Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter June 11, 2013

Phase-field approach to martensitic phase transformations: Effect of martensite–martensite interface energy

  • Valery I. Levitas and Mahdi Javanbakht

Abstract

A generalization of the phase-field theory for multivariant martensitic phase transformations is suggested that allows one to vary martensite–martensite interface energy independent of energy for austenite–martensite interfaces. The finite element method is utilized to solve the coupled phase-field and elasticity equations. Width and energy of the austenite–martensite interfaces are determined. Splitting of the martensite–martensite interface into two austenite–martensite interfaces, leading to barrierless austenite nucleation, is obtained. The effect of the martensite–martensite interface energy and grain size on the stationary and non-stationary nanostructure inside the transforming grain embedded in the austenitic matrix is determined. Some nano-structures differ essentially from the prediction of crystallographic theory. Relationships between the number of twins in grain vs. grain size, and width of twin vs. its length are found. Two unexpected stress-relaxation mechanisms at the boundary of transforming grain are revealed.


* Correspondence address, Prof. Valery I. Levitas 2351 Howe Hall Department of Aerospace Engineering Iowa State University, Ames, Iowa 50011-2161, USA Tel.: +1 515 294 9691 Fax: +1 801 788 0026 E-mail:

Dedicated to Prof. F. D. Fischer on the occasion of his 70th birthday


References

[1] A.L.Roytburd, J.Slutsker: J. Appl. Phys.77 (1995) 27452750.10.1063/1.358744Search in Google Scholar

[2] H.Petryk, S.Stupkiewicz, G.Maciejewski: J. Mech. Phys. Solids.58 (2010) 373389.10.1016/j.jmps.2009.11.004Search in Google Scholar

[3] H.Petryk, S.Stupkiewicz: J. Mech. Phys. Solids.58 (2010) 390408.10.1016/j.jmps.2009.11.003Search in Google Scholar

[4] T.Waitz, T.Antretter, F.D.Fischer, H.P.Karnthaler: Mater. Sci. Tech.24 (2008) 934940.10.1179/174328408X302620Search in Google Scholar

[5] F.D.Fischer, T.Waitz, D.Vollath, N.K.Simha: Prog. Mater. Sci.53 (2008) 481.10.1016/j.pmatsci.2007.09.001Search in Google Scholar

[6] J.Slutsker, A.Artemev, A.L.Roytburd: Acta Mater.52 (2004) 1731.10.1016/j.actamat.2003.12.015Search in Google Scholar

[7] G.R.Barsch, J.A.Krumhansl: Phys. Rev. Lett.53 (1984) 1069.10.1103/PhysRevLett.53.1069Search in Google Scholar

[8] Y.M.Jin, A.Artemev, A.G.Khachaturyan: Acta Mater.49 (2001) 2309.10.1016/S1359-6454(01)00108-2Search in Google Scholar

[9] L.Q.Chen: Annu. Rev. Mater. Res.32 (2002) 113.10.1146/annurev.matsci.32.112001.132041Search in Google Scholar

[10] A.E.Jacobs, S.H.Curnoe, R.C.Desai: Phys. Rev. B68 (2003) 224104.10.1103/PhysRevB.68.224104Search in Google Scholar

[11] Y.Z.Wang, A.G.Khachaturyan: Mater. Sci. Eng. A55 (2006) 483.Search in Google Scholar

[12] W.Zhang, Y.M.Jin, A.G.Khachaturyan: Acta Mater.49 (2007) 565.10.1016/j.actamat.2006.08.050Search in Google Scholar

[13] T.Lookman, A.Saxena, R.C.Albers: Phys. Rev. Lett.100 (2008) 145504.10.1103/PhysRevLett.100.145504Search in Google Scholar PubMed

[14] V.I.Levitas, D.L.Preston: Phys. Rev. B66 (2002) 134206.10.1103/PhysRevB.66.134206Search in Google Scholar

[15] V.I.Levitas, D.L.Preston: Phys. Rev. B66 (2002) 134207.10.1103/PhysRevB.66.134207Search in Google Scholar

[16] V.I.Levitas, D.L.Preston, D.-W.Lee: Phys. Rev. B68 (2003) 134201.10.1103/PhysRevB.68.134201Search in Google Scholar

[17] K.Bhattacharya: Microstructure of Martensite, University Press Oxford, Oxford (2003).Search in Google Scholar

[18] V.I.Levitas, V.A.Levin, K.M.Zingerman, E.I.Freiman: Phys. Rev. Lett.103 (2009) 025702.10.1103/PhysRevLett.103.025702Search in Google Scholar PubMed

[19] A.V.Idesman, J.-Y.Cho, V.I.Levitas: Appl. Phys. Lett.93 (2008) 043102.10.1063/1.2955514Search in Google Scholar

[20] V.I.Levitas, D.-W.Lee: Phys. Rev. Lett.99 (2007) 245701.10.1103/PhysRevLett.99.245701Search in Google Scholar PubMed

[21] V.I.Levitas, D.-W.Lee, D.L.Preston: Int. J. Plasticity.26 (2010) 395422.10.1016/j.ijplas.2009.08.003Search in Google Scholar

[22] V.I.Levitas, M.Javanbakht: Phys. Rev. Lett.105 (2010) 165701.10.1103/PhysRevLett.105.165701Search in Google Scholar PubMed

[23] V.I.Levitas, K.Samani: Nature Communications2 (2011), 284.10.1038/ncomm1275Search in Google Scholar

[24] V.I.Levitas, A.V.Idesman, D.L.Preston: Phys. Rev. Lett.93 (2004) 105701.10.1103/PhysRevLett.93.105701Search in Google Scholar

[25] COMSOL, Inc.: website: www.comsol.com.Search in Google Scholar

[26] F.Falk: Arch. Mech.15 (1983) 6384.Search in Google Scholar

[27] H.L.Duan, J.Wang, B.L.Karihaloo: Adv. Appl. Mech.42 (2008) 1.10.1016/S0065-2156(08)00001-XSearch in Google Scholar

[28] Y.L.Li, S.Y.Hu, L.Q.Chen: J. Appl. Phys.97 (2005) 034112.10.1063/1.1849820Search in Google Scholar

[29] J.Hlinka, P.Márton: Phys. Rev. B74 (2006) 104104.10.1103/PhysRevB.74.104104Search in Google Scholar

[30] S.Rubini, P.Ballone: Phys. Rev. B48 (1993) 99111.10.1103/PhysRevB.48.99Search in Google Scholar

[31] V.I.Levitas, D.L.Preston: Phys. Lett. A343 (2005) 3239.10.1016/j.physleta.2005.05.034Search in Google Scholar

[32] H.Xu, S.Tan, I.Mueller: Z. Metallkd.89 (1998) 5964.Search in Google Scholar

[33] V.I.Levitas: Phys. Rev. Lett.95 (2005) 075701.10.1103/PhysRevLett.95.075701Search in Google Scholar PubMed

[34] V.I.Levitas, B.F.Henson, L.B.Smilowitz, B.W.Asay: Phys. Rev. Lett.92 (2004) 235702.10.1103/PhysRevLett.92.235702Search in Google Scholar PubMed

[35] T.Waitz, T.Antretter, F.D.Fischer, N.K.Simha, H.P.Karnthaler: J. Appl. Phys. Solids.55 (2007) 419444.10.1016/j.jmps.2006.06.006Search in Google Scholar

[36] L.C.Brinson, I.Schmidt, R.Lammering: J. Mech. Phys. Solids.52 (2004) 1549.10.1016/j.jmps.2004.01.001Search in Google Scholar

[37] M.Porta, T.Castan, P.Lloveras, T.Lookman, A.Saxena, S.R.Shenoy: Phys. Rev. B79 (2009) 214117.10.1103/PhysRevB.79.214117Search in Google Scholar

[38] Y.Ni, A.G.Khachaturyan: Nat. Mater.8 (2009) 410414.10.1038/nmat2431Search in Google Scholar PubMed

[39] B.Horovitz, G.R.Barsch, J.A.Krumhansl: Phys. Rev. B43 (1991) 1021.10.1103/PhysRevB.43.1021Search in Google Scholar

Received: 2010-11-24
Accepted: 2011-4-4
Published Online: 2013-06-11
Published in Print: 2011-06-01

© 2011, Carl Hanser Verlag, München

Downloaded on 29.3.2024 from https://www.degruyter.com/document/doi/10.3139/146.110529/pdf
Scroll to top button