**6.3. {031}<100> recrystallization texture**

In Section 5.4 the (123)[-6-3 4] rolling to (031)[100] Rex orientation transformation was discussed. Here we discuss the {123}<634> rolling to {031}<100> Rex orientation transformation. Figure 43b shows the shear strain rates as a function of strain for the (123)[6 3-4] crystal, which was calculated by the *ε*13 and *ε*<sup>23</sup> relaxed strain rate sensitive model. The figure indicates that the S orientation is not stable with respect to the strain. Therefore, we calculate AMSD using the shear strain rates of 0.014, 0.01, 0.006 (0.007 was used in Section 5.4), and 0.003 at zero strain on the C, J, M, and B active slip systems (Figure 43b). AMSD is 0.014 [10-1] + 0.01 ×0.577 [110] + 0.006 × 0.577 [110] + 0.003 [0 1-1] = [0.023 0.0122 –0.017], where the factor 0.577 originates from the fact that the (1-1 1) and (1-1-1) slip planes share the [110] slip direction (Eq. 7). The [0.023 0.0122 –0.017] AMSD is parallel to the [0.7397 0.3924 –0.5467] unit vector. Following the method explained in Figure 6, we obtain Figure 45. Therefore, the (123)[6 3-4] rolling orientation is calculated to transform to the Rex texture as explained in Eq. 9. The calculated results are as follows:

Recrystallization Textures of Metals and Alloys http://dx.doi.org/10.5772/54123 37


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

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%

In Section 5.4 the (123)[-6-3 4] rolling to (031)[100] Rex orientation transformation was discussed. Here we discuss the {123}<634> rolling to {031}<100> Rex orientation transformation. Figure 43b shows the shear strain rates as a function of strain for the (123)[6 3-4] crystal, which was calculated by the *ε*13 and *ε*<sup>23</sup> relaxed strain rate sensitive model. The figure indicates that the S orientation is not stable with respect to the strain. Therefore, we calculate AMSD using the shear strain rates of 0.014, 0.01, 0.006 (0.007 was used in Section 5.4), and 0.003 at zero strain on the C, J, M, and B active slip systems (Figure 43b). AMSD is 0.014 [10-1] + 0.01 ×0.577 [110] + 0.006 × 0.577 [110] + 0.003 [0 1-1] = [0.023 0.0122 –0.017], where the factor 0.577 originates from the fact that the (1-1 1) and (1-1-1) slip planes share the [110] slip direction (Eq. 7). The [0.023 0.0122 –0.017] AMSD is parallel to the [0.7397 0.3924 –0.5467] unit vector. Following the method explained in Figure 6, we obtain Figure 45. Therefore, the (123)[6 3-4] rolling orientation is calculated to transform to the Rex texture as explained in Eq. 9. The calculated results are as

the [1-1 2] RD. Thus, AMSD = [0-1 1] + [101] = [1-1 2] is the same as RD.

Mn alloy.

follows:

**6.3. {031}<100> recrystallization texture**

36 Recent Developments in the Study of Recrystallization

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 {123}<412> crystal. 32 Book Title 1 The calculated result means that rolled fcc metal with the (123)[6 3-4] orientation transforms to (- 2 0.1156 3.5441 1.1947)[7.8 0.1455 0.3263] (-1 31 10)[54 1 2] after Rex. For polycrystalline metals, 3 the {123}<634> deformation texture transforms to the {-0.1156 3.5441 1.1947}<7.8 0.1455 0.3263> 4 {1 31 10}<54 1 2> Rex texture. The Rex texture is shown in Figure 46a. If the {-0.1156 3.5441 5 1.1947}<7.8 0.1455 0.3263> orientations are expressed as Gaussian peaks with scattering angle of 6 10°, the Rex texture is very well approximated by the {310}<001> texture as shown in Figure 46b. 7 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]. 19 **Figure 45.** Orientation relationship between deformed and Rexed states [61].

8 {123}<412> crystal.

40

41 It is noted that the highest density component in the deformation texture does not always dominate the 42 Rex texture. All the components in the deformation texture are not in equal position to nucleate and 43 grow the corresponding components in the Rex texture. The brass component has the highest density, 44 but has lowest stored energy or the Taylor factor, while the copper component has the lowest density, **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 can be approximated by {310}<001> [61].

45 but has the highest stored energy or the Taylor factor. If grains with the Goss or cube orientation 46 survived during rolling, they must have undergone plane strain compression. They could undergo 47 recovery and act as nuclei for Rex during annealing. This is the reason why the cube Rex texture 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 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 Rex texture in the Cu-4%Mn alloy among the three Cu-Mn alloys.

texture change after annealing. Microstructures and hardness tests of the surface layer before

**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‐

2/

ee<sup>1113</sup>

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

1.225 1.225 1.225 1.225 1.225

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

**dε13/dε<sup>11</sup> γ(1) γ(2) γ(3) γ(4)**

1.225 1.225 1.225 1.225 1.225 0.245 1.120 1.466 1.837 1.986 0.245 1.120 1.466 1.837 1.986

Recrystallization Textures of Metals and Alloys

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

39

0/ ee<sup>1113</sup>

and after annealing indicated Rex occurring after annealing [64].

tion of 70% were used [63].

0.5 1.0 1.2 √2 1.5
