Nanoscale Phase Field Modeling and Simulations of Martensitic Phase Transformations and Twinning at Finite Strains

  • Anup BasakEmail author
  • Valery I. LevitasEmail author
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)


A thermodynamically consistent phase field approach to martensitic phase transformations for a system with austenite and two martensitic variants has been developed. The model considers two order parameters, describing austenite \( \leftrightarrow \) martensite and variant \( \leftrightarrow \) variant transformations, respectively. The coexistence of three phases at a single material point are consistently penalized. Twinning in the nanoscale sample was studied for two different kinematic models (KMs) for the transformation stretch tensor \( {\mathbf{U}}_{t} \). In KM-I, \( {\mathbf{U}}_{t} \) is taken as a linear combination of the Bain strains, and in KM-II, \( {\mathbf{U}}_{t} \) is an exponential of the logarithm of the Bain stretch tensors. For these two KMs and for an additional model based on simple shear, analytical solutions for elastic stresses within a variant-variant boundary in an infinite twinned sample are presented. The results can be easily generalized for an arbitrary number of variants. They are crucial for further development of phase field approaches to multivariant martensitic transformations coupled to mechanics.


Phase field Martensitic transformation Twinning Interfacial stress Finite strain 



The authors gratefully acknowledge the supports from NSF (CMMI-1536925 and DMR-1434613), ARO (W911NF-12-1-0340), and Iowa State University (Schafer 2050 Challenge Professorship and Vance Coffman Faculty Chair Professorship). Simulations were performed at Extreme Science and Engineering Discovery Environment (XSEDE), allocations TG-MSS140033 and MSS170015.


  1. 1.
    Jin YM, Artemev A, Khachaturyan AG (2001) Acta Mater 49:2309–2320CrossRefGoogle Scholar
  2. 2.
    Chen LQ (2002) Annu Rev Mater Res 32:113–140CrossRefGoogle Scholar
  3. 3.
    Levitas VI, Preston DL (2002) Phys Rev B 66:134207CrossRefGoogle Scholar
  4. 4.
    Clayton JD, Knap J (2011) Physica D 240:841–858CrossRefGoogle Scholar
  5. 5.
    Hildebrand FE, Miehe C (2012) Philos Mag 92:1–41CrossRefGoogle Scholar
  6. 6.
    Levitas VI, Roy AM, Preston DL (2013) Phys Rev B 88:054113CrossRefGoogle Scholar
  7. 7.
    Levitas VI (2014) J Mech Phys Solids 70:154–189CrossRefGoogle Scholar
  8. 8.
    Levitas VI, Roy AM (2015) Phys Rev B 91:174109CrossRefGoogle Scholar
  9. 9.
    Tůma K, Stupkiewicz S, Petryk H (2016) J Mech Phys Solids 95:284–307CrossRefGoogle Scholar
  10. 10.
    Steinbach I (2009) Model Simul Mater Sci Eng 17:073001CrossRefGoogle Scholar
  11. 11.
    Jog CS (2007) Foundations and applications of mechanics. Volume I: continuum mechanics. Narosa, New DelhiGoogle Scholar
  12. 12.
    Bhattacharya K (2004) Microstructure of martensite: why it forms and how it gives rise to the shape-memory effect. Oxford University Press, OxfordGoogle Scholar
  13. 13.
    Bangerth W, Davydov D, Heister T, Heltai L, Kanschat G, Kronbichler M, Maier M, Turcksin B, Wells D (2016) J Numer Math 24 version 8.4Google Scholar
  14. 14.
    Basak A, Levitas VI (2017) Acta Mater 139:174–187CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringIowa State UniversityAmesUSA
  2. 2.Departments of Aerospace Engineering, Mechanical Engineering, and Material Science and EngineeringIowa State UniversityAmesUSA
  3. 3.Ames Laboratory, Division of Materials Science and EngineeringAmesUSA

Personalised recommendations