Evolution of shear texture according to shear strain ratio in rolled FCC metal sheets

METALS AND MATERIALS International, Vol. 12, No. 1 (2006), pp. 21~26

Evolution of Shear Texture According to Shear Strain Ratio

in Rolled FCC Metal Sheets

Hyo Tae Jeong1,*, Su Dong Park2, and Tae Kwon Ha1

1Dept. of Metal and Materials Engineering, Kangnung National University,

120, Gangneung Daehangno, Gangneung-si, Gangwon 210-702, Korea

2Advanced Electrical Materials Group, Korea Electrotechnology Research Institute,

28-1, Seongju-dong, Changwon-si, Gyeongnam 641-120, Korea

The shear textures developed in the surface layer by rolling procedures consist mainly of {001}<110> and {111} orientations in FCC metal sheets, but the orientation components of shear textures vary with the rolling conditions. That is, either a single orientation component or a mixture of components can be developed depending on the rolling conditions. The purpose of this study is to analyze the various shear deformation textures in rolled FCC metal sheets.

Keywords: texture, shear strain ratio, computer simulation, rolling, FCC

1. INTRODUCTION

Many experimental and theoretical studies have been con-ducted on the development of homogeneous rolling textures of FCC metals. Experimental findings on homogeneous roll-ing textures have revealed Cu orientation {112}<111>, S orientation {123}<412>, etc [1,2]. Simulations of texture development based on the full constraints and relaxed con-straints Taylor-Bishop-Hill model shows that D orientation {4 4 11}<11 11 8>, S orientation, and Cu orientation develop during plane strain compression [3-9]. However, experimen-tal rolling processes give rise to through-thickness inhomo-geneous rolling texture due to the deformation geometry and friction between the rolls and sheet [10-13]. In FCC metals, the shear textures consist mainly of {001}<110>, {111}<112>, and {111}<110> orientations. However, the shear textures vary with the rolling condition. Specifically, either a single component or mixtures of {001}<110>, {111}<112>, and {111}<110> orientations can develop according to the roll-ing conditions.

The shear texture developed in the surface layer of a rolled sheet is attributed to the shear strain caused by friction between a roll and a sheet. The types of shear textures vary with the magnitude of shear strain. The magnitude of shear strain in the surface layer depends on the friction coefficient, the rolling temperature, the rolling speed, and the geometri-cal parameters such as the size of rolls, the reduction per pass, the total reduction, the initial thickness of the sheet, etc. In this study, the initial sheet thickness and the reduction per pass were varied so as to obtain different shear deformation. V ariation of geometrical parameters was expressed as a form of l/d parameter.

The variation of the shear deformation texture was mea-sured according to the l/d parameters and simulated accord-ing to the shear strain ratio of dε13/d. From the analysis of stable orientation and rotation rate of crystals, it is shown that shear texture formed during rolling varies with the shear strain ratio, dε13/d.

2. EXPERIMENTAL PROCEDURE

Commercial purity aluminum sheets were cold rolled using a mill with 127 mm diameter rolls. The shear strain in the sur-face layer of the sheet during rolling was controlled by the l/d value, where l and d are, respectively, the roll-material contact length projected on the rolling direction and the mean value of the sheet thickness before and after rolling. The l/d parameter can be expressed as follows:

(1)

where R is the radius of the roll and h i and h f are the sheet thickness before and after rolling. The l/d value was con-trolled by the initial thickness of the sheet and the reduction per pass, as shown in Fig. 1.

ε

ε

l d?R h i h f

–

()h i h f

–

()24?

–

h i h f

+

()2?

-------------------------------------------------------

=

*Corresponding author: htjeong@kangnung.ac.kr

22Hyo Tae Jeong et al.

Three different rolling schedules are given in Table 1.Fig. 2 shows the l/d values as a function of reduction for each rolling schedule. The l/d values in each rolling schedule were kept approximately constant by changing the reduction per pass in each rolling procedure. The reduction per pass in each rolling procedure was determined along the equal l/d parameter line in Fig. 1. The average l/d values in the rolling schedule A, B, and C were 0.55, 2.62, and 4.77, respectively. The (111), (200), and (220) pole figures were measured using

the Schulz reflection method up to a tilting angle of 80o

.Figs. 3(a), (b), and (c) show the (111) pole figures obtained at the surface of the specimen rolled by schedules A, B, and C in Table 1. Figure 3(d) was obtained at the surface of an asymmetrically rolled aluminum specimen. Asymmetric rolling gives rise to relatively uniform shear deformation through the sheet’s thickness.

3. DISCUSSION AND RESULTS

It is well known that the l/d parameter is correlated with the shear strain in rolling deformation. The shear texture developed when the l/d parameter was smaller or larger than a specific value. However, the specific value of the l/d parameter has been defined in various ways by different researchers [11-13]. Recently, the relationship between the l/d parameter and shear strain was studied by Um et al . [18].

The results of this study indicate that the shear strain compo-nent in the rolling procedure increases as the value of the l/d parameter increases. Specifically, specimen A, which had the lowest l/d parameter of 0.55, displayed homogeneous

rolling texture while shear texture further developed as the

Fig. 1. Map of l/d parameter as a function of initial thickness and reduction per pass.

Table 1. Rolling schedules of aluminum sheets

Total Reduction Average l/d Sheet thickness (mm)

A 80 %0.55 6.3 -(0.15/pass) → 5.35 -(0.1/pass) → 3.95 -(0.05/pass) →2.95 -(0.025/pass) → 1.95 -(0.015/pass) → 1.43 -(0.01/pass) → 1.26

B 80 % 2.62 2.95→2.25→1.80→1.56→1.37→1.23→1.06→0.90→0.79→0.74→0.69→0.63→0.60

C

74 %

4.77

3.4

→1.7→0.9

Fig. 2. V alues of l/d as a

function of rolling reduction for rolling schedules of A, B, and C in Table 1.

Fig. 3. Measured (111) pole figures of surface layers of cold rolled aluminum sheets: (a) specimen A, (b) specimen B, (c) specimen C in Table 1, and (d) asymmetrically rolled sheet.

Evolution of Shear Texture according to Shear Strain Ratio in Rolled FCC Metal Sheets 23

l/d parameter increased in a range larger than a specific value.

An arbitrary deformation can be achieved by five active slip systems. The five active slip systems may not be deter-mined uniquely. Many methods have been suggested to solve this problem. Selection of one set of five slip systems that give the same minimum sum of shear strain may be achieved by the secondary work minimization principle [14], the random choice method [15], the strain rate sensitiv-ity method [16], the averaging method [17], etc. In this study, the random choice method is employed. However, as in the present study, when the stable orientation is deter-mined by rolling reduction containing shear strain with respect to TD//<110> orientations, there are four active slip systems instead of five. Therefore, the uniqueness in the Taylor model is achieved and all of the methods yield the same result.

The homogeneous rolling texture can be better simulated by the relaxed constraints model, in which some of the shear strain components are relaxed, rather than the full constraints model, where the strains of each grain are the same as the external strains. However, the full constraints model is used in the present study for analyzing stable shear texture by defining the shear strain components in the rolling proce-dures.

3.1. Experimental texture

For the specimen rolled by schedule A, the average value of l/d parameters is 0.55. The texture of Fig. 3(a) resembles homogenous rolling texture composed of {112}<111>, {4 411}<11 11 8> and {123}<634> orientations. The average value of l/d parameters in rolling schedule B is 2.62 and the texture of Fig. 3(b) is approximated by the {001}<110> ori-entation. However, the texture of the sample shown in Fig.3(c), which was rolled by rolling schedule C with an average l/d parameter of 4.77, is approximated by {001}<110> and {111} orientations. The texture of the sample in Fig.3(d) is also approximated by {001}<110> and {111}orientations. It is noted that the {111} texture is stron-ger in Fig. 3(d) than in Fig. 3(c).

3.2. Calculation of stable orientation

The stable orientation as a function of shear strain in roll-ing can be determined through a plot of rotation rate against orientation or rotation angle. The rotation rate with respect to effective strain may be defined by d ε13/d , where d is the effective strain. The effective strain is defined as follows:

d =(2)

Most parts of the sheet in rolling are subject to the following

strain state:

d ε11=?d ε33≠0, d ε31≠0, d ε22=d ε23=d ε12=0(3)

In this case, the effective strain becomes

(4)

The effective strains of external deformations were set to 2/ in order to compare rotation rates for different shear strains. Since the stable orientation can vary with effective strain, the effective strains of deformations should be set to be equal in order to analyze the stable orientation precisely.Therefore, the ratio of shear strain to effective strain, d ε13/d , is defined as a measure of shear strain, d ε13. In plane strain deformation without shear strain d ε13/d =0 while in pure shear strain deformation d ε13/d =.

Figure 4 shows the rotation rate, d ω/, of crystal orien-tation as a function of rotation angle for different shear strain ratios. The orientation with a positive rotation rate rotates to a positive rotation angle and vice versa. Therefore, the orien-tations for which the slope of the curve of the rotation rate against ω is negative at a zero rotation rate is stable whereas the orientation for which the slope of the curve is positive at zero rotation rate is meta-stable. When TD//[110] and the

orientation at a rotation angle w of 0o

is (001)[1 10], the crystal orientation is expressed as follows:

(5)Crystal orientations are shown in Table 2 according to the rotation angles. D orientation, {4 4 11}<11 11 8>, is calcu-lated to be the stable orientation for plane strain compression.However, the shear strain d ε13 makes the stable orientation

εεε23

------d ε11d ε22–()2d ε22d ε33–()2d ε33d ε

11–()2

++[6d ε232d ε312d ε122

++()2+]

12

?d ε23

------d ε112d ε312+()

12

?=3εεε34?εg ω()sin ω2----------sin ω2----------cos ω????cos ω2-----------–cos ω2

-----------–sin ω=Fig. 4. Rotation rates, d ω13/d , as a function of rotation angle for various d ε13/d values.

εε

24Hyo Tae Jeong et al.

rotate from the D orientation about the TD//<110> direction. Therefore, the orientations rotated about TD//<110> were calculated in order to determine the stable orientation as a function of shear strain, dε13.

The deformation texture was simulated as a function of

dε13/d with 978 randomly distributed single crystals and presented using Gauss type functions of w o=10o. Calcula-

tion was performed up to an effective strain of 2.30 without

shear strains and up to an effective strain of 3.46 (97% reduction) as a function of dε13/d.

3.3. Changes of stable orientation according to the shear

strain ratio

Figure 4 shows that the plot of the rotation rate against the rotation angle shifts to the negative rotation angle direction

with an increasing dε13/d value and the plot of pure shear deformation shifts by ?45o from that of plane strain com-

pression. The shifting angle of the plot in Fig. 4 is shown in Fig. 5 as a function of dε13/d. The stable orientation at var-ious dε13/d can be analyzed from Figs. 4 and 5. The rotation of symmetric D orientation, which is known as stable orien-tation under plane strain compression, is analyzed as a func-tion of dε13/d.

The stable orientation, which has a zero rotation rate and a negative slope, as shown in Fig. 4, varies with the dε13/d value. This change of the stable orientation is shown in the (111) pole figure of Fig. 6. In Fig. 6, two symmetric D orien-tations of (4 4 11)[11 11 8] and (4 4 11)[11 11 8], which are at rotation angles of 27.2o and 152.8o with (001)[1 10], respec-tively, become asymmetrical stable orientations at some val-ues of dε13/d. The sign of the rotation angle also changes depending on dε13/d.

For the (4 4 11)[11 11 8] orientation, the stable orientation moves in the negative angular direction and changes from the (4 4 11)[11 11 8] to (1 1 10)[5 51] orientation as the dε13/d value or the shear strain ratio increases from 0 to . As the shear strain ratio increases from to , the sta-ble orientation moves in the positive angular direction and changes from (111)[1 1 2] to (11

)[1 1]. That is, the stable orientations of (111)[1 1 2] and (11)[1 1] are obtained at a shear strain ratio of and , respec-tively.

ε

ε

ε

ε

ε

ε

ε

ε

ε

ε

23?

23?34?

22

22

23?34?

Fig. 5. Shifting angle, Δω, in Fig. 2 as a function of dε13/d.ε

Table 2. Crystal orientations as a function of rotation angle about [110] direction from (001)[1 10] orientation.

Rotation angle, ωOrientation Rotation angle, ωOrientation

0.0 o(0 0 1)[11 0]95.1 o(8 8 1)[1 1 16]

10.0 o(1 1 8)[44 1]98.0 o(5 5 1)[1 1 10]

15.8 o(1 1 5)[55 1]100.0 o(4 4 1)[1 1 8]

19.5 o(1 1 4)[22 1]103.3 o(3 3 1)[1 1 6]

25.2 o(1 1 3)[33 1]109.5 o(2 2 1)[1 1 4]

27.2 o(4 4 11)[1111 8]113.0 o(5 5 3)[3 3 10]

35.3 o(1 1 2)[11 1]117.9 o(4 4 3)[3 3 8]

40.3 o(3 3 5)[55 6]125.3 o(1 1 1)[1 1 2]

43.3 o(2 2 3)[33 4]133.3 o(3 3 4)[2 2 3]

46.7 o(3 3 4)[22 3]136.7 o(2 2 3)[3 3 4]

54.7 o(1 1 1)[11 2]139.7 o(3 3 5)[5 5 6]

62.1 o(4 4 3)[33 8]144.7 o(1 1 2)[1 1 1]

67.0 o(5 5 3)[33 10]152.8 o(4 4 11)[11 11 8]

70.5 o(2 2 1)[11 4]154.8 o(1 1 3)[3 3 2]

76.7 o(3 3 1)[11 6]160.5 o(1 1 4)[2 2 1]

80.0 o(4 4 1)[11 8]164.2 o(1 1 5)[5 5 2]

82.0 o(5 5 1)[11 10]170.0 o(1 1 8)[4 4 1]

84.9 o(8 8 1)[11 16]180.0 o(0 0 1)[1 1 0]

90.0 o(1 1 0)[0 0 1]

Evolution of Shear Texture according to Shear Strain Ratio in Rolled FCC Metal Sheets25

For the (4G4G11)[11G11G8] orientation, the stable orientation moves in the negative angular direction from (4G4G11)[11G11G8] to (111)[112] as the shear strain ratio increases from 0 to . As the shear strain ratio increases from to

, the stable orientation moves in the positive angular direction from (001)[110] to (229)[994]

Figure 7 shows the angles of stable orientation from D ori-entations as a function of shear strain ratio. When the crystal of (4G4G11)[1111G8] orientation was subjected to plane strain compression including shear strain, the sign of the rotation angle to stable orientation changes abruptly from negative to positive at a shear strain ratio of . The rotation angle to stable orientation decreased from 0o to ?35.3o with increas-ing shear strain ratio from 0 to . The rotation angle to stable orientation was decreased from 27.5o to 17.8o with increasing shear strain ratio from . Meanwhile, when the crystal of (4G4G11)[11G11G8] orienta-tion was subjected to plane strain compression including shear strain, the sign of the rotation angle to stable orienta-tion was changed abruptly from negative to positive at a shear strain ratio of . The rotation angle to stable orienta-tion decreases from 0o to ?27.5o with increasing shear strain ratio from G0 to . The rotation angle to stable orienta-tion decreases from 27.2o to 9.8o with increasing shear strain ratio from .

In Fig. 6, the change of stable orientation depending on the shear strain ratio can be classified into three regions, because the shear strain ratios, at which the sign of the rotation angle to stable orientation changes abruptly, are different in two symmetric D orientations, that is, and . When the shear strain ratio is lower than or higher than , the {001}<110> and {111}<112> components are stable. When the shear

strain ratio is higher than and lower than

, only the {001}<110> is stable.

There-

fore, the stable orientation under plane strain compression

including shear strain varies with the shear strain ratio, and

the shear texture of surface layer of rolled specimen may be

the {001}<110> orientation,

or a mixture of {001}<110>

and {111}<112> orientations.

3.4. Shear deformation dependent rolling texture

In order to elucidate the evolution of the textures in Fig. 3,

a texture simulation has been performed using the Taylor-

Bishop-Hill full constraint method, where the initial texture

12?12?

34?

23?

23?

23?

12?

12?

12?

12?23?

12?23?

12?

23?

Fig. 7. Rotation angle from D{4 4 11}<11 11 8> orientation as a func-

tion of dε13/d.ε

Fig. 6. (111) pole figures of stable orientation as a function of dε13/d.ε

Fig. 8. Calculated (111) pole figures of FCC metal sheets rolled by

=4.0~4.3 with dε13/d of (a) 0.0, (b) 0.7047, (c) 0.7206 and (d) 0.8187.

Simulation was carried out based on the full constraint model with

978 orientations, and each orientation is replaced by a Gauss type

function with a half width of 10o.

ε

ε

26Hyo Tae Jeong et al.

was assumed to be 987 randomly distributed orientations. The simulated results are shown in Fig. 8. Figure 8(a) shows the simulated (111) pole figure obtained when the initial sheet is subjected to plane strain deformation up to =2.30 (90% reduction) without shear strain and the 987 orienta-tions are each replaced by a Gauss type function with a half width of 10o. The simulated texture in Fig. 8(a) is similar to the experimental texture in Fig. 3(a).

Figures 8(b), (c), and (d) are calculated for a plane strain deformation up to =4.0~4.3 (97~98 % reduction), where dε13/d is 0.7047, 0.7206, and 0.8187, respectively, after deformation without shear strain. The dε13/d values of 0.7047 and 0.7206 are slightly smaller and larger than

, respectively. The value of 0.8187 is slightly larger than . As already explained, abrupt changes in the rotation angle and direction take place, and hence severe tex-ture changes occur at dε13/d values of and . In Fig. 8(b), (001)[110] and (111)[112] orientations develop whereas only the (001)[110] orientation is observed in Fig. 8(c) and the (1G1G10)[551] and (344)[851] orientations in Fig. 8(d).

4. CONCLUSIONS

1. Due to the non-orthorhombic symmetry of the shear deformation in inhomogeneous rolling, the (4G4G11)[11 11G8] and (4G4G11)[11G11G8] orientations, equally stable in the case of plane strain compression, evolved into other asymmetric orientations for inhomogeneous rolling.

2. As the shear strain increases, the stable orientations change in such a way that new stable orientations are obtained by rotation of old stable orientations about the TD//<110> direction. The rotating direction of stable orientations changes when the shear strain ratio reaches a critical value. The critical values are and for the (4G4G11)[11 11G8] and (4G4G11)[11G11G8] orientations, respectively. The results indicated that the com-bined orientations of the (4G4G11)[11 11G8] and (4G4G11)[11G11G8] orientations evolved into 3 types of shear textures depending on shear strains.

3. When the dε13/d value is smaller than or larger than , the shear texture is approximated by {001}<110>the {001}<110> is stable for

4. In order to develop the shear texture of {111}, it is necessary to find the optimized dε13/d value. ACKNOWLEDGMENT

This study has been supported by the Korea Electrotech-nology Research Institute.

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ε

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