Home A continuum based microstructure model of inhomogeneous hardening and recovery as a pre-stage of recrystallization nucleation
Article
Licensed
Unlicensed Requires Authentication

A continuum based microstructure model of inhomogeneous hardening and recovery as a pre-stage of recrystallization nucleation

Dedicated to Professor Dr. H.-P. Degischer on the occasion of his 65th birthday
  • Werner Mitter and Christof Sommitsch
Published/Copyright: May 18, 2013
Become an author with De Gruyter Brill
Author Information
International Journal of Materials Research
From the journal International Journal of Materials Research Volume 101 Issue 9

Abstract

Starting from the fundamental relation between the diffusion flux of point defects (vacancies, interstitials) and the gradient of the diffusion potential the diffusion equation is set up and applied to the calculation of the concentrations of both types of point defects. Thereby, all possible sources and sinks and their mutual effects are taken into consideration. These equations are coupled with the equations for the temporal derivatives of dislocation density, porosity, pore size and temperature. For the close-up region of spherical inhomogeneities (pores, hard inclusions) and a grain boundary this system of six partial differential equations is solved numerically. For simplicity a one dimensional model in space is used and uniaxial tension or pure shear load is assumed. Hardening and the simultaneous recovery are characterized by the local and temporal development of the point defect concentrations and especially of the dislocation density, which is proportional to the intrinsic strain energy. The gradients of both strain energy and lattice rotation determine the formation and growth of recrystallization nuclei. It is the aim of this work to present a new mathematical model and also to give a perceptual general view on the concerted action of the fundamental physical processes, which necessarily lead to hardening, recovery (softening) and recrystallization nucleation. Moreover it seems to be a basis of a future general theory of microstructure changes.

Keywords: Hardening; Recovery; Recrystallization nucleation
∗ Correspondence address, Univ.-Prof. Dr. Christof Sommitsch Institute for Materials Science and Welding Christian Doppler Laboratory for Materials Modelling and Simulation Graz University of TechnologyKopernikusgasse 24, A-8010 Graz, Austria Tel.: +43 (0) 316 873 7180 Fax: +43 (0) 316 873 7187 E-mail:

References

[1] P.Haasen: Physikalische Metallkunde, Springer-Verlag, Berlin (1974).10.1007/978-3-642-96199-1Search in Google Scholar

[2] G.Joos: Lehrbuch der theoretischen Physik, Akademische Verlagsgesellschaft Geest&Portig, Leipzig (1959).Search in Google Scholar

[3] C.Schäfer: Einführung in die theoretische Physik, Band I, Walter de Gruyter, Berlin und Leipzig (1929).Search in Google Scholar

[4] W.Mitter, C.Sommitsch: Zur Theorie der Gefügeänderungen in Metallen: Verfestigung, Erholung, Korngrenzenbewegung und Rekristallisation, Teil 1: Ein kontinuumstheoretisches Modell von inhomogener Verfestigung und Erholung als Vorstufe für die Bildung von Rekristallisationskeimen, in: C.Sommitsch, K.Reichmann, F.Hofer (Eds.), Monographic Series TU Graz, Advanced Materials Science, Vol. 1, Verlag der Technischen Universität Graz, Graz (2010), in press.Search in Google Scholar

[5] J.W.Cahn: Acta Met.10 (1962) 789.10.1016/0001-6160(62)90092-5Search in Google Scholar

[6] M.Millitzer, W.P.Sun, J.J.Jonas: Acta Metall. Mater.42 (1994) 133.Search in Google Scholar

[7] D.Hull: Introduction to Dislocations, 2nd Ed., Pergamon Press, Oxford (1975).Search in Google Scholar

[8] E.Macherauch, H.Wohlfahrt, U.Wolfstieg: HTM28 (1973) 201.Search in Google Scholar

[9] H.P.Stüwe: Acta Met.13 (1965) 1337.10.1016/0001-6160(65)90045-3Search in Google Scholar

[10] P.Täubert: Metallphysik, Verlag Harry Deutsch, Zürich und Frankfurt/M. (1964).Search in Google Scholar

[11] G.Gottstein: Rekristallisation metallischer Werkstoffe, Deutsche Gesellschaft für Metallkunde e.V., Oberursel (1984).Search in Google Scholar

[12] J.Grewen, J.Huber, in: F.Haessner (Ed.), Recrystallization of Metallic Materials, Dr. Riederer Verlag GmbH, Stuttgart (1978) 115.Search in Google Scholar

[13] W.Pantleon, P.Klimanek: Comput. Mater. Sci.3 (1994) 223.Search in Google Scholar

[14] J.P.Stark: Solid State Diffusion, John Wiley & Sons Inc., New York (1976).Search in Google Scholar

[15] W.Gao, A.Belyakov, H.Miura, T.Sakai: Mater. Sci. Eng. A265 (1999) 233.Search in Google Scholar

[16] T.Antretter: personal communication.Search in Google Scholar

[17] F.J.Humphreys, P.S.Bate: Scripta Mater.48 (2003) 173.Search in Google Scholar

[18] F.J.Humphreys, M.Hatherly: Recrystallization and Related Annealing Phenomena, 2nd ed., Elsevier, London (2004).Search in Google Scholar

[19] G.E.R.Schulze: Metallphysik, Akademie-Verlag, Berlin (1967).Search in Google Scholar

[20] F.J.Humphreys: Acta Met.27 (1979) 1801.10.1016/0001-6160(79)90071-3Search in Google Scholar

[21] A.P.Clarke, F.J.Humphreys, P.S.Bate: Mater. Sci. Forum, Vols.426–432 (2003) 399.Search in Google Scholar

[22] P.N.Kalu, F.J.Humphreys, in: N. Hansen and T. Leffers (Eds.), Proceedings of the 7th Riso International Symposium on Metallurgy and Materials Science, Riso National Laboratories, Roskilde (1986) 385.Search in Google Scholar

[23] P.N.Kalu, F.J.Humphreys, in: J.B. Bilde-Sorensen (Ed.), Proceedings of the 10th Riso International Symposium on Metallurgy and Materials Science, Riso National Laboratories, Roskilde (1989) 415.Search in Google Scholar

[24] Q.Liu, Z.Yao, A.Godfrey, W.Liu: J. Alloys Compd.482 (2009) 264.Search in Google Scholar

[25] G.A.Zickler, R.Schnitzer, R.Radis, R.Hochfellner, R.Schweins, M.Stockinger, H.Leitner: Mater. Sci. Eng. A523 (2009) 295.Search in Google Scholar

[26] F.J.Humphreys, M.G.Ardakani: Acta Metal. Mater.42 (1994) 749.Search in Google Scholar

[27] F.J.Humphreys, P.N.Kalu: Acta Metall. Mater.38 (1990) 917.Search in Google Scholar

[28] F.J.Humphreys, A.T.Stewart: Surface Science31 (1972) 389.Search in Google Scholar

[29] M.Ferry, F.J.Humphreys: Acta Mater.44 (1996) 3089.Search in Google Scholar

[30] M.L.Bhatia, R.W.Cahn: Proc. R. Soc. A362 (1978) 341.Search in Google Scholar

[31] F.J.Humphreys: Acta Mater.45 (1997) 4231.10.1016/S1359-6454(97)00070-0Search in Google Scholar

[32] F.J.Humphreys: Acta Mater.45 (1997) 5031.10.1016/S1359-6454(97)00173-0Search in Google Scholar

Received: 2010-3-12
Accepted: 2010-6-28
Published Online: 2013-05-18
Published in Print: 2010-09-01

© 2010, Carl Hanser Verlag, München

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. Hans-Peter Degischer – 65th birthday
  5. Basic
  6. X-ray and neutron imaging – Complementary techniques for materials science and engineering
  7. Fast in-situ X-ray micro tomography characterisation of microstructural evolution and strain-induced damage in alloys at various temperatures
  8. Thermo-kinetic computer simulation of differential scanning calorimetry curves of AlMgSi alloys
  9. Influence of stacking fault energy and alloying on stage V hardening of HPT-deformed materials
  10. Thermo-physical properties of silver/carbon fibre composites
  11. Influence of reinforcement contiguity on the thermal expansion of alumina particle reinforced aluminium composites
  12. A continuum based microstructure model of inhomogeneous hardening and recovery as a pre-stage of recrystallization nucleation
  13. Applied
  14. Metal foams – towards microcellular materials
  15. Gigacycle fatigue response of tool steels produced by powder metallurgy compared to ingot metallurgy tool steels
  16. Characterization of the microstructure and damage mechanisms in a Ti6Al4V alloy modified with 1 wt.% B
  17. Structural and age hardening characteristics of near eutectic Al–Si alloys
  18. Stress-corrosion cracking susceptibility of AZ31 alloy after varied heat-treatment in 3.5 wt.% NaCl solution
  19. Tensile deformation behavior of AA5083-H111 at cold and warm temperatures
  20. Experimental investigation of thermal fatigue behaviour of header tube to stub welded joint in power plants
  21. Synthesis and characterization of nanostructured Cu/ZnO/Al2O3 from lyotropic liquid crystalline templates
  22. DGM News
  23. Personal
https://doi.org/10.3139/146.110383
Keywords for this article
Hardening; Recovery; Recrystallization nucleation

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. Hans-Peter Degischer – 65th birthday
  5. Basic
  6. X-ray and neutron imaging – Complementary techniques for materials science and engineering
  7. Fast in-situ X-ray micro tomography characterisation of microstructural evolution and strain-induced damage in alloys at various temperatures
  8. Thermo-kinetic computer simulation of differential scanning calorimetry curves of AlMgSi alloys
  9. Influence of stacking fault energy and alloying on stage V hardening of HPT-deformed materials
  10. Thermo-physical properties of silver/carbon fibre composites
  11. Influence of reinforcement contiguity on the thermal expansion of alumina particle reinforced aluminium composites
  12. A continuum based microstructure model of inhomogeneous hardening and recovery as a pre-stage of recrystallization nucleation
  13. Applied
  14. Metal foams – towards microcellular materials
  15. Gigacycle fatigue response of tool steels produced by powder metallurgy compared to ingot metallurgy tool steels
  16. Characterization of the microstructure and damage mechanisms in a Ti6Al4V alloy modified with 1 wt.% B
  17. Structural and age hardening characteristics of near eutectic Al–Si alloys
  18. Stress-corrosion cracking susceptibility of AZ31 alloy after varied heat-treatment in 3.5 wt.% NaCl solution
  19. Tensile deformation behavior of AA5083-H111 at cold and warm temperatures
  20. Experimental investigation of thermal fatigue behaviour of header tube to stub welded joint in power plants
  21. Synthesis and characterization of nanostructured Cu/ZnO/Al2O3 from lyotropic liquid crystalline templates
  22. DGM News
  23. Personal
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 27.10.2025 from https://www.degruyterbrill.com/document/doi/10.3139/146.110383/html
Scroll to top button