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Continuum Mechanics and Thermodynamics

, Volume 29, Issue 3, pp 805–834 | Cite as

Thermomechanical couplings in shape memory alloy materials

  • D. Soldatos
  • S. P. Triantafyllou
  • V. P. Panoskaltsis
Original Article
  • 164 Downloads

Abstract

In this work, we address several theoretical and computational issues which are related to the thermomechanical modeling of shape memory alloy materials. More specifically, in this paper we revisit a non-isothermal version of the theory of large deformation generalized plasticity which is suitable for describing the multiple and complex mechanisms occurring in these materials during phase transformations. We also discuss the computational implementation of a generalized plasticity-based constitutive model, and we demonstrate the ability of the theory in simulating the basic patterns of the experimentally observed behavior by a set of representative numerical examples.

Keywords

Shape memory alloys Shape memory effect Pseudoelasticity Generalized plasticity Invariance Balance energy equation Thermomechanical state equations Isothermal split Thermomechanical couplings 

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References

  1. 1.
    Agelet de Saracibar, C., Cervera, M., Chiumenti, M.: On the constitutive modeling of coupled thermomechanical phase-change problems. Int. J. Plast. 17, 1565–1622 (2001)CrossRefGoogle Scholar
  2. 2.
    Anand, L., Gurtin, M.E.: Thermal effects in the superelasticity of crystalline shape-memory materials. J. Mech. Phys. Solids 51, 1015–1058 (2003)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Andani, T.A., Alipour, A., Elahinia, M.: Coupled rate-dependent superelastic behavior of shape memory alloy bars induced by combined axial-torsional loading: a semi-analytic modeling. J. Intell. Mater. Syst. Struct. 24, 1995–2007 (2013)CrossRefGoogle Scholar
  4. 4.
    Armero, F., Simo, J.C.: A priori stability estimates and unconditionally stable product formula algorithms for non-linear coupled thermoplasticity. Int. J. Plast. 9, 149–182 (1993)CrossRefGoogle Scholar
  5. 5.
    Auricchio, F., Fugazza, D., DesRoches, R.: Rate-dependent thermo-mechanical modeling of superelastic shape-memory alloys for seismic applications. J. Intell. Mater. Syst. Struct. 19, 47–61 (2008)CrossRefGoogle Scholar
  6. 6.
    Ball, J.M., James, R.D.: Fine phase mixtures and minimizers of energy. Arch. Rat. Mech. Anal. 100, 13–52 (1987)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Boyd, J.G., Lagoudas, D.C.: A thermodynamic constitutive model for shape memory alloy materials. Part I. The monolithic shape memory alloy. Int. J. Plast. 12, 805–842 (1994)CrossRefGoogle Scholar
  8. 8.
    Boyd, J.C., Lagoudas, D.C.: Thermodynamical response of shape memory composites. J. Intell. Mater. Syst. Struct. 5, 333–346 (1994)CrossRefGoogle Scholar
  9. 9.
    Christ, D., Reese, S.: A finite element model for shape-memory alloys considering thermomechanical couplings at large strains. Int. J. Solids Struct. 46, 3694–3709 (2009)CrossRefGoogle Scholar
  10. 10.
    Earman, J.: Laws, symmetry and symmetry breaking: Invariance, conservation principles and objectivity. Philos. Sci. 71, 1227–1241 (2004)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fosdick, R.L., Serrin, J.: Global properties of continuum thermodynamic processes. Arch. Rat. Mech. Anal. 59, 97–109 (1975)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Ganghoffer, J.F.: Symmetries in mechanics: from field theories to master responses in the constitutive modeling of materials. In: Ganghoffer, J.F., Mladenov, I. (eds.) Similarity and Symmetry Methods, Applications in Elasticity and Mechanics of Materials, pp. 271–351. Springer, New York (2014)Google Scholar
  13. 13.
    Grabe, C., Bruhns, O.T.: On the viscous and strain rate dependent behavior of polycrystalline NiTi. Int. J. Solids Struct. 45, 1876–1895 (2008)CrossRefGoogle Scholar
  14. 14.
    Holzapfel, G.A.: Nonlinear Solid Mechanics. A Continuum Approach for Engineering. Wiley, West Sussex (2000)zbMATHGoogle Scholar
  15. 15.
    Huo, Y., Müller, I.: Nonequilibrium thermodynamics of pseudoelasticity. Cont. Mech. Thermodyn. 5, 163–204 (1993)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Kamlah, M., Haupt, P.: On the macroscopic description of stored energy and self heating during plastic deformation. Int. J. Plast. 13, 893–911 (1998)CrossRefGoogle Scholar
  17. 17.
    Lagoudas, D.C., Bo, Z., Qidwai, M.A.: A unified constitutive model for SMA and finite element analysis of active metal matrix composites. Mech. Compos. Mater. Struct. 3, 153–179 (1996)CrossRefGoogle Scholar
  18. 18.
    Leclercq, S., Lexcellent, C.: A general macroscopic description of the thermomechanical behavior of shape memory alloys. J. Mech. Phys. Solids 44, 953–980 (1996)ADSCrossRefGoogle Scholar
  19. 19.
    Leo, P.H., Shield, T.W., Bruno, O.P.: Transient heat transfer effects on the pseudoelastic behavior of shape-memory wires. Acta Metall. Mater. 41, 2477–2485 (1993)CrossRefGoogle Scholar
  20. 20.
    Lu, Z.K., Weng, G.J.: Martensitic transformation and stress–strain relations of shape-memory alloys. J. Mech. Phys. Solids 45, 1905–1921 (1997)ADSCrossRefGoogle Scholar
  21. 21.
    Lubliner, J.: Non-isothermal generalized plasticity. In: Bui, H.D., Nyugen, Q.S. (eds.) Thermomechanical Couplings in solids, pp. 121–133. North-Holland, Amsterdam (1987)Google Scholar
  22. 22.
    Lubliner, J., Auricchio, F.: Generalized plasticity and shape memory alloys. Int. J. Solids Struct. 33, 991–1004 (1996)CrossRefGoogle Scholar
  23. 23.
    Marsden, J.E., Hughes, T.J.R.: Mathematical Foundations of Elasticity. Dover Publications, New York (1994)zbMATHGoogle Scholar
  24. 24.
    McKelvey, A.L., Ritchie, R.O.: On the temperature dependence of the superelastic strength and the prediction of the theoretical uniaxial transformation strain in Nititol. Philos. Mag. 80, 1759–1768 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    Meyers, A., Xiao, H., Bruhns, O.: Elastic stress ratcheting and corotational stress rates. Tech. Mech. 23, 92–102 (2003)Google Scholar
  26. 26.
    Mirzaeifar, R., DesRoches, R., Yavari, A.: Analysis of the rate-dependent coupled thermomechanical response of shape memory alloy bars and wires in tension. Cont. Mech. Thermodyn. 23, 363–385 (2011)CrossRefGoogle Scholar
  27. 27.
    Morin, C., Moumni, Z., Zaki, W.: Thermomechanical coupling in shape memory alloys under cyclic loadings: experimental analysis and constitutive modeling. Int. J. Plast. 27, 1959–1980 (2011)CrossRefGoogle Scholar
  28. 28.
    Müller, I.: On the size of the hysteresis in pseudoelasticity. Cont. Mech. Thermodyn. 1, 125–142 (1989)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Müller, C., Bruhns, O.T.: A thermodynamic finite-strain model for pseudoelastic shape memory alloys. Int. J. Plast. 22, 1658–1682 (2006)CrossRefGoogle Scholar
  30. 30.
    Naghdi, P.M.: A critical review of the state of finite plasticity. Z. Angew. Math. Phys. 41, 315–387 (1990)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Olson, G.B., Cohen, M.: Kinetics of strain-induced martensitic nucleation. Metall. Trans. A 6A, 791–795 (1975)ADSCrossRefGoogle Scholar
  32. 32.
    Panoskaltsis, V.P.: Mechanics of shape memory alloys—constitutive modeling and numerical implications. In: Dr. Fernandes, F.M.B. (ed.) Shape Memory Alloys—Processing, Characterization and Applications. ISBN: 978-953-51-1084-2, In Tech doi: 10.5772/52228 (2013)
  33. 33.
    Panoskaltsis, V.P., Bahuguna, S., Soldatos, D.: On the thermomechanical modeling of shape memory alloys. Int. J. Non-Linear Mech. 39, 709–722 (2004)CrossRefGoogle Scholar
  34. 34.
    Panoskaltsis, V.P., Soldatos, D., Triantafyllou, S.P.: Generalized plasticity theory for phase transformations. In: Guagliano, M. (ed.) 11th International Conference on the Mechanical Behavior of Materials, Milano, Italy, 5–9 June 2011, pp. 3104–3108. Procedia Engineering (2011)Google Scholar
  35. 35.
    Panoskaltsis, V.P., Soldatos, D., Triantafyllou, S.P.: A new model for shape memory alloy materials under general states of deformation and temperature conditions. In: Boudouvis, A.G., Stavroulakis, G.E. (eds.) 7th GRACM International Congress on Computational Mechanics, Athens, Greece (2011)Google Scholar
  36. 36.
    Panoskaltsis, V.P., Polymenakos, L.C., Soldatos, D.: The concept of physical metric in the thermomechanical modeling of phase transformations with emphasis on shape memory alloy materials. ASME J. Eng. Mater. Technol. 135(2), 021016 (2013). doi: 10.1115/1.4023780 CrossRefGoogle Scholar
  37. 37.
    Panoskaltsis, V.P., Soldatos, D.: A phenomenological constitutive model of non-conventional elastic response. Int. J. Appl. Mech. 5, 1350035 (2013)CrossRefGoogle Scholar
  38. 38.
    Panoskaltsis, V.P., Soldatos, D., Triantafyllou, S.P.: On phase transformations in shape memory alloy materials and large deformation generalized plasticity. Cont. Mech. Thermodyn. 26, 811–831 (2014)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Panoskaltsis, V.P., Polymenakos, L.C., Soldatos, D.: Large deformation constitutive theory for a two-phase shape memory alloy. Eng. Trans. 62, 355–380 (2014)Google Scholar
  40. 40.
    Peyroux, R., Chrysochoos, A., Light, C., Löbel, M.: Thermomechanical couplings and pseudoelasticity of shape memory alloys. Int. J. Eng. Sci. 36, 489–509 (1998)CrossRefGoogle Scholar
  41. 41.
    Rahuadj, R., Ganghoffer, J.F., Cunat, C.: A thermodynamic approach with internal variables using Lagrange formalism. Part I: general framework. Mech. Res. Commun. 30, 109–117 (2003)CrossRefGoogle Scholar
  42. 42.
    Rahuadj, R., Ganghoffer, J.F., Cunat, C.: A thermodynamic approach with internal variables using Lagrange formalism. Part 2: continuous symmetries in the case of the time–temperature equivalence. Mech. Res. Commun. 30, 119–123 (2003)CrossRefGoogle Scholar
  43. 43.
    Raniecki, B., Lexcellent, C., Tanaka, K.: Thermodynamic models of pseudoelastic behaviour of shape memory alloys. Arch. Mech. 44(3), 261–284 (1992)MathSciNetzbMATHGoogle Scholar
  44. 44.
    Raniecki, B., Lexcellent, C.: RL models of pseudoelasticity and their specification for some shape memory solids. Eur. J. Mech. A Solids 12(1), 21–50 (1994)zbMATHGoogle Scholar
  45. 45.
    Raniecki, B., Lexcellent, C.: Thermodynamics of isotropic pseudoelasticity in shape memory alloys. Eur. J. Mech. A Solids 17, 185–205 (1998)CrossRefGoogle Scholar
  46. 46.
    Romero, I.: A characterization of conserved quantities in non-equilibrium thermodynamics. Entropy 15, 5580–5596 (2013)ADSCrossRefGoogle Scholar
  47. 47.
    Rosakis, P., Rosakis, A.J., Ravichandran, G., Hodowany, J.: A thermodynamic internal variable model for partition of plastic work into heat and stored energy in metals. J. Mech. Phys. Solids 48, 581–607 (2000)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    Simo, J.C., Miehe, C.: Associative couple thermoplasticity at finite strains: formulation, numerical analysis and implementation. Comput. Methods Appl. Mech. Eng. 98, 41–104 (1992)ADSCrossRefGoogle Scholar
  49. 49.
    Speicher, M., Hodgson, D.E., DesRoches, R., Leon, R.T.: Shape memory alloy tension/compression device for seismic retrofit of buildings. J. Mater. Eng. Perform. 18, 746–753 (2009)CrossRefGoogle Scholar
  50. 50.
    Smallman, R.E., Bishop, R.J.: Modern Physical Metallurgy and Materials Engineering, 6th edn. Butterworth-Heinemann, Stoneham (2000)Google Scholar
  51. 51.
    Stumpf, H., Hoppe, U.: The application of tensor analysis on manifolds to nonlinear continuum mechanics—invited survey article. Z. Agnew. Math. Mech. 77, 327–339 (1997)CrossRefGoogle Scholar
  52. 52.
    Thamburaja, P.: A finite-deformation-based theory for shape-memory alloys. Int. J. Plast. 26, 1195–1219 (2010)CrossRefGoogle Scholar
  53. 53.
    Yavari, A., Marsden, J.E., Ortiz, M.: On spatial and material covariant balance laws in elasticity. J. Math. Phys. 47, 1–53 (2006)MathSciNetCrossRefGoogle Scholar
  54. 54.
    Yin, Y.M., Weng, G.J.: Micromechanical study of thermomechanical characteristics of polycrystals shape-memory alloy films. Thin Solid Films 376, 198–207 (2000)ADSCrossRefGoogle Scholar
  55. 55.
    Yu, C., Kang, G., Kan, Q., Zhu, Y.: Rate dependent cyclic deformation of super-elastic NiTi shape memory alloy: thermo-mechanical coupled and physical mechanism-based constitutive model. Int. J. Plast. 72, 60–90 (2015)CrossRefGoogle Scholar
  56. 56.
    Zaki, W., Morin, C., Moumni, Z.: A simple 1D model with thermomechanical coupling for superelastic SMAs. In: IOP Conference Series: Materials Science and Engineering. 10, 021149 (2010)Google Scholar
  57. 57.
    Ziołkowski, A.: Three-dimensional phenomenological thermodynamical model of pseudoelasticity of shape memory alloys at finite strains. Cont. Mech. Thermodyn. 19, 379–398 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Civil EngineeringDemokritos University of ThraceXanthiGreece
  2. 2.Department of Civil EngineeringUniversity of NottinghamNottighamUK

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