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Kinetic Monte Carlo Modeling of Martensitic Phase Transformation Dynamics

  • Ying ChenEmail author
Reference work entry
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Abstract

Martensitic transformation is, on the one hand, a pervasive deformation mechanism in both structural and functional materials, and on the other hand, a first-order phase transition that is diffusionless. The transformation from one crystal structure to another takes place by a volumetric change and a large shear. As a result, modeling of the martensitic transformation process requires an integration of thermodynamic, kinetic, and mechanical considerations. Moreover, the transformation process is intrinsically stochastic. Not only is there a competition between nucleation and propagation modes, but there are also competitions among different ways of transformation and different regions for transformation. In this chapter, an integrated thermodynamic and Kinetic Monte Carlo (KMC) treatment of martensitic transformation is presented. Modeling martensitic transformation as a unit process, the free energy function for potential transformation of each unit is determined. Stress and strain distributions are predicted by the Finite Element method after each unit transformation and are incorporated in the free energy function. A KMC algorithm that incorporates the free energy function in the rate formula is invoked to select a unit to transform and advance the time. The modeling formulation is described in detail, so is the simulation algorithm. Examples of transformation dynamics modeled by this method will be shown.

Notes

Acknowledgments

Y. Chen acknowledges the support from the US National Science Foundation with award number DMR-1352524.

References

  1. Bonnot E, Vives E, Mañosa L, Planes A, Romero R (2008) Acoustic emission and energy dissipation during front propagation in a stress-driven martensitic transition. Phys Rev B 78:094104ADSCrossRefGoogle Scholar
  2. Bulatov VV, Argon AS (1994a) a stochastic-model for continuum elastoplastic behavior.1. Numerical approach and strain localization. Model Simul Mater Sci Eng 2:167–184. https://doi.org/10.1088/0965-0393/2/2/001ADSCrossRefGoogle Scholar
  3. Bulatov VV, Argon AS (1994b) a stochastic-model for continuum elastoplastic behavior. 2. A study of the glass-transition and structural relaxation. Model Simul Mater Sci Eng 2:185–202. https://doi.org/10.1088/0965-0393/2/2/002ADSCrossRefGoogle Scholar
  4. Bulatov VV, Argon AS (1994c) a stochastic-model for continuum elastoplastic behavior. 3. Plasticity in ordered versus disordered solids. Model Simul Mater Sci Eng 2:203–222. https://doi.org/10.1088/0965-0393/2/2/003ADSCrossRefGoogle Scholar
  5. Chatterjee A, Voter AF (2010) Accurate acceleration of kinetic Monte Carlo simulations through the modification of rate constants. J Chem Phys 132:194101. https://doi.org/10.1063/1.3409606ADSCrossRefGoogle Scholar
  6. Chen Y, Schuh CA (2011) Size effects in shape memory alloy microwires. Acta Mater 59:537–553. https://doi.org/10.1016/j.actamat.2010.09.057CrossRefGoogle Scholar
  7. Chen Y, Schuh CA (2015) A coupled kinetic Monte Carlo–finite element mesoscale model for thermoelastic martensitic phase transformations in shape memory alloys. Acta Mater 83:431–447. https://doi.org/10.1016/j.actamat.2014.10.011CrossRefGoogle Scholar
  8. Gall K, Sehitoglu H (1999) The role of texture in tension–compression asymmetry in polycrystalline NiTi. Int J Plast 15:69–92. https://doi.org/10.1016/S0749-6419(98)00060-6CrossRefzbMATHGoogle Scholar
  9. Gall K, Lim TJ, McDowell DL, Sehitoglu H, Chumlyakov YI (2000) The role of intergranular constraint on the stress-induced martensitic transformation in textured polycrystalline NiTi. Int J Plast 16:1189–1214. https://doi.org/10.1016/s0749-6419(00)00007-3CrossRefzbMATHGoogle Scholar
  10. Guda Vishnu K, Strachan A (2012) Size effects in NiTi from density functional theory calculations. Phys Rev B 85:014114ADSCrossRefGoogle Scholar
  11. Homer ER, Schuh CA (2009) Mesoscale modeling of amorphous metals by shear transformation zone dynamics. Acta Mater 57:2823–2833. https://doi.org/10.1016/j.actamat.2009.02.035CrossRefGoogle Scholar
  12. Homer ER, Rodney D, Schuh CA (2010) Kinetic Monte Carlo study of activated states and correlated shear-transformation-zone activity during the deformation of an amorphous metal. Phys Rev B 81:064204 https://doi.org/10.1103/PhysRevB.81.064204
  13. Jaworski A, Ankem S (2005) The effect of α phase on the deformation mechanisms of β titanium alloys. J Mater Eng Perform 14:755. https://doi.org/10.1361/105994905x75565CrossRefGoogle Scholar
  14. Jin YM, Artemev A, Khachaturyan AG (2001) Three-dimensional phase field model of low-symmetry martensitic transformation in polycrystal: simulation of ζ′2 martensite in AuCd alloys. Acta Mater 49:2309–2320. https://doi.org/10.1016/S1359-6454(01)00108-2CrossRefGoogle Scholar
  15. Juan JS, No ML, Schuh CA (2009) Nanoscale shape-memory alloys for ultrahigh mechanical damping. Nat Nanotechnol 4:415–419ADSCrossRefGoogle Scholar
  16. Karaca HE, Karaman I, Basaran B, Lagoudas DC, Chumlyakov YI, Maier HJ (2007) On the stress-assisted magnetic-field-induced phase transformation in Ni2MnGa ferromagnetic shape memory alloys. Acta Mater 55:4253–4269. https://doi.org/10.1016/j.actamat.2007.03.025CrossRefGoogle Scholar
  17. Kastner O, Eggeler G, Weiss W, Ackland GJ (2011) Molecular dynamics simulation study of microstructure evolution during cyclic martensitic transformations. J Mech Phys Solids 59:1888–1908. https://doi.org/10.1016/j.jmps.2011.05.009ADSCrossRefzbMATHGoogle Scholar
  18. Kriven W (1995) Displacive transformations and their applications in structural ceramics. J Phys IV 5:C8-101–C8-110Google Scholar
  19. Lagoudas DC (2008) Shape memory alloys: modeling and engineering applications. Springer, BostonzbMATHGoogle Scholar
  20. Lagoudas D, Hartl D, Chemisky Y, Machado L, Popov P (2012) Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys. Int J Plast 32-33:155–183. https://doi.org/10.1016/j.ijplas.2011.10.009CrossRefGoogle Scholar
  21. Levitas VI, Levin VA, Zingerman KM, Freiman EI (2009) Displacive phase transitions at large strains: phase-field theory and simulations. Phys Rev Lett 103:025702ADSCrossRefGoogle Scholar
  22. Levitas VI, Roy AM, Preston DL (2013) Multiple twinning and variant-variant transformations in martensite: phase-field approach. Phys Rev B 88:054113ADSCrossRefGoogle Scholar
  23. Mamivand M, Asle Zaeem M, El Kadiri H, Chen L-Q (2013) Phase field modeling of the tetragonal-to-monoclinic phase transformation in zirconia. Acta Mater 61:5223–5235. https://doi.org/10.1016/j.actamat.2013.05.015CrossRefGoogle Scholar
  24. Mamivand M, Asle Zaeem M, El Kadiri H (2014) Phase field modeling of stress-induced tetragonal-to-monoclinic transformation in zirconia and its effect on transformation toughening. Acta Mater 64:208–219. https://doi.org/10.1016/j.actamat.2013.10.031CrossRefGoogle Scholar
  25. Manchiraju S, Anderson PM (2010) Coupling between martensitic phase transformations and plasticity: a microstructure-based finite element model. Int J Plast 26:1508–1526. https://doi.org/10.1016/j.ijplas.2010.01.009CrossRefzbMATHGoogle Scholar
  26. Manchiraju S, Gaydosh D, Benafan O, Noebe R, Vaidyanathan R, Anderson PM (2011) Thermal cycling and isothermal deformation response of polycrystalline NiTi: simulations vs. experiment. Acta Mater 59:5238–5249. https://doi.org/10.1016/j.actamat.2011.04.063CrossRefGoogle Scholar
  27. Ortín J, Planes A (1988) Thermodynamic analysis of thermal measurements in thermoelastic martensitic transformations. Acta Metall 36:1873–1889CrossRefGoogle Scholar
  28. Otsuka K, Wayman CM (1998) Shape memory materials. Cambridge University Press, CambridgeGoogle Scholar
  29. Otsuka K, Wayman CM, Nakai K, Sakamoto H, Shimizu K (1976) Superelasticity effects and stress-induced martensitic transformations in Cu-Al-Ni alloys. Acta Metall 24:207–226CrossRefGoogle Scholar
  30. Otsuka K, Sakamoto H, Shimizu K (1979) Successive stress-induced martensitic transformations and associated transformation pseudoelasticity in Cu-Al-Ni alloys. Acta Metall 27:585–601CrossRefGoogle Scholar
  31. Ozdemir N, Karaman I, Mara NA, Chumlyakov YI, Karaca HE (2012) Size effects in the superelastic response of Ni54Fe19Ga27 shape memory alloy pillars with a two stage martensitic transformation. Acta Mater 60:5670–5685. https://doi.org/10.1016/j.actamat.2012.06.035CrossRefGoogle Scholar
  32. Patoor E, El Amrani M, Eberhardt A, Berveiller M (1995) Determination of the origin for the dissymmetry observed between tensile and compression tests on shape memory alloys. J Phys IV 5:C2-495–C2-500Google Scholar
  33. Sedlák P, Seiner H, Landa M, Novák V, Sittner P, Mañosa L (2005) Elastic constants of bcc austenite and 2H orthorhombic martensite in CuAlNi shape memory alloy. Acta Mater 53:3643–3661CrossRefGoogle Scholar
  34. Tadaki T, Otsuka K, Shimizu K (1988) Shape memory alloys. Annu Rev Mater Sci 18:25–45ADSCrossRefGoogle Scholar
  35. Tao K, Choo H, Li H, Clausen B, Jin J-E, Lee Y-K (2007) Transformation-induced plasticity in an ultrafine-grained steel: an in situ neutron diffraction study. Appl Phys Lett 90:101911ADSCrossRefGoogle Scholar
  36. Tatar C, Kazanc S (2012) Investigation of the effect of pressure on thermodynamic properties and thermoelastic phase transformation of CuAlNi alloys: a molecular dynamics study. Curr Appl Phys 12:98–104. https://doi.org/10.1016/j.cap.2011.04.050ADSCrossRefGoogle Scholar
  37. Ueland SM, Chen Y, Schuh CA (2012) Oligocrystalline shape memory alloys. Adv Funct Mater 22:2094–2099. https://doi.org/10.1002/adfm.201103019CrossRefGoogle Scholar
  38. Van Humbeeck J, Delaey L (1981) The influence of strain-rate, amplitude and temperature on the hysteresis of a pseudoelastic Cu-Zn-Al single crystal. J Phys Colloq 42:C5-1007–C5-1011Google Scholar
  39. Wechsler MS, Lieberman DS, Read TA (1953) On the theory of the formation of martensite. Trans AIME J Met 197:1503–1515Google Scholar
  40. Wollants P, Roos JR, Delaey L (1993) Thermally- and stress-induced thermoelastic martensitic transformations in the reference frame of equilibrium thermodynamics. Prog Mater Sci 37:227–288CrossRefGoogle Scholar
  41. Wood AJM, Clyne TW (2006) Measurement and modelling of the nanoindentation response of shape memory alloys. Acta Mater 54:5607–5615. https://doi.org/10.1016/j.actamat.2006.08.013CrossRefGoogle Scholar
  42. Yin H, Yan Y, Huo Y, Sun Q (2013) Rate dependent damping of single crystal CuAlNi shape memory alloy. Mater Lett 109:287–290. https://doi.org/10.1016/j.matlet.2013.07.062CrossRefGoogle Scholar
  43. Zhong Y, Gall K, Zhu T (2012) Atomistic characterization of pseudoelasticity and shape memory in NiTi nanopillars. Acta Mater 60:6301–6311. https://doi.org/10.1016/j.actamat.2012.08.004CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringRensselaer Polytechnic InstituteTroyUSA

Section editors and affiliations

  • Ying Chen
    • 1
  • Eric Homer
    • 2
  • Christopher A. Schuh
    • 3
  1. 1.Department of Materials Science and EngineeringRensselaer Polytechnic InstituteTroyUSA
  2. 2.Department of Mechanical EngineeringBingham Young UniversityProvoUSA
  3. 3.Department of Materials Science and EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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