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On the emergence of new surface grains during superplastic deformation
Scripta mater. 44 (2001) 2611–2615 www.elsevier.com/locate/scriptamat
ON THE EMERGENCE OF NEW SURFACE GRAINS DURING SUPERPLASTIC DEFORMATION Atul H. Chokshi Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India (Received November 17, 2000) (Accepted in revised form January 30, 2001) Keywords: Superplasticity; Grain growth; Surface grains
1. Introduction Superplasticity, the ability of some polycrystalline materials to exhibit large elongations to failure offers an attractive and cost effective means for forming some components with complex shapes, and it is being used currently in several aerospace and other applications [1–3]. Although the phenomenon has been studied extensively since the 1960’s [1,2,4 –7], the fundamental rate controlling deformation mechanism has not yet been unambiguously identified. One of the key microstructural observations following superplastic deformation is the retention of an equiaxed grain size following large elongations. Ashby and Verrall [8] developed a topological model for superplasticity that was able to account for the retention of an equiaxed grain size during superplasticity. However, Spingarn and Nix [9] pointed out some limitations in the model developed by Ashby and Verrall [8], and they suggested an alternate model developed by Lee [10] for the retention of an equiaxed grain size during superplasticity. However, the topological models discussed above are two-dimensional in nature. Most early studies on superplasticity indicated that there was very limited grain growth during superplastic deformation. As noted by Hazzledine and Newburry [11], the increase in surface area during superplastic deformation must be accompanied by the emergence of new surface grains. Gifkins [12] and later Langdon [13] modified the above topological models to account for the emergence of new surface grains. Geckinli [14] has developed a three-dimensional grain boundary sliding model for superplasticity that explicitly accounts for the emergence of new surface grains. Clearly, the emergence of new surface grains appears to be an important topological aspect of superplastic deformation. In addition, the appearance of new surface grains also places a constraint on measurements of grain boundary sliding [15]. There have now been detailed measurements of changes in the grain size during superplastic deformation, which indicate that there is substantial grain growth during superplastic deformation [16,17]. The present report is a reappraisal of the emergence of new surface grains during superplasticity. It is demonstrated that, in general, there is no need to explicitly account for the emergence of new surface grains, in view of the extensive grain growth accompanying superplastic deformation.
1359-6462/01/$–see front matter. © 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(01)00949-6
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Figure 1. Variation in the experimentally observed ratio df/d0 with strain for several superplastic materials; the solid line represents condition for no new grains to emerge on the tensile surface.
2. Analysis and Discussion For a tensile specimen surface with initial length L0 and width W0, deformation to a strain ⑀ will lead to a new length L (⫽L0 exp ⑀) and width W (⫽W0 exp (⫺⑀/2). If d0 is the initial grain size and df is the grain size at strain ⑀, then the following condition needs to be satisfied for no new grains to emerge on the surface: L 0W 0/d 02 ⫽ LW/d ƒ2
(1)
df/d0 ⫽ exp共 ⑀ / 2兲
(2)
which can be expressed as
It follows from eqn. 2 that when the ratio df/d0 ⬍ exp (⑀/2), grain growth will not be sufficient to fill up the increase in surface area, and new grains will have to emerge on the surface. On the other hand, when df/d0 ⬎ exp (⑀/2), no new grains will need to emerge and in fact some grains that were present originally will have to disappear. Figure 1 presents experimental data from a wide range of superplastic materials, in the form of the variation in the ratio df/d0 with true strain ⑀; the solid line represents eqn. 2. Shown in Fig. 1 are experimental data for a high purity Zn-22% Al eutectoid alloy [18] and a Cu-based alloy CDA 638 [19]; for the copper alloy, only the data at the lowest and highest strain rate are shown for the sake of clarity. Also included in Fig. 1 are data from a superplastic 3 mol% yttria stabilized tetragonal zirconia (3YTZ), a 2.5 mol% yttria stabilized tetragonal zirconia (2.5 YTZ) and alumina [20 –22]. Inspection of Fig. 1 indicates that the experimental data are substantially above the solid line, implying that some original grains must disappear during superplastic deformation. The experimental data shown in Fig. 1 encompass a wide range of superplastic materials including a quasi-single phase Cu alloy [19], a microduplex Zn-22% Al alloy [18], as well as zirconia and alumina ceramics [20 –22]. The elongations to failure in these materials also encompass a wide range from ⬍50% for alumina to ⬎1000% for
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Figure 2. Schematic 2-D illustration of possible microstructural changes: (a) initial microstructure, and microstructure following (b) Lifshitz sliding, (c) Rachinger sliding and (d) superplastic deformation.
zirconia and the Zn-Al alloy. Therefore, the trend shown in Fig. 1 is considered to represent superplasticity in general, so that some grain growth appears to be common in all superplastic materials. 2.1. Significance of Grain Growth The present analysis suggests that there is no need to account explicitly for the emergence of new surface grains during superplasticity. In addition, the significant grain growth occurring during superplasticity must lead to the removal of some grains that were present before deformation. In this context, it is to be noted that grain growth will also lead to grain switching [23], so that there may be the appearance of some new grains on the surface because of this process. The topological models developed by Ashby and Verall [8] as well as Lee [10] involve one grain switching event for a strain of 0.55. Calculations indicate that a relatively small amount of grain growth of ⬃10% will lead to the removal of more than ⬃20% of the grains present in the specimen before superplastic deformation, which is likely to provide sufficient number of grain switching events to maintain an equiaxed grain size. From Fig. 1 it is clear that eqn. 2 represents a lower limit for grain growth during superplasticity. Calculations with eqn. 2 indicate that grain growth by 10% will occur within strains of ⬃0.2, so that grain growth is a very potent means for enabling grain rearrangement and the maintenance of an equiaxed grain size. Models for superplasticity have frequently invoked diffusion creep, in view of the lack of significant intragranular dislocation activity. One of the major criticisms against diffusion creep is the retention of an equiaxed grain size after substantial superplastic deformation, as predicted originally [24]. However, as noted elsewhere [23], the occurrence of grain growth can lead to substantial grain rearrangement and switching, so that an equiaxed grain size can be retained even during deformation by diffusion creep. The observed lack of a stress exponent of one during superplasticity, as predicted by diffusion creep, may be a consequence of an interface reaction controlled diffusion creep process [25] or deformation involving a combination of diffusion creep and dislocation creep [26]. 2.2. Implications for Grain Boundary Sliding Since diffusion creep also involves grain boundary sliding [27,28], it is necessary to distinguish between the operation of grain boundary sliding as an independent mechanism and as a process associated with diffusion creep [24 ]: these two processes are referred to as Rachinger sliding [29] and Lifshitz sliding [27]. One of the means suggested earlier for distinguishing between Rachinger and Lifshitz sliding is to examine the microstructure after tensile deformation. Figure 2 illustrates the microstructural changes anticipated from these two processes. Lifshitz sliding will result in the elongation of grains along the tensile axis and the retention of the same grain neighbors (Fig. 2b), whereas Rachinger sliding will lead to a retention of the initial equiaxed microstructure, grain switching and rearrangement (Fig. 2c), and in 3-D an increase in the number of grains on the surface. Since grains retain their original equiaxed
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shapes after substantial superplastic deformation, it has been concluded generally that Rachinger sliding is involved in superplastic deformation. However, as noted elsewhere [23] and in the present study, the significant grain growth occurring during superplastic deformation can lead to substantial grain rearrangement so that an equiaxed grain size can also be retained with Lifshitz sliding. Consequently, the retention of an equiaxed grain size with a reduction in the number of grains on the specimen surface (Fig. 2d) cannot be used to rule out Lifshitz sliding and diffusion creep. In fact, recent studies on superplastic ceramics such as alumina [22,30] and zirconia [31,32], where intragranular dislocation mobility is limited, have attributed superplastic deformation to Coble diffusion creep [33], and a model for superplasticity has been developed recently explicitly involving grain growth and diffusion creep [34]. 3. Summary and Conclusions It has generally been considered necessary to account for the emergence of new surface grains in 3-d topological models of superplasticity. A reappraisal of this phenomenon indicates that it is generally not necessary to explicitly incorporate the appearance of new surface grains in view of the significant grain growth accompanying superplastic deformation; in fact, many of the grains originally present prior to superplastic deformation must disappear due to grain growth. Calculations indicate that grain growth is a very potent means for producing grain rearrangement and switching, which enables the retention of an equiaxed grain size. Finally, the lack of grain elongation does not necessarily preclude the occurrence of diffusion creep process during superplastic deformation. Acknowledgment This work was supported by the Department of Science and Technology with an award of a Swarnajayanti Young Investigator Fellowship. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
A. H. Chokshi, A. K. Mukherjee, and T. G. Langdon, Mater. Sci. Eng. R10, 238 (1993). T. G. Nieh, J. Wadsworth, and O. D. Sherby, Superplasticity in Metals and Ceramics, Cambridge University Press, UK (1997). A. J. Barnes, in Superplasticity—Current Status and Future Potential, ed. P. B. Berbon, M. Z. Berbon, T. Sakuma, and T. G. Langdon, MRS Symp. Proc. 601, 207 (2000). J. W. Edington, K. N. Melton, and C. P. Cutler, Prog. Mater. Sci. 21, 63 (1976). A. K. Mukherjee, Annu. Rev. Mater. Sci. 9, 191 (1979). K. A. Padmanabhan and G. J. Davies, Superplasticity, Springer-Verlag, Berlin, Germany (1980). O. D. Sherby and J. Wadsworth, Prog. Mater. Sci. 33, 169 (1989). M. F. Ashby and R. A. Verrall, Acta Metall. 21, 149 (1973). J. R. Spingarn and W. D. Nix, Acta Metall. 26, 1389 (1978). D. Lee, Metall. Trans. 1, 309 (1970). P. M. Hazzledine and D. E. Newburry, in Grain Boundary Structure and Properties, ed. G. A. Chadwick and D. A. Smith, p. 235, Academic Press, London (1976). R. C. Gifkins, J. Mater. Sci. 13, 1926 (1978). T. G. Langdon, Metals Forum. 4, 14 (1981). A. E. Geckinli, Metal Sci. 17, 12 (1983). Z.-R. Lin, A. H. Chokshi, and T. G. Langdon, J. Mater. Sci. 23, 2712 (1988). C. H. Caceres and D. S. Wilkinson, Acta Metall. 32, 415 (1984). T. Sakuma, Mater. Sci. Forum. 204 –206, 109 (1996).
Vol. 44, No. 11
18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.
EMERGENCE OF NEW SURFACE GRAINS
X.-G. Jiang, S. T. Yang, J. C. Earthman, and F. A. Mohamed, Metall. Mater. Trans. 27A, 863 (1996). D. S. Wilkinson and C. H. Caceres, Acta Metall. 32, 1335 (1984). D. J. Schissler, A. H. Chokshi, T. G. Nieh, and J. Wadsworth, Acta Metall. Mater 39, 3227 (1991). K. Kajihara, Y. Yoshizawa, and T. Sakuma, Acta Metall. Mater. 43, 1235 (1995). R. S. Kottada and A. H. Chokshi, Acta Mater. 48, 3905 (2000). A. H. Chokshi, Scripta Mater. 42, 241 (2000). W. R. Cannon, Phil. Mag. 25, 1489 (1972). M. F. Ashby, Scripta Metall. 3, 837 (1969). A. K. Ghosh and R. Raj, Acta Mater. 29, 607 (1981). I. M. Lifshitz, Sov. Phys. JETP. 17, 909 (1963). R. Raj and M. F. Ashby. Metall. Trans. 2, 1113 (1971). W. A. Rachinger, J. Inst. Metals. 81, 33 (1952–53). R. S. Kottada and A. H. Chokshi, Key Eng. Mater. 171–174, 779 (2000). M. Z. Berbon and T. G. Langdon, Acta Mater. 47, 2485 (1999). I. Charit and A. H. Chokshi, Acta Mater. submitted for publication. R. L. Coble, J. Appl. Phys. 34, 1679 (1963). M. J. Mayo and J. R. Seidensticker, MRS Symp. Proc. 601, 181 (2000).
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ON THE EMERGENCE OF NEW SURFACE GRAINS DURING SUPERPLASTIC DEFORMATION Atul H. Chokshi Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India (Received November 17, 2000) (Accepted in revised form January 30, 2001) Keywords: Superplasticity; Grain growth; Surface grains
1. Introduction Superplasticity, the ability of some polycrystalline materials to exhibit large elongations to failure offers an attractive and cost effective means for forming some components with complex shapes, and it is being used currently in several aerospace and other applications [1–3]. Although the phenomenon has been studied extensively since the 1960’s [1,2,4 –7], the fundamental rate controlling deformation mechanism has not yet been unambiguously identified. One of the key microstructural observations following superplastic deformation is the retention of an equiaxed grain size following large elongations. Ashby and Verrall [8] developed a topological model for superplasticity that was able to account for the retention of an equiaxed grain size during superplasticity. However, Spingarn and Nix [9] pointed out some limitations in the model developed by Ashby and Verrall [8], and they suggested an alternate model developed by Lee [10] for the retention of an equiaxed grain size during superplasticity. However, the topological models discussed above are two-dimensional in nature. Most early studies on superplasticity indicated that there was very limited grain growth during superplastic deformation. As noted by Hazzledine and Newburry [11], the increase in surface area during superplastic deformation must be accompanied by the emergence of new surface grains. Gifkins [12] and later Langdon [13] modified the above topological models to account for the emergence of new surface grains. Geckinli [14] has developed a three-dimensional grain boundary sliding model for superplasticity that explicitly accounts for the emergence of new surface grains. Clearly, the emergence of new surface grains appears to be an important topological aspect of superplastic deformation. In addition, the appearance of new surface grains also places a constraint on measurements of grain boundary sliding [15]. There have now been detailed measurements of changes in the grain size during superplastic deformation, which indicate that there is substantial grain growth during superplastic deformation [16,17]. The present report is a reappraisal of the emergence of new surface grains during superplasticity. It is demonstrated that, in general, there is no need to explicitly account for the emergence of new surface grains, in view of the extensive grain growth accompanying superplastic deformation.
1359-6462/01/$–see front matter. © 2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S1359-6462(01)00949-6
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Vol. 44, No. 11
Figure 1. Variation in the experimentally observed ratio df/d0 with strain for several superplastic materials; the solid line represents condition for no new grains to emerge on the tensile surface.
2. Analysis and Discussion For a tensile specimen surface with initial length L0 and width W0, deformation to a strain ⑀ will lead to a new length L (⫽L0 exp ⑀) and width W (⫽W0 exp (⫺⑀/2). If d0 is the initial grain size and df is the grain size at strain ⑀, then the following condition needs to be satisfied for no new grains to emerge on the surface: L 0W 0/d 02 ⫽ LW/d ƒ2
(1)
df/d0 ⫽ exp共 ⑀ / 2兲
(2)
which can be expressed as
It follows from eqn. 2 that when the ratio df/d0 ⬍ exp (⑀/2), grain growth will not be sufficient to fill up the increase in surface area, and new grains will have to emerge on the surface. On the other hand, when df/d0 ⬎ exp (⑀/2), no new grains will need to emerge and in fact some grains that were present originally will have to disappear. Figure 1 presents experimental data from a wide range of superplastic materials, in the form of the variation in the ratio df/d0 with true strain ⑀; the solid line represents eqn. 2. Shown in Fig. 1 are experimental data for a high purity Zn-22% Al eutectoid alloy [18] and a Cu-based alloy CDA 638 [19]; for the copper alloy, only the data at the lowest and highest strain rate are shown for the sake of clarity. Also included in Fig. 1 are data from a superplastic 3 mol% yttria stabilized tetragonal zirconia (3YTZ), a 2.5 mol% yttria stabilized tetragonal zirconia (2.5 YTZ) and alumina [20 –22]. Inspection of Fig. 1 indicates that the experimental data are substantially above the solid line, implying that some original grains must disappear during superplastic deformation. The experimental data shown in Fig. 1 encompass a wide range of superplastic materials including a quasi-single phase Cu alloy [19], a microduplex Zn-22% Al alloy [18], as well as zirconia and alumina ceramics [20 –22]. The elongations to failure in these materials also encompass a wide range from ⬍50% for alumina to ⬎1000% for
Vol. 44, No. 11
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2613
Figure 2. Schematic 2-D illustration of possible microstructural changes: (a) initial microstructure, and microstructure following (b) Lifshitz sliding, (c) Rachinger sliding and (d) superplastic deformation.
zirconia and the Zn-Al alloy. Therefore, the trend shown in Fig. 1 is considered to represent superplasticity in general, so that some grain growth appears to be common in all superplastic materials. 2.1. Significance of Grain Growth The present analysis suggests that there is no need to account explicitly for the emergence of new surface grains during superplasticity. In addition, the significant grain growth occurring during superplasticity must lead to the removal of some grains that were present before deformation. In this context, it is to be noted that grain growth will also lead to grain switching [23], so that there may be the appearance of some new grains on the surface because of this process. The topological models developed by Ashby and Verall [8] as well as Lee [10] involve one grain switching event for a strain of 0.55. Calculations indicate that a relatively small amount of grain growth of ⬃10% will lead to the removal of more than ⬃20% of the grains present in the specimen before superplastic deformation, which is likely to provide sufficient number of grain switching events to maintain an equiaxed grain size. From Fig. 1 it is clear that eqn. 2 represents a lower limit for grain growth during superplasticity. Calculations with eqn. 2 indicate that grain growth by 10% will occur within strains of ⬃0.2, so that grain growth is a very potent means for enabling grain rearrangement and the maintenance of an equiaxed grain size. Models for superplasticity have frequently invoked diffusion creep, in view of the lack of significant intragranular dislocation activity. One of the major criticisms against diffusion creep is the retention of an equiaxed grain size after substantial superplastic deformation, as predicted originally [24]. However, as noted elsewhere [23], the occurrence of grain growth can lead to substantial grain rearrangement and switching, so that an equiaxed grain size can be retained even during deformation by diffusion creep. The observed lack of a stress exponent of one during superplasticity, as predicted by diffusion creep, may be a consequence of an interface reaction controlled diffusion creep process [25] or deformation involving a combination of diffusion creep and dislocation creep [26]. 2.2. Implications for Grain Boundary Sliding Since diffusion creep also involves grain boundary sliding [27,28], it is necessary to distinguish between the operation of grain boundary sliding as an independent mechanism and as a process associated with diffusion creep [24 ]: these two processes are referred to as Rachinger sliding [29] and Lifshitz sliding [27]. One of the means suggested earlier for distinguishing between Rachinger and Lifshitz sliding is to examine the microstructure after tensile deformation. Figure 2 illustrates the microstructural changes anticipated from these two processes. Lifshitz sliding will result in the elongation of grains along the tensile axis and the retention of the same grain neighbors (Fig. 2b), whereas Rachinger sliding will lead to a retention of the initial equiaxed microstructure, grain switching and rearrangement (Fig. 2c), and in 3-D an increase in the number of grains on the surface. Since grains retain their original equiaxed
2614
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Vol. 44, No. 11
shapes after substantial superplastic deformation, it has been concluded generally that Rachinger sliding is involved in superplastic deformation. However, as noted elsewhere [23] and in the present study, the significant grain growth occurring during superplastic deformation can lead to substantial grain rearrangement so that an equiaxed grain size can also be retained with Lifshitz sliding. Consequently, the retention of an equiaxed grain size with a reduction in the number of grains on the specimen surface (Fig. 2d) cannot be used to rule out Lifshitz sliding and diffusion creep. In fact, recent studies on superplastic ceramics such as alumina [22,30] and zirconia [31,32], where intragranular dislocation mobility is limited, have attributed superplastic deformation to Coble diffusion creep [33], and a model for superplasticity has been developed recently explicitly involving grain growth and diffusion creep [34]. 3. Summary and Conclusions It has generally been considered necessary to account for the emergence of new surface grains in 3-d topological models of superplasticity. A reappraisal of this phenomenon indicates that it is generally not necessary to explicitly incorporate the appearance of new surface grains in view of the significant grain growth accompanying superplastic deformation; in fact, many of the grains originally present prior to superplastic deformation must disappear due to grain growth. Calculations indicate that grain growth is a very potent means for producing grain rearrangement and switching, which enables the retention of an equiaxed grain size. Finally, the lack of grain elongation does not necessarily preclude the occurrence of diffusion creep process during superplastic deformation. Acknowledgment This work was supported by the Department of Science and Technology with an award of a Swarnajayanti Young Investigator Fellowship. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
A. H. Chokshi, A. K. Mukherjee, and T. G. Langdon, Mater. Sci. Eng. R10, 238 (1993). T. G. Nieh, J. Wadsworth, and O. D. Sherby, Superplasticity in Metals and Ceramics, Cambridge University Press, UK (1997). A. J. Barnes, in Superplasticity—Current Status and Future Potential, ed. P. B. Berbon, M. Z. Berbon, T. Sakuma, and T. G. Langdon, MRS Symp. Proc. 601, 207 (2000). J. W. Edington, K. N. Melton, and C. P. Cutler, Prog. Mater. Sci. 21, 63 (1976). A. K. Mukherjee, Annu. Rev. Mater. Sci. 9, 191 (1979). K. A. Padmanabhan and G. J. Davies, Superplasticity, Springer-Verlag, Berlin, Germany (1980). O. D. Sherby and J. Wadsworth, Prog. Mater. Sci. 33, 169 (1989). M. F. Ashby and R. A. Verrall, Acta Metall. 21, 149 (1973). J. R. Spingarn and W. D. Nix, Acta Metall. 26, 1389 (1978). D. Lee, Metall. Trans. 1, 309 (1970). P. M. Hazzledine and D. E. Newburry, in Grain Boundary Structure and Properties, ed. G. A. Chadwick and D. A. Smith, p. 235, Academic Press, London (1976). R. C. Gifkins, J. Mater. Sci. 13, 1926 (1978). T. G. Langdon, Metals Forum. 4, 14 (1981). A. E. Geckinli, Metal Sci. 17, 12 (1983). Z.-R. Lin, A. H. Chokshi, and T. G. Langdon, J. Mater. Sci. 23, 2712 (1988). C. H. Caceres and D. S. Wilkinson, Acta Metall. 32, 415 (1984). T. Sakuma, Mater. Sci. Forum. 204 –206, 109 (1996).
Vol. 44, No. 11
18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.
EMERGENCE OF NEW SURFACE GRAINS
X.-G. Jiang, S. T. Yang, J. C. Earthman, and F. A. Mohamed, Metall. Mater. Trans. 27A, 863 (1996). D. S. Wilkinson and C. H. Caceres, Acta Metall. 32, 1335 (1984). D. J. Schissler, A. H. Chokshi, T. G. Nieh, and J. Wadsworth, Acta Metall. Mater 39, 3227 (1991). K. Kajihara, Y. Yoshizawa, and T. Sakuma, Acta Metall. Mater. 43, 1235 (1995). R. S. Kottada and A. H. Chokshi, Acta Mater. 48, 3905 (2000). A. H. Chokshi, Scripta Mater. 42, 241 (2000). W. R. Cannon, Phil. Mag. 25, 1489 (1972). M. F. Ashby, Scripta Metall. 3, 837 (1969). A. K. Ghosh and R. Raj, Acta Mater. 29, 607 (1981). I. M. Lifshitz, Sov. Phys. JETP. 17, 909 (1963). R. Raj and M. F. Ashby. Metall. Trans. 2, 1113 (1971). W. A. Rachinger, J. Inst. Metals. 81, 33 (1952–53). R. S. Kottada and A. H. Chokshi, Key Eng. Mater. 171–174, 779 (2000). M. Z. Berbon and T. G. Langdon, Acta Mater. 47, 2485 (1999). I. Charit and A. H. Chokshi, Acta Mater. submitted for publication. R. L. Coble, J. Appl. Phys. 34, 1679 (1963). M. J. Mayo and J. R. Seidensticker, MRS Symp. Proc. 601, 181 (2000).
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