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Stress Relaxation by Transformation Plasticity under the Martensitic Transformation in Steels

  • D. Ivanov and L. Markegård
Published/Copyright: April 14, 2016

Abstract

Transformation plasticity is considered as a phenomenon limiting the actual stress for any specified strain rate under conditions of phase transformation. A one-dimensional model of a steel bar strained under martensitic transformation is provided. Discussion is limited to a series of accepted assumptions, such as athermal kinetics of martensite transformation, monotonic evolution of temperature and constant transformation plasticity parameter. An equivalent tangent modulus is deduced indicating the decisive parameters influencing the softening modes. The obtained model is utilized together with well-known transformation plasticity laws and martensite transformation kinetics to demonstrate an actual softening of steels under the martensitic transformation.

Kurzfassung

Umwandlungsplastizität wird als ein Phänomen betrachtet, das die aktuelle Spannung während einer Phasenumwandlung unabhängig von der vorherrschenden Dehnrate begrenzt. Im Rahmen dieser Arbeit wird ein eindimensionales Modell eines beanspruchten Stahlstabs unter martensitischer Umwandlung vorgestellt. Der Ansatz ist durch eine Reihe von akzeptierten Annahmen begrenzt wie eine athermische Kinetik der Martensitumwandlung, monotone Temperaturentwicklung und konstanter Parameter der Umwandlungsplastizität. Es wird ein äquivalenter Tangentenmodul abgeleitet, der die entscheidenden Parameter erkennen lässt, die die Entfestigung beeinflussen. Das so erhaltene Modell wird mit verschiedenen in der Literatur vorliegenden Beschreibungen der Umwandlungsplastizität und der Kinetik der Martensitbildung genutzt, um eine Entfestigung von Stählen während der martensitischen Umwandlung aufzuzeigen.


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References

1. Gautier, E.; Zhang, J. S.; Zhang, X. M.: Martensitic Transformation under Stress in Ferrous Alloys. Mechanical Behaviour and Resulting Morphologies. J. Phys. IV France05 (1995) C8, pp. 4150, 10.1051/jp4:1995805Gautier, E.; Zhang, J. S.; Zhang, X. M.: Martensitic Transformation under Stress in Ferrous Alloys. Mechanical Behaviour and Resulting Morphologies. J. Phys. IV France05 (1995) C8, pp. 4150, 10.1051/jp4:1995805Search in Google Scholar

2. Videau, J.-C.; Cailletaud, G.; Pineau, A.: Experimental Study of the Transformation-Induced Plasticity in a Cr-Ni-Mo-Al-Ti Steel. J. Phys. IV France06 (1996) C1, pp. 465474, 10.1051/jp4:1996145Videau, J.-C.; Cailletaud, G.; Pineau, A.: Experimental Study of the Transformation-Induced Plasticity in a Cr-Ni-Mo-Al-Ti Steel. J. Phys. IV France06 (1996) C1, pp. 465474, 10.1051/jp4:1996145Search in Google Scholar

3. Otsuka, T.; AkashiT.; Ogawa, S.; Imai, T.; Egami, A.: Effect of Volume Expansion on Transformation Plasticity during Ferrite and Martensite Transformation of Steel. J. Soc. Mater. Sci.60 (2011) 10, pp. 937942, 10.2472/jsms.60.937Otsuka, T.; AkashiT.; Ogawa, S.; Imai, T.; Egami, A.: Effect of Volume Expansion on Transformation Plasticity during Ferrite and Martensite Transformation of Steel. J. Soc. Mater. Sci.60 (2011) 10, pp. 937942, 10.2472/jsms.60.937Search in Google Scholar

4. Liebaut, C.; Gautier, E.; SimonA.: Premiers resultats portant sur letude rheologique dun acier Fe-C pendant sa transformation de phase. Rev. Phys. Appl.23 (1988) 4, pp. 703703, 10.1051/rphysap:01988002304070300Liebaut, C.; Gautier, E.; SimonA.: Premiers resultats portant sur letude rheologique dun acier Fe-C pendant sa transformation de phase. Rev. Phys. Appl.23 (1988) 4, pp. 703703, 10.1051/rphysap:01988002304070300Search in Google Scholar

5. Gautier, E.; Denis, S.; Liebaut, C.; Sjöström, S.; Simon, A.: Mechanical behaviour of Fe-C alloys during phase transformations. J. Phys. IV France04 (1994) C3, pp. 279284, 10.1051/jp4:1994338Gautier, E.; Denis, S.; Liebaut, C.; Sjöström, S.; Simon, A.: Mechanical behaviour of Fe-C alloys during phase transformations. J. Phys. IV France04 (1994) C3, pp. 279284, 10.1051/jp4:1994338Search in Google Scholar

6. Greenwood, G. W.; Johnson, R. H.: The Deformation of Metals Under Small Stresses During Phase Transformations. Proc. Royal Society A: Mathematical, Physical and Engineering Sciences283 (1965) 1394, pp. 403422, 10.1098/rspa.1965.0029Greenwood, G. W.; Johnson, R. H.: The Deformation of Metals Under Small Stresses During Phase Transformations. Proc. Royal Society A: Mathematical, Physical and Engineering Sciences283 (1965) 1394, pp. 403422, 10.1098/rspa.1965.0029Search in Google Scholar

7. Magee, C. L.: Transformation kinetics, microplasticity and aging of martensite in Fe-31 Ni. Tech. rep. (1966), DTIC DocumentMagee, C. L.: Transformation kinetics, microplasticity and aging of martensite in Fe-31 Ni. Tech. rep. (1966), DTIC DocumentSearch in Google Scholar

8. Kim, W.-B.; Na, S.-J.: A study of residual stresses in the surface hardening of a blade mould by high frequency induction heating. Surf. Coat. Techn.58 (1993) 2, pp. 129136, 10.1016/0257-8972(93)90184-pKim, W.-B.; Na, S.-J.: A study of residual stresses in the surface hardening of a blade mould by high frequency induction heating. Surf. Coat. Techn.58 (1993) 2, pp. 129136, 10.1016/0257-8972(93)90184-pSearch in Google Scholar

9. Inoue, T.: Mechanics and Characteristics of Transformation Plasticity and Metallo-thermo-mechanical Process Simulation. Procedia Eng.10 (2011), pp. 37933798, 10.1016/j.proeng.2011.06.001Inoue, T.: Mechanics and Characteristics of Transformation Plasticity and Metallo-thermo-mechanical Process Simulation. Procedia Eng.10 (2011), pp. 37933798, 10.1016/j.proeng.2011.06.001Search in Google Scholar

10. Inoue, T.; HidetoW.: Unified theory of transformation plasticity and the effect on quenching simulation. Strojarstvo: časopis za teoriju i praksu u strojarstvu53 (2011) 1, pp. 1118Inoue, T.; HidetoW.: Unified theory of transformation plasticity and the effect on quenching simulation. Strojarstvo: časopis za teoriju i praksu u strojarstvu53 (2011) 1, pp. 1118Search in Google Scholar

11. Ju, D. Y.; Zhang, W. M.; Zhang, Y.: Modeling and experimental verification of martensitic transformation plastic behavior in carbon steel for quenching process. Mat. Sci. Eng. A438–440 (2006), pp. 246250, 10.1016/j.msea.2006.01.125Ju, D. Y.; Zhang, W. M.; Zhang, Y.: Modeling and experimental verification of martensitic transformation plastic behavior in carbon steel for quenching process. Mat. Sci. Eng. A438–440 (2006), pp. 246250, 10.1016/j.msea.2006.01.125Search in Google Scholar

12. Kang, S.-H.; Im, Y.-T.: Three-dimensional thermo-elastic-plastic finite element modeling of quenching process of plain-carbon steel in couple with phase transformation. International Journal of Mechanical Sciences49 (2007) 4, pp. 423439, 10.1016/j.ijmecsci.2006.09.014Kang, S.-H.; Im, Y.-T.: Three-dimensional thermo-elastic-plastic finite element modeling of quenching process of plain-carbon steel in couple with phase transformation. International Journal of Mechanical Sciences49 (2007) 4, pp. 423439, 10.1016/j.ijmecsci.2006.09.014Search in Google Scholar

13. Ivanov, D.; Markegård, L.; Asperheim, J. I.; Kristoffersen, H: Simulation of Stress and Strain for Induction-Hardening Applications. J. Mat. Eng. Perform.22 (2013) 11, pp. 32583268, 10.1007/s11665-013-0645-5Ivanov, D.; Markegård, L.; Asperheim, J. I.; Kristoffersen, H: Simulation of Stress and Strain for Induction-Hardening Applications. J. Mat. Eng. Perform.22 (2013) 11, pp. 32583268, 10.1007/s11665-013-0645-5Search in Google Scholar

14. Nallathambi, A. K.; Kaymak, Y.; Specht, E.; Bertram, A.: Sensitivity of material properties on distortion and residual stresses during metal quenching processes. J. Mater. Process. Techn.210 (2010) 2, pp. 204211, 10.1016/j.jmatprotec.2009.09.001Nallathambi, A. K.; Kaymak, Y.; Specht, E.; Bertram, A.: Sensitivity of material properties on distortion and residual stresses during metal quenching processes. J. Mater. Process. Techn.210 (2010) 2, pp. 204211, 10.1016/j.jmatprotec.2009.09.001Search in Google Scholar

15. Hayama, T.: Effect of Residual Stress on Fatigue Strength of Induction-Hardened Steel. Bulletin of JSME18 (1975) 125, pp. 11941200, 10.1299/jsme1958.18.1194Hayama, T.: Effect of Residual Stress on Fatigue Strength of Induction-Hardened Steel. Bulletin of JSME18 (1975) 125, pp. 11941200, 10.1299/jsme1958.18.1194Search in Google Scholar

16. Webster, G. A.; Ezeilo, A. N.: Residual stress distributions and their influence on fatigue lifetimes. Int. J. Fatigue23 (2001), pp. 375383, 10.1016/s0142-1123(01)00133-5Webster, G. A.; Ezeilo, A. N.: Residual stress distributions and their influence on fatigue lifetimes. Int. J. Fatigue23 (2001), pp. 375383, 10.1016/s0142-1123(01)00133-5Search in Google Scholar

17. Shaw, B. A.; Aylott, C.; O’Hara, P.; Brimble, K.: The role of residual stress on the fatigue strength of high performance gearing. Int. J. Fatigue25 (2003) 9, pp. 12791283, 10.1016/j.ijfatigue.2003.08.014Shaw, B. A.; Aylott, C.; O’Hara, P.; Brimble, K.: The role of residual stress on the fatigue strength of high performance gearing. Int. J. Fatigue25 (2003) 9, pp. 12791283, 10.1016/j.ijfatigue.2003.08.014Search in Google Scholar

18. Torres, M. A. S.; Voorwald, H. J. C.: An evaluation of shot peening, residual stress and stress relaxation on the fatigue life of AISI 4340 steel. Int. J. Fatigue24 (2002) 8, pp. 877886, 10.1016/s0142-1123(01)00205-5Torres, M. A. S.; Voorwald, H. J. C.: An evaluation of shot peening, residual stress and stress relaxation on the fatigue life of AISI 4340 steel. Int. J. Fatigue24 (2002) 8, pp. 877886, 10.1016/s0142-1123(01)00205-5Search in Google Scholar

19. Benedetti, M.; Fontanari, V.; Höhn, B. R.; Oster, P.; Tobie, T.: Influence of shot peening on bending tooth fatigue limit of case hardened gears. Int. J. Fatigue24 (2002) 11, pp. 11271136, 10.1016/s0142-1123(02)00034-8Benedetti, M.; Fontanari, V.; Höhn, B. R.; Oster, P.; Tobie, T.: Influence of shot peening on bending tooth fatigue limit of case hardened gears. Int. J. Fatigue24 (2002) 11, pp. 11271136, 10.1016/s0142-1123(02)00034-8Search in Google Scholar

20. Pereloma, E.; Edmonds, D. V. (Eds.): Phase Transformations in Steels: Diffusionless transformations, high strength steels, modelling and advanced analytical techniques. Vol. 2, Woodhead Publishing, Cambridge, UK, 2012, p. 45Pereloma, E.; Edmonds, D. V. (Eds.): Phase Transformations in Steels: Diffusionless transformations, high strength steels, modelling and advanced analytical techniques. Vol. 2, Woodhead Publishing, Cambridge, UK, 2012, p. 4510.1533/9780857096104Search in Google Scholar

21. Koistinen, D. P.; Marburger, R. E.: A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metall.7 (1959) 1, pp. 5960, 10.1016/0001-6160(59)90170-1Koistinen, D. P.; Marburger, R. E.: A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metall.7 (1959) 1, pp. 5960, 10.1016/0001-6160(59)90170-1Search in Google Scholar

22. Ferguson, B. L.; Li, Z.; Freborg, A. M.: Modeling heat treatment of steel parts. Comp. Mat. Sci.34 (2005) 3, pp. 274281, 10.1016/j.commatsci.2005.02.005Ferguson, B. L.; Li, Z.; Freborg, A. M.: Modeling heat treatment of steel parts. Comp. Mat. Sci.34 (2005) 3, pp. 274281, 10.1016/j.commatsci.2005.02.005Search in Google Scholar

23. Lee, M. G.; Kim, S. J.; Han, H. N.; Jeong, W. C.: Implicit finite element formulations for multi-phase transformation in high carbon steel. Int. J. Plast.25 (2009) 9, pp. 17261758, 10.1016/j.ijplas.2008.11.010Lee, M. G.; Kim, S. J.; Han, H. N.; Jeong, W. C.: Implicit finite element formulations for multi-phase transformation in high carbon steel. Int. J. Plast.25 (2009) 9, pp. 17261758, 10.1016/j.ijplas.2008.11.010Search in Google Scholar

24. Yang, H. S.; Bhadeshia, H. K. D. H.: Austenite grain size and the martensite-start temperature. Scripta mater.60 (2009) 7, pp. 493495, 10.1016/j.scriptamat.2008.11.043Yang, H. S.; Bhadeshia, H. K. D. H.: Austenite grain size and the martensite-start temperature. Scripta mater.60 (2009) 7, pp. 493495, 10.1016/j.scriptamat.2008.11.043Search in Google Scholar

25. Lambers, H. G.; Tschumak, S.; Maier, H. J.; Canadinc, D.: Pre-deformation-transformation plasticity relationship during martensitic transformation. Mat. Sci. Eng. A527 (2010) 3, pp. 625633, 10.1016/j.msea.2009.08.038Lambers, H. G.; Tschumak, S.; Maier, H. J.; Canadinc, D.: Pre-deformation-transformation plasticity relationship during martensitic transformation. Mat. Sci. Eng. A527 (2010) 3, pp. 625633, 10.1016/j.msea.2009.08.038Search in Google Scholar

26. Mioković, T.; Schulze, V.; Vöhringer, O.; Löhe, D.: Prediction of phase transformations during laser surface hardening of AISI 4140 including the effects of inhomogeneous austenite formation. Mat. Sc. Eng. A435 (2006), pp. 547555, 10.1016/j.msea.2006.07.037Mioković, T.; Schulze, V.; Vöhringer, O.; Löhe, D.: Prediction of phase transformations during laser surface hardening of AISI 4140 including the effects of inhomogeneous austenite formation. Mat. Sc. Eng. A435 (2006), pp. 547555, 10.1016/j.msea.2006.07.037Search in Google Scholar

27. Lee, S. J.; Lee, Y. K.: Effect of austenite grain size on martensitic transformation of a low alloy steel. Materials Science Forum475 (2005), pp. 31693172, 10.4028/www.scientific.net/msf.475-479.3169Lee, S. J.; Lee, Y. K.: Effect of austenite grain size on martensitic transformation of a low alloy steel. Materials Science Forum475 (2005), pp. 31693172, 10.4028/www.scientific.net/msf.475-479.3169Search in Google Scholar

28. Jung, M.; Kang, M.; Lee, Y. K.: Finite-element simulation of quenching incorporating improved transformation kinetics in a plain medium-carbon steel. Acta Mater.60 (2012) 2, pp. 525536, 10.1016/j.actamat.2011.10.007Jung, M.; Kang, M.; Lee, Y. K.: Finite-element simulation of quenching incorporating improved transformation kinetics in a plain medium-carbon steel. Acta Mater.60 (2012) 2, pp. 525536, 10.1016/j.actamat.2011.10.007Search in Google Scholar

29. Leblond, J. B.; Devaux, J.; Devaux, J. C.: Mathematical modelling of transformation plasticity in steels I: case of ideal-plastic phases. Int. J. Plasticity5 (1989) 6, pp. 551572, 10.1016/0749-6419(89)90001-6Leblond, J. B.; Devaux, J.; Devaux, J. C.: Mathematical modelling of transformation plasticity in steels I: case of ideal-plastic phases. Int. J. Plasticity5 (1989) 6, pp. 551572, 10.1016/0749-6419(89)90001-6Search in Google Scholar

30. Taleb, L.; Petit, S.: New investigations on transformation induced plasticity and its interaction with classical plasticity. Int. J. Plasticity22 (2006) 1, pp. 110130, 10.1016/j.ijplas.2005.03.012Taleb, L.; Petit, S.: New investigations on transformation induced plasticity and its interaction with classical plasticity. Int. J. Plasticity22 (2006) 1, pp. 110130, 10.1016/j.ijplas.2005.03.012Search in Google Scholar

31. Suhr, B.; Frerichs, F.; Hüßler, I.; Wolff, M.: Evaluation of models for martensitic transformation and TRIP via comparison of experiments and simulations. Proc. 2nd Int. Conf. IDE 2008, 17–18.09.08, Bremen, H.-W. Zoch, Th.Luebben (Eds.), 2008, pp. 421429Suhr, B.; Frerichs, F.; Hüßler, I.; Wolff, M.: Evaluation of models for martensitic transformation and TRIP via comparison of experiments and simulations. Proc. 2nd Int. Conf. IDE 2008, 17–18.09.08, Bremen, H.-W. Zoch, Th.Luebben (Eds.), 2008, pp. 421429Search in Google Scholar

32. Abrassart, F.: Stress-induced γ → α martensitic transformation in two carbon stainless steels. Application to trip steels. Metall. Trans.4 (1973) 9, pp. 22052216, 10.1007/bf02643289Abrassart, F.: Stress-induced γ → α martensitic transformation in two carbon stainless steels. Application to trip steels. Metall. Trans.4 (1973) 9, pp. 22052216, 10.1007/bf02643289Search in Google Scholar

33. Sjöström, S.: Interactions and constitutive models for calculating quench stresses in steel. Mat. Sci. Techn.1 (1985) 10, pp. 823829, 10.1179/026708385790124099Sjöström, S.: Interactions and constitutive models for calculating quench stresses in steel. Mat. Sci. Techn.1 (1985) 10, pp. 823829, 10.1179/026708385790124099Search in Google Scholar

34. Satoh, K.: Transient thermal stresses of weld heat-affected zone by both-ends-fixed bar analogy. Trans. Jap. Weld. Soc.3 (1972) 1, pp. 125134Satoh, K.: Transient thermal stresses of weld heat-affected zone by both-ends-fixed bar analogy. Trans. Jap. Weld. Soc.3 (1972) 1, pp. 125134Search in Google Scholar

35. Petit-Grostabussiat, S.; Taleb, L.; Jullien, J. F.: Experimental results on classical plasticity of steels subjected to structural transformations. Int. J. Plasticity20 (2004) 8, pp. 13711386, 10.1016/j.ijplas.2003.07.003Petit-Grostabussiat, S.; Taleb, L.; Jullien, J. F.: Experimental results on classical plasticity of steels subjected to structural transformations. Int. J. Plasticity20 (2004) 8, pp. 13711386, 10.1016/j.ijplas.2003.07.003Search in Google Scholar

36. Deng, D.: FEM prediction of welding residual stress and distortion in carbon steel considering phase transformation effects. Mater. Design30 (2009) 2, pp. 359366, 10.1016/j.matdes.2008.04.052Deng, D.: FEM prediction of welding residual stress and distortion in carbon steel considering phase transformation effects. Mater. Design30 (2009) 2, pp. 359366, 10.1016/j.matdes.2008.04.052Search in Google Scholar

37. Ju, W. Q.; Guillet, A.; Taleb, L.: Influence of the austenite grain size on the mechanical behavior of steels undergoing phase changes: analyses through Satoh tests. Proc. 2nd Int. Conf. on Distortion Engineering, 17–19.09.08, Bremen, H.-W. Zoch, Th.Luebben (Eds.), 2008, pp. 35562Ju, W. Q.; Guillet, A.; Taleb, L.: Influence of the austenite grain size on the mechanical behavior of steels undergoing phase changes: analyses through Satoh tests. Proc. 2nd Int. Conf. on Distortion Engineering, 17–19.09.08, Bremen, H.-W. Zoch, Th.Luebben (Eds.), 2008, pp. 35562Search in Google Scholar

Published Online: 2016-04-14
Published in Print: 2016-04-15

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