Skip to main content

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 163))

  • 1911 Accesses

Abstract

In this chapter we present MD simulations of martensitic phase transformations in 2D Lennard–Jones (L–J) crystals. A binary L–J potential is used to describe a square-to-hexagonal transformation by shear-and-shuffle processes. The model material is capable of the complex thermo-mechanical coupling present in SMA—pseudo-plasticity, pseudo-elasticity and the shape memory effect [1, 2].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. O. Kastner, Molecular dynamics of a 2D model of the shape memory effect. Part II: thermodynamics of a small system. Continuum Mech. Therm. 18(1–2), 63–81 (2006)

    Google Scholar 

  2. O. Kastner, G. Eggeler, Molecular dynamics simulations of the shape memory effect in a chain of Lennard-Jones crystals. MMMS 6(1), 78–91 (2010)

    Google Scholar 

  3. O. Kastner, Molecular dynamics of a 2D model of the shape memory effect. Part I: model and simulations. Continuum Mech. Therm. 15(5), 487–502 (2003)

    Google Scholar 

  4. U. Pinsook, G.J. Ackland, Simulation of martensitic microstructural evolution in zirconium. Phys. Rev. B 58(17), 11252 (1998)

    Google Scholar 

  5. U. Pinsook, G.J. Ackland, Atomistic simulation of shear in a martensitic twinned microstructure. Phys. Rev. B 62(9), 5427–5434 (2000)

    Google Scholar 

  6. T. Suzuki, M. Shimono, A simple model for martensitic transformations. J. Phy. IV France 112, 129–132 (2003)

    Article  Google Scholar 

  7. X.D. Ding, T. Suzuki, X.B. Ren, J. Sun, K. Otsuka, Precursors to stress-induced martensitic transformations and associated superelasticity: molecular dynamics simulations and an analytical theory. Phys. Rev. B 74, 104–111 (2006)

    Google Scholar 

  8. F.E. Hildebrand, R. Abeyaratne, An atomistic investigation of the kinetics of detwinning. J. Mech. Phys. Solids 56(4), 1296–1319 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. R.S. Elliott, J.A. Shaw, N. Triantafyllidis, Stability of thermally-induced martensitic transformations in bi-atomic crystals. J. Mech. Phys. Solids 50, 2463–2493 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. M. Born, K. Huang, Dynamical Theory of Crystal Lattices. International Series of Monographs on Physics (Oxford University Press, New York, 1954)

    Google Scholar 

  11. D.C. Swift, G.J. Ackland, A. Hauer, G.A. Kyrala, First principles equations of state for simulations of shock waves. Phys. Rev. B 64, 214107 (2001)

    Article  ADS  Google Scholar 

  12. J. Solyom, Fundamentals of the Physics of Solids, Volume 1: Structure and Dynamics (Springer, Berlin, 2007)

    Google Scholar 

  13. E.A. Mastny, J.J. de Pablo, Melting line of the Lennard-Jones system. J. Chem. Phys. 127, 104504 (2007)

    Google Scholar 

  14. I. Müller, P. Villaggio, A model for an elastic-plastic body. Arch. Rational. Mech. Anal. 65(1), 25–46 (1977)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. G. Puglisi, L. Truskinovsky, Mechanics of a discrete chain with bi-stable elements. J. Mech. Phys. Solids 48(1), 1–27 (January 2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. I. Müller, A model for a body with shape-memory. Arch. Ration. Mech. An. 70, 61–77 (1979)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. A. Vainchtein, T. Healey, P. Rosakis, L. Truskinovsky, The role of the spinodal region in one-dimensional martensitic phase transitions. Phys. D 115(1–2), 29–48 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  19. I. Müller, S. Seelecke, Thermodynamic aspects of shape memory alloys. Math. Comput. Model. 34, 1307–1355 (2001)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kastner, O. (2012). 2D Model Material. In: First Principles Modelling of Shape Memory Alloys. Springer Series in Materials Science, vol 163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28619-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28619-3_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28618-6

  • Online ISBN: 978-3-642-28619-3

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics