Startseite Misorientations and geometrically necessary dislocations in deformed copper crystals: A microstructural analysis of X-ray rocking curves
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Misorientations and geometrically necessary dislocations in deformed copper crystals: A microstructural analysis of X-ray rocking curves

  • Haël Mughrabi EMAIL logo und Bernhard Obst
Veröffentlicht/Copyright: 16. Februar 2022
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International Journal of Materials Research
Aus der Zeitschrift International Journal of Materials Research Band 96 Heft 7

Abstract

In this study, the deformation-induced misorientations that are typically found in face-centred cubic single crystals deformed in single slip into stage II (and early stage III) of the work-hardening curve are discussed with respect to the experimentally observed broadening of X-ray rocking curves. By making use of well-established empirical relationships between characteristic features of the microstructure and the flow stress, some of the ambiguities of earlier interpretations of rocking curves could be avoided, and relationships between the half-widths of the rocking curves, the density of geometrically necessary dislocations, and the flow stress could be derived for both the tilt misorientations due to the kink bands lying perpendicular to the primary Burgers vector and the twist misorientations originating from the dislocation networks (grids, sheets) lying parallel to the primary glide plane. An evaluation of largely unpublished experimental rocking-curve data obtained on different crystallographic sections of deformed copper single crystals yielded a linear relationship between the broadening of the rocking curves and the flow stress. In terms of the predictions of the model developed, this implies that the ratio of the density of the geometrically necessary dislocations (that are responsible for the misorientations) to the total dislocation density remains constant during deformation, at least up to flow stresses of about 50 MPa. The absolute densities of the geometrically necessary dislocations are found to be a small fraction (at most ca. 5%) of the total dislocation densities. In terms of the evolution laws of deformation-induced dislocation boundaries proposed in the literature, it is concluded that both kink bands and grids/ sheets follow the characteristics of so-called geometrically necessary boundaries.

Keywords: X-ray rocking curve broadening; Lattice misorientations; Plastic deformation; Deformed crystals; Geometrically necessary dislocations
Prof. Haël Mughrabi Institut für Werkstoffwissenschaften Lehrstuhl Allgemeine Werkstoffeigenschaften Universität Erlangen-Nürnberg Martensstrasse 5, D-91058 Erlangen, Germany Tel.: +49 9131 852 7482 Fax: +49 9131 852 7504

Dedicated to Professor Dr.-Ing. habil. Dr. h. c. Heinrich Oettel on the occasion of his 65th birthday

References

[1] U. Essmann: Phys. Stat. Sol. 12 (1965) 707 and 723.10.1002/pssb.19650120218Suche in Google Scholar

[2] Z.S. Basinski: Disc. Faraday Society 38 (1964) 93.10.1039/df9643800093Suche in Google Scholar

[3] J.W. Steeds: Proc. Roy. Soc. A 292 (1966) 343.10.1098/rspa.1966.0139Suche in Google Scholar

[4] A. Seeger, in: J.P. Hirth, J. Weertman (Eds.), Work-Hardening, Gordon & Breach (1968) 27.Suche in Google Scholar

[5] H. Mughrabi, in: A.S. Argon (Ed.), Constitutive Equations in Plasticity, The MIT Press, Cambridge, Massachusetts, and London, England (1975) 199.Suche in Google Scholar

[6] P.B. Hirsch, in: B. Chalmers, R. King (Eds.), Progress in Metal Physics, Vol. 6, Pergamon Press (1956) 283.10.1016/0502-8205(56)90008-9Suche in Google Scholar

[7] M. Wilkens, in: N. Hessel Anderson et al. (Eds.), Microstructural Characterization of Materials by Non-Microscopical Techniques, Proc. of 5th Risoe Int. Symp. on Metallurgy and Materials Science, Risoe National Laboratory, Roskilde, Denmark (1984) 153.Suche in Google Scholar

[8] M. Wilkens, K. Eckert: Z. Naturforschung 19a (1964) 459.10.1515/zna-1964-0410Suche in Google Scholar

[9] M. Wilkens: Can. J. Phys. 45 (1967) 567.10.1139/p67-049Suche in Google Scholar

[10] B. Obst: Untersuchung der Versetzungsanordnung in plastisch verformten Kupfer-Einkristallen mit Hilfe von Ätzgrübchen und röntgenographischer Abbildung, Diplomarbeit, Techn. Hochschule Stuttgart (1966).Suche in Google Scholar

[11] B. Obst, H. Auer, M. Wilkens: Mater. Sci. Eng. 3 (1968/69) 41.10.1016/0025-5416(68)90031-1Suche in Google Scholar

[12] H. Oettel: Kristall und Technik 12 (1977) 275.10.1002/crat.19770120308Suche in Google Scholar

[13] N. Koch, H. Oettel, P. Klimanek, J. Ohser: Z. Metallkd. 78 (1987) 310.10.1515/ijmr-1987-780502Suche in Google Scholar

[14] M.F. Ashby: Phil. Mag. 21 (1970) 399.10.1080/14786437008238426Suche in Google Scholar

[15] N.A. Fleck, G.M. Muller, M.F. Ashby, J.W. Hutchinson: Acta met. mater. 42 (1994) 475.10.1016/0956-7151(94)90502-9Suche in Google Scholar

[16] Viewpoint Set No. 28: Geometrically Necessary Dislocations and Size Dependent Plasticity, organized by A. Needleman, J. Gil Se-villano, Scripta mater. 48 (2003) 109.10.1016/S1359-6462(02)00336-6Suche in Google Scholar

[17] H. Mughrabi, T. Ungár, M. Wilkens: Scripta metall. 17 (1983) 797.10.1016/0036-9748(83)90496-9Suche in Google Scholar

[18] R.I. Barabash, P. Klimanek: J. Appl. Cryst. 32 (1999) 1050.10.1107/S0021889899010237Suche in Google Scholar

[19] R. Barabash, P. Klimanek: Z. Metallkd. 92 (2001) 70.Suche in Google Scholar

[20] D. Breuer, P. Klimanek, W. Pantleon: J. Appl. Crystallogr. 33 (2000) 1284.10.1107/S0021889800008256Suche in Google Scholar

[21] M. Wilkens, K. Herz, H. Mughrabi: Z. Metallkd. 71 (1980) 376.10.1515/ijmr-1980-710606Suche in Google Scholar

[22] D. Ottenhaus: Röntgenographische Bestimmung von Versetzungsverteilungen und inneren Spannungen in plastisch verformten Einkristallen, Doctoral Thesis, Universität Stuttgart (1987).Suche in Google Scholar

[23] M. Wilkens, T. Ungár, H. Mughrabi: Phys. Stat. Sol. (a) 104 (1987) 157.10.1002/pssa.2211040111Suche in Google Scholar

[24] W. Pantleon: Solid State Phenomena 87 (2002) 73.10.4028/www.scientific.net/SSP.87.73Suche in Google Scholar

[25] H. Strunk, U. Essmann: Z. Metallkd. 60 (1969) 367.10.1515/ijmr-1969-600506Suche in Google Scholar

[26] S. Mader: Z. Phys. 149 (1957) 73.10.1007/BF01325693Suche in Google Scholar

[27] H. Mughrabi: Phil. Mag. 23 (1971) 931.10.1080/14786437108216996Suche in Google Scholar

[28] H. Mughrabi, T. Ungár, in: F.R.N. Nabarro, M.S. Duesberry (Eds.), Dislocations in Solids, Vol. 11, Elsevier Science B. V. (2002) 343.10.1016/S1572-4859(02)80011-0Suche in Google Scholar

[29] F.R.N. Nabarro, Z.S. Basinski, D.B. Holt: Adv. Phys. 13 (1964) 193.10.1080/00018736400101031Suche in Google Scholar

[30] D.B. Holt: J. Appl. Phys. 41 (1970) 3197.10.1063/1.1659399Suche in Google Scholar

[31] J.T. Fourie: Phil. Mag. 17 (1968) 148.10.1080/14786436808223026Suche in Google Scholar

[32] H. Mughrabi: Phys. Stat. Sol. (b) 44 (1971) 391.10.1002/pssb.2220440140Suche in Google Scholar

[33] M.O. Bargouth: Diplomarbeit Thesis, Technische Hochschule Stuttgart (1967).Suche in Google Scholar

[34] H. Mughrabi: Acta metall. 31 (1983) 1367.10.1016/0001-6160(83)90007-XSuche in Google Scholar

[35] D. Kuhlmann-Wilsdorf, N. Hansen: Scripta metall. mater. 25 (1991) 1557.10.1016/0956-716X(91)90451-6Suche in Google Scholar

[36] N. Hansen: Metall. Mater. Trans. A 32 (2001) 2917.10.1007/s11661-001-0167-xSuche in Google Scholar

[37] N. Hansen, X. Huang, D.A. Hughes: Mater. Sci. Eng. A 317 (2001) 3.10.1016/S0921-5093(01)01191-1Suche in Google Scholar

[38] D.A. Hughes, N. Hansen: Acta mater. 48 (2000) 2985.10.1016/S1359-6454(00)00082-3Suche in Google Scholar

[39] O.B. Pedersen, A.T. Winter: Acta metall. 30 (1982) 711.10.1016/0001-6160(82)90120-1Suche in Google Scholar

[40] R. Zauter, F. Petry, M. Bayerlein, C. Sommer, H.-J. Christ, H. Mughrabi: Phil. Mag. 66 (1992) 425.10.1080/01418619208201567Suche in Google Scholar

[41] Z.F. Zhang, Z.G. Wang: Phil. Mag. Letters 78 (1998) 105.10.1080/095008398178084Suche in Google Scholar

[42] S.F. Nielsen, E.M. Lauridsen, D. Juul-Jensen: Mater. Sci. Eng. 319–321 (2001) 179.10.1016/S0921-5093(01)01056-5Suche in Google Scholar

[43] R.I. Barabash, G.E. Ice, B.C. Larson, W. Yang, in: Fundamental Materials Research Series: “From Proteins to Semiconductors: Beyond the Average Structure”, Kluwer Academic/Plenum Publishers (2002) 49.10.1007/978-1-4615-0613-3_4Suche in Google Scholar

[44] W. Pantleon, H.F. Poulsen, J. Almer, U. Lienert: Mater. Sci. Eng. A 387 (2004) 339.10.1016/j.msea.2004.02.080Suche in Google Scholar

[45] T. Ungár, H. Mughrabi, M. Wilkens: Acta metall. 30 (1982) 1861.10.1016/0001-6160(82)90026-8Suche in Google Scholar

[46] H. Mughrabi: Phys. Stat. Sol. 39 (1970) 317.10.1002/pssb.19700390133Suche in Google Scholar

[47] R.I. Barabash, G.E. Ice, J.W.L. Pang: Mater. Sci. Eng. A, in press.Suche in Google Scholar

[48] C. Lang, W. Schneider, H. Mughrabi: Acta metall. mater. 43 (1995) 1751.10.1016/0956-7151(94)00407-9Suche in Google Scholar
  1. 1

    In an Eshelby-type approach [39], the value of the Eshelby elastic accommodation factor, which is derived from continuum mechanics could be replaced in a formal manner by an “effective” value. Strictly speaking, however, such modifications and relaxations of the internal stresses which occur by dislocation rearrangements, as discussed here, can simply not be accounted for in a continuum approach.

Received: 2005-03-02
Accepted: 2005-04-11
Published Online: 2022-02-16

© 2005 Carl Hanser Verlag, München

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. Heinrich Oettel – 65 Jahre
  4. Articles Basic
  5. Misorientations and geometrically necessary dislocations in deformed copper crystals: A microstructural analysis of X-ray rocking curves
  6. Microstructure and lattice defects in highly deformed metals by X-ray diffraction whole powder pattern modelling
  7. Magnetoplasticity
  8. Articles Applied
  9. Finite-element analysis of the hot-pressing consolidation of continuous Al2O3 fibers-reinforced NiAl composites
  10. Modelling the stress state of a thermal barrier coating system at high temperatures
  11. Impedance spectroscopy of thermal barrier coatings as non-destructive evaluation tool for failure detection
  12. Diffraction by image processing and its application in materials science
  13. On the preferred orientation in Ti1–xAlxN and Ti1–x–yAlxSiyN thin films
  14. Boron segregation and creep in ultra-fine grained tempered martensite ferritic steels
  15. Numeric simulation of the α/γ-phase ratio of ferritic-austenitic duplex steels
  16. Deformation behaviour and microscopic investigations of cyclically loaded railway wheels and tyres
  17. Similarity considerations on the simulation of turning processes of steels
  18. Crack-tip residual stresses and crack propagation in cyclically-loaded specimens under different loading modes
  19. On the effect of oxide scale stability on the internal nitridation process in high-temperature alloys
  20. Nitriding behaviour of the intermetallic alloy FeAl
  21. Material-related fundamentals of cutting techniques for GaAs wafer manufacturing
  22. Determination of RuAl phase boundaries in binary Ru–Al phase diagram at room temperature and 1200 °C
  23. On the Orowan stress in intermetallic ODS alloys and its superposition with grain size and solid solution hardening
  24. Effects of particle reinforcement on creep behaviour of AlSi1MgCu
  25. Effect of preaging on the precipitation behaviour of AlMgSi1
  26. Corrosion behaviour of hard coatings on Mg substrates
  27. Phase transformations in creep resistant MgYNdScMn alloy
  28. Notifications/Mitteilungen
  29. Personal/Personelles
  30. Press/Presse
  31. Conferences
https://doi.org/10.1515/ijmr-2005-0122
Schlagwörter für diesen Artikel
X-ray rocking curve broadening; Lattice misorientations; Plastic deformation; Deformed crystals; Geometrically necessary dislocations

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. Heinrich Oettel – 65 Jahre
  4. Articles Basic
  5. Misorientations and geometrically necessary dislocations in deformed copper crystals: A microstructural analysis of X-ray rocking curves
  6. Microstructure and lattice defects in highly deformed metals by X-ray diffraction whole powder pattern modelling
  7. Magnetoplasticity
  8. Articles Applied
  9. Finite-element analysis of the hot-pressing consolidation of continuous Al2O3 fibers-reinforced NiAl composites
  10. Modelling the stress state of a thermal barrier coating system at high temperatures
  11. Impedance spectroscopy of thermal barrier coatings as non-destructive evaluation tool for failure detection
  12. Diffraction by image processing and its application in materials science
  13. On the preferred orientation in Ti1–xAlxN and Ti1–x–yAlxSiyN thin films
  14. Boron segregation and creep in ultra-fine grained tempered martensite ferritic steels
  15. Numeric simulation of the α/γ-phase ratio of ferritic-austenitic duplex steels
  16. Deformation behaviour and microscopic investigations of cyclically loaded railway wheels and tyres
  17. Similarity considerations on the simulation of turning processes of steels
  18. Crack-tip residual stresses and crack propagation in cyclically-loaded specimens under different loading modes
  19. On the effect of oxide scale stability on the internal nitridation process in high-temperature alloys
  20. Nitriding behaviour of the intermetallic alloy FeAl
  21. Material-related fundamentals of cutting techniques for GaAs wafer manufacturing
  22. Determination of RuAl phase boundaries in binary Ru–Al phase diagram at room temperature and 1200 °C
  23. On the Orowan stress in intermetallic ODS alloys and its superposition with grain size and solid solution hardening
  24. Effects of particle reinforcement on creep behaviour of AlSi1MgCu
  25. Effect of preaging on the precipitation behaviour of AlMgSi1
  26. Corrosion behaviour of hard coatings on Mg substrates
  27. Phase transformations in creep resistant MgYNdScMn alloy
  28. Notifications/Mitteilungen
  29. Personal/Personelles
  30. Press/Presse
  31. Conferences
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