**6. Cold-rolled polycrystalline fcc metals and alloys**

### **6.1. Cube recrystallization texture**

The rolling texture of fcc sheet metals with medium to high stacking fault energies is known to consist of the brass orientation {011}<211>, the Cu orientation {112}<111>, the Goss orienta‐ tion {011}<100>, the S orientation {123}<634>, and the cube orientation {100}<001>. The fiber connecting the brass, Cu, and S orientations in the Euler space is called the β fiber. Major components of the plane-strain rolling texture of polycrystalline Al and Cu are known to be the Cu and S orientations. The Rex texture of rolled Al and Cu sheets is well known to be the cube texture. The 40°<111> orientation relationship between the S texture and the cube texture has been taken as a proof of OG, and has made one believe that the S orientation is more responsible for the cube Rex texture. OG is claimed to be associated with grain boundary mobility anisotropy. However, experimental data indicate that the Cu texture is responsible for the cube texture. For an experimental result of Table 3, the deformation texture is not strongly developed below a reduction of 73% and its Rex texture is approximately random. At a reduction of 90%, a strong Cu texture is obtained and its Rex texture is a strong cube texture. For 95% cold rolled Al-0 to 9%Mg alloy after annealing at 598K for 0.5 to 96 h, the highest density in the Cu component in the deformation texture and the highest density in the cube component in Rex textures were observed at about 3% Mg (Figure 37). This implies that the Cu component is responsible for the cube component. However, these cannot prove that the Cu texture is responsible for the cube texture because deformation components with the highest density are not always linked with highest Rex components [47].

The calculated Rex orientation is (0.049 3.543–1.192)[7.801-0.017-0.275] ≈ (0 3-1)[100]. Similarly the (321)[-436] crystal is calculated to have slip systems of (111)[-101], (111)[-110], (-1-1 1)[011], and (-1 1-1)[011], on which the shear strain rates at *dε*11=0 are 0.014, 0.003, 0.01, and 0.007, respectively. The (321)[-436] is calculated to transform to the (-0.049 3.543-1.192)[7.801 0.017 -0.275] ≈ the (0 3-1)[100] Rex texture. This result is understandable from the fact that the (0 3-1) [100] orientation is symmetrical with respect to TD as shown in Figure 36b and the deformation orientations, (123)[-6-3 4] and (321)[-436], are also symmetrical with respect to TD as shown in Figure 35b. The {112}<111> rolling orientation to the {001}<100> Rex orientation transformation

According to the discussion in Section 6.1, if the cube oriented regions are generated during rolling, they are likely to survive and act as nuclei and grow at the expense of neighboring {112}<111> region during annealing because the region tend to transform to the {001}<100> orientation to reduce energy. The grown-up cube grains will grow at the expense of grains having other orientations such as the {123}<634> orientation, resulting in the {001}<100> texture after Rex, even though the Cu orientation is a minor component in the deformation texture. Meanwhile, the main S component in the deformation texture can form its own Rex texture, the near (0 3-1)[100] orientation. In this case, the Rex texture may be approximated by main (001)[100] and minor (0 3-1)[001] components. Figure 36b shows the texture calculated assuming Gaussian scattering (half angle=10°) of these components with the intensity ratio of (001)[100]: (0 3-1)[001] = 2 : 1. It is interesting to note that the cube peaks diffuse rightward under the influence of the minor (0 3-1)[100] component in agreement with experimental result

The rolling texture of fcc sheet metals with medium to high stacking fault energies is known to consist of the brass orientation {011}<211>, the Cu orientation {112}<111>, the Goss orienta‐ tion {011}<100>, the S orientation {123}<634>, and the cube orientation {100}<001>. The fiber connecting the brass, Cu, and S orientations in the Euler space is called the β fiber. Major components of the plane-strain rolling texture of polycrystalline Al and Cu are known to be the Cu and S orientations. The Rex texture of rolled Al and Cu sheets is well known to be the cube texture. The 40°<111> orientation relationship between the S texture and the cube texture has been taken as a proof of OG, and has made one believe that the S orientation is more responsible for the cube Rex texture. OG is claimed to be associated with grain boundary mobility anisotropy. However, experimental data indicate that the Cu texture is responsible for the cube texture. For an experimental result of Table 3, the deformation texture is not strongly developed below a reduction of 73% and its Rex texture is approximately random. At a reduction of 90%, a strong Cu texture is obtained and its Rex texture is a strong cube texture. For 95% cold rolled Al-0 to 9%Mg alloy after annealing at 598K for 0.5 to 96 h, the highest density in the Cu component in the deformation texture and the highest density in the

is discussed based on SERM in Section 6.1.

30 Recent Developments in the Study of Recrystallization

**6. Cold-rolled polycrystalline fcc metals and alloys**

in Figure 34c.

**6.1. Cube recrystallization texture**

Changes in orientation densities of 95% rolled Cu during annealing at 400 to 500 °C (Figure 38), 95% rolled AA8011 Al alloy during annealing at 350 °C (Figure 39a), and 95% rolled Fe-50%Ni alloy during annealing at 600℃ (Figure 39b), and 95% rolled Cu after heating to 150 to 300℃ at a rate of 2.5 K/s followed by quenching showing that the Cu component disappears most rapidly when the cube orientation started to increase [52]. These results imply that the Cu component is responsible for the cube Rex texture. Rex is likely to occur first in high strain energy regions. It is known that the energy stored in highly deformed crystals is proportional to the Taylor factor (Σ*dγ*(*k*) */dεij* with *γ* and *εij* being shear strains on slip systems *k* and strains of specimen, respectively). The Taylor factor is calculated to be 2.45 for the cube oriented fcc crystal using the full constraints model, 3.64 for the Cu oriented fcc crystal using the ε<sup>13</sup> relaxed constraints rate sensitive model, 3.24 for the S oriented fcc crystal using the *ε*13 and *ε*23 relaxed constraints rate sensitive model, and 2.45 for the brass orientation using the ε12 and ε23 relaxed constraints rate sensitive model. In the rate sensitive model calculation, the rate sensitivity index was 0.01 and each strain step in rolling was 0.025. The measured stored energies for 99.99% Al crystals channel-die compressed by a strain of 1.5 showed that the Cu oriented region had higher energies than the S oriented region [53]. The Taylor factors and the measured stored energies indicate that the driving force for Rex is higher in the Cu oriented grains than in the S oriented grains. Therefore, the Cu component in the deformation texture is more responsible for the cube Rex texture than the S component.


**Table 3.** Texture component strength of high purity OFE copper [46]

The copper to cube texture transition was first explained by SERM [4], and elaborated later [54]. The orientations of the (112)[1 1-1] and (123)[6 3-4] Cu single crystals remain stable in the center layer for all degree of rolling [55]. The Cu orientation (112)[1 1-1] is calculated to be stable by the *ε*13 relaxed constraint model [56,57]. For the (112)[1 1-1] crystal, the active slip systems are calculated by the RC model to be (-1 1-1)[110], (1-1-1)[110], (111)[1 0-1], and (111) [0 1-1], on which shear strain rates are the same regardless of reduction ratio. Almost the same

8 9

27

texture.

Rex or recovery (1st priority in Section 2).

**6.2. Goss recrystallization texture**

result is obtained by ε13, ε23 relaxed constraints rate sensitive model [54]. The slip directions are chosen to be at acute angles with RD (Section 2). To calculate AMSD, the active slip systems are weighted by the shear strain rates on them. AMSD is calculated to be [0 1-1] + [1 0-1] + 0.577 × 2[110] ≈ 2 [1 1-1]. Here the factor 0.577 is related to the fact that the slip direction [110] is shared by the (-1 1-1) and (1-1-1) slip planes (Eq. 7). The [1 1-1] direction is equivalent to **A** in Figure 6. **S** becomes [1-1 0] because it is one of slip directions nearest to 90° with **A**. In fact. **S** is normal to **A**, so **S** becomes **B** and **C** = **A**×**B** = [-1-1-2]. Since MYMDs are <100>, the Rex orientation is calculated using Eq. 9 to be (0 0-1)[100], which is equivalent to (001)[100]. In conclusion, the (112)[1 1-1] deformation texture is calculated to change to the (001)[100] Rex

Recrystallization Textures of Metals and Alloys

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

33

The above calculation indicates that the Cu orientation tends to turn into the cube orientation during annealing. In order for the transformation to occur, the cube oriented nuclei are needed, whether they may be generated from the deformed matrix or already existing cube bands. In order for the cube bands to be nuclei, they must be stable during annealing. The cube orien‐ tation (001)[100] is calculated by the full constrains method to be metastable with respect to plane strain compression, with active slip systems being (111)[1 0-1], (1 1-1)[101], (1-1-1)[101], and (1-1 1)[1 0-1] on which the shear strain rates are the same. If cube oriented grains survive after rolling, they must have undergone the plane strain compression with the slip systems. Therefore, AMSD is [1 0-1] + [101] + [101] + [1 0-1] = [400] // [100]. This is MYMD of Cu. Since AMSD is the same as the MYMD, the cube texture is expected to remain unchanged whether

SERM does not tell us how the cube oriented nuclei form. If the cube oriented grains survived during rolling, they are likely to survive and act as nuclei and grow at the expense of neigh‐ boring Cu oriented grains during annealing, because the Cu oriented grains tend to transform to the cube orientation. The grown up cube grains will grow at the expense of grains having other orientations such as the S and brass orientations, resulting in the cube texture after Rex.

The evolution of rolling textures in copper alloys depends strongly on their SFEs. A continuous transition from the copper orientation to the brass orientation tends to occur with increasing content of alloying elements or decreasing SFE. However, Mn can be dissolved in copper up to 12 at.% without significantly changing SFE unlike various Cu alloys [58]. Engler [59,60] studied the influence of Mn on the deformation and Rex behavior of Cu-4 to 16%Mn alloys, as this should yield a clear separation of the effects caused by the changes in SFE from those due to other factors. It is particularly interesting that the alloys develop a deformation texture in which the density of the brass orientation can be higher than the densities of the copper orientation and the S orientation despite the fact that SFEs of the alloys are almost the same as that of pure Cu. The brass orientation is obtained in many Cu alloys with low SFEs, which is well known to transforms to the {236}<385> orientation. However, the Cu-Mn alloys do not develop the {236}<385> orientation after Rex. The texture transformation cannot be well

This discussion applies to other fcc metals with high stacking fault energy (SFE).

explained by 40° <111> relation between the deformation and Rex textures.

**Figure 37.** Effect of Mg content on (a) densities of {112}<111>, {123}<634>, and {110}<112> orientations in Al-Mg alloys cold rolled by 95% and on (b) density of {001}<100> orientation in specimens annealed at 598 K for 0.5, 4, and 96 h [48]. 6 7

**Figure 38.** Changes in densities of copper Cu, S, brass Bs, and cube orientations in 95% cold rolled copper during an‐ nealing at (a) 400, (b) 450, and (c) 500 °C [49]. 18 19 time, min time, min time, min

20 Figure 38. Changes in densities of copper Cu, S, brass Bs, and cube orientations in 95% cold rolled

21 copper during annealing at (a) 400, (b) 450, and (c) 500C [49].

**Figure 39.** a) Changes in densities of cube, brass, copper and S orientations in 95% cold-rolled AA8011 Al alloy during an‐ nealing at 350 oC [50]. (b) Evolution of bulk textures in 90% cold-rolled Fe-50%Ni alloy during annealing at 600 ºC [51].

result is obtained by ε13, ε23 relaxed constraints rate sensitive model [54]. The slip directions are chosen to be at acute angles with RD (Section 2). To calculate AMSD, the active slip systems are weighted by the shear strain rates on them. AMSD is calculated to be [0 1-1] + [1 0-1] + 0.577 × 2[110] ≈ 2 [1 1-1]. Here the factor 0.577 is related to the fact that the slip direction [110] is shared by the (-1 1-1) and (1-1-1) slip planes (Eq. 7). The [1 1-1] direction is equivalent to **A** in Figure 6. **S** becomes [1-1 0] because it is one of slip directions nearest to 90° with **A**. In fact. **S** is normal to **A**, so **S** becomes **B** and **C** = **A**×**B** = [-1-1-2]. Since MYMDs are <100>, the Rex orientation is calculated using Eq. 9 to be (0 0-1)[100], which is equivalent to (001)[100]. In conclusion, the (112)[1 1-1] deformation texture is calculated to change to the (001)[100] Rex texture.

The above calculation indicates that the Cu orientation tends to turn into the cube orientation during annealing. In order for the transformation to occur, the cube oriented nuclei are needed, whether they may be generated from the deformed matrix or already existing cube bands. In order for the cube bands to be nuclei, they must be stable during annealing. The cube orien‐ tation (001)[100] is calculated by the full constrains method to be metastable with respect to plane strain compression, with active slip systems being (111)[1 0-1], (1 1-1)[101], (1-1-1)[101], and (1-1 1)[1 0-1] on which the shear strain rates are the same. If cube oriented grains survive after rolling, they must have undergone the plane strain compression with the slip systems. Therefore, AMSD is [1 0-1] + [101] + [101] + [1 0-1] = [400] // [100]. This is MYMD of Cu. Since AMSD is the same as the MYMD, the cube texture is expected to remain unchanged whether Rex or recovery (1st priority in Section 2).

SERM does not tell us how the cube oriented nuclei form. If the cube oriented grains survived during rolling, they are likely to survive and act as nuclei and grow at the expense of neigh‐ boring Cu oriented grains during annealing, because the Cu oriented grains tend to transform to the cube orientation. The grown up cube grains will grow at the expense of grains having other orientations such as the S and brass orientations, resulting in the cube texture after Rex. This discussion applies to other fcc metals with high stacking fault energy (SFE).

#### **6.2. Goss recrystallization texture**

**Figure 37.** Effect of Mg content on (a) densities of {112}<111>, {123}<634>, and {110}<112> orientations in Al-Mg alloys cold rolled by 95% and on (b) density of {001}<100> orientation in specimens annealed at 598 K for 0.5, 4, and 96 h [48].

10 Figure 37. Effect of Mg content on (a) densities of {112}<111>, {123}<634>, and {110}<112> 11 orientations in Al-Mg alloys cold rolled by 95% and on (b) density of {001}<100> orientation in

min time, min time, min time,

**Figure 38.** Changes in densities of copper Cu, S, brass Bs, and cube orientations in 95% cold rolled copper during an‐

time, min time, min time, min

Cube Bs Cu S

**Figure 39.** a) Changes in densities of cube, brass, copper and S orientations in 95% cold-rolled AA8011 Al alloy during an‐ nealing at 350 oC [50]. (b) Evolution of bulk textures in 90% cold-rolled Fe-50%Ni alloy during annealing at 600 ºC [51].

20 Figure 38. Changes in densities of copper Cu, S, brass Bs, and cube orientations in 95% cold rolled

1 10 100 1000

time, min

a b

*gf* )(

*f* (*g*)

Running Title

32 Recent Developments in the Study of Recrystallization

nealing at (a) 400, (b) 450, and (c) 500 °C [49].

*f* (*g*)

17

0

12 specimens annealed at 598 K for 0.5, 4, and 96 h [48].

21 copper during annealing at (a) 400, (b) 450, and (c) 500C [49].

a b c

a b c

27

The evolution of rolling textures in copper alloys depends strongly on their SFEs. A continuous transition from the copper orientation to the brass orientation tends to occur with increasing content of alloying elements or decreasing SFE. However, Mn can be dissolved in copper up to 12 at.% without significantly changing SFE unlike various Cu alloys [58]. Engler [59,60] studied the influence of Mn on the deformation and Rex behavior of Cu-4 to 16%Mn alloys, as this should yield a clear separation of the effects caused by the changes in SFE from those due to other factors. It is particularly interesting that the alloys develop a deformation texture in which the density of the brass orientation can be higher than the densities of the copper orientation and the S orientation despite the fact that SFEs of the alloys are almost the same as that of pure Cu. The brass orientation is obtained in many Cu alloys with low SFEs, which is well known to transforms to the {236}<385> orientation. However, the Cu-Mn alloys do not develop the {236}<385> orientation after Rex. The texture transformation cannot be well explained by 40° <111> relation between the deformation and Rex textures.

 

Figure 40 shows the orientation densities f(g) along the β-fiber of Cu-4%Mn, Cu-8%Mn, and Cu-16%Mn alloys after rolling reductions of 50 to 97.5%. The figure indicates that with increasing Mn content and rolling reduction the brass orientation tends to dominate the rolling texture. The brass orientation in the Cu-Mn alloys is particularly interesting because the transformation of the orientation to the Rex texture will not be complicated by twinning as in low SFE alloys. Figure 41 shows {111} pole figures of the three Cu-Mn alloys rolled by 97.5% after complete Rex by annealing for 1000 s at 450 °C. In Cu-4%Mn the texture maximum lies in the cube-orientation. In Cu-8%Mn the texture maximum has shifted from the cube orienta‐ tion to an orientation which can be approximated by the {013}<100> orientation. In Cu-16%Mn the texture maximum is in the Goss orientation. The orientation density ratios among the copper, S, and brass components in the rolling texture are shown in Figure 42. The density ratio of the brass to S component increases from about 1 to 2, the density ratio of the S to copper component increases from about 5 to 8, and the density ratio of the brass to copper component increases from about 5 to 18 with increasing Mn content from 4 to 16% in the Cu- Mn alloy. The density ratio of the S to copper and that of the brass to copper component are lowest in

Book Title

SFEs of the alloys are almost the same as that of pure Cu. The brass orientation is obtained in many Cu alloys with low SFEs, which is well known to transforms to the {236}<385> orientation.

the Cu-Mn alloys do not develop the {236}<385> orientation after Rex. The texture transformation

Figure 40 shows the orientation densities f(g) along the -fiber of Cu-4%Mn, Cu-8%Mn, and Cu-16%Mn alloys after rolling reductions of 50 to 97.5%. The figure indicates that with increasing Mn content and rolling reduction the brass orientation tends to dominate the rolling texture. The brass orientation in the Cu-Mn alloys is particularly interesting because the transformation of the orientation to the Rex texture will not be complicated by twinning as in low SFE alloys. Figure 41 shows {111} pole figures of the three Cu-Mn alloys rolled by 97.5% after complete Rex by annealing for 1000s at 450C. In Cu-4%Mn the texture maximum lies in the cube-orientation. In Cu-8%Mn the texture maximum has shifted from the cube orientation to an orientation which can be approximated by the {013}<100> orientation. In Cu-16%Mn the texture maximum is in the Goss orientation. The orientation density ratios among the copper, S, and brass components in the rolling texture are shown in Figure 42. The density ratio of the brass to S component increases from about 1 to 2, the density ratio of the S to copper component increases from about 5 to 8, and the density ratio of the brass to copper component increases from about 5 to 18 with increasing Mn content from 4 to 16% in the Cu-

cannot be well explained by 40<111> relation between the deformation and Rex textures.

 e

> e

*d d*

**Figure 43.** dγ/dε<sup>11</sup> (dε11=0.01) vs. ε11 curves on active slip systems of (a) (111)[0-1 1] and (-1-1 1)[101] of (110)[1-1 2] crystal and of (b) J (1-1-1)[110], B (111)[0 1-1], M (-1 1-1)[110], and C (111)[1 0-1] of (123)[6 3-4]. Values of dγ/dε11 on

Figure 43. *dγ/dε*11 (*dε*11=0.01) vs. *ε*<sup>11</sup> curves on active slip systems of (a) (111)[0-1 1] and (-1-1 1)[101] of (110)[1-1 2] crystal and of (b) J (1-1-1)[110], B (111)[0 1-1], M (-1 1-1)[110], and C (111)[1 0-1] of (123)[6 3-4]. Values of *dγ/dε*<sup>11</sup> on B, M, J, and C are 0.003, 0.006, 0.01, and 0.014,

Recrystallization Textures of Metals and Alloys

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

e

RD

(110)[001]

e

*d d*

b

b

Figure 44. {110}<112> rolling and {110}<001> Rex textures of Cu-1% P alloy [62].

e

e

B, M, J, and C are 0.003, 0.006, 0.01, and 0.014, respectively, at ε11=0 [61].

RD

{110} 112

**Figure 44.** {110}<112> rolling and {110}<001> Rex textures of Cu-1% P alloy [62].

4%Mn and highest in 16%Mn.

However,

 e

> e

*d d*

a

*d d*

a

respectively, at *ε*11=0 [61].

**Figure 40.** β-fiber intensity lines of Cu-4%Mn, Cu-8%Mn, and Cu-16%Mn alloys after rolling reductions from 50 to 97.5% [59]. 

**Figure 41.** pole figures of (a) Cu-4%Mn, (b) Cu-8%Mn, and (c) Cu-16%Mn alloys after complete Rex (97.5% rolling, annealing for 1000 s at 450 °C) [60]. Figure 41. (111) pole figures of (a) Cu-4%Mn, (b) Cu-8%Mn, and (c) Cu-16%Mn alloys after a 4.2 max b 3.3 max c 3.3 max

complete Rex (97.5% rolling, annealing for 1000 s at 450 °C) [60].

Figure 42. Orientation density ratios (ODR) among brass B, S, and copper C components in rolling texture (Figure 40) as a function of Mn concentration in Cu-Mn alloy [61]. can be higher than the densities of the copper orientation and the S orientation despite the fact that **Figure 42.** Orientation density ratios (ODR) among brass B, S, and copper C components in rolling texture (Figure 40) as a function of Mn concentration in Cu-Mn alloy [61].

Figure 40 shows the orientation densities f(g) along the β-fiber of Cu-4%Mn, Cu-8%Mn, and Cu-16%Mn alloys after rolling reductions of 50 to 97.5%. The figure indicates that with increasing Mn content and rolling reduction the brass orientation tends to dominate the rolling texture. The brass orientation in the Cu-Mn alloys is particularly interesting because the transformation of the orientation to the Rex texture will not be complicated by twinning as in low SFE alloys. Figure 41 shows {111} pole figures of the three Cu-Mn alloys rolled by 97.5% after complete Rex by annealing for 1000 s at 450 °C. In Cu-4%Mn the texture maximum lies in the cube-orientation. In Cu-8%Mn the texture maximum has shifted from the cube orienta‐ tion to an orientation which can be approximated by the {013}<100> orientation. In Cu-16%Mn the texture maximum is in the Goss orientation. The orientation density ratios among the copper, S, and brass components in the rolling texture are shown in Figure 42. The density ratio of the brass to S component increases from about 1 to 2, the density ratio of the S to copper component increases from about 5 to 8, and the density ratio of the brass to copper component increases from about 5 to 18 with increasing Mn content from 4 to 16% in the Cu- Mn alloy. The density ratio of the S to copper and that of the brass to copper component are lowest in 4%Mn and highest in 16%Mn. 30 Book Title 1 SFEs of the alloys are almost the same as that of pure Cu. The brass orientation is obtained in many 2 Cu alloys with low SFEs, which is well known to transforms to the {236}<385> orientation. 3 However, 4 the Cu-Mn alloys do not develop the {236}<385> orientation after Rex. The texture transformation 5 cannot be well explained by 40<111> relation between the deformation and Rex textures. 6 Figure 40 shows the orientation densities f(g) along the -fiber of Cu-4%Mn, Cu-8%Mn, and Cu-7 16%Mn alloys after rolling reductions of 50 to 97.5%. The figure indicates that with increasing Mn 8 content and rolling reduction the brass orientation tends to dominate the rolling texture. The brass 9 orientation in the Cu-Mn alloys is particularly interesting because the transformation of the 10 orientation to the Rex texture will not be complicated by twinning as in low SFE alloys. Figure 41 11 shows {111} pole figures of the three Cu-Mn alloys rolled by 97.5% after complete Rex by annealing

for 1000s at 450C. In Cu-4%Mn the texture maximum lies in the cube-orientation. In Cu-8%Mn the texture maximum has shifted from the cube orientation to an orientation which can be approximated by the {013}<100> orientation. In Cu-16%Mn the texture maximum is in the Goss orientation. The orientation density ratios among the copper, S, and brass components in the rolling texture are shown

**Figure 43.** dγ/dε<sup>11</sup> (dε11=0.01) vs. ε11 curves on active slip systems of (a) (111)[0-1 1] and (-1-1 1)[101] of (110)[1-1 2] crystal and of (b) J (1-1-1)[110], B (111)[0 1-1], M (-1 1-1)[110], and C (111)[1 0-1] of (123)[6 3-4]. Values of dγ/dε11 on B, M, J, and C are 0.003, 0.006, 0.01, and 0.014, respectively, at ε11=0 [61]. 24 25 Figure 43. *dγ/dε*11 (*dε*11=0.01) vs. *ε*<sup>11</sup> 26 curves on active slip systems of (a) (111)[0-1 1] and (-1-1 27 1)[101] of (110)[1-1 2] crystal and of (b) J (1-1-1)[110], B (111)[0 1-1], M (-1 1-1)[110], and C 11 e<sup>11</sup> b e a

(111)[1 0-1] of (123)[6 3-4]. Values of *dγ/dε*<sup>11</sup> 28 on B, M, J, and C are 0.003, 0.006, 0.01, and 0.014,

**Figure 44.** {110}<112> rolling and {110}<001> Rex textures of Cu-1% P alloy [62].

39 Figure 44. {110}<112> rolling and {110}<001> Rex textures of Cu-1% P alloy [62].

**Figure 40.** β-fiber intensity lines of Cu-4%Mn, Cu-8%Mn, and Cu-16%Mn alloys after rolling reductions from 50 to

16 Figure 40. β-fiber intensity lines of Cu-4%Mn, Cu-8%Mn, and Cu-16%Mn alloys after rolling

29

a 4.2 max b 3.3 max c 3.3 max

**Figure 41.** pole figures of (a) Cu-4%Mn, (b) Cu-8%Mn, and (c) Cu-16%Mn alloys after complete Rex (97.5% rolling,

<sup>16</sup> B/C

28 complete Rex (97.5% rolling, annealing for 1000 s at 450 °C) [60].

4 8 12

ODR

as a function of Mn concentration in Cu-Mn alloy [61].

38 texture (Figure 40) as a function of Mn concentration in Cu-Mn alloy [61].

27 Figure 41. (111) pole figures of (a) Cu-4%Mn, (b) Cu-8%Mn, and (c) Cu-16%Mn alloys after

a 4.2 max b 3.3 max c 3.3 max

37 Figure 42. Orientation density ratios (ODR) among brass B, S, and copper C components in rolling

<sup>4</sup> 8 12 <sup>16</sup> <sup>0</sup>

% Mn

S/C

B/S

39 can be higher than the densities of the copper orientation and the S orientation despite the fact that

**Figure 42.** Orientation density ratios (ODR) among brass B, S, and copper C components in rolling texture (Figure 40)

97.5% [59].

annealing for 1000 s at 450 °C) [60].

Running Title

34 Recent Developments in the Study of Recrystallization

17 reductions from 50 to 97.5% [59].

Comparison of the Rex textures with the corresponding deformation textures indicates that the brass component in the deformation texture seems to be responsible for the Goss compo‐ nents in the Rex texture. In what follows, the Rex textures are discussed based on SERM [61]. In order to find which component in the rolling texture is responsible for the Goss Rex texture, the brass rolling texture is first examined because it is the highest component in the deformation texture of Cu-16% Mn alloy, which changed to the Goss texture when an‐ nealed. When fcc crystals with the (110)[1-1 2] orientation are plane strain compressed along the [110] direction and elongated along the [1-1 2] direction, the relation between the strain *ε*<sup>11</sup> of specimen and shear strain rates *dγ/dε*<sup>11</sup> on active slip systems was calculated by the *ε*<sup>13</sup> and *ε*23 relaxed strain rate sensitive model. Figure 43a shows the calculated results, which indicate that active slip systems are (111)[0-1 1] and (-1-1 1)[101] and their shear strain rates do not vary with strain of specimen indicating that the brass orientation is stable with re‐ spect to the strain. It is noted that the active slip directions were chosen to be at acute with the [1-1 2] RD. Thus, AMSD = [0-1 1] + [101] = [1-1 2] is the same as RD.

(

0.7397 0.3924 −0.5467 0.0812 0.7545 0.6513 0.6684 −0.5263 0.5263

compressed {123}<412> crystal.

8 {123}<412> crystal.

40

can be approximated by {310}<001> [61].

)(1 2 3

) =( <sup>−</sup>0.1156 3.5441 1.1947

) (0.7397 0.3924 <sup>−</sup>0.5467 0.0812 0.7545 0.6513 0.6684 −0.5263 0.5263

[0.7397 0.3924 -0.5467] <sup>d</sup> //[100] <sup>r</sup>

[0.0812 0.7545 0.6513] <sup>d</sup> //[001] B <sup>r</sup>

The calculated result means that rolled fcc metal with the (123)[6 3-4] orientation transforms to (-0.1156 3.5441 1.1947)[7.8 0.1455 0.3263] ≈ (-1 31 10)[54 1 2] after Rex. For polycrystalline metals, the {123}<634> deformation texture transforms to the {-0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> ≈ {1 31 10}<54 1 2> Rex texture. The Rex texture is shown in Figure 46a. If the {-0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> orientations are expressed as Gaussian peaks with scattering angle of 10°, the Rex texture is very well approximated by the {310}<001> texture as shown in Figure 46b. This texture is similar to Figure 27 which shows the Rex texture of the plane strain

32 Book Title

The calculated result means that rolled fcc metal with the (123)[6 3-4] orientation transforms to (- 0.1156 3.5441 1.1947)[7.8 0.1455 0.3263] (-1 31 10)[54 1 2] after Rex. For polycrystalline metals, the {123}<634> deformation texture transforms to the {-0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> {1 31 10}<54 1 2> Rex texture. The Rex texture is shown in Figure 46a. If the {-0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> orientations are expressed as Gaussian peaks with scattering angle of 10°, the Rex texture is very well approximated by the {310}<001> texture as shown in Figure 46b. This texture is similar to Figure 27 which shows the Rex texture of the plane strain compressed

18 Figure 45. Orientation relationship between deformed and Rexed states [61].

<sup>b</sup> <sup>a</sup>

96.3 <sup>O</sup>

<sup>A</sup> <sup>O</sup>

[0.6684 -0.5263 0.5263] <sup>d</sup> //[010]r <sup>C</sup>

<sup>b</sup> <sup>a</sup>

**Figure 45.** Orientation relationship between deformed and Rexed states [61].

[0 1 1]

37 Figure 46. (a) (111) pole figure of {0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> ≈ {1 31 10}<54 1 2>. 38 (b) Sum of {0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> expressed as Gaussian peaks with scattering

It is noted that the highest density component in the deformation texture does not always dominate the Rex texture. All the components in the deformation texture are not in equal position to nucleate and grow the corresponding components in the Rex texture. The brass 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

**Figure 46.** (a) (111) pole figure of {0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> ≈ {1 31 10}<54 1 2>. (b) Sum of {0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> expressed as Gaussian peaks with scattering angle of 10°. Calculated orientation

It is noted that the highest density component in the deformation texture does not always dominate the Rex texture. All the components in the deformation texture are not in equal position to nucleate and grow the corresponding components in the Rex texture. The brass

39 angle of 10°. Calculated orientation can be approximated by {310}<001> [61].

)( 6 3 −4

]100)[310(

]100)[310(

) =( 7.8 0.1455 0.3263 )

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

37

Recrystallization Textures of Metals and Alloys

According to SERM, AMSD is parallel to MYMD of Rexed grain, the <100> directions in fcc metals. Therefore, the Rexed grains will have the (hk0)[001] orientation. The 2nd priority in Section 2 gives rise to the (110)[001] orientation because the (110) plane is shared by the de‐ formed and Rexed grains. That is, the (110)[1-1 2] rolling texture transforms to the (110)[001] Rex texture. Similarly, for the (011)[2-1 1] crystal, equally active slip systems of (111)[1-1 0] and (1-1-1)[101] are obtained. Therefore, the (011)[2-1 1] rolling texture is calculated to trans‐ form to the (011)[100] Rex texture. It is concluded that the Goss Rex texture is linked with the brass rolling texture. The Goss orientation is stable with respect to plane strain compres‐ sion and thermally stable (Section 5.1). Therefore, the Goss grains that survived during roll‐ ing are likely to act as nuclei during subsequent Rex and will grow at the expense of surrounding brass grains which are destined to change to assume the Goss orientation.

Figure 44 shows the rolling and Rex textures of Cu-1% P alloy sheet. The {110}<112> rolling texture changes to the (110)[001] texture after Rex. This is another example of the transition from the {110}<112> rolling texture to the {110}<001> Rex texture as explained in the Cu-16% Mn alloy.
