Startseite A critical analysis of the composite model as applied to high-temperature creep of Al and an Al–Mg alloy
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A critical analysis of the composite model as applied to high-temperature creep of Al and an Al–Mg alloy

  • M. Zehetbauer EMAIL logo , E. Schafler , F. Dobeš und K. Milička
Veröffentlicht/Copyright: 11. Januar 2022
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International Journal of Materials Research
Aus der Zeitschrift International Journal of Materials Research Band 97 Heft 3

Abstract

The composite model which has been created by Mughrabi, and developed by several other researchers, is analyzed with respect to high-temperature creep of Al and an Al– Mg alloy. Data for structural parameters such as local and global internal stresses, and dislocation densities have been obtained from X-ray line profile analyses and stress dip tests. Based on the composite model, quantitative relations have been derived which convert the internal stresses gained from X-ray profile analysis into those obtained from stress dip tests. This allowed for a detailed check of the composite model and its formalism describing local and global external and internal stresses, and local and global dislocation densities, during creep at high temperatures. While the local and global internal stresses show an excellent coincidence, the dislocation densities and subboundary volume fractions derived from experiment and modelling show certain deviations; however, these can be related to simplifications of equations used which are not part of the composite model.

Keywords: Internal stresses; Stress dip test; X-ray Bragg profile analysis
Ao. Univ. Prof. Dr. Michael Zehetbauer Universität Wien Institut für Materialphysik Boltzmanngasse 5, A-1090 Wien, Austria Tel.: +43 1 4277 51443 Fax: +43 1 4277 51440

Dedicated to Professor Dr. Gernot Kostorz on the occasion of his 65th birthday

  1. The investigation was performed within the frame of a joint Austrian – Czech project granted by the Austrian Institute for East and South Europe. Partial support of the Grant Agency of the Czech Academy of Science within grants A2041202 and A2041203 is gratefully acknowledged. M.Z. and E.S. are grateful to the Austrian Science Fund (FWF) which provided finances under project P 17095 N02.

References

[1] H. Mughrabi, in: P. Haasen, V. Gerold, G. Kostorz (Eds.), Strength of Metals and Alloys (Proc. ICSMA 5), Vol. 3, Pergamon Press, New York, (1980) 1615.Suche in Google Scholar

[2] W.D. Nix, B. Ilschner, in: P. Haasen, V. Gerold, G. Kostorz (Eds.), Strength of Metals and Alloys (Proc. ICSMA 5), Vol. 3, Pergamon Press, New York, (1980) 1503.10.1016/B978-1-4832-8412-5.50243-5Suche in Google Scholar

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

[4] H. Mughrabi: phys. stat. sol. (a) 104 (1987) 107.10.1002/pssa.2211040108Suche in Google Scholar

[5] H. Mughrabi: Mater. Sci. Eng. A 317 (2001) 171.10.1016/S0921-5093(01)01173-XSuche in Google Scholar

[6] M. Meier, W. Blum: Mater. Sci. Eng. A 164 (1993) 290.10.1016/0921-5093(93)90680-DSuche in Google Scholar

[7] M. Meier, Q. Zhu, W. Blum: Z. Metallkd. 84 (1993) 263.10.1515/ijmr-1993-840411Suche in Google Scholar

[8] F. Dobes, W. Blum: phys. stat. sol. A 144 (1994) 343.10.1002/pssa.2211440213Suche in Google Scholar

[9] M. Zehetbauer: Acta metall. mater. 41 (1993) 589.10.1016/0956-7151(93)90089-BSuche in Google Scholar

[10] R. Sedlacek: Scripta metall. mater. 33 (1995) 283.10.1016/0956-716X(95)00136-JSuche in Google Scholar

[11] M. Zehetbauer, T. Ungár, R. Král, A. Borbély, E. Schafler, B. Ortner, H. Amenitsch, S. Bernstorff: Acta mater. 47 (1999) 1053.10.1016/S1359-6454(98)00366-8Suche in Google Scholar

[12] C.N. Ahlquist, W.D. Nix: Scripta metall. 3 (1969) 679.10.1016/0036-9748(69)90076-3Suche in Google Scholar

[13] O.D. Sherby, P.M. Burke: Prog. Mater. Sci. 13 (1968) 325.10.1016/0079-6425(68)90024-8Suche in Google Scholar

[14] T. Ungár, I. Groma, M. Wilkens: J. Appl. Cryst. 22 (1989) 26.10.1107/S0021889888009720Suche in Google Scholar

[15] I. Groma, T. Ungár, M. Wilkens: J. Appl. Cryst. 21 (1988) 47.10.1107/S0021889887009178Suche in Google Scholar

[16] M. Wilkens: phys. stat. sol. (a) 2 (1970) 359.10.1002/pssa.19700020224Suche in Google Scholar

[17] T. Ungár, I. Dragomir, A. Révész, A. Borbély: J. Appl. Cryst 32 (1999) 992.10.1107/S0021889899009334Suche in Google Scholar

[18] T. Ungár, H. Mughrabi, D. Rönnpagel, M. Wilkens: Acta metall. 32 (1984) 333.10.1016/0001-6160(84)90106-8Suche in Google Scholar

[19] M. Müller, M. Zehetbauer, A. Borbély, T. Ungár: Z. Metallkd. 86 (1995) 827.10.1515/ijmr-1995-861205Suche in Google Scholar

[20] E. Nes, K. Marthinsen: Mater. Sci. Eng. A 322 (2002) 176.10.1016/S0921-5093(01)01130-3Suche in Google Scholar

[21] W. Blum, in: R.W. Cahn, P. Haasen E.J. Cramer (Eds.), Materials Science and Technology, Vol. 6, VCH Wiley, Weinheim (1993) 359.Suche in Google Scholar

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

[23] F.F. Lavrentev: Mater. Sci. Eng. 46 (1980) 19110.1016/0025-5416(80)90175-5Suche in Google Scholar

[24] W. Blum, in: T.G. Langdon, H.D. Merchant, J.G. Morris, M.A. Zaidi (Eds.), Hot Deformation of Aluminium Alloys, The Minerals, Metals & Materials Society, Warrendale (Pasadena, USA) (1991) 81.Suche in Google Scholar

[25] G. Schoeck, R. Frydman, phys. stat. sol. B 53 (1972) 661.10.1002/pssb.2220530227Suche in Google Scholar

[26] F. Dobeš, A. Orlová: Mater. Sci. Eng. A 125 (1990) 61.10.1016/0921-5093(90)90178-6Suche in Google Scholar

Appendix

In the following, a procedure is described for the modeling of local stresses which starts from the principles of composite models [7, 8] for high temperature steady state creep.

In steady state, the overall nonelastic strain rate is given by the sum of contributions from motion of free dislocations, ε˙c, and from subgrain boundary migration, ε˙m, and the contributions are coupled by [7]: ε˙c:ε˙m=9:1. The contribution from the motion of free dislocations is the same in both hard and soft regions and is given by

(A1) ε˙c=bρcVc/MT

In pure aluminum, the velocity of dislocations in subgrain interiors is expressed by Eq. (6b). The strain rate due to migration of subgrain boundaries can also be described by the Orowan equation

(A2) ε˙m=bρSBVm/MT

The velocity of subgrain boundary migration is written as

(A3) Vm=Vm0sWsinh(bAwσwMTkT)

where vm0 is a temperature dependent pre-exponential term.

The calculation starts for given external conditions, i. e. temperature and applied stress (523 K, 20 MPa and 673 K, 2.5 MPa). For a chosen applied stress, the value of local stress σw and of volume fraction fw as derived from X-ray measurements are taken (cf. Table 1). The values of microstructural quantities w, ρc and s are calculated by means of the above Eqs. (8), (24) and (25). Then the ratio of the preexponential terms for the chosen temperature, vm0/vs0, is calculated. For the next applied stress, only the volume fraction from X-ray measurements is taken. From equations (A1) to (A3), the coupling condition ε˙c:ε˙m=9:1 and the condition of mechanical equilibrium Eq. (3), the local stresses σw and σc are found numerically. The results of calculations are presented in Fig. 5. It can be seen that with the exception of one data point (673 K, 5 MPa), the local stress values estimated from X-ray measurements and those found by modeling follow the same tendency.

In the modeling of the Al –Mg behaviour, the dislocation velocity in subgrain interiors is governed by a viscous glide mechanism [7]

(A4) Vc=Bσc*

where B is a temperature dependent constant. The modeling procedure is analogous to that in pure Al. The results are given in Fig. 5. The calculated relative stress in hard regions, σw/σ, decreases with the increasing applied stress in agreement with both data from X-ray measurements and the previous model of Meier et al. [7].

Received: 2005-09-19
Accepted: 2006-01-02
Published Online: 2022-01-11

© 2006 Carl Hanser Verlag, München

Artikel in diesem Heft

  1. Frontmatter
  2. Professor Dr. Gernot Kostorz 65 years
  3. Dislocation micromechanisms under single slip conditions
  4. Characterisation of short-range order using dislocations
  5. Between microscopic and mesoscopic descriptions of twin–twin interaction
  6. Influence of the thermoelastic effect on the acoustic properties of pure metals at low temperatures
  7. Recent progress in the area of bulk metallic glasses
  8. Formation of the ABC6-type ordered structure in fcc alloys
  9. Short-range order in Fe-21.9 at.% Al
  10. Criteria for developing castable, creep-resistant aluminum-based alloys – A review
  11. Phase decomposition and precipitation of metastable A2 phase in B2 ordered Co–Al–Fe alloys
  12. Atomic migration and ordering phenomena in bulk and thin films of FePd and FePt
  13. Late-stage coarsening of oil droplets of excess oil in microemulsions following a temperature quench
  14. Small-angle scattering from spherical particles on randomly oriented interfaces
  15. Ripening of L12 Ni3Ti precipitates in the framework of the trans-interface diffusion-controlled theory of particle coarsening
  16. Texture evolution in equiaxed polycrystalline L10-ordered FePd during coarsening at 600 °C
  17. Modulated structures in amorphous films of Cr-silicide prepared by electron-beam-deposition
  18. Early stages of nucleation and growth of Guinier –Preston zones in Al–Zn–Mg and Al–Zn–Mg–Cu alloys
  19. Experimental and theoretical characterization of Al3Sc precipitates in Al–Mg–Si–Cu–Sc–Zr alloys
  20. Ag2Al plates in Al–Ag alloys
  21. A critical analysis of the composite model as applied to high-temperature creep of Al and an Al–Mg alloy
  22. Damage behaviour of an Al2O3 particle-reinforced 6061 alloy induced by monotonic and cyclic deformation
  23. Deformation behaviour of ultrafine-grained magnesium with 3 vol.% graphite
  24. Press/Presse
  25. Conferences/Konferenzen
  26. Frontmatter
  27. Editorial
  28. Professor Dr. Gernot Kostorz 65 years
  29. Articles BBasic
  30. Dislocation micromechanisms under single slip conditions
  31. Characterisation of short-range order using dislocations
  32. Between microscopic and mesoscopic descriptions of twin–twin interaction
  33. Influence of the thermoelastic effect on the acoustic properties of pure metals at low temperatures
  34. Recent progress in the area of bulk metallic glasses
  35. Formation of the ABC6-type ordered structure in fcc alloys
  36. Short-range order in Fe-21.9 at.% Al
  37. Criteria for developing castable, creep-resistant aluminum-based alloys – A review
  38. Phase decomposition and precipitation of metastable A2 phase in B2 ordered Co–Al–Fe alloys
  39. Atomic migration and ordering phenomena in bulk and thin films of FePd and FePt
  40. Late-stage coarsening of oil droplets of excess oil in microemulsions following a temperature quench
  41. Small-angle scattering from spherical particles on randomly oriented interfaces
  42. Ripening of L12 Ni3Ti precipitates in the framework of the trans-interface diffusion-controlled theory of particle coarsening
  43. Articles AApplied
  44. Texture evolution in equiaxed polycrystalline L10-ordered FePd during coarsening at 600 °C
  45. Modulated structures in amorphous films of Cr-silicide prepared by electron-beam-deposition
  46. Early stages of nucleation and growth of Guinier –Preston zones in Al–Zn–Mg and Al–Zn–Mg–Cu alloys
  47. Experimental and theoretical characterization of Al3Sc precipitates in Al–Mg–Si–Cu–Sc–Zr alloys
  48. Ag2Al plates in Al–Ag alloys
  49. A critical analysis of the composite model as applied to high-temperature creep of Al and an Al–Mg alloy
  50. Damage behaviour of an Al2O3 particle-reinforced 6061 alloy induced by monotonic and cyclic deformation
  51. Deformation behaviour of ultrafine-grained magnesium with 3 vol.% graphite
  52. Notifications/Mitteilungen
  53. Press/Presse
  54. Conferences/Konferenzen
https://doi.org/10.1515/ijmr-2006-0053
Schlagwörter für diesen Artikel
Internal stresses; Stress dip test; X-ray Bragg profile analysis

Artikel in diesem Heft

  1. Frontmatter
  2. Professor Dr. Gernot Kostorz 65 years
  3. Dislocation micromechanisms under single slip conditions
  4. Characterisation of short-range order using dislocations
  5. Between microscopic and mesoscopic descriptions of twin–twin interaction
  6. Influence of the thermoelastic effect on the acoustic properties of pure metals at low temperatures
  7. Recent progress in the area of bulk metallic glasses
  8. Formation of the ABC6-type ordered structure in fcc alloys
  9. Short-range order in Fe-21.9 at.% Al
  10. Criteria for developing castable, creep-resistant aluminum-based alloys – A review
  11. Phase decomposition and precipitation of metastable A2 phase in B2 ordered Co–Al–Fe alloys
  12. Atomic migration and ordering phenomena in bulk and thin films of FePd and FePt
  13. Late-stage coarsening of oil droplets of excess oil in microemulsions following a temperature quench
  14. Small-angle scattering from spherical particles on randomly oriented interfaces
  15. Ripening of L12 Ni3Ti precipitates in the framework of the trans-interface diffusion-controlled theory of particle coarsening
  16. Texture evolution in equiaxed polycrystalline L10-ordered FePd during coarsening at 600 °C
  17. Modulated structures in amorphous films of Cr-silicide prepared by electron-beam-deposition
  18. Early stages of nucleation and growth of Guinier –Preston zones in Al–Zn–Mg and Al–Zn–Mg–Cu alloys
  19. Experimental and theoretical characterization of Al3Sc precipitates in Al–Mg–Si–Cu–Sc–Zr alloys
  20. Ag2Al plates in Al–Ag alloys
  21. A critical analysis of the composite model as applied to high-temperature creep of Al and an Al–Mg alloy
  22. Damage behaviour of an Al2O3 particle-reinforced 6061 alloy induced by monotonic and cyclic deformation
  23. Deformation behaviour of ultrafine-grained magnesium with 3 vol.% graphite
  24. Press/Presse
  25. Conferences/Konferenzen
  26. Frontmatter
  27. Editorial
  28. Professor Dr. Gernot Kostorz 65 years
  29. Articles BBasic
  30. Dislocation micromechanisms under single slip conditions
  31. Characterisation of short-range order using dislocations
  32. Between microscopic and mesoscopic descriptions of twin–twin interaction
  33. Influence of the thermoelastic effect on the acoustic properties of pure metals at low temperatures
  34. Recent progress in the area of bulk metallic glasses
  35. Formation of the ABC6-type ordered structure in fcc alloys
  36. Short-range order in Fe-21.9 at.% Al
  37. Criteria for developing castable, creep-resistant aluminum-based alloys – A review
  38. Phase decomposition and precipitation of metastable A2 phase in B2 ordered Co–Al–Fe alloys
  39. Atomic migration and ordering phenomena in bulk and thin films of FePd and FePt
  40. Late-stage coarsening of oil droplets of excess oil in microemulsions following a temperature quench
  41. Small-angle scattering from spherical particles on randomly oriented interfaces
  42. Ripening of L12 Ni3Ti precipitates in the framework of the trans-interface diffusion-controlled theory of particle coarsening
  43. Articles AApplied
  44. Texture evolution in equiaxed polycrystalline L10-ordered FePd during coarsening at 600 °C
  45. Modulated structures in amorphous films of Cr-silicide prepared by electron-beam-deposition
  46. Early stages of nucleation and growth of Guinier –Preston zones in Al–Zn–Mg and Al–Zn–Mg–Cu alloys
  47. Experimental and theoretical characterization of Al3Sc precipitates in Al–Mg–Si–Cu–Sc–Zr alloys
  48. Ag2Al plates in Al–Ag alloys
  49. A critical analysis of the composite model as applied to high-temperature creep of Al and an Al–Mg alloy
  50. Damage behaviour of an Al2O3 particle-reinforced 6061 alloy induced by monotonic and cyclic deformation
  51. Deformation behaviour of ultrafine-grained magnesium with 3 vol.% graphite
  52. Notifications/Mitteilungen
  53. Press/Presse
  54. Conferences/Konferenzen
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