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Kinetics on the micro- and macro-levels in polycrystalline alloy materials during martensitic transformation

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Summary

Kinetics is studied during the martensitic transformation on both the micro- and macro-level from the thermomechanical point of view. A variant, a smallest microstructure element in an alloy, is assumed to transform at a burst when a transformation condition expressed by means of the driving force is satisfied. It has a micro-fraction showing 1 (transformed) or 0 (yet untransformed). The macrofraction, which represents a certain extent of transformation in a representative volume composed of a large enough number of variants, is derived by performing an ensemble average of the micro-fraction over the representative volume. The progress of the macro-fraction during thermomechanical loading is shown to be governed by a differential equation, the solution of which could be reduced to the conventional transformation kinetics discussed in the fields of metallurgy and transformation thermomechanics. A linear relation is derived between the increments of the macroscopic transformation strain and of the macro-fraction.

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References

  1. Tanaka, K., Nagaki, S.: A thermomechanical description of materials with internal variables in the process of phase transitions. Ing. Arch.51, 287–299 (1982).

    Google Scholar 

  2. Tanaka, K., Kobayashi, S., Sato, Y.: Thermomechanics of transformation pseudoelasticity and shape memory effect in alloys. Int. J. Plasticity2, 59–72 (1986).

    Google Scholar 

  3. Abeyaratne, R., Knowles, J. K.: A continuum model of a thermoelastic solid capable of undergoing phase transitions. J. Mech. Phys. Solids.41, 541–571 (1993).

    Google Scholar 

  4. Fischer, F. D., Berveiller, M., Tanaka, K., Oberaigner, E. R.: Continuum mechanical aspects of phase transformations in solids. Arch. Appl. Mech.64, 54–85 (1993).

    Google Scholar 

  5. Olson, G. B., Roitburd, A. L.: Martensitic nucleation. In: Martensite (Olson, G. B., Owen, W. S., eds.), pp. 149–174. Materials Park, Ohio: ASM International 1993.

    Google Scholar 

  6. Grujicic, M., Ling, H. C., Haezebrouck, D. M., Owen, W. S.: The growth of martensite. In: Martensite (Olson, G. B., Owen, W. S., eds.), pp. 175–196. Materials Park, Ohio: ASM International 1993.

    Google Scholar 

  7. Heidug, W., Lehner, F. K.: Thermodynamics of coherent phase transformations in nonhydrostatically stressed solids. Pure Appl. Geophys.123, 91–98 (1985).

    Google Scholar 

  8. Abeyaratne, R., Knowles, J. K.: On the driving traction acting on a surface of strain discontinuity in a continuum. J. Mech. Phys. Solids38, 345–360 (1990).

    Google Scholar 

  9. Liu, I.-S.: On interface equilibrium and inclusion problems. Continuum Mech. Thermodyn.4, 177–186 (1992).

    Google Scholar 

  10. Raniecki, B., Tanaka, K.: On the thermodynamic driving force for martensitic transformations. In: Residual stresses — 3 Hujiwara, H., Abe, T., Tanaka, K., eds.), Vol. 1, pp. 196–201. London, New York: Elsevier 1992.

    Google Scholar 

  11. Lexcellent, C., Torra, V.: Micromechanics of shape memory alloys Cu−Zn−Al single crystal: Experiments and modelling. In: MECAMAT 93, Int. Seminar on Micromechanics of Materials, pp. 234–245. Paris: Editions Eyrolles 1993.

    Google Scholar 

  12. Tamura, I.: Deformation-induced martensitic transformation and transformation-induced plasticity in steels. Metal Sci.16, 245–253 (1982).

    Google Scholar 

  13. Wang, Z. G., Inoue, T.: Analyses of temperature, structure and stress during quenching of steel with consideration for stress dependence of transformation kinetics. J. Soc. Mater. Sci. Jpn.32, 991–996 (1983).

    Google Scholar 

  14. Nishiyama, Z.: Martensitic transformation. New York: Academic Press 1978.

    Google Scholar 

  15. Kaufmann, L., Hilbert, M.: Thermodynamics of martensitic transformation. In: Martensite (Olson, G. B., Owen, W. S., eds.), pp. 41–58. Materials Park, Ohio: ASM International 1993.

    Google Scholar 

  16. Magee, C. L.: The nucleation of martensite. In: Phase transformations (Aaronson, H. I., ed.), pp. 115–156. Materials Park, Ohio: ASM 1969.

    Google Scholar 

  17. De Groot, S. R., Mazur, P.: Non-equlibrium thermodynamics. Amsterdam: North-Holland 1962.

    Google Scholar 

  18. Inoue, T., Raniecki, B.: Determination of thermal-hardening stresses in steels by use of thermoplasticity theory. J. Mech. Phys. Solids26, 187–212 (1978).

    Google Scholar 

  19. Tanaka, K., Sato, Y.: A mechanical view of transformation-induced plasticity. Ing. Arch.55, 147–155 (1985).

    Google Scholar 

  20. Tanaka, K.: A phenomenological description on thermomechanical behavior of shape memory alloys. J. Pressure Vessel Tech.112, 158–163 (1990).

    Google Scholar 

  21. Fischer, F. D., Tanaka, K.: A micromechanical model for the kinetics of martensitic transformation. Int. J. Solids Struct.29, 1723–1728 (1992).

    Google Scholar 

  22. Marchand, J. P.: Distributions, and outline. Amsterdam: North-Holland 1962.

    Google Scholar 

  23. Koistinen, D. P., Marburger, R. E.: A general prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steel. Acta Metall.7, 59 (1959).

    Google Scholar 

  24. Hill, R.: Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids11, 357–372 (1963).

    Google Scholar 

  25. Mori, T., Wakashima, K.: Successive iteration method in the evaluation of averaged field in elastically inhomogeneous materials. In: Micromechanics and inhomogeneity (Weng, G. J., Taya, H., Abe, H., eds.), pp. 269–282. New York: Springer (1990).

    Google Scholar 

  26. Kröner, E.: Statistical continuum mechanics. Wien, New York: Springer 1972.

    Google Scholar 

  27. Patoor, E., Eberhardt, A., Berveiller, M.: Thermomechanical behavior by martensitic transformation in single and polycrystals. In: Proc. 8th RISO Int. Symp., pp. 465–470, Riso 1987.

  28. Wakashima, K., Tsukamoto, H., Choi, B. H.: Elastic and thermoelastic properties of metal matrix composite with discontinuous fibers or particles. In: Proc. Korea-Japan Metal Symp. Composite Materials, Seoul/Korea, pp. 102–112, 1988.

  29. Benveniste, Y., Dvorak, G. J.: On a correspondence between mechanical and thermal effects in two-phase composite. In: Micromechanics and inhomogeneity (Wang, G. J., Taya, H., Abe, H., eds.), pp. 65–82. New York: Springer 1990.

    Google Scholar 

  30. Eshelby, J. D.: The determination of the elastic field on an ellipsoidal inclusion and related problems. Proc. R. Soc. London Ser.A241, 376–396 (1957).

    Google Scholar 

  31. Withers, P. J., Stobbs, W. M., Pedersen, O. B.: The application of the Eshelby method of internal stress determination to short fibre metal matrix composites. Acta Metall.37, 3061–3084 (1989).

    Google Scholar 

  32. Tanaka, K., Hasegawa, D., Böhm, H. J., Fischer, F. D.: Overall thermomechanical behavior of shape memory alloys; a micromechanical approach based on mean field theory. Mat. Sci. Res. Int.1, 23–30 (1995).

    Google Scholar 

  33. Patel, J. R., Cohen, M.: Criterion for the action of applied stress in the martensitic transformation. Acta Metall.1, 531–538 (1953).

    Google Scholar 

  34. Gautier, E., Zhang, X. M., Simon, A.: Role of internal stress state on transformation induced plasticity and transformation mechanisms during the progress of stress induced phase transformation. In: International Conference on Residual Stresses (ICRS2), (Beck, G., Denis, S., Simon, A., eds.), pp. 777–783. London, New York: Elsevier 1989.

    Google Scholar 

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Author notes

  1. K. Tanaka

    Present address: Department of Aerospace Engineering, Tokyo Metropolitan Institute of Technology, Hino/Tokyo, Japan

  2. E. R. Oberaigner

    Present address: Institute of Mechanics, University for Mining and Metallurgy, Franz-Josef-Strasse 18, A-8700, Leoben, Austria

  3. F. D. Fischer

    Present address: Christian Doppler Laboratory for Micromechanics of Materials, University for Mining and Metallurgy, Franz-Josef-Strasse 18, A-8700, Leoben, Austria

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    1. K. Tanaka
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    2. E. R. Oberaigner
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    3. F. D. Fischer
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    Tanaka, K., Oberaigner, E.R. & Fischer, F.D. Kinetics on the micro- and macro-levels in polycrystalline alloy materials during martensitic transformation. Acta Mechanica 116, 171–186 (1996). https://doi.org/10.1007/BF01171428

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