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The effect of strain path on microstructure and texture development in copper single crystals with (110)[001]and (110)[11̄0]initial orientations
Scripta Materialia, Vol. 35, No. 3, pp. 417-422, 1996 Elsevier Science Ltd Copyright Q 1996 Acta Metallurgica Inc. Printed in the USA. All rights reserved 1359-6462/96 $12.00 + .OO
Pergamon PI1 S1359-6462(96)00132-7
THE EFFECT OF STRAIN PATH ON MICROSTRUCTURE AND TEXTURE DEVELOPMENT IN COPPER SINGLE CRYSTALS WITH (iio)[ooi] AND (iio)[iio] INITIAL ORIENTATIONS Miroslaw Wr6be1, Stanislaw Dymek and Marek Blicharski Academy of Mining and Metallurgy, al. Mickiewicza 30, 30-059 Krakow, Poland (Received September 2 1, 1995) (Accepted March 5, 1996) Introduction
It has been shown that the localization of deformation can be induced by a change in strain path [l-4]. Changes in strain path can also influence evolution of deformation texture. However, the correspondence between microstructure and crystallographic texture evolution in metals under complex loading paths has been generally neglected in studies of plastic deformation. The change in microstructure found recently in austenitic stainless steel single crystals with the initial orientation (11 O)[OOl] subjected to cross-rolling [3] suggested that the analogous experiment on crystals with higher stacking fault energies would shed new light on the influence of strain path changes on microstructure and texture development. The aim of the present work is to examine the structural and textural changes induced by changes in the direction of plastic flow in select copper single crystals, i.e. crystals deforming by dislocation glide. In contrast to other studies on changes in strain path, the present study considers the effect of secondary deformation mode on resulting microstructure. Material and Exuerimental
Procedure
Copper single crystals with (1 lO)[OOl]and (1 lO)[ 1TO]initial orientations were rolled and/or compressed in a channel die at room temperature. Such orientations and deformation paths were selected in order to reproduce a similar experiment performed with low stacking fault energy single crystals [3]. By analogy to rolling, the direction of plastic flow during channel die compression is termed the rolling direction (RD), the compression direction is the normal direction (ND) and the direction perpendicular to the channel side walls is the transverse direction (TD). The single crystal bar with the orientation (1 lO)[OOl]was uniformly rolled to 50% reduction and then cut into two parts. The first part was rolled an additional 30% and the second part was compressed in a channel die to the same reduction in thickness. In both cases, the new direction of plastic flow (RD2) was the former transverse direction (TD 1). Thus the new orientation was (1 10)[ 1TO]. The single crystal with the initial orientation (1 10)[1TO]was deformed only in the channel die to 65% reduction of thickness, i.e. 417
418
TEXTURE DEVELOPMENT
IN Cu
Vol. 35. No. 3
to the same amount of deformation experienced by the samples deformed in two-step procedure (50% + 30%). Friction between the sample and the walls of the channel die was reduced by wrapping samples with teflon tape. The surfaces of each sample deformed in the channel die were polished prior to deformation. This enabled further examination of these surfaces by light microscopy. Transmission electron microscope investigations were performed on longitudinal and transverse sections of the deformed specimens. The {11 l} pole figures were obtained from sections parallel to the rolling plane. Results and Discussion
Figure 1 shows the {1 1 1} pole figures from the deformed single crystals. Plastic Flow Alow
the 10011 Direction
Rolling in this direction does not alter the initial orientation (Figure la). This result is consistent with earlier work [5,6] and confirms that slip occurs in four mutually symmetrical systems producing selfcompensating orientation changes. Such a deformation mode leads to a uniform dislocation microstructure, identical with that described in Ref. [6,7]. Plastic Flow Alow
the I1 iO1 After Flow Along the 10011 Direction
The overall character of texture taken from samples deformed along [00 l] and next along [ 1iO] remains the same with main maxima located close to the initial orientations (Figures lb, lc). Analysis of deformation in the plane strain compression state based on the modified Taylor model by Chin et al. [8] indicates that in the case of the (1 lO)[l TO] orientation slip can occur simultaneously in two directions on each out of four possible {11 1 } planes. No change of the new (1 lO)[ 1TO]orientation after
Figure 1. The (111) pole figures of the examined crystals: a) unidirectionally rolled along [OOl] direction, reduction 50%; b) rolled as in a) with further 30% deformation in the channel die along [ITO]direction; c) rolled as in a) with further rolling along [110] direction with additional reduction of 30%; d) deformed in orientation (1 lO)[lTO] by the channel die compression with 65% reduction of thickness.
Figure 2. Typical dislocation structure after crossrolling (50% along [OOl]followed by 30% along the RD2 parallel to the TDl), section perpendicular to the RDl.
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TEXTURE DEVELOPMENT IN Cu
419
Figure 3. An example of a deformation twin in the cross-rolled specimen with corresponding selected area diffraction pattern, section perpendicular to the RDl.
additional 30% reduction indicates that the identical average strains take place in the mutually symmetrical slip systems as ASSUMed by Chin et al. [S]. However, the texture exhibits orientation scattering around components originated during unidirectional deformation (Figures 1b, 1c). The character of scattering is different for each sample. The extent of scattering is much greater for the rolled specimen (Figure lc) and comprises twin orientations emerging close to the {22 1} < 11O> positions. The same positions correspond to twins predicted for metals with low stacking fault energy and experimentally confirmed in Co-8%Fe single crystals deformed 10% by channel die compression [8]. After additional rolling along the [ 1TO] direction slight sample broadening (-6%) was observed. Consequently the rolling was not strictly a pure plane strain deformation. Nevertheless, the microstructure was relatively homogeneous. Dislocation bands in two directions symmetrical to the RD were the predominant feature of the structure (Figure 2). Only sporadically, clusters of microbands resembling shear bands were observed. Some extremely thin twins were occasionally found (Figure 3) but the overall density of twins was very low. The presence of twins, an unusual result, was confirmed by means of selected area diffraction and bright/dark field technique. This finding may explain the character of orientation scattering on the pole figures (Figure lc). The occurrence of twinning can be justified by the fact that the orientation (1 10)[ 1TO]is regarded as a “hard” one, i.e., because of the orientation factor, the external stresses to activate slip are relatively high - almost double that of the (1 lO)[OOl] orientation [8]. Moreover, as the initial dislocation structure developed in the first stage of deformation can act as a barrier to dislocation motion occurring in the second deformation the critical resolved shear stress for slip may in fact be comparable to the twinning stress. Further deformation in the channel die with flow along the [ 1TO]direction, on the other hand, provides orientation scattering related to rotation about the RD2 and leads to very inhomogeneous structure in the entire sample (Figure 4). Two families of broad shear bands angled at approximately &33o to the FUI2 were observed on longitudinal sections (sections perpendicular to the TD2). The directions of shear bands are not parallel to the traces of { 111) planes indicating a non-crystallographic character of these shear bands. In the (1 10)[1TO]oriented crystal the traces of {11 1 } planes are parallel or perpendicular to the RD on the section in question (Figure 5). The substructure of such shear bands consists of small dislocation cells with high crystallographic misorientations. The misorientation is evident from the large stretching of spots on diffraction patterns (Figure 6). Contrary to the cross-rolled sample, no indication of twinning,
lmm Figure 4. Microstructure of the cross-deformed crystal in the channel die (RD2 parallel to TDl) after initial rolling along the [OOl] direction; The figure depicts the entire side surface of the specimen, section perpendicular to the RDl, light microscope.
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TEXTURE DEVELOPMENT IN Cu
Figure 5. Simple sketch showing layout of
slip planes
Vol. 35. No. 3
in the (110)[110] oriented single crystal.
either in the pole figures or in the microstructure, was found. One can speculate that twinning did not take place because of some unfavored factors. One such possibility is that almost the entire deformation took place within shear bands. Additionally, the stress field is much more homogeneous during channel die compression such that slip is favored as the deformation mechanism. Also, the constraint of deformation components of the strain field: eTD_rD and eND.TD can be unfavorable for twinning, as was found in austenitic stainless steel single crystals [3]. The substantial difference between microstructures of rolled (no shear bands) and compressed in channel die (well-defined, typical shear bands) samples is interesting as both types of deformation produce equal reduction in specimen thickness. This may arise from different way of applying strain and different constraints imposed on deformed samples: during rolling strain is applied gradually on the specimen length and the specimen can deform more freely (broadening was allowed and shear strain in the plane perpendicular to the RD was constrained only partially) while during channel die compression the entire specimen is deformed at once with only one possible direction of plastic flow. Deformation bv Channel Die ComDression with Plastic Flow Along the I1TO1Direction Deformation of the single crystal with (1 lO)[ l-n] initial orientation by channel die compression with 65% reduction of thickness brings about rotation of the initial orientation around the ND by approximately 3 5 o toward the orientation near to (1 lO)[ 1TT] (Figure 1d). The unexpected rotation, which was not observed after two step deformation, is likely a result of the different amount of strain applied to the (1 10)[ 1TO] orientation. Also a significant shear strain in planes perpendicular to the ND was found. Both, the rotation and the shear strain in the specimen deformed to 65% indicate, that at deformation greater than 50% different average values of strains took place in the mutually symmetrical systems. The above
Figure 6. Transmission electron micrographs of the microstructure from the Figure 4: a) broad shear band (A) and matrix (B); b) structure of the broad shear band at higher magnification with corresponding dieaction pattern. Section perpendicular to the TD2.
Vol. 35, No. 3
TEXTURE DEVELOPMENT
IN Cu
421
Figure 7. The microstructure of the channel die deformedcrystalwiththe initialorientation(1 lO)[lTO]: a) deformation 50%, b) deformation 65%; sections perpendicular to the TD.
considerations b;ing the conclusion that the (1 10)[ 1TO]orientation does not change for small amounts of deformation. This observation is in agreement with the work of Chin et al. [8]. However, our results (Figure Id) also shows that a definite orientation change occurs at higher strains. Up to the 50% reduction in thickness, no evidence of inhomogeneous deformation in the form of shear bands was observed (Figure 7a) but an additional 30% deformation led to the formation of well-defmed shear bands (Figure 7b). These shear bands, conspicuous at the compression surface, cease in central part of the specimen. Electron microscopy revealed strongly recovered cell structure both in matrix or shear bands indicating explicit dynamical effects during deformation of this particular orientation (Figure 8). Conclusions Texture and microstructure development in similar plane strain deformations is still affected by the degree of ca’nstraint imposed on the deformed sample. For copper single crystals with initial (1 lO)[OOl] orientation, rolling followed by cross rolling produced uniform microstructure with a minor amount of twinning. Changes (scattering) of the crystallographic orientation in the cross-rolled specimens may be associated with the occurrence of extremely thin deformation twins. For crystals Ithatwere rolled and then deformed in channel die compression shear bands were observed on longitudinal sections. The intersection of the shear bands with the longitudinal sample surface did not correspond to any {11l} trace. TEM investigation of the shear bands showed that the bands were comprised of fine, highly misoriented dislocation cells. Furthermore, the {111) pole figures indicated the presence of the established texture with main maxima located close to the initial orientations. Pole figures obtained by one-step deformation by channel die compression of the (1 lO)[ITO]oriented crystal showed that the initial orientation was not stable. After 65% reduction an approximately 35 o rotation about ND was found. Up to the 50% deformation no evidence of inhomogeneous deformation was found.
Figure 8. Transmission electron micrograph of the sample from Figure 7a. Section perpendicular to the TD.
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Acknowledements This work has been sponsored by Polish Scientific Research Committee (KEIN) under the grant No. 3 P407 060 04. The authors are grateful to Dr. Maniawski and Dr. Kwiatkowska fi-om the Institute of Nuclear Physics (KIT&W, Poland) for their valuable help and assistance in preparing the single crystals for this investigation.
References
2. 3. 4. 5. 6. I. 8.
A. Korbel, in: ‘ildvunces in Crystar Plastici@“, p. 43, Proc. Symp. in Honor of Prof. Z. Basinski held in conjunction with the 4th Canadian Mat. Sci. Conf., Kingston, Ontario, ed. D.S. Wilkinson and Z. Basinski, (1992). S. Thuillier and E.F. Rauch, Acta Metull. Muter. 42, 1973(1994). M. Wr6bel, S. Dymek, M. Blicharski and J. Driver, Scripta Metull. Muter. 32, 1985(1995). F. Dobrzadskiand W. Bochniak, Scriptu Metull. Muter. 32,2067 (1995). W. ~atas, M. Wr6bel and S. Gorczyca, Archives ofMetdlwgy, 32,530 (1987). M. Wr&el, S. Dymek, M. Blicharski and S. Gorczyca, Textires undhficrostructures, 10,9 (1988). M. WI-&XI,S. Dymek, M. Blicharski and S. Gorczyca, Z Metullkmde, 85,415 (1994). G.Y. Chin, W.F. Hosford and D.R. Mendorf, Proc. Roy. Sot. A 309,433 (1969).
Pergamon PI1 S1359-6462(96)00132-7
THE EFFECT OF STRAIN PATH ON MICROSTRUCTURE AND TEXTURE DEVELOPMENT IN COPPER SINGLE CRYSTALS WITH (iio)[ooi] AND (iio)[iio] INITIAL ORIENTATIONS Miroslaw Wr6be1, Stanislaw Dymek and Marek Blicharski Academy of Mining and Metallurgy, al. Mickiewicza 30, 30-059 Krakow, Poland (Received September 2 1, 1995) (Accepted March 5, 1996) Introduction
It has been shown that the localization of deformation can be induced by a change in strain path [l-4]. Changes in strain path can also influence evolution of deformation texture. However, the correspondence between microstructure and crystallographic texture evolution in metals under complex loading paths has been generally neglected in studies of plastic deformation. The change in microstructure found recently in austenitic stainless steel single crystals with the initial orientation (11 O)[OOl] subjected to cross-rolling [3] suggested that the analogous experiment on crystals with higher stacking fault energies would shed new light on the influence of strain path changes on microstructure and texture development. The aim of the present work is to examine the structural and textural changes induced by changes in the direction of plastic flow in select copper single crystals, i.e. crystals deforming by dislocation glide. In contrast to other studies on changes in strain path, the present study considers the effect of secondary deformation mode on resulting microstructure. Material and Exuerimental
Procedure
Copper single crystals with (1 lO)[OOl]and (1 lO)[ 1TO]initial orientations were rolled and/or compressed in a channel die at room temperature. Such orientations and deformation paths were selected in order to reproduce a similar experiment performed with low stacking fault energy single crystals [3]. By analogy to rolling, the direction of plastic flow during channel die compression is termed the rolling direction (RD), the compression direction is the normal direction (ND) and the direction perpendicular to the channel side walls is the transverse direction (TD). The single crystal bar with the orientation (1 lO)[OOl]was uniformly rolled to 50% reduction and then cut into two parts. The first part was rolled an additional 30% and the second part was compressed in a channel die to the same reduction in thickness. In both cases, the new direction of plastic flow (RD2) was the former transverse direction (TD 1). Thus the new orientation was (1 10)[ 1TO]. The single crystal with the initial orientation (1 10)[1TO]was deformed only in the channel die to 65% reduction of thickness, i.e. 417
418
TEXTURE DEVELOPMENT
IN Cu
Vol. 35. No. 3
to the same amount of deformation experienced by the samples deformed in two-step procedure (50% + 30%). Friction between the sample and the walls of the channel die was reduced by wrapping samples with teflon tape. The surfaces of each sample deformed in the channel die were polished prior to deformation. This enabled further examination of these surfaces by light microscopy. Transmission electron microscope investigations were performed on longitudinal and transverse sections of the deformed specimens. The {11 l} pole figures were obtained from sections parallel to the rolling plane. Results and Discussion
Figure 1 shows the {1 1 1} pole figures from the deformed single crystals. Plastic Flow Alow
the 10011 Direction
Rolling in this direction does not alter the initial orientation (Figure la). This result is consistent with earlier work [5,6] and confirms that slip occurs in four mutually symmetrical systems producing selfcompensating orientation changes. Such a deformation mode leads to a uniform dislocation microstructure, identical with that described in Ref. [6,7]. Plastic Flow Alow
the I1 iO1 After Flow Along the 10011 Direction
The overall character of texture taken from samples deformed along [00 l] and next along [ 1iO] remains the same with main maxima located close to the initial orientations (Figures lb, lc). Analysis of deformation in the plane strain compression state based on the modified Taylor model by Chin et al. [8] indicates that in the case of the (1 lO)[l TO] orientation slip can occur simultaneously in two
Figure 1. The (111) pole figures of the examined crystals: a) unidirectionally rolled along [OOl] direction, reduction 50%; b) rolled as in a) with further 30% deformation in the channel die along [ITO]direction; c) rolled as in a) with further rolling along [110] direction with additional reduction of 30%; d) deformed in orientation (1 lO)[lTO] by the channel die compression with 65% reduction of thickness.
Figure 2. Typical dislocation structure after crossrolling (50% along [OOl]followed by 30% along the RD2 parallel to the TDl), section perpendicular to the RDl.
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TEXTURE DEVELOPMENT IN Cu
419
Figure 3. An example of a deformation twin in the cross-rolled specimen with corresponding selected area diffraction pattern, section perpendicular to the RDl.
additional 30% reduction indicates that the identical average strains take place in the mutually symmetrical slip systems as ASSUMed by Chin et al. [S]. However, the texture exhibits orientation scattering around components originated during unidirectional deformation (Figures 1b, 1c). The character of scattering is different for each sample. The extent of scattering is much greater for the rolled specimen (Figure lc) and comprises twin orientations emerging close to the {22 1} < 11O> positions. The same positions correspond to twins predicted for metals with low stacking fault energy and experimentally confirmed in Co-8%Fe single crystals deformed 10% by channel die compression [8]. After additional rolling along the [ 1TO] direction slight sample broadening (-6%) was observed. Consequently the rolling was not strictly a pure plane strain deformation. Nevertheless, the microstructure was relatively homogeneous. Dislocation bands in two directions symmetrical to the RD were the predominant feature of the structure (Figure 2). Only sporadically, clusters of microbands resembling shear bands were observed. Some extremely thin twins were occasionally found (Figure 3) but the overall density of twins was very low. The presence of twins, an unusual result, was confirmed by means of selected area diffraction and bright/dark field technique. This finding may explain the character of orientation scattering on the pole figures (Figure lc). The occurrence of twinning can be justified by the fact that the orientation (1 10)[ 1TO]is regarded as a “hard” one, i.e., because of the orientation factor, the external stresses to activate slip are relatively high - almost double that of the (1 lO)[OOl] orientation [8]. Moreover, as the initial dislocation structure developed in the first stage of deformation can act as a barrier to dislocation motion occurring in the second deformation the critical resolved shear stress for slip may in fact be comparable to the twinning stress. Further deformation in the channel die with flow along the [ 1TO]direction, on the other hand, provides orientation scattering related to rotation about the RD2 and leads to very inhomogeneous structure in the entire sample (Figure 4). Two families of broad shear bands angled at approximately &33o to the FUI2 were observed on longitudinal sections (sections perpendicular to the TD2). The directions of shear bands are not parallel to the traces of { 111) planes indicating a non-crystallographic character of these shear bands. In the (1 10)[1TO]oriented crystal the traces of {11 1 } planes are parallel or perpendicular to the RD on the section in question (Figure 5). The substructure of such shear bands consists of small dislocation cells with high crystallographic misorientations. The misorientation is evident from the large stretching of spots on diffraction patterns (Figure 6). Contrary to the cross-rolled sample, no indication of twinning,
lmm Figure 4. Microstructure of the cross-deformed crystal in the channel die (RD2 parallel to TDl) after initial rolling along the [OOl] direction; The figure depicts the entire side surface of the specimen, section perpendicular to the RDl, light microscope.
420
TEXTURE DEVELOPMENT IN Cu
Figure 5. Simple sketch showing layout of
slip planes
Vol. 35. No. 3
in the (110)[110] oriented single crystal.
either in the pole figures or in the microstructure, was found. One can speculate that twinning did not take place because of some unfavored factors. One such possibility is that almost the entire deformation took place within shear bands. Additionally, the stress field is much more homogeneous during channel die compression such that slip is favored as the deformation mechanism. Also, the constraint of deformation components of the strain field: eTD_rD and eND.TD can be unfavorable for twinning, as was found in austenitic stainless steel single crystals [3]. The substantial difference between microstructures of rolled (no shear bands) and compressed in channel die (well-defined, typical shear bands) samples is interesting as both types of deformation produce equal reduction in specimen thickness. This may arise from different way of applying strain and different constraints imposed on deformed samples: during rolling strain is applied gradually on the specimen length and the specimen can deform more freely (broadening was allowed and shear strain in the plane perpendicular to the RD was constrained only partially) while during channel die compression the entire specimen is deformed at once with only one possible direction of plastic flow. Deformation bv Channel Die ComDression with Plastic Flow Along the I1TO1Direction Deformation of the single crystal with (1 lO)[ l-n] initial orientation by channel die compression with 65% reduction of thickness brings about rotation of the initial orientation around the ND by approximately 3 5 o toward the orientation near to (1 lO)[ 1TT] (Figure 1d). The unexpected rotation, which was not observed after two step deformation, is likely a result of the different amount of strain applied to the (1 10)[ 1TO] orientation. Also a significant shear strain in planes perpendicular to the ND was found. Both, the rotation and the shear strain in the specimen deformed to 65% indicate, that at deformation greater than 50% different average values of strains took place in the mutually symmetrical systems. The above
Figure 6. Transmission electron micrographs of the microstructure from the Figure 4: a) broad shear band (A) and matrix (B); b) structure of the broad shear band at higher magnification with corresponding dieaction pattern. Section perpendicular to the TD2.
Vol. 35, No. 3
TEXTURE DEVELOPMENT
IN Cu
421
Figure 7. The microstructure of the channel die deformedcrystalwiththe initialorientation(1 lO)[lTO]: a) deformation 50%, b) deformation 65%; sections perpendicular to the TD.
considerations b;ing the conclusion that the (1 10)[ 1TO]orientation does not change for small amounts of deformation. This observation is in agreement with the work of Chin et al. [8]. However, our results (Figure Id) also shows that a definite orientation change occurs at higher strains. Up to the 50% reduction in thickness, no evidence of inhomogeneous deformation in the form of shear bands was observed (Figure 7a) but an additional 30% deformation led to the formation of well-defmed shear bands (Figure 7b). These shear bands, conspicuous at the compression surface, cease in central part of the specimen. Electron microscopy revealed strongly recovered cell structure both in matrix or shear bands indicating explicit dynamical effects during deformation of this particular orientation (Figure 8). Conclusions Texture and microstructure development in similar plane strain deformations is still affected by the degree of ca’nstraint imposed on the deformed sample. For copper single crystals with initial (1 lO)[OOl] orientation, rolling followed by cross rolling produced uniform microstructure with a minor amount of twinning. Changes (scattering) of the crystallographic orientation in the cross-rolled specimens may be associated with the occurrence of extremely thin deformation twins. For crystals Ithatwere rolled and then deformed in channel die compression shear bands were observed on longitudinal sections. The intersection of the shear bands with the longitudinal sample surface did not correspond to any {11l} trace. TEM investigation of the shear bands showed that the bands were comprised of fine, highly misoriented dislocation cells. Furthermore, the {111) pole figures indicated the presence of the established texture with main maxima located close to the initial orientations. Pole figures obtained by one-step deformation by channel die compression of the (1 lO)[ITO]oriented crystal showed that the initial orientation was not stable. After 65% reduction an approximately 35 o rotation about ND was found. Up to the 50% deformation no evidence of inhomogeneous deformation was found.
Figure 8. Transmission electron micrograph of the sample from Figure 7a. Section perpendicular to the TD.
422
TEXTURE DEVELOPMENT IN Cu
Vol. 35, No. 3
Acknowledements This work has been sponsored by Polish Scientific Research Committee (KEIN) under the grant No. 3 P407 060 04. The authors are grateful to Dr. Maniawski and Dr. Kwiatkowska fi-om the Institute of Nuclear Physics (KIT&W, Poland) for their valuable help and assistance in preparing the single crystals for this investigation.
References
2. 3. 4. 5. 6. I. 8.
A. Korbel, in: ‘ildvunces in Crystar Plastici@“, p. 43, Proc. Symp. in Honor of Prof. Z. Basinski held in conjunction with the 4th Canadian Mat. Sci. Conf., Kingston, Ontario, ed. D.S. Wilkinson and Z. Basinski, (1992). S. Thuillier and E.F. Rauch, Acta Metull. Muter. 42, 1973(1994). M. Wr6bel, S. Dymek, M. Blicharski and J. Driver, Scripta Metull. Muter. 32, 1985(1995). F. Dobrzadskiand W. Bochniak, Scriptu Metull. Muter. 32,2067 (1995). W. ~atas, M. Wr6bel and S. Gorczyca, Archives ofMetdlwgy, 32,530 (1987). M. Wr&el, S. Dymek, M. Blicharski and S. Gorczyca, Textires undhficrostructures, 10,9 (1988). M. WI-&XI,S. Dymek, M. Blicharski and S. Gorczyca, Z Metullkmde, 85,415 (1994). G.Y. Chin, W.F. Hosford and D.R. Mendorf, Proc. Roy. Sot. A 309,433 (1969).