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The effect of rolling geometry on the distribution of deformed cube structure and its recrystallisation kinetics
HATERIAIS SCIENCE & ENGRIEERIWG ELSEVIER
Materials Science and Engineering A257 (1998) 198-203
A --
The effect of rolling geometry on the distribution of deformed cube structure and its recrystallisation kinetics C.S. Lee *: F.C. Ng, KC.
Lee
Abstract The microstructure. distribution and recrystallisation kinetics of cube-oriented deformation structures in copper cold roiled at two different rolling geometries were studied. It was found that a suitable amount of redundant shear strain during rolling increases the density and volume fraction of the cube-oriented deformation structure. In addition, the cube-oriented structure at the rolling sheet surface. where the redundant shear strain is generally larger than that at the centre region, was found to have a smaller average misorientation angle from the exact cube orientation. Irrespective to these factors, the cube-oriented structure formed by rolling at a high redundant shear condition recrystaliscs much slower than that formed at a lower redundant shear condition. On the other hand. this observation is consistent with the fact that the 25-40” (111) misorientation relationship between the cube-oriented structures and their neighbours is least frequently found in the regions of large redundant shear. That is, many of the cube-oriented structures formed with a high redundant shear do not have neighbours with the favourable X-40” (I 11) misorientation relationship for high rate of grain boundary migration during recrystallisation. Q 1998ElsevierScienceS.A. All rights reserved. Ke~~oucls: Rolling geometry; Cube structure; Recrystallisation
1. Introduction The studies of cube recrystallisation continued for several decades and
texture has been these works have
been comprehensively summarised in two recent publications [1,2]. A major theme of these works has been on establishing whether the oriented nucleation (ON) or the oriented growth (OG) is more important. On the
other hand, recent works by Duggan et al. [3:4] suggested that both the ON and OG factors are essential during
recrystallisation.
It was considered
(DK) model [7]. It has also been pointed out that redundant shear strain during the rolling deformation can influence the formation of the cube-oriented deformation structure [S]. It is the purpose of the present work to present experimental data on how the distribution, microstructure and subsequent recrystallisation kinetics of the cube-oriented deformation structure are influenced by the amount of redundant shear strain during rolling.
that the cube
recrystallisation texture in cold rolled FCC materials is formed by a preferential growth of the cube-oriented nuclei (ON factor) into their immediate neighbours which are of orientations 30-40” rotated about a (11 l} pole of the {lOO~(OOl) orientation (OG factor). The existence of the cube-oriented structure with 30-40” (111) rotated neighbour have been theoretically predicted by Lee et al. [5] using either a deformation banding (DB) model [6] or the Dillamore and Katoh * Corresponding author. Fax: + 852 27887830. e-mail: apcslee@ cityu.edu.hk
2. Experimental The initial material was high purity ( > 99.99%) copper with a weak initial texture and an average grain size of 100 pm. Samples were cold rolled to 90% thickness reduction at two rolling geometries with two rolling mills of different roller diameters to produce different amount of redundant shear strain (Table 1). In Table 1, ys is the ratio of the geometrical redundant shear strain to the normal rolling strain; (1and 1 are, respectively the specimen thickness and the projected length of contact between roller and specimen.The more commonly used
0921-5093/98/S - see front matter 0 1998 Elsevier Science S.A. Ail rights reserved. PII 50921-5093(98)00842-9
C.S. LEE et al. / Milterials
Science
rind Engimering
A257
(1998)
199
198-203
Table 1 Details of rolling condition Sample
Average yF
Roller diameter
No. of pass to 90% reduction
lld
Large shear sample Small shear sample
0.938 0.231
105 mm 254 mm
152 15
0.53 2.16
l/n parameter, which equals 1/2y, [9], is also tabled for reference. For both rolling conditions, ample kerosene was used for lubrication. A crystallographic etch, which preferentially exposes { 111 j planes, was used to reveal microstructural as well as orientation information in the rolled materials [lo]. All microstructural and orientation measurements were performed on the plane 45” to the rolling plane and the longitudinal section as it is the plane on which the cube-oriented structure can be best resolved by the crystallographic etch. The number and volume fraction of cube-oriented deformation structures were measured at different positions namely, surface, l/4 thickness, and centre, along the thickness direction of the cold rolled samples. In order to take into account that some cube bands are slightly off the ideal cube orientation, weighting factors of 1, 0.5 and 0.25 have been applied. respectively to bands of O-5, 5-10 and 10-15” misorientation from the IlOO}(OOl) orientation. The resulting data shown in Table 2 are average values from five specimens measured throughout the sample thickness (i.e. a total sampling distance of 4.5 mm in the thickness direction for each rolling condition). Misorientation relationship between the cube-oriented structures and their immediate neighbours was determined by measuring orientations of 50 immediate neighbours of the cube structures for both rolling conditions at both the surface and centre regions. For the determination of the percentage of cube bandneighbouring band pairs which have the 25-40” (111) misorientation, the pairs were counted only if the one of the (111) pole of the neighbouring band is within 15” of one of the (111) pole of the cube band and that the rotation about their nearly common (111) pole is within 25-40”. In fact, due to the limited orientation resolution of the present method and the scattering nature of the orientation distribution, the description of the 25-40” (11 l} misorientation used here is over specifying. According to the authors experience, most of these neighbouring bands can be more accurately referred as near S-oriented band. The description of 25-40” (111) misorientation is used here simply because it is a more commonly used description in the field. Recrystallisation kinetics was studied by measuring the volume fraction of the recrystallised regions upon annealing the cold rolled samples at 150°C for various durations.
3. Results and discussions After 90% rolling, the microstructure consists of long thin bands of different orientations. Cube-oriented bands in the cold rolled samples are shown in Fig. 1. For the sample rolled at ys = 0.231 (small redundant shear), the cube-oriented bands are m l-3 pm thick (Fig. l(a)). No apparent difference was observed from the cube-oriented bands found at different thickness positions. For the sample rolled at yn = 0.938 (large redundant shear), the cube-oriented bands found near the centre layer of the rolled sheet have a microstructure similar to that of the cube-oriented bands in the sample rolled at ys = 0.231. However, in the surface layers of the sheet rolled at yg = 0.938, the cube-oriented bands were found clustering together (Fig. l(b)). Occasionally, splitting of thick cube-oriented bands into two or more cube-oriented bands (marked by white arrows in Fig. l(b)) was observed. The average number and volume fraction of the cube-oriented bands at different thickness positions of the cold rolled samples are summarised in Table 2. It is clear from the table that both the number and the volume fraction of cube-oriented structure are higher in the sample rolled at yy = 0.938. For this sample, the number and volume fraction of cube-oriented bands also increase from the rolling sheet centre towards the surface region. For the sample rolled at y: = 0.231, the number and volume fraction of cube-oriented bands have their maxima at the l/4 thickness.position. This influence by the thickness position has been studied theoretically by Lee et al. [S] and was found to be dependent on both the geometrical shear yr and the frictional shear, yP However, as there is little knowledge on the experimental frictional shear: no direct comparison can be made between the experimental results and the theoretical prediction’. M&orientation of the near-cube bands from the exact { lOO}(OOl) orientation as a function of the position along the specimen thickness direction is shown in Fig. 2. It can be seen that the misorientation angle is mainly determined by the thickness position and is the largest near the sheet centre where the shear strain should be a minimum. ’ On the other hand, it is not difficult to fit the theoretical prediction to the experimental data by choosing a suitable frictional shear profile. It is not done here as it is not considered to be very meaningful.
200
C.S. Lee et al. /Mnterinis
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A257
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Table 2 Number and volume fraction of the cube-oriented structure at different thickness position of copper cold rolled 90% at two different rolling conditions Sample
y, = 0.23 1
ye = 0.938
Thickness position
No. of cube band
Vol. fraction of cube band”
No. of cube band
Vol. fraction of cube band*
Surface 114 Thickness Centre Total
7.7 11.1 6.1 24.9
1.0 1.4 0.7 3.1
16.6 11.9 7.2 35.7
2.2 1.5 1.0 4.1
ri With respect to the whole sample instead of just the particular thickness position.
The orientation relationship between the cube-oriented bands and their immediate neighbours was determined from 50 cube bands at two different thickness positions for each rolling condition and is listed in Table 3. It should be noted that orientations of the neighbours of the cube bands were determined from the crystallographic etching patterns which spatial resolution is in the order of a micron. As the band structure in the present studies has a thickness range of - 0.5 to
3 pm, thus, orientations were determined near the limit of the etching technique. The orientation accuracy here was estimated to be - 15” only. (For the case of near cube orientations, an accuracy of 3-5” can be obtained as the observation plane was selected such that both the angular and spatial resolutions are highest for the cube orientation.) In fact, in about a quarter of the neighbours of the cube-oriented bands, no resolvable etching pattern can be obtained. These unresolvable patterns were not counted in the present studies. For these limitations, the data shown in Table 3 are considered to be qualitative rather than quantitative. In fact, Ihe authors have tried to determine the misorientation with the electron back scattering pattern (EBSP) technique. However, due to the high plastic strain and small band thickness, most of the deformed structures do not give good enough diffraction patterns for orientation determination. Of course, this problem can be solved by slightly annealing the deformed materials, but then it will lead to growth of some cube-oriented nuclei and thus eliminates part of the information [4], On the other hand, if the misorientation is determined by electron diffraction with a transmission electron microscope, it will be a very extensive work for sampling throughout the sample thickness. Hence, it is considered that the present etching technique is a reasonable compromise 10 c
b) Fig. 1. Cube-oriented bands (marked with asterisks) in 90% cold rolled copper (rolling direction parallel to micron marker). (a) ye= 0.231, taken from the centre layer of the rolling sheet. (b) 7, = 0.938, taken from near the rolling sheet surface. A thick cube-oriented band on the left is splitting into two near cube bands (marked with white arrows) on the right.
su fface
114 thickness Thickness Position
centre
Fig. 2. A graph of the average misorientation angle from the exact { lOOt(OO1) orientation of the near-cube band at different positions in the specimens.
C.S. Lee et al. /Maarerials
Science
am’ Engineerir7g
A257
(1998)
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198-203
Table 3 Percentage of the cube-neighbour pair with the special 2540” (111) rotation relationship at different thickness positions of copper cold rolled 90% at two different rolling conditions Sample
ys = 0.23 1
Thickness position
Surface
Centre
Surface
Centre
40
40
22
36
‘% of the cube-neighbour
pair with 2540” (111) rotation relationship
between accuracy, completeness of data and the amount of effort involved. Nevertheless, data in Table 3 suggest that the surface region of the sample rolled at yg = 0.938 has a much lower percentage of the special 25-40” (111) special misorientation relationship among the cube-neighbour pairs. In fact, many cube bands at the surface of the s/~= 0.938 sample are clustered together (Fig. l(b)) and have neighbours only slightly misoriented (i.e. the neighbours are itself near cube bands). If the cubecube pairs were also considered, the percentage of 25-40” (111) misorientation relationship at the surface of the yp = 0.938 sample should be even lower than the present value (22%) shown in Table 3. Upon annealing at 150°C the dominant recrystallisation textures are the cube texture in both samples. The volume fraction of recrystallised regions as a function of annealing time is shown in Fig. 3. Clearly the sample rolled at small ys recrystallised much faster. Fig. 4(a) and (b) show through-thickness micrographs of the partially recrystallised samples rolled, respectively at ye = 0.231 and 0.938. The recrystallised cube grains in Fig. 4(a) and (b) are outlined in the schematic diagram Fig. 4(c) and (d), respectively. It is clear from Fig. 4 that a relatively homogeneous distribution of cube recrystallised grains was found in the ye = 0.231 sample. On the other hand, in the yp = 0.938 sample, the recrystallised cube grains are concentrated in the centre region. This is consistent with the observation that the surface region of the yg = 0.938 sample has the smallest proportion of the 25-40” (111) misoriented 90 g c .$ 0 b2 g
80 70 60 50 40 30
yg = 0.938
boundaries in the cube-neighbour pairs. Thus, the favourable oriented growth condition is least fulfilled and resulting in a much lower recrystallisation rate. The present results indicate that a suitable amount of redundant shear strain can increase the number and volume fraction of the cube-oriented bands in cold rolled copper. This observation agrees with the predicted stabilising effect on the cube-oriented grain by the redundant shear [8]. The splitting of the thick cube-oriented bands into several thin bands and the clustering of the thin cube bands (Fig. l(b)) in regions of large shear suggest that the thick cube bands have been homogeneously deforming to a relatively high strain (say 80-90% cold rolling). On the other hand, in regions where the redundant shear is low, homogeneously deforming cube grains are not stable and would split into deformation bands at a much lower strain by the mechanisms proposed by Dillamore and Katoh or Lee et al. [5]. Hence, thick or clustered cube bands were seldom observed in the small shear regions. It has also been pointed out [5] that both the DK [7] and the DB [6] banding models can predict the formation of the cube-neighbour pairs with the 30-40” (111) misorientation relationship. Hence, the delay in banding due to the stabilising effect on the cube-oriented grains by the redundant shear will also delay the formation of the 30-40” (111) misorientation relationship in the cubeneighbour pairs. The present works also suggest that the formation of cube recrystallisation texture is mainly controlled by the amount of cube bands with the 30-40” (111) misorientation relationship with their neighbours. Whereas, the overall density, volume fraction and orientation accuracy of the cube bands only play a secondary role.
4. Conclusions
3 20
0
150
And%ng
Timk”fmin]
Fig. 3. A graph of the volume fraction of the recrystallised region as a function of annealing time.
It is confirmed that a suitable amount of redundant shear during rolling can stabilise the cube-oriented grains. More cube-oriented bands were found in the sample rolled with a larger amount of redundant shear. In addition, the average misorientation of the cube bands from the exact {lOO}(OOl) orientation was found to be smaller in the rolling sheet surface where the redundant shear is large. On the other hand, the
d
Fig. 4. Through-thickness micrographs showing the distribution of the recrystallised cube grains in (a) sample rolled at j)F = 0.231 after 3 min arm&q at 1 50°C: ib) sample rolled at ;lp = 0.938 after 21 min annealing at 150°C; (c) and (d) are the schematic diagrams of, respectively (a) and (b) with the recrystallised cube grains outlined. (rolling direction parallel to micron marker).
percentage of the cube-neighbour pairs having the 2540” (Ill) misorientation relationship is smallest in the surface region of the sample rolled with a large amount of redundant shear. The recrystallisation rate is also the slowest at this region, It is concluded that the formation of cube annealing texture is dominantly controlled by amount of cube-neighbour pairs having the 30-40” (111) misorientation relationship. The number. volume fraction and orientation accuracy of
the cube bands in the deformed structure only play a secondary role.
Acknowledgements CSL would like to acknowledge Croucher Foundation for financial support through a research grant number 900001.
C.S. Lee et d. I Muterids
Science
References [l] F.J. Humphreys, M. Hatherly, Recrystallisation and Related Annealing Phenomena, Pergmon, 1995. [?I R. Cdhn, in: R. Cahn, P. Haasen (Eds.), Physical Metallurgy, 4th edn., vol. 3, Elsevier, Amsterdam, 1996, p. 2400. 131 B.J. Duggan, M. Sindel, G.D. Kiihlhoff, K. Liicke, Acta Metall. 38 (1990) 103. [4] B.J. Duggan, K. Liicke, G.D. Kiihlhoff, C.S. Lee, Acta Metall.
n17d Engil7eering
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(1998)
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203
41 (1921) 1993. [5] C.S. Lee. R.E. Smallman, B.J. Duggan, Scripta Metall. Mater. 29 (1993) 43. [6] C.S. Lee, B.J. Duggan, Acta Metall. Mater. 41 (1993) 2691. [7] I.L. Dillamore. H. Katoh, Mater. Sci. 8 (1974) 73. [8] C.S. Lee, R.E. Smallman, B.J. Duggan, Mater. Sci. Technol. 10 (1994) 149. [9] C.S. Lee, B.J. Duggan, Metall. Trans. 22A (1991) 2637. [IO] G.D. Kiihlhoff, X. Sun, K. Liicke, Proc. 8th Int Conf. on Textures of Materials, 1988. p. 183.
Materials Science and Engineering A257 (1998) 198-203
A --
The effect of rolling geometry on the distribution of deformed cube structure and its recrystallisation kinetics C.S. Lee *: F.C. Ng, KC.
Lee
Abstract The microstructure. distribution and recrystallisation kinetics of cube-oriented deformation structures in copper cold roiled at two different rolling geometries were studied. It was found that a suitable amount of redundant shear strain during rolling increases the density and volume fraction of the cube-oriented deformation structure. In addition, the cube-oriented structure at the rolling sheet surface. where the redundant shear strain is generally larger than that at the centre region, was found to have a smaller average misorientation angle from the exact cube orientation. Irrespective to these factors, the cube-oriented structure formed by rolling at a high redundant shear condition recrystaliscs much slower than that formed at a lower redundant shear condition. On the other hand. this observation is consistent with the fact that the 25-40” (111) misorientation relationship between the cube-oriented structures and their neighbours is least frequently found in the regions of large redundant shear. That is, many of the cube-oriented structures formed with a high redundant shear do not have neighbours with the favourable X-40” (I 11) misorientation relationship for high rate of grain boundary migration during recrystallisation. Q 1998ElsevierScienceS.A. All rights reserved. Ke~~oucls: Rolling geometry; Cube structure; Recrystallisation
1. Introduction The studies of cube recrystallisation continued for several decades and
texture has been these works have
been comprehensively summarised in two recent publications [1,2]. A major theme of these works has been on establishing whether the oriented nucleation (ON) or the oriented growth (OG) is more important. On the
other hand, recent works by Duggan et al. [3:4] suggested that both the ON and OG factors are essential during
recrystallisation.
It was considered
(DK) model [7]. It has also been pointed out that redundant shear strain during the rolling deformation can influence the formation of the cube-oriented deformation structure [S]. It is the purpose of the present work to present experimental data on how the distribution, microstructure and subsequent recrystallisation kinetics of the cube-oriented deformation structure are influenced by the amount of redundant shear strain during rolling.
that the cube
recrystallisation texture in cold rolled FCC materials is formed by a preferential growth of the cube-oriented nuclei (ON factor) into their immediate neighbours which are of orientations 30-40” rotated about a (11 l} pole of the {lOO~(OOl) orientation (OG factor). The existence of the cube-oriented structure with 30-40” (111) rotated neighbour have been theoretically predicted by Lee et al. [5] using either a deformation banding (DB) model [6] or the Dillamore and Katoh * Corresponding author. Fax: + 852 27887830. e-mail: apcslee@ cityu.edu.hk
2. Experimental The initial material was high purity ( > 99.99%) copper with a weak initial texture and an average grain size of 100 pm. Samples were cold rolled to 90% thickness reduction at two rolling geometries with two rolling mills of different roller diameters to produce different amount of redundant shear strain (Table 1). In Table 1, ys is the ratio of the geometrical redundant shear strain to the normal rolling strain; (1and 1 are, respectively the specimen thickness and the projected length of contact between roller and specimen.The more commonly used
0921-5093/98/S - see front matter 0 1998 Elsevier Science S.A. Ail rights reserved. PII 50921-5093(98)00842-9
C.S. LEE et al. / Milterials
Science
rind Engimering
A257
(1998)
199
198-203
Table 1 Details of rolling condition Sample
Average yF
Roller diameter
No. of pass to 90% reduction
lld
Large shear sample Small shear sample
0.938 0.231
105 mm 254 mm
152 15
0.53 2.16
l/n parameter, which equals 1/2y, [9], is also tabled for reference. For both rolling conditions, ample kerosene was used for lubrication. A crystallographic etch, which preferentially exposes { 111 j planes, was used to reveal microstructural as well as orientation information in the rolled materials [lo]. All microstructural and orientation measurements were performed on the plane 45” to the rolling plane and the longitudinal section as it is the plane on which the cube-oriented structure can be best resolved by the crystallographic etch. The number and volume fraction of cube-oriented deformation structures were measured at different positions namely, surface, l/4 thickness, and centre, along the thickness direction of the cold rolled samples. In order to take into account that some cube bands are slightly off the ideal cube orientation, weighting factors of 1, 0.5 and 0.25 have been applied. respectively to bands of O-5, 5-10 and 10-15” misorientation from the IlOO}(OOl) orientation. The resulting data shown in Table 2 are average values from five specimens measured throughout the sample thickness (i.e. a total sampling distance of 4.5 mm in the thickness direction for each rolling condition). Misorientation relationship between the cube-oriented structures and their immediate neighbours was determined by measuring orientations of 50 immediate neighbours of the cube structures for both rolling conditions at both the surface and centre regions. For the determination of the percentage of cube bandneighbouring band pairs which have the 25-40” (111) misorientation, the pairs were counted only if the one of the (111) pole of the neighbouring band is within 15” of one of the (111) pole of the cube band and that the rotation about their nearly common (111) pole is within 25-40”. In fact, due to the limited orientation resolution of the present method and the scattering nature of the orientation distribution, the description of the 25-40” (11 l} misorientation used here is over specifying. According to the authors experience, most of these neighbouring bands can be more accurately referred as near S-oriented band. The description of 25-40” (111) misorientation is used here simply because it is a more commonly used description in the field. Recrystallisation kinetics was studied by measuring the volume fraction of the recrystallised regions upon annealing the cold rolled samples at 150°C for various durations.
3. Results and discussions After 90% rolling, the microstructure consists of long thin bands of different orientations. Cube-oriented bands in the cold rolled samples are shown in Fig. 1. For the sample rolled at ys = 0.231 (small redundant shear), the cube-oriented bands are m l-3 pm thick (Fig. l(a)). No apparent difference was observed from the cube-oriented bands found at different thickness positions. For the sample rolled at yn = 0.938 (large redundant shear), the cube-oriented bands found near the centre layer of the rolled sheet have a microstructure similar to that of the cube-oriented bands in the sample rolled at ys = 0.231. However, in the surface layers of the sheet rolled at yg = 0.938, the cube-oriented bands were found clustering together (Fig. l(b)). Occasionally, splitting of thick cube-oriented bands into two or more cube-oriented bands (marked by white arrows in Fig. l(b)) was observed. The average number and volume fraction of the cube-oriented bands at different thickness positions of the cold rolled samples are summarised in Table 2. It is clear from the table that both the number and the volume fraction of cube-oriented structure are higher in the sample rolled at yy = 0.938. For this sample, the number and volume fraction of cube-oriented bands also increase from the rolling sheet centre towards the surface region. For the sample rolled at y: = 0.231, the number and volume fraction of cube-oriented bands have their maxima at the l/4 thickness.position. This influence by the thickness position has been studied theoretically by Lee et al. [S] and was found to be dependent on both the geometrical shear yr and the frictional shear, yP However, as there is little knowledge on the experimental frictional shear: no direct comparison can be made between the experimental results and the theoretical prediction’. M&orientation of the near-cube bands from the exact { lOO}(OOl) orientation as a function of the position along the specimen thickness direction is shown in Fig. 2. It can be seen that the misorientation angle is mainly determined by the thickness position and is the largest near the sheet centre where the shear strain should be a minimum. ’ On the other hand, it is not difficult to fit the theoretical prediction to the experimental data by choosing a suitable frictional shear profile. It is not done here as it is not considered to be very meaningful.
200
C.S. Lee et al. /Mnterinis
Science
md Engineering
A257
(1998)
198-203
Table 2 Number and volume fraction of the cube-oriented structure at different thickness position of copper cold rolled 90% at two different rolling conditions Sample
y, = 0.23 1
ye = 0.938
Thickness position
No. of cube band
Vol. fraction of cube band”
No. of cube band
Vol. fraction of cube band*
Surface 114 Thickness Centre Total
7.7 11.1 6.1 24.9
1.0 1.4 0.7 3.1
16.6 11.9 7.2 35.7
2.2 1.5 1.0 4.1
ri With respect to the whole sample instead of just the particular thickness position.
The orientation relationship between the cube-oriented bands and their immediate neighbours was determined from 50 cube bands at two different thickness positions for each rolling condition and is listed in Table 3. It should be noted that orientations of the neighbours of the cube bands were determined from the crystallographic etching patterns which spatial resolution is in the order of a micron. As the band structure in the present studies has a thickness range of - 0.5 to
3 pm, thus, orientations were determined near the limit of the etching technique. The orientation accuracy here was estimated to be - 15” only. (For the case of near cube orientations, an accuracy of 3-5” can be obtained as the observation plane was selected such that both the angular and spatial resolutions are highest for the cube orientation.) In fact, in about a quarter of the neighbours of the cube-oriented bands, no resolvable etching pattern can be obtained. These unresolvable patterns were not counted in the present studies. For these limitations, the data shown in Table 3 are considered to be qualitative rather than quantitative. In fact, Ihe authors have tried to determine the misorientation with the electron back scattering pattern (EBSP) technique. However, due to the high plastic strain and small band thickness, most of the deformed structures do not give good enough diffraction patterns for orientation determination. Of course, this problem can be solved by slightly annealing the deformed materials, but then it will lead to growth of some cube-oriented nuclei and thus eliminates part of the information [4], On the other hand, if the misorientation is determined by electron diffraction with a transmission electron microscope, it will be a very extensive work for sampling throughout the sample thickness. Hence, it is considered that the present etching technique is a reasonable compromise 10 c
b) Fig. 1. Cube-oriented bands (marked with asterisks) in 90% cold rolled copper (rolling direction parallel to micron marker). (a) ye= 0.231, taken from the centre layer of the rolling sheet. (b) 7, = 0.938, taken from near the rolling sheet surface. A thick cube-oriented band on the left is splitting into two near cube bands (marked with white arrows) on the right.
su fface
114 thickness Thickness Position
centre
Fig. 2. A graph of the average misorientation angle from the exact { lOOt(OO1) orientation of the near-cube band at different positions in the specimens.
C.S. Lee et al. /Maarerials
Science
am’ Engineerir7g
A257
(1998)
201
198-203
Table 3 Percentage of the cube-neighbour pair with the special 2540” (111) rotation relationship at different thickness positions of copper cold rolled 90% at two different rolling conditions Sample
ys = 0.23 1
Thickness position
Surface
Centre
Surface
Centre
40
40
22
36
‘% of the cube-neighbour
pair with 2540” (111) rotation relationship
between accuracy, completeness of data and the amount of effort involved. Nevertheless, data in Table 3 suggest that the surface region of the sample rolled at yg = 0.938 has a much lower percentage of the special 25-40” (111) special misorientation relationship among the cube-neighbour pairs. In fact, many cube bands at the surface of the s/~= 0.938 sample are clustered together (Fig. l(b)) and have neighbours only slightly misoriented (i.e. the neighbours are itself near cube bands). If the cubecube pairs were also considered, the percentage of 25-40” (111) misorientation relationship at the surface of the yp = 0.938 sample should be even lower than the present value (22%) shown in Table 3. Upon annealing at 150°C the dominant recrystallisation textures are the cube texture in both samples. The volume fraction of recrystallised regions as a function of annealing time is shown in Fig. 3. Clearly the sample rolled at small ys recrystallised much faster. Fig. 4(a) and (b) show through-thickness micrographs of the partially recrystallised samples rolled, respectively at ye = 0.231 and 0.938. The recrystallised cube grains in Fig. 4(a) and (b) are outlined in the schematic diagram Fig. 4(c) and (d), respectively. It is clear from Fig. 4 that a relatively homogeneous distribution of cube recrystallised grains was found in the ye = 0.231 sample. On the other hand, in the yp = 0.938 sample, the recrystallised cube grains are concentrated in the centre region. This is consistent with the observation that the surface region of the yg = 0.938 sample has the smallest proportion of the 25-40” (111) misoriented 90 g c .$ 0 b2 g
80 70 60 50 40 30
yg = 0.938
boundaries in the cube-neighbour pairs. Thus, the favourable oriented growth condition is least fulfilled and resulting in a much lower recrystallisation rate. The present results indicate that a suitable amount of redundant shear strain can increase the number and volume fraction of the cube-oriented bands in cold rolled copper. This observation agrees with the predicted stabilising effect on the cube-oriented grain by the redundant shear [8]. The splitting of the thick cube-oriented bands into several thin bands and the clustering of the thin cube bands (Fig. l(b)) in regions of large shear suggest that the thick cube bands have been homogeneously deforming to a relatively high strain (say 80-90% cold rolling). On the other hand, in regions where the redundant shear is low, homogeneously deforming cube grains are not stable and would split into deformation bands at a much lower strain by the mechanisms proposed by Dillamore and Katoh or Lee et al. [5]. Hence, thick or clustered cube bands were seldom observed in the small shear regions. It has also been pointed out [5] that both the DK [7] and the DB [6] banding models can predict the formation of the cube-neighbour pairs with the 30-40” (111) misorientation relationship. Hence, the delay in banding due to the stabilising effect on the cube-oriented grains by the redundant shear will also delay the formation of the 30-40” (111) misorientation relationship in the cubeneighbour pairs. The present works also suggest that the formation of cube recrystallisation texture is mainly controlled by the amount of cube bands with the 30-40” (111) misorientation relationship with their neighbours. Whereas, the overall density, volume fraction and orientation accuracy of the cube bands only play a secondary role.
4. Conclusions
3 20
0
150
And%ng
Timk”fmin]
Fig. 3. A graph of the volume fraction of the recrystallised region as a function of annealing time.
It is confirmed that a suitable amount of redundant shear during rolling can stabilise the cube-oriented grains. More cube-oriented bands were found in the sample rolled with a larger amount of redundant shear. In addition, the average misorientation of the cube bands from the exact {lOO}(OOl) orientation was found to be smaller in the rolling sheet surface where the redundant shear is large. On the other hand, the
d
Fig. 4. Through-thickness micrographs showing the distribution of the recrystallised cube grains in (a) sample rolled at j)F = 0.231 after 3 min arm&q at 1 50°C: ib) sample rolled at ;lp = 0.938 after 21 min annealing at 150°C; (c) and (d) are the schematic diagrams of, respectively (a) and (b) with the recrystallised cube grains outlined. (rolling direction parallel to micron marker).
percentage of the cube-neighbour pairs having the 2540” (Ill) misorientation relationship is smallest in the surface region of the sample rolled with a large amount of redundant shear. The recrystallisation rate is also the slowest at this region, It is concluded that the formation of cube annealing texture is dominantly controlled by amount of cube-neighbour pairs having the 30-40” (111) misorientation relationship. The number. volume fraction and orientation accuracy of
the cube bands in the deformed structure only play a secondary role.
Acknowledgements CSL would like to acknowledge Croucher Foundation for financial support through a research grant number 900001.
C.S. Lee et d. I Muterids
Science
References [l] F.J. Humphreys, M. Hatherly, Recrystallisation and Related Annealing Phenomena, Pergmon, 1995. [?I R. Cdhn, in: R. Cahn, P. Haasen (Eds.), Physical Metallurgy, 4th edn., vol. 3, Elsevier, Amsterdam, 1996, p. 2400. 131 B.J. Duggan, M. Sindel, G.D. Kiihlhoff, K. Liicke, Acta Metall. 38 (1990) 103. [4] B.J. Duggan, K. Liicke, G.D. Kiihlhoff, C.S. Lee, Acta Metall.
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