)[-1-1 1] = [0.0801 -0.2129 -0.0801] // [1 -2.658 -1] or (0.0536 + 0.0086 + 0.0843)[1-1 1] + (0.0368 + 0.0148 + 0.0148)[1 1-1] = [0.2129 - 0.0801 0.0801] // [2.658 -1 1]. The second term direction in AMSD is determined physically with reference to Figure 55a. For the first term direction of [1-1 1], the angle between the [1-1 1] direction and TD [-1-1 2.4] direction is less than 90°. Therefore, the angle between the [-1-1 2.4] direction and the second direction, [-1-1 1] or [1 1-1], should be larger than 90o and so the [1 1-1] direction is chosen.

38 Book Title

(111)[1 1 0]

fiber

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

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

1

0 30 60 90

)] appears to be linked to the {665}<110> deformation texture

)]. Let the (665)[1-1 0] orientation be an ideal orienta‐

 10 s 20 s 30 s 50 s 100 s 120 s 150 s 200 s 400 s 1000 s

19 Figure 53. Orientation densities along and γ fibers for IF steel sheets cold-rolled by 80% and

**Figure 53.** Orientation densities along α and γ fibers for IF steel sheets cold-rolled by 80% and subsequently annealed

These two slip systems are depicted as locating in the opposite sides of the rolling plane as shown in Figure 54a, and they are physically equivalent. They may not be activated homoge‐ neously, even though they are equally activated macroscopically. In this case, AMSD is [1-1-1] or [1-1 1]. It should be mentioned that all active slip directions are not summed unlike fcc metals in which all slip directions are related to each other through associated slip planes. Figure 54b shows angular relationships among MYMD [100], ND [111], and RD [2-1-1] in the (111)[2-1-1] grains, whose orientation has been supposed to be the Rex texture of the (111)[1-1 0] rolling texture. It can be seen that [1-1 1] in Figure 54a is not parallel to [100] in Figure 54b. According to SERM, the {111}<110> rolling texture is not likely to link with the {111}<112> Rex

0

21 pancake relaxations (*ε*13 and *ε*23 are relaxed.). The active slip systems of the (111)[1-1 0] crystal are 22 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

(k) 23 / *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 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 -

These two slip systems are depicted as locating in the opposite sides of the rolling plane as shown in Figure 54a, and they are physically equivalent. They may not be activated homogeneously, even though they are equally activated macroscopically. In this case, AMSD is [1-1-1] or [1-1 1]. It should be mentioned that all active slip directions are not summed unlike fcc metals in which all slip directions are related to each other through associated slip planes. Figure 54b shows angular relationships among MYMD [100], ND [111], and RD [2-1-1] in the (111)[2-1-1] grains, whose orientation has been supposed to be the Rex texture of the (111)[1-1 0] rolling texture. It can be seen that [1-1 1] in Figure 54a is not parallel to [100] in Figure 54b. According to SERM, the {111}<110>

37 Examining the experimental results more closely, the evolution of the {665}<1 1 2.4> Rex texture

Examining the experimental results more closely, the evolution of the {665}<1 1 2.4> Rex texture

tion representing the {665}<110> deformation texture. The (665)[1-1 0] orientation is calculated to be stable using the rate sensitive slip with pancake relaxations. Calculated active slip systems and their activities in the (665)[1-1 0] crystal are given in Table 5. Active slip directions are [1-1-1], [1-1 1], and [1 1-1]. It is noted that the [1-1-1] and [1-1 1] slip directions are chosen to be at acute angles with RD and physically equivalent. The [1 1-1] direction is normal to RD. The relationship between various directions is shown in Figure 55. AMSD is therefore (0.0536 + 0.0086 + 0.0843)[1-1-1] + (0.0368 + 0.0148 + 0.0148)[-1-1 1] = [0.0801 -0.2129 -0.0801] // [1 -2.658 -1] or (0.0536 + 0.0086 + 0.0843)[1-1 1] + (0.0368 + 0.0148 + 0.0148)[1 1-1] = [0.2129 - 0.0801 0.0801] // [2.658 -1 1]. The second term direction in AMSD is determined physically with reference to Figure 55a. For the first term direction of [1-1 1], the angle between the [1-1 1] direction and TD [-1-1 2.4] direction is less than 90°. Therefore, the angle between the [-1-1 2.4] direction and the second direction, [-1-1 1] or [1 1-1], should be larger than 90o and so the [1 1-1] direction is

<sup>2</sup> 38 )=(90,59.4,45)] appears to be linked to the {665}<110> deformation texture

 39 )=(0,59.5,45) or (54.8,58.7,50)]. Let the (665)[1-1 0] orientation be an ideal orientation representing the {665}<110> deformation texture. The (665)[1-1 0] orientation is calculated to be stable using the rate sensitive slip with pancake relaxations. Calculated active slip systems and their activities in the (665)[1-1 0] crystal are given in Table 4. Active slip directions are [1-1-1], [1-1 1], and [1 1-1]. It is noted that the [1-1-1] and [1-1 1] slip directions are chosen to be at acute angles with RD and physically equivalent. The [1 1-1] direction is normal to RD. The relationship between various directions is shown in Figure 55. AMSD is therefore (0.0536 + 0.0086 + 0.0843)[1-1-1] + (0.0368 + 0.0148 + 0.0148)[-1-1 1] = [0.0801 -0.2129 -0.0801] // [1 -2.658 -1] or

20 subsequently annealed at 695°C for 10 to 1000 s [71].

0 30 60 90

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

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

fiber

44 Recent Developments in the Study of Recrystallization

36 rolling texture is not likely to link with the {111}<112> Rex texture.

,58.7o ,50o

) or (54.8o

strain rates *dγ*

0

27 0.1682)[1-1 1]

at 695°C for 10 to 1000 s [71].

f(g)

[(1,,

texture.

chosen.

[(1,,

,59.4o ,45o

,59.5o ,45o

[(*φ*1,Φ,*φ*2)=(90o

[(*φ*1,Φ,*φ*2)=(0o

**Figure 54.** Angular relationships (a) among AMSD, ND, and RD in rolled (111)[1-1 0] crystal and. (b) among MYMD, ND, and RD in (111)[2-1-1] crystal.


**Table 5.** Shear strain rates on slip systems in plane strain compressed (665)[1-1 0] crystal calculated based on rate sensitive pancake model [71]

For the (665)[-1-1 2.4] orientation as an orientation representing the {665}<1 1 2.4> Rex texture, the angles among ND, TD, RD, and [001] are shown in Figure 55b. Comparison of Figures 55a and 55b shows that AMSD in the deformed specimen is almost parallel to [001], MYMD of iron, in the Rexed specimen. This is compatible with SERM. In other words, the transformation from the (665)[1-1 0] deformation orientation to the (665)[1-1 2.4] Rex orientation is compatible with SERM. The deformed matrix and Rexed grains share the [665] ND (2nd priority in Section 2). Taking symmetry into account, the {665}<110> rolling texture is calculated to transform to the {665}<1 1 2.4> Rex texture, in agreement with the experimental result. This transformation relationship may be approximated by the transformation from the {111}<110> deformation texture to the {111}<112> Rex texture.

The {111}<112> orientation is not stable with respect to plane-strain compression. However, if the orientation survived during rolling, grains with the orientation must have been planestrain compressed. The plane-strain compressed (111)[1 1-2] crystal is calculated, by the full constrains model, to have slip systems of (110)[1-1-1] and (110) [-1 1-1], whose activities are the same, if we consider slip systems on one side of the rolling plane. It is noted that the slip directions are at acute angles to RD and on the same slip plane. AMSD is calculated to be [1-1-1] + [-1 1-1] = [0 0-2], which is parallel to a MYMD (Figure 56a). Therefore, the {111}<112> deformation texture is likely to remain unchanged during annealing (1st priority in Section 2). The {111}<112> grains may act as nuclei.

Yoshinaga et al. [74] observed that a {111}<112> nucleation texture was strongly formed in 65% rolled iron electrodeposit with a weak {111}<112> texture, resulting in the {111}<112> Rex texture, whereas a {111}<110> nucleation texture was formed in 80% rolled electrodeposit having a strong{111}<112> texture, resulting in the {111}<110> Rex texture. They noted the importance of the nucleation texture in the Rex texture formation and attributed to the {111}<110> Rex texturing in the 80% rolled sheet to higher mobility of grain boundaries between the {111}<110> grains and the{111}<112> deformed matrix. They did not account for the differences in nucleation texture between the 65% and 80% rolled sheets.

As the Rexed {665}<1 1 2.4> and {111}<112> grains grow, they are likely to meet the α fiber grains. If the Rexed grains are not in a favorable orientation relationship with the α fiber grains, they may not grow at the expense of the α fiber grains. This is discussed in the next section.

Recrystallization Textures of Metals and Alloys

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

47

Park et al. [75,76] discussed orientation relationships between the rolling and Rex textures in rolled IF steel sheets based on both SERM and the conventional OG, in which the α-fiber roll‐ ing texture was assumed to transform to the γ-fiber Rex texture. The {001}<110> and {112} <110>rolling orientations, which are main components in the α-fiber texture, are calculated to be stable using the full constraints Taylor model. For the (001)[110] orientation as an orienta‐ tion representing the {001}<110> orientation, active slip systems are calculated to be (1 1-2) [111] and (112)[1 1-1] from the full constraints Taylor model. Therefore, AMSD can be [111] or [1 1-1]. Figure 57a shows the angular relation between the [111] direction and the (001)[110] specimen axes. Figure 57b shows the angular relation between the [001] direction, which is a MYMD, and the axes of the specimen with the (111)[-1-1 2] Rex texture. It can be seen from Fig‐ ure 57 that AMSD in the deformed state is parallel to MYMD in the Rexed state and TD is shared by the deformed and Rexed states (2nd priority in Section 2). Taking the symmetry into account, the {001}<110> deformation texture is calculated to transform into the {111}<112> Rex texture. This transformation was observed in the experimental results (Figures 52 and 53, [75], [77]). It is often addressed that the {001}<110> orientation is difficult to be Rexed. It may be at‐

For the (558)[1-1 0] orientation as an orientation representing the {558}<110> orientation, active slip systems are calculated to be 2.283(101)[1-1-1], (101)[-1-1 1], 2.283(0-1-1)[1-1 1], and (0-1-1) [1 1-1] from the full constraints Taylor model, where the factor 2.283 in front of slip systems in‐ dicates that their activities are 2.283 times higher than other slip systems [66]. The slip systems reduce effectively to (101)[1-2.56-1] and (0-1-1)[2.56-1 1]. Therefore, AMSD becomes [1-2.56-1] or [2.56 -1 1]. Figure 58 shows that the [1-2.56-1] direction in the (558)[1-10] crystal is nearly par‐ allel to MYMD in the Rexed state, and the [101] direction is shared by the deformed and Rexed states (2nd priority in Section 2). Taking the symmetry into account, the {558}<110> deforma‐ tion texture is calculated to transform into the {334}<483> Rex texture. This transformation rela‐ tion was observed in the experimental result. The {334}<483> orientation is away from the {111}<112> orientation. An exact correspondence between the (112)[-110] deformation and

74.54

ND//[111]

10]1TD//[

26.35

MYMD//[001]

(111)

2]11RD//[

tributed to the fact that the orientation has a low Taylor factor [66].

(-2.45 2 –2.45)[1 2.45 1] Rex orientations can be seen in Figure 59.

AMSD//[111]

(001)

RD//[110]

**Figure 57.** AMSD in (001)[110] rolled crystal and MYMD in (111)[-1-1 2] Rexed crystal [71].

74.54

ND//[001]

10]1TD//[

26.35

**8.2. Recrystallization in α fiber grains**

**Figure 55.** (a) AMSD in (665)[1-1 0] rolled crystal; (b) MYMD in (665)[-1-1 2.4] Rexed crystal [71].

**Figure 56.** Explanation of {111}<112> rolling texture changing to {111}<112> or {111}<110> after Rex. F'B' and F'D' are MYMDs in Rexed state and are almost parallel to AMSDs, FB and FD, in deformed state, respectively [5].

According to SERM, the {111}<112> deformation texture is likely to remain unchanged after Rex because AMSD in the deformed state is parallel to MYMD, as mentioned above. If the activities of the slip systems of (110)[-1 1-1] and (110)[1-1-1] in Figure 56a are well balanced, MYMD becomes [0 0-1]. This may be the case in the 65% rolled sheet. As the rolling reduction increases, the balance can be broken. When the (110)[1-1-1] slip system is two times more active than the (110)[-1 1-1] system, AMSD is parallel to the [1-1-3] direction (2[1-1-1] + [-1 1-1] = [1-1 -3]). Similarly if the (110)[-1 1-1] system is two times more active than the (110)[1-1-1] slip system, AMSD is parallel to the [-1 1-3] direction. These directions are shown in Figure 56a. If one of the two slips takes place in one layer and another one does in another layer and so on, as in *ε*23 relaxation, the rolling texture macroscopically appears the same as in the balanced slip. When these AMSDs are made to be parallel to MYMD, one of the <100> directions, as shown in Figures 56b and 56c, we come to the result that the {111}<112> rolling texture is linked with the {111}<32 31 1> Rex texture that is approximated by the {111}<110> texture.

As the Rexed {665}<1 1 2.4> and {111}<112> grains grow, they are likely to meet the α fiber grains. If the Rexed grains are not in a favorable orientation relationship with the α fiber grains, they may not grow at the expense of the α fiber grains. This is discussed in the next section.

#### **8.2. Recrystallization in α fiber grains**

texture, whereas a {111}<110> nucleation texture was formed in 80% rolled electrodeposit having a strong{111}<112> texture, resulting in the {111}<110> Rex texture. They noted the importance of the nucleation texture in the Rex texture formation and attributed to the {111}<110> Rex texturing in the 80% rolled sheet to higher mobility of grain boundaries between the {111}<110> grains and the{111}<112> deformed matrix. They did not account for the

59

ND//[665]

90

)111(

b ND//[111]

1]-31-RD//[32

0] 1TD//[1

31

b

21] 11-TD//[-10

F

O

MYMD//[001]

(665)

2.4] 11RD//[

)111(

D

1]-31-RD//[32

differences in nucleation texture between the 65% and 80% rolled sheets.

0] 1RD//[1

**Figure 55.** (a) AMSD in (665)[1-1 0] rolled crystal; (b) MYMD in (665)[-1-1 2.4] Rexed crystal [71].

ND//[111]

ND//[111] c

O

OA//FC//[0 0-1], OC//[-1 1-1], EC//[1-1-1], FB//[1-1-3], FD//[-1 1-3], FB//[0-1 0], FD//[100] BFC=CFD=25.2, (FB,TD)=64.8, (FB,RD)=42.4, (OA,RD)=35.3, (FD,TD)=115.2 (FD,RD)=42.4, (FB,TD)=64.7, (FB,RD)=45.9, (FD,TD)=115.9, (FD,RD)=44

**Figure 56.** Explanation of {111}<112> rolling texture changing to {111}<112> or {111}<110> after Rex. F'B' and F'D'

According to SERM, the {111}<112> deformation texture is likely to remain unchanged after Rex because AMSD in the deformed state is parallel to MYMD, as mentioned above. If the activities of the slip systems of (110)[-1 1-1] and (110)[1-1-1] in Figure 56a are well balanced, MYMD becomes [0 0-1]. This may be the case in the 65% rolled sheet. As the rolling reduction increases, the balance can be broken. When the (110)[1-1-1] slip system is two times more active than the (110)[-1 1-1] system, AMSD is parallel to the [1-1-3] direction (2[1-1-1] + [-1 1-1] = [1-1 -3]). Similarly if the (110)[-1 1-1] system is two times more active than the (110)[1-1-1] slip system, AMSD is parallel to the [-1 1-3] direction. These directions are shown in Figure 56a. If one of the two slips takes place in one layer and another one does in another layer and so on, as in *ε*23 relaxation, the rolling texture macroscopically appears the same as in the balanced slip. When these AMSDs are made to be parallel to MYMD, one of the <100> directions, as shown in Figures 56b and 56c, we come to the result that the {111}<112> rolling texture is linked

<sup>B</sup> <sup>F</sup>

21] 11-TD//[-10

are MYMDs in Rexed state and are almost parallel to AMSDs, FB and FD, in deformed state, respectively [5].

with the {111}<32 31 1> Rex texture that is approximated by the {111}<110> texture.

a

)111(

AMSD//[2.6 1]16 (665)

1]1[1

60

2.4] 11TD//[

0] 1-TD//[1

F

O

ND//[665]

46 Recent Developments in the Study of Recrystallization

31

2]-1 RD//[1

E D C B A

a

)110(

85

17.60

Park et al. [75,76] discussed orientation relationships between the rolling and Rex textures in rolled IF steel sheets based on both SERM and the conventional OG, in which the α-fiber roll‐ ing texture was assumed to transform to the γ-fiber Rex texture. The {001}<110> and {112} <110>rolling orientations, which are main components in the α-fiber texture, are calculated to be stable using the full constraints Taylor model. For the (001)[110] orientation as an orienta‐ tion representing the {001}<110> orientation, active slip systems are calculated to be (1 1-2) [111] and (112)[1 1-1] from the full constraints Taylor model. Therefore, AMSD can be [111] or [1 1-1]. Figure 57a shows the angular relation between the [111] direction and the (001)[110] specimen axes. Figure 57b shows the angular relation between the [001] direction, which is a MYMD, and the axes of the specimen with the (111)[-1-1 2] Rex texture. It can be seen from Fig‐ ure 57 that AMSD in the deformed state is parallel to MYMD in the Rexed state and TD is shared by the deformed and Rexed states (2nd priority in Section 2). Taking the symmetry into account, the {001}<110> deformation texture is calculated to transform into the {111}<112> Rex texture. This transformation was observed in the experimental results (Figures 52 and 53, [75], [77]). It is often addressed that the {001}<110> orientation is difficult to be Rexed. It may be at‐ tributed to the fact that the orientation has a low Taylor factor [66].

For the (558)[1-1 0] orientation as an orientation representing the {558}<110> orientation, active slip systems are calculated to be 2.283(101)[1-1-1], (101)[-1-1 1], 2.283(0-1-1)[1-1 1], and (0-1-1) [1 1-1] from the full constraints Taylor model, where the factor 2.283 in front of slip systems in‐ dicates that their activities are 2.283 times higher than other slip systems [66]. The slip systems reduce effectively to (101)[1-2.56-1] and (0-1-1)[2.56-1 1]. Therefore, AMSD becomes [1-2.56-1] or [2.56 -1 1]. Figure 58 shows that the [1-2.56-1] direction in the (558)[1-10] crystal is nearly par‐ allel to MYMD in the Rexed state, and the [101] direction is shared by the deformed and Rexed states (2nd priority in Section 2). Taking the symmetry into account, the {558}<110> deforma‐ tion texture is calculated to transform into the {334}<483> Rex texture. This transformation rela‐ tion was observed in the experimental result. The {334}<483> orientation is away from the {111}<112> orientation. An exact correspondence between the (112)[-110] deformation and (-2.45 2 –2.45)[1 2.45 1] Rex orientations can be seen in Figure 59.

**Figure 57.** AMSD in (001)[110] rolled crystal and MYMD in (111)[-1-1 2] Rexed crystal [71].

[111] directions. They are calculated to be the (112) and/or (1 1-2) planes. The related slip sys‐ tems are therefore (112)[-1-1 1] and (1 1-2)[111]. These systems are physically equivalent. There‐ fore, it is sufficient to choose one of them. Let us choose the [111] direction. The [111] direction and other related directions and planes are shown in Figure 60a. The [111] direction is on ND-

Rolled

(101)

ND//[545]

1]-1 TD//[1

ND//[112]

1]-0 TD//[1

a b c

which is the usually observed angle between the shear band and RD.

5.60

xedRe

**Figure 60.** Correspondence between AMSD in rolled state (top), MYMD in Rexed state (bottom) in orientation rela‐ tionships between (a) (001)[110] roll ↔ (111)[-1-1 2] Rex, (b) (112)[-110] roll ↔ (545)[-2 5-2] Rex, (c) (114)[-110] roll

If the [111] direction in the deformed state is set to be parallel to MYMD [001] in the Rexed state, the (111) plane becomes parallel to the rolling plane and the [-1-1 2] direction becomes parallel to RD in the Rexed state, giving rise to the (111)[-1-1 2] Rex texture as shown in Figure 60a. This result is the same as that obtained based on the full-constraints Taylor mod‐ el (Figure 57). Therefore, the {001}<110> may be responsible for the measured {111}<112> Rex texture. It is noted that the [-110] TD is shared by both the deformed and Rexed states (2nd priority in Section 2). It is also noted that the angle between AMSD and RD is about 30o

Other examples in Figure 60 are self-explainable. In all the examples except Figure 60d, the <110> directions are shared by the deformed and Rexed states. In fact, the Rex textures in Figure 60b and 60c are very similar. This is the reason why there exists an angular relation between the deformed and Rexed states about the <110> axes (Table 6). This has often been interpreted to be associated with CSL boundaries. However, there is no consistency in the CSL boundaries. Anyhow the high density orientations along the α fiber change to near

As the Rexed γ fiber grains grow, they are likely to meet the α fiber grains. Main components in α fiber including the {112}<110> orientation are predicted to tend to change to near {111}<112> orientations according to SERM. Therefore, the {111}<112> Rexed grains will grow at the ex‐ pense of the α fiber grains with little disturbance of orientation. It is interesting to note that SERM can satisfy the relation between the deformation and Rex textures in the nucleation and growth stages. The two prominent components, (334)[4-8 3] and (554)[-2-2 5], in the Rex texture are related to the (558)[1-1 0] and (112)[1-1 0] components in the rolling texture, respectively.

MYMD//[010 ] 5.29 )545(

AMSD//[-12 1] <sup>30</sup>


01) 1( )112(

5.19 - ]111[

2]-5 RD//[-2

4.13 40]-19-TD//[67

67) 0 40( )556(

4) 1-3( )114(

36

3.57

ND//[556]

1]-2 TD//[2

35

11 - ]232[ <sup>57</sup>

ND//[114]

MYMD//[010 ]

AMSD//[-111]

Recrystallization Textures of Metals and Alloys

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

49


5]-7 RD//[-1

RD plane. Therefore, it is likely to be AMSD.

MYMD//[001 ] 26.35 10) 1( )111(

2] 1-RD//[-1

AMSD//[111]

]110//[RD

2)-1 1( )001(

ND//[111]

TD//[-110]

26.35

ND//[001]

TD//[-110]

{111}<112> orientations on Rex.

↔ (556)[-1 7-5] Rex.

**Figure 58.** AMSD in (558)[1-1 0] rolled crystal and MYMD in (334)[4-8 3] Rexed crystal [71].

**Figure 59.** AMSD in (112)[-110] rolled crystal and MYMD in (-2.45 2 -2.45)[1 2.45 1] Rexed crystal [71].

Park et al. [75] studied relationships between rolling and Rex textures of IF steel. When the {112}<110>, {225}<110>, and {112}<110> components had the highest density in cold rolling texture, the {567}<943>, {223}<472>, and {554}<225> components had the highest density in Rex texture, respectively. Rolling and Rex textures of low carbon steel (C in solution), and Fe-16%Cr and Fe-3%Si steels indicate that the strong rolling texture components {001}<110> and {112}<110> have an effect on the evolution of a very strong Rex texture {111}<112> [77].

Park et al. [76] investigated the macrotexture changes in 75% cold-rolled IF steel with an‐ nealing time at 650ºC along the α-fiber. The cold rolling texture showed the development of the α fiber as typical in bcc steels. The orientation densities of the α-fiber increased slightly after annealing for 300 s. This is a well-known recovery phenomenon. A part of the α-fiber, near {114}<110>, substantially decreased after annealing for 1000 s. EBSD analysis indicated that the {556}<175> Rex component was formed at the expense of the {114}<110> deformation component. This texture transformation could be explained by SERM. Relationships be‐ tween various rolling and Rex textures are summarized in Table 6.

These results can be explained based on SERM [4,75,76]. Figure 60 shows drawings relating the rolling texture components to the Rex texture components. AMSDs can be easily obtained by choosing the <111> directions, the slip directions in bcc metals, closest to 45o to the compression axis without calculation of rolling deformation. For the cold rolling texture (001)[110], TD is cal‐ culated by the vector product of [110] and [001] to be [-110]. The <111> directions closest to 45o with the [001] compression axis are [-111], [-1-1 1], and [111]. The [-111] direction is likely to con‐ tribute to spread of the width of sheets. Therefore, slip along the [-111] direction is unlikely. The effective slip planes are likely to be parallel to TD and contain the [111] and [-1-1 1] slip direc‐ tions. The planes are those normal to the vector product of the [-110] TD and the [-1-1 1] and/or [111] directions. They are calculated to be the (112) and/or (1 1-2) planes. The related slip sys‐ tems are therefore (112)[-1-1 1] and (1 1-2)[111]. These systems are physically equivalent. There‐ fore, it is sufficient to choose one of them. Let us choose the [111] direction. The [111] direction and other related directions and planes are shown in Figure 60a. The [111] direction is on ND-RD plane. Therefore, it is likely to be AMSD.

32

30

01]1TD//[

]2.45 2 2.45ND//[

MYMD//[0 0]1

MYMD//[0 0]1

1] 2.45 RD//[1

to the compression

(101)~ (334)

83 3]8RD//[4

(101)

» 01]1[36] 7 41TD//[

ND//[334]

6.30

30

]1TD//[11

ND//[112]

3.86 0]1RD//[1

]1 2.56 AMSD//[1

**Figure 58.** AMSD in (558)[1-1 0] rolled crystal and MYMD in (334)[4-8 3] Rexed crystal [71].

21]1AMSD//[

tween various rolling and Rex textures are summarized in Table 6.

choosing the <111> directions, the slip directions in bcc metals, closest to 45o

(101) (112)

0]1RD//[1

**Figure 59.** AMSD in (112)[-110] rolled crystal and MYMD in (-2.45 2 -2.45)[1 2.45 1] Rexed crystal [71].

Park et al. [75] studied relationships between rolling and Rex textures of IF steel. When the {112}<110>, {225}<110>, and {112}<110> components had the highest density in cold rolling texture, the {567}<943>, {223}<472>, and {554}<225> components had the highest density in Rex texture, respectively. Rolling and Rex textures of low carbon steel (C in solution), and Fe-16%Cr and Fe-3%Si steels indicate that the strong rolling texture components {001}<110> and {112}<110> have an effect on the evolution of a very strong Rex texture {111}<112> [77]. Park et al. [76] investigated the macrotexture changes in 75% cold-rolled IF steel with an‐ nealing time at 650ºC along the α-fiber. The cold rolling texture showed the development of the α fiber as typical in bcc steels. The orientation densities of the α-fiber increased slightly after annealing for 300 s. This is a well-known recovery phenomenon. A part of the α-fiber, near {114}<110>, substantially decreased after annealing for 1000 s. EBSD analysis indicated that the {556}<175> Rex component was formed at the expense of the {114}<110> deformation component. This texture transformation could be explained by SERM. Relationships be‐

These results can be explained based on SERM [4,75,76]. Figure 60 shows drawings relating the rolling texture components to the Rex texture components. AMSDs can be easily obtained by

axis without calculation of rolling deformation. For the cold rolling texture (001)[110], TD is cal‐ culated by the vector product of [110] and [001] to be [-110]. The <111> directions closest to 45o with the [001] compression axis are [-111], [-1-1 1], and [111]. The [-111] direction is likely to con‐ tribute to spread of the width of sheets. Therefore, slip along the [-111] direction is unlikely. The effective slip planes are likely to be parallel to TD and contain the [111] and [-1-1 1] slip direc‐ tions. The planes are those normal to the vector product of the [-110] TD and the [-1-1 1] and/or

(101)~ (558)

5] 4 4TD//[

ND//[558]

48 Recent Developments in the Study of Recrystallization

**Figure 60.** Correspondence between AMSD in rolled state (top), MYMD in Rexed state (bottom) in orientation rela‐ tionships between (a) (001)[110] roll ↔ (111)[-1-1 2] Rex, (b) (112)[-110] roll ↔ (545)[-2 5-2] Rex, (c) (114)[-110] roll ↔ (556)[-1 7-5] Rex.

If the [111] direction in the deformed state is set to be parallel to MYMD [001] in the Rexed state, the (111) plane becomes parallel to the rolling plane and the [-1-1 2] direction becomes parallel to RD in the Rexed state, giving rise to the (111)[-1-1 2] Rex texture as shown in Figure 60a. This result is the same as that obtained based on the full-constraints Taylor mod‐ el (Figure 57). Therefore, the {001}<110> may be responsible for the measured {111}<112> Rex texture. It is noted that the [-110] TD is shared by both the deformed and Rexed states (2nd priority in Section 2). It is also noted that the angle between AMSD and RD is about 30o which is the usually observed angle between the shear band and RD.

Other examples in Figure 60 are self-explainable. In all the examples except Figure 60d, the <110> directions are shared by the deformed and Rexed states. In fact, the Rex textures in Figure 60b and 60c are very similar. This is the reason why there exists an angular relation between the deformed and Rexed states about the <110> axes (Table 6). This has often been interpreted to be associated with CSL boundaries. However, there is no consistency in the CSL boundaries. Anyhow the high density orientations along the α fiber change to near {111}<112> orientations on Rex.

As the Rexed γ fiber grains grow, they are likely to meet the α fiber grains. Main components in α fiber including the {112}<110> orientation are predicted to tend to change to near {111}<112> orientations according to SERM. Therefore, the {111}<112> Rexed grains will grow at the ex‐ pense of the α fiber grains with little disturbance of orientation. It is interesting to note that SERM can satisfy the relation between the deformation and Rex textures in the nucleation and growth stages. The two prominent components, (334)[4-8 3] and (554)[-2-2 5], in the Rex texture are related to the (558)[1-1 0] and (112)[1-1 0] components in the rolling texture, respectively.


in {001}<110> to {112}<110> accompanied by a strong increase in γ-fiber {111}<112> and/or

**Figure 62.** (a) φ<sup>2</sup> =45° ODF section of center of Mo sheet annealed for 1h at 925°C and (b) orientation density along α-

The deformation texture of rolled Mo sheets was characterized by a weak γ-fiber and α-fiber with a strong {100}<110> component [79]. Full Rex does not change the rolling texture but reduces its intensity (Figure 62). This result is compatible with SERM considering that the <111> directions are not only slip directions, which is approximately AMSD (Figure 60a, top), but also MYMD of Mo (*A*<0 in Table 7) (1st priority in Section 2). The decrease in orientation density

Since the slip systems of W are {112}<111> [80], it is predicted that the {001}<110> component dominates the rolling texture as shown in Figure 60a. Figure 63a shows the rolling texture which is dominated by the {100}<011> component as predicted. The deformation texture is approximately randomized after Rex (Figure 63b). This is compatible with SERM because W

**Material Temp., K f** *S11* **f** *S44* **f S12** *A* **Reference**

13.966 14.025 14.184 14.409

9.158 9.242 9.823

6.158 6.218 6.553 7.375 -3.150 -3.224 -3.274 -3.357



Recrystallization Textures of Metals and Alloys

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

51

0.7052 0.7092 0.7824

0.9948 1.0113 1.0710 1.2662 82

83

{554}<225> due to Rex. The Rex behavior is readily understood from Figure 60 [4, 75].

b a

110}001{ 110}001{

during annealing may be attributed to *A* being close to unity.

is almost isotropic in its elastic properties (*A*≈1 in Table 7).

8.137 8.297 8.408 8.576

2.607 2.655 3.010

2.398 2.454 2.711 3.509

> 273 373 973

**Table 7.** *Sij* (GPa-1) and *A*=2(*S*11-*S*12)/*S*44 for Ta, Mo, and W. f =1000

110}110{

Ta

Mo

W

fiber in central zone of Mo sheet annealed at 850°C [79].

110}111{ 110}112{

**Table 6.** Orientation relationships (OR) between major components which dominate rolling and Rex textures.

**Figure 61.** Orientation densities along α- and β- fibers for 70% rolled and annealed Ta [78].

#### **8.3. Recrystallization in non-ferrous bcc metals**

The texture evolution in Ta after 70% rolling and subsequent annealing at various temperatures is shown in Figure 61 [78]. The rolling texture of Ta is characterized by a partial α-fiber extending from {001}<110> to {111}<110> and a complete γ-fiber {111}<uvw>. The major deformation texture components are {112}<110> and {001}<110> as in steel. MYMD of Ta is <100> (A>0 in Table 6), the development of the Rex texture is expected to be similar to that in steel. It can be seen that an enhancement of {001}<110> due to recovery and a strong decrease in {001}<110> to {112}<110> accompanied by a strong increase in γ-fiber {111}<112> and/or {554}<225> due to Rex. The Rex behavior is readily understood from Figure 60 [4, 75].

**Rolling texture Component**

50 Recent Developments in the Study of Recrystallization

**Rex texure Component**

{114}<110> {556}<175> 35 36

**RD↔AMSD (°)**

{112}<110> {567}<943> 30 29 30°<110> Σ19a(26.5°<110>)

{225}<110> {223}<472> 35.3 32.6 25°<110> Σ19a(26.5°<110>)

{112}<110> {554}<225> 30 29.5 35°<110> Σ9(38.9°<110>)

{001}<110> {111}<112> 35.3 35.3 55°<110> Σ11(50.5°<110>)

{558}<110> {334}<483> 30.6 32 29°<110> Σ19a (26.5°<110>

**Table 6.** Orientation relationships (OR) between major components which dominate rolling and Rex textures.

**Figure 61.** Orientation densities along α- and β- fibers for 70% rolled and annealed Ta [78].

The texture evolution in Ta after 70% rolling and subsequent annealing at various temperatures is shown in Figure 61 [78]. The rolling texture of Ta is characterized by a partial α-fiber extending from {001}<110> to {111}<110> and a complete γ-fiber {111}<uvw>. The major deformation texture components are {112}<110> and {001}<110> as in steel. MYMD of Ta is <100> (A>0 in Table 6), the development of the Rex texture is expected to be similar to that in steel. It can be seen that an enhancement of {001}<110> due to recovery and a strong decrease

**8.3. Recrystallization in non-ferrous bcc metals**

**RD↔MYMD (°)**

**Observed OR**

**Coincidence site lattice relation**

**Figure 62.** (a) φ<sup>2</sup> =45° ODF section of center of Mo sheet annealed for 1h at 925°C and (b) orientation density along αfiber in central zone of Mo sheet annealed at 850°C [79].

The deformation texture of rolled Mo sheets was characterized by a weak γ-fiber and α-fiber with a strong {100}<110> component [79]. Full Rex does not change the rolling texture but reduces its intensity (Figure 62). This result is compatible with SERM considering that the <111> directions are not only slip directions, which is approximately AMSD (Figure 60a, top), but also MYMD of Mo (*A*<0 in Table 7) (1st priority in Section 2). The decrease in orientation density during annealing may be attributed to *A* being close to unity.

Since the slip systems of W are {112}<111> [80], it is predicted that the {001}<110> component dominates the rolling texture as shown in Figure 60a. Figure 63a shows the rolling texture which is dominated by the {100}<011> component as predicted. The deformation texture is approximately randomized after Rex (Figure 63b). This is compatible with SERM because W is almost isotropic in its elastic properties (*A*≈1 in Table 7).


**Table 7.** *Sij* (GPa-1) and *A*=2(*S*11-*S*12)/*S*44 for Ta, Mo, and W. f =1000

components are calculated to result from the {112}<111> and (123)[-6-3 4] components in

Recrystallization Textures of Metals and Alloys

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53

**8.** The {011}<211>, {112}<111>, and {123}<634> components in the rolling texture of coldrolled polycrystalline fcc metals and alloys with medium to high stacking fault energy are respectively linked with the {011}<100>, {100}<001>, and {031}<100> component in the Rex

**9.** The {111}<112> bcc crystal undergoing plane strain rolling can develop three different Rex textures of {441}<118>≈ {110}<001>, {111}<112>, and ~{111}<110> depending on local slip

**10.** The {665}<110>, {001}<110>, {558}<110>, {112}<110>, {114}<110> components in the rolling texture of steel are respectively linked with the {665}<1 1 2.4>, {111}<112>, {334}<483>,

**13.** The rolling texture of W transforms to a texure which can be approximated by random

This study was supported by a grant (0592-20120019) from POSCO and a grant(0417-20110114)

Department of Materials Science and Engineering, Seoul National University, Seoul, Repub‐

[1] Burgers WG, Louwerse PC. Über den Zusammenhang zwischen Deformationsvorgang und Rekristallisationstextur bei Aluminium. Zeitschrift für Physik 1931; 61 605-678.

[2] Barrett CS. Recrystallization texture in aluminum after compression. Trans AIME 1940;

systems and their activities in the same gloval deformation.

{545}<252>, {556}<175> components in the Rex texture.

**11.** The rolling and Rex textures of Ta are similar to those of steel.

**12.** Full Rex of Mo does not change the rolling texture but reduces its intensity.

from Center for Iron & Steel Research of RIAM in Seoul National University.

the deformation textures, respectively.

orientation distribution after Rex.

Dong Nyung Lee and Heung Nam Han

**Acknowledgements**

**Author details**

lic of Korea

**References**

137 128-145.

texture.

**Figure 63.** Pole figure of W sheet (a) after cold rolling by 96% and (b) subsequent annealing at 2000 °C for 30 min [81]. Max intensity: (a) >16 and (b) >4. Contour levels: 1/2, 1, 2, 4, 8, 16.
