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ISSN 0031918X, The Physics of Metals and Metallography, 2012, Vol. 113, No. 8, pp. 810–816. © Pleiades Publishing, Ltd., 2012. Original Russian Text © N.M. Shkatulyak, A.A. Bryukhanov, M. Rodman, V.V. Usov, M. Schaper, G. Haferkamp, V.A. Nastasyuk, 2012, published in Fizika Metallov i Metallovedenie, 2012, Vol. 113, No. 8, pp. 853–859.

STRENGTH AND PLASTICITY

Reverse Bending Effect on the Texture, Structure, and Mechanical Properties of Sheet Copper N. M. Shkatulyaka, A. A. Bryukhanova, M. Rodmanb, V. V. Usova, M. Schaperb, G. Haferkampb, and V. A. Nastasyuka aUshinskii

SouthUkrainian National Pedagogical University, ul. Staroportofrankovskaya 26, Odessa, 65020 Ukraine b Institute of Materials Science, Leibnitz University of Hanover, 30823 Gasen, Germany Received November 7, 2011; in final form, December 28, 2011

Abstract—The effect of reverse roomtemperature bending on the crystallographic texture, metallographic structure, and mechanical properties of preliminarily rolled and annealed sheets of copper has been studied. It has been found that the type of the initial structure and the texture represented by the {001}具100典 recrystal lization orientation, remains of the deformation texture {112}具111典, and twin orientations do not change; only the ratio of these orientations changes in the process of the reverse bending, which naturally leads to changes in the mechanical properties. Keywords: copper, rolling, annealing, reverse bending, structure, texture, twins, anisotropy, mechanical prop erties DOI: 10.1134/S0031918X1208011X

1. INTRODUCTION Copper and its alloys represent one of the major groups of commercial metals. They are widely used due to their excellent electrical and thermal conduc tivity, sufficient corrosion resistance, relative ease of manufacture, high strength, and fatigue resistance [1]. The world consumption of copper is growing con stantly; by 2010, it has reached 19.2 million tons. Cop per is used mainly in the electronic and communica tion fields (42%), building industry (28%), mechani cal engineering (12%), industrial machinery (9%), and in the production of consumer goods (9%). For aluminum, copper, and their alloys, combined pro cesses of casting and rolling [2] are becoming increas ingly popular. In this method, a continuously cast workpiece is cut into pieces of required length or a thin strip is wound into a coil for cold rolling [3]. Most of the modern technologies for processing sheet metal include mechanical and thermal treat ment, which inevitably results in the generation of internal stresses in the material and warping of the resulting parts. The intensity of these effects depends on the chemical composition, initial parameters of the stress state of the metal, and some other characteris tics. As a consequence, there arise a number of diffi culties associated with the subsequent processing of these parts, formation of a desired geometry, and the appearance of defective products [4]. Therefore, before using coil metal, the metallurgists subject it to straightening on a leveling machine. In the course of straightening, the material is subjected to reverse

bending (RB), which ensures good planeness. This treatment minimizes the level of internal residual stresses in the metal and provides necessary planar characteristics, which significantly facilitates the sub sequent metal processing and positively affects the quality of finished products [4, 5]. As a result of plastic deformation in the process of straightening, there, of course, occurs a change in the metal structure and in its mechanical properties. The effect of RB on the structure and properties of metals and alloys was investigated in many studies. For example, in [6], the authors investigated RB in con nection with the texture and elastic properties of low carbon steel and revealed the effect of twinning on the change in the character of the anisotropy of elastic properties of the steel. A series of works was devoted to the investigation of the effect of RB on the structure and mechanical prop erties of a hexagonal magnesium alloy AZ31. In [7], the authors supposed that twinning can affect the reduction in the yield stress of the AZ31 alloy sub jected to a small number of RB cycles. The authors of [8] calculated the mechanical properties of single crystal AZ31 alloy and the values of properties for var ious directions in the sheet plane and in the perpen dicular direction for different numbers of RB cycles. In [9], the authors studied the development of texture and the mechanisms of its formation upon deforma tion by reverse bending of AZ31 sheets. No data on the complex studies of how RB affects the texture, struc

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ture, and mechanical properties of copper strips and their anisotropy are available in the literature. The aim of this paper is to study the effect of defor mation by reverse bending on the crystallographic tex ture, metallographic structure, and mechanical prop erties of rolled and annealed strips of commercially pure copper. 2. EXPEREMENTAL As the material for the study, strips of copper of grade M0 (0.004 Fe, 0.002 Ni, 0.003 Zn, 0.001 Sn, 0.002 Sb, 0.001 As, 0.003 Pb, 0.003 S, 0.04 O, 99.93 Cu + Ag, wt %) were used [10]. The asdelivered copper strips 1 mm thick were annealed in a vacuum at 350°C for 1 h. The process of sheet straightening was simulated with RB using a specially constructed machine. The diameter of the bending roller was 50 mm. The speed of the metal during bending was ~150 mm/s. The samples for mechanical tests (in the rolling direction (RD), diagonal direction (DD) at 45° to RD, and transverse direction (TD)) and the samples for texture and structure studies were cut (threes par ties for each test) from the initial sheet and from sheets subjected to bending using 0.5, 1, 3, and 5 cycles. The mechanical tests were performed on a 250N5A WN:143331 tensile machine with an ID:0 WN:805506 20 kN effort sensor at room temperature for samples cut in the RD, TD, and DD. The length and width of the gage part of the samples was 15 and 12.5 mm, respectively. The values of the mechanical properties were taken by averaging values over three series of tests of the samples in each direction. Before examining the texture, the samples were chemically polished to a depth of 0.1 mm to remove the distorted surface layer. The crystallographic tex ture was investigated by recording inverse pole figures (IPFs) in the normal and rolling directions using a DRON3m diffractometer in the filtered Mo Kα radi ation on both surfaces of the samples after the above mentioned numbers of the cycles and after 0.25 cycle. The sample without texture was produced from fine recrystallized copper filings. In order to ensure a flat surface after 0.25cycle bending for taking IPFs, a composite sample was manufactured from pieces 3 mm wide, which were cut across the metal strips. To take IPFs in the RD, we also produced composite samples. The metallographic structure was studied in the reflection mode from the butt surfaces of the samples cut in the RD and TD on a Neophot 21 optical micro scope. 3. RESULTS AND DISCUSSION Figure 1 shows IPFs of the copper samples. It is seen that the texture types of the initial sample and samples after RB are similar. THE PHYSICS OF METALS AND METALLOGRAPHY

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The microstructure of the copper samples is shown in Fig. 2. The strength properties are presented in Fig. 3; the plastic properties, in Fig. 4. It is seen from Figs. 1a and 1b that the texture of the original sample is represented mainly by cube {001}〈100〉 orientation, by the remains of the rolling texture {112}〈111〉 and {012}〈120〉; {012}〈121〉; {012}〈100〉; {012}〈123〉; {331}〈110〉; {331}〈013〉; {331}〈123〉 orienta tions. In the corresponding micrographs (Figs. 2a, 2b), annealing twins are observed. The presence of a cube orientation in the annealing texture and of annealing twins in corresponding micrographs indicates that the initial material was recrystallized [11]. The formation of the above cube orientations and {012}〈uv w〉 texture components during copper recrys tallization, as was described in the earlier work [12], can be activated by untwinning of the rolling texture com ponent {112}〈111〉 through the inverse Rowland trans formation. Later, this has also been demonstrated upon the recrystallization annealing of preliminarily rolled copper bicrystals with the initial twin orientations (112)[11 1 ]/(112)[1 1 1 ] and (1 1 0)[112]/( 1 10)[112] in [13]. The formation of the {331}〈uv w〉 orientations was described in the study of texture in copper rolled to 90% (in thickness) and annealed for halfhour at 250°С [14]. Together with the cube component, the recrystalli zation texture of copper contains {122}〈212〉 orienta tions, which are twinned with respect to the cube ori entation [15, 16]. As was said above, twins in the cop per microstructure were found in our study as well (Figs. 2a, 2b). On the one hand, it is impossible to quantitatively analyze 〈221〉 poles in the IPFs of an fcc metal because of the ambiguity of their indexing (superposition of 511 and 333 reflections, and 600 and 442 reflections). On the other hand, the 〈221〉directions are deviated from 〈331〉 directions shown in the IPFs by an angle of ≈6.3°. In [17], the authors performed a thorough analysis of twin maxima in direct experimental pole figures in a coarsegrained rolled copper with grain sizes of 50 and 500 μm and in a fully annealed copper. The analysis has shown that the exact location of the twin maxima in the pole fig ures deviates from the ideal positions of {122}〈212〉 twins by 2°–3° to 9°, depending on the degree of pre liminary rolling. This makes it possible to suppose that our original micrographs of the initial recrystallized copper sample (Figs. 2a, 2b) depicts annealing twins with orientations close to {122}〈212〉, which in the IPFs corresponding to the normal direction (ND) lie in the region of spread of the 331 pole (Figs. 1a, 1b). After 0.25cycle bending, some overall reduction in the pole density is observed in the IPFs, which indi cates an enhanced spread of the texture (Figs. 1c–1e). With an increase in the number of RB cycles to three, the number of twins tends to increase in the cor responding micrographs (Figs. 2c–2j). This is accom Vol. 113

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ND

RD

(a)

111

533 2.43 211 1.52 2 1 733 1.49 311 0.78 321

0.54

100

1 0.58 1.55 0.86 931 0.26 1 531 3 1 0.87 1.13 0.75 0.51 5.60

331

110

100

310 210 320

111

(c)

111

0.94

931 100

0.76

0.76 1.39 531 1

331

0.90

110

3 0.42 1.07 1.16 0.70 3.57

100

100

0.49 1.66

0.64

110

100

100

0.75

110

100

1 0.56 1.46

0.56

0.82

110

100

1

100

0.671

531 1

2 3 0.09 0.21 0.96 0.66 3.84

310 210 320

110

100

0.84

1.27

0.67 110

1.52

1 3 1.19 1 0.65 0.77 1.07 3.34

0.68

110

310 210 320

331

0.97

0.79

0.98 110

100

3 3.51

1 1.21 1 0.72 0.91 1.12

311

1 0.66 2.69 1.36 531 1 2 4 0.16 0.25 0.96 0.65 0.63 4.20

0.82

2.43 533 211 1.53 2 1.51 733 321 0.86 1.01

931 100

110

(n)

111

331

110

331

310 210 320

(m)

0.64

0.82 0.83

531

931

310 210 320

310 210 320

331

(k)

3 1.23 0.78 3.67

0.78 0.89

0.85

331

531 1 0.89 1.14

0.77

110

310 210 320

(p)

111

(q)

533 2.78 211 1.81 2 1 1.78 733 321 0.88 311 1.05

331

931

100

0.79 0.81

531

2.35 533 211 1.49 2 1 733 1.48 321 0.73 311

0.69 1.74 531 1

0.43

0.88

111

111

331

(h)

(j)

533 0.31 211 0.45 0.98 733 321 0.15 311

1.13 733 321 0.26 311 2.72

0.47

4 0.19 4.83 1 0.89 1.35 0.72

(o)

533 0.45 211 0.65

0.49

0.79

1 5 0.22 5.05 1 0.91 1.17 0.76

931

111

0.99

733 1.19 1 321 0.39 311

531

310 210 320

931

331

931

111

331

0.45 110

111

533 0.33 211 0.47

733 1.26 0.50 1 321 311

100

1.14 1 1.82 1.5 0.61 0.67 1.04

531

(l)

331

533 2.27 211 1.48 2 1 733 1.47 321 0.67 311

310 210 320

0.82

0.78

531

(g)

0.65 1.53

1 4 0.42 4.81 1 0.83 1.22 0.33

0.46 533 211 0.46

1 4 0.25 1.07 1.13 0.70 4.91

100

0.57 0.83

310 210 320

310 210 320

111

931

110

531

931

310 210 320

0.98

0.96

0.69

331

531

0.54

0.83

533 0.36 211 0.53 1.06 733 321 0.68 1 311 1

1 0.56 1.65

1 4 0.31 4.51 1 0.99 1.22 0.77

1

931

111

0.30 533 211 0.44 1.31 733 0.70 1 321 311

931

0.98

331

531 1

(i)

111

0.93

1.48 1 733 0.88 321 311

310 210 320

931

(e)

111 533 2.09 211 1.42 2

0.73 1.41

0.33 1.13 1.19 0.90

0.59

331

310 210 320

0.51

(d)

111

531

1 5 0.09 1.09 1.27 0.47 5.35

310 210 320

0.44 533 211 0.57 733 1.21 321 311 0.49 1 1

0.34 533 211 0.51 733 1.32 0.52 1 321 311 1

931

3.57 3

(f)

111

0.92

1.06

931 1

310 210 320

0.63

0.93 0.95 331 0.79 0.57 931 531 1.24 4 0.88 1.11 0.79 4.85 1 0.62 110

533 0.42 211 0.67 733 1.32 321 0.34 311 1

533 0.68 211 0.65 733 1.38 0.33 1 321 311 0.81

(b)

111

533 0.24 0.41 211 733 1 1.15 0.52 321 311

0.85 0.89 331 0.89 531 1 1.18 1 2 0.81 0.91 1.15 0.78 2.53 110

931

110

100

310 210 320

Fig. 1. Experimental inverse pole figures of copper sheets: (a, b) initial state; (c–r) after reverse bending using (c–e) 1/4, (f–h) 1/2, (i–k), (l–n) 3, and (o–r) 5 cycles. THE PHYSICS OF METALS AND METALLOGRAPHY

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813

(а)

20 µm (b)

20 µm

(c)

20 µm (d)

20 µm

(e)

20 µm (f)

20 µm

(g)

20 µm (h)

20 µm

(i)

20 µm (j)

20 µm

Fig. 2. Copper microstructure: (a, b) initial state; (c–j) after reverse bending using (c, d) 1/2, (e, f) 1, (g, h) 3; and (i, j) 5 cycles. The length of the scale bar in the bottom righthand corner of the images corresponds to 20 µm. The lefthand panel corresponds to the section perpendicular to the RD; the righthand panel, to the section perpendicular to the TD. THE PHYSICS OF METALS AND METALLOGRAPHY

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σ0.2, MPa

195

3 1

2

3 1

2

2 3

2

1

3 12

1

190

3

185 180 0

1 Cycles Z

3

5 (b)

60 50 40 30 20 10 0

2 1

0

3

2

2 1

3

0.5

1

3

1 Cycles Z

2 1

3

3

2 1

3

5

Fig. 4. Variation of the relative elongation at fracture of copper as a function of the number of RB cycles. (1), (2), and (3) correspond to the measurements made in RD, DP, and TD, respectively.

σu, MPa

260 250 240 230 220 210 200

0.5

Δl/l, %

(a)

200

0

0.5

1 Cycles Z

3

5

Fig. 3. Dependence of (a) the yield stress and (b) ultimate strength of copper on the number of RB cycles. (1), (2), and (3) correspond to the measurements made in the RD, DD, and TD, respectively.

panied by an increase in the pole density at the 210 and 331 points in the IPFs taken in the ND (Figs. 1f–1n). The bending deformation can be simulated as a combination of tension of the convex side and com pression on the concave side of the strip. The authors of [11] have analyzed the possibility of deformation induced twinning in fcc metals under tension and compression. It was shown that, since the twinning in the fcc structure is always preceded by slip [11], the twinning plane is ( 1 11), and that Shockley and Frank partial dislocations are formed [11] in the process of twinning. These partials act as twinning dislocations under compression for the initial orientations that in the unit triangle of the standard stereographic projec tion are adjacent to the 011 pole, and, under tension, for the orientations adjacent to 001. Thus, under com pression, we should expect the formation of twins with orientations that lie near the 331 pole; and under ten sion, in the region bounded by the 210, 931, 311, and 211 poles [11]. These orientations are present in our IPFs (Fig. 1), as was mentioned above. Thus, in the RB process there occurs deformationinduced twin ning, which becomes somewhat weaker as the number of RB cycles increases to 5 (Figs. 2i, 2j). An increase in the number of RB cycles to 5 leads to a weakening of the cube texture and of the pole den sity of twin orientations. However, against the general weakening of the texture, orientations of a deforma tion texture of the {135}〈211〉 type are seen to become developed (Figs. 1m–1r), which was established as the major component of the rolling texture of copper as long ago as in early works on the texture [18, 19].

The above changes in the texture regularly affect the mechanical properties (Figs. 3, 4). As can be seen, an anisotropy of mechanical properties is observed in the plane of the sheets. Thus, the yield strength σ0.2 is minimum in the RD; and is maximum in the original sheets and after 0.5, 1, and 5 cycles in the TD, and after three cycles of RB, in the DD. Simultaneously, the ultimate strength σu is maximum in the RD; minimum, in the DD; and it takes intermediate values in the TD (Fig. 3). The rela tive elongation shows the opposite trend with respect to σu (Fig. 4). The magnitude of the anisotropy can be repre sented quantitatively by an anisotropy factor η = Fmax − Fmin × 100%, where F is the value of a corre Fmin sponding property. In the initial material, η = 3.13% for σ0.2 and 6.72% for σu. After a 0.5cycle RB, these values decreased to 2.6 and 5.46%, respectively, which can be attributed to an increase in the texture spread, as was mentioned above. With increasing number of RB cycles, the anisotropy factor was 3.16 and 5.04% for σ0.2 and σu, respectively. After five RB cycles, the anisotropy factors decreased to 2.09 and 2.9%, respec tively, which corresponds to the above mentioned gen eral texture weakening. A similar trend is characteristic of the elongation. Its anisotropy factor is maximum in the initial strip (24.7%) and is minimum after three RB cycles (22.9%). After five cycles, it increases slightly (23.7%) (Fig. 4). Let us analyze the observed anisotropy of mechan ical properties and its variation in relation to the crys tallographic texture after the corresponding RB cycles. The change in texture can be quantitatively described by variations of the normalized values of the pole den sity Prel in the IPFs (ND) (see Fig. 1) that is greater than unity, which corresponds to a textureless sample. In other words, we take the approach in which it is assumed that the contribution to the mechanical properties comes only from those components of the

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texture whose pole density is greater than unity. In this case it is necessary to produce a renormalization of the pole density with allowance for only the above compo nents of the texture. To this end, we first average the values of the pole density (which exceed unity) obtained for both sides of each sheet after each num ber of RB cycles in the IPFs (ND) (see Fig. 1). Thus, ND we find the average values of the pole densities P100 ND ND , and P211 for the initial sample and the samples P210 after the appropriate number of RB cycles. As a nor malization factor, we use the sum of the average values ND of the above pole densities for an appropriate Phkl number of cycles. Now, let us define the relative con ND tribution to the texture from each density Phkl for each ND number of cycles by dividing by the sum Phkl ; i.e.,

Normalized values of the pole density that are greater than unity in the IPFs in the ND

∑

∑

we find the ratio

ND Phkl for the corresponding RB ND Phkl

∑

cycle. In principle, the latter ratio means the volume fraction of the corresponding component of the tex ture in the above approximation. The contribution from each component of the texture to the mechanical prop erties will now be considered in the form of sums of prod ND ucts of Phkl and its volume fractions

ND Phkl , that is, in ND Phkl

∑

⎛ ND P ND ⎞ the following form: Prel = ⎜ Phkl × hkl ND ⎟, which will ⎜ Phkl ⎟⎠ ⎝ be called the normalized values of the pole density Prel.

∑

∑

The abovementioned normalized values of the pole density that are greater than unity are presented in the table. A comparison of Prel with the corresponding values of the strength properties has shown that there exist statistically significant linear correlations between Prel, on the one hand, and the σ0.2 and σu values averaged over the direction of measurement shown in Fig. 3, on the other hand. We obtained the following regression equations with reliability indices of the approximation 2 = 0.77 and Ru2 = 0.80: R0.2

σ 0.2 = 2.64 ( Prel ) + 185.3; σ u = 2.69 ( Prel ) + 234.2. Thus, the observed anisotropy of the mechanical properties and its change with increasing number of RB cycles are largely specified by the corresponding changes in the texture. The RB exerts a most pronounced effect on those structure parameters and mechanical properties that are sensitive to small tensile strains. These are the tex ture, tensile strength, and relative elongation. There fore, the most significant changes in these characteris tics were observed during the first three cycles of RB. THE PHYSICS OF METALS AND METALLOGRAPHY

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Cycles

Prel

0

3.86

0.25

2.38

0.5

3.28

1

3.22

3

3.32

5

2.71

4. CONCLUSIONS (1) It has been established that the initial copper strips after the rolling and annealing at 350°С for 1 h are recrys tallized. The texture of the initial strips is presented mainly by the {001}〈100〉 cube orientation; remains of the rolling texture {112}〈111〉; orientations {012}〈120〉; {012}〈121〉; {012}〈100〉; {012}〈123〉; {331}〈110〉; {331}〈013〉 and {331}〈123〉; and a twinning orientation close to {122}〈212〉. The twins were found in the corre sponding micrographs of the initial strips. (2) It has been shown that the reverse bending (RB) results in the development of deformationinduced twinning, which proceeds most intensely during the first three RB cycles. An increase in the number of RB cycles to five leads to a weakening of the cube texture and of the pole density of twin orientations and to the development of a deformationinduced texture of the {135}〈211〉 type. (3) The presence of anisotropy of mechanical properties in both the original copper strips and in strips subjected to RB with various numbers of cycles has been established. The anisotropy factor was found to be minimum after five cycles of RB. (4) Statistically significant linear correlations have been found between the normalized values of the pole density Prel exceeding unity in the IPFs (ND), on the one hand, and the σ0.2 and σu values averaged over the directions of measurement, on the other hand. The reliability factors of the approximation were 0.77 and 0.80, respectively. (5) It is shown that the greatest changes in the structure and mechanical properties occurred during the first three–five cycles of RB. REFERENCES 1. Copper and Copper Alloys. http://www.keytomet als.com/Article27.html 2. Continuous Melting. http://bse.scilib.com/article 081225.html 3. Copper in Architecture. http://www.knowhouse.ru/pdf books/copperbook.pdf Vol. 113

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4. Technology of Correction in ARKU Rolls. http://www.tkzentrum.ru/equipment/arku/item17/ 5. Straightening Machines. http://www.tehnoinfa.ru/ kuznechnoeoborudovanie/109.html 6. A. A. Bryukhanov, Yu. V. Zil’berg, M. Shaper, S. I. Iovchev, M. Rodman, and D. Rodman, “Influence of Sign Variable Bending Deformation on Texture and Anisotropy of Elastic Properties of Low Carbon Steel Sheets,” Mater. Sci., No. 10, 33–38 (2010). 7. Yu. V. Zil’berg, F.V. Bakh, D. Borman, M. Rodman, M. Shaper, and M. Hepke, “Effect of Alternating Bending on the Structure and Properties of Strips from AZ31 Magnesium Alloy,” Met. Sci. Heat Treat. 51, 170–175 (2009). 8. A. A. Bryukhanov, P. P. Stoyanov, Yu. V. Zil’berg, and D. Rodman, “Anisotropy of Mechanical Properties of Magnesium Alloy AZ31 Sheets as a Result of SignVari able Bending Deformation,” Metallurg. Mining Ind. 2, 215–219 (2010). 9. A. A. Bryukhanov, M. Rodman, A. F. Tarasov, P. P. Stoyanov, M. Shaper, and D. Bormann, “Mecha nism of the Plastic Deformation of the AZ31 Alloy upon LowCycle Reverse Bending,” Phys. Met. Metal logr. 111, 623–629 (2011). 10. Marks of Copper. http://weldzone.info/technol ogy/materials/144cu/798markimodi 11. Ya. D. Vishnyakov, A. A. Babareko, S. A. Vladimirov, and I. V. Egiz, Teoriya obrazovaniya tekstur v metallakh

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i splavakh (Texture Formation Theory in Metals and Alloys) (Nauka, Moscow, 1979) [in Russian]. C. A. Verbraak, “The Formation of Cube Recrystalliza tion Textures by 112 Slip,” Acta Metall. 6, 580–597 (1958). W. F. Hellerph, C. A. Verbraaks, and B. H. Kolster, “Recrystallization at Grain Boundaries in Deformed Copper Bicrystals,” Acta Metall. 32, 1391–1406 (1984). T. Kamijo “Study on the Inverse Rowland Mechanism for the Nucleation of a Cube Recrystallization Tex ture,” J. Jpn. Inst. Metals 31, 741–746 (1967). W. Mao, “Formation of Recrystallization Cube Texture in High Purity FaceCentered Cubic Metal Sheets,” J. Mater. Eng. Perf. 8, 557–560 (1999). K. Sztwiertnia, “Orientation Aspects of the Recrystal lization Nucleation in Highly Deformed Polycrystal line Copper,” Mater. Sci. Forum 467–470, 99–107 (2004). M. Sindel, G. D. Kohlhoff, K. Lücke, and B. J. Dug gan, “Development of Cube Texture in Coarse Grained Copper,” Text. Microstruct. 12, 37–46 (1990). C. S. Barrett and W. Steadman, “Structure of Copper after Rolling,” Trans. AIME 147, 57–64 (1942). H. Hu, P. R. Sperry, and P. A. Beck, “Rolling Textures in FaceCentered Cubic Metals,” J. Met., No. 1, 76–81 (1952).

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