Skip to main content

Advertisement

SpringerLink
Log in

Rate dependence of temperature fields and energy dissipations in non-static pseudoelasticity

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

The temperature fields and the energy dissipations of shape memory alloys during the stress-induced martensitic transformations are studied theoretically and experimentally. The effect of the loading rate is analyzed. It was found that the temperature field inside a shape memory alloy sample varies strongly in space and time. The increase rate of the temperature is given by the difference between the rate of the latent heat release and the rate of the heat convection and conduction. The notion and the rate dependence of the energy dissipation are discussed in connection with the stress–strain hysteresis, the entropy production, and the Clausius–Duhem inequality.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Otsuka K., Wayman C.M.: Shape Memory Materials. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  2. Delaey L., Krishnan R.V., Tas H., Warlimon H.: Thermoelasticity, pseudoelasticity and memory effects associated with martensitic transformations, part 1. Structural and microstructural changes associated with transformations. J. Mater. Sci. 9(9), 1521–1535 (1974)

    Article  ADS  Google Scholar 

  3. Bhattacharya, K. (eds): Microstructure of Martensite. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

  4. Müller I., Wilmanski K.: A model for phase-transition in pseudoelastic bodies. Nuovo Cimento B 57(2), 283–318 (1980)

    Article  ADS  Google Scholar 

  5. Van Humbeeck J., Delaey L.: The influence of strain-rate, amplitude and temperature on the hysteresis of a pseudoelastic Cu-Zn-Al single-crystal. J. Phys. Paris 42(Nc5), 1007–1011 (1981)

    Article  Google Scholar 

  6. Müller I., Xu H.: On the pseudo-elastic hysteresis. Acta Metall. Mater. 39(3), 263–271 (1991)

    Article  Google Scholar 

  7. Dutkiewicz J., Kato H., Miura S., Messerschmidt U., Bartsch M.: Structure changes during pseudoelastic deformation of CuAlMn single crystals. Acta Mater. 44(11), 4597–4609 (1996)

    Article  Google Scholar 

  8. Fang D.N., Lu W., Hwang K.C.: Pseudoelastic behavior of a CuAlNi single crystal under uniaxial loading. Metall. Mater. Trans. A 30(8), 1933–1943 (1999)

    Article  Google Scholar 

  9. Vivet A., Orgeas L., Lexcellent C., Favier D., Bernardini J.: Shear and tensile pseudoelastic behaviours of CuZnAl single crystals. Scripta Mater. 45(1), 33–40 (2001)

    Article  Google Scholar 

  10. Brinson L.C., Schmidt I., Lammering R.: Stress-induced transformation behavior of a polycrystalline NiTi shape memory alloy: micro and macromechanical investigations via in situ optical microscopy. J. Mech. Phys. Solids 52(7), 1549–1571 (2004)

    Article  ADS  MATH  Google Scholar 

  11. Grabe C., Bruhns O.T.: Tension/torsion tests of pseudoelastic, polycrystalline NiTi shape memory alloys under temperature control. Mater. Sci. Eng. Struct. 481, 109–113 (2008)

    Article  Google Scholar 

  12. Müller I.: On the size of the hysteresis in pseudoelasticity. Continuum Mech. Thermodyn. 1, 125–142 (1989)

    Article  ADS  Google Scholar 

  13. Peng C., Wang X.Y., Huo Y.Z.: Characteristics of stress-induced transformation and microstructure evolution in Cu-based SMA. Acta Mech. Solida Sin. 21(1), 1–8 (2008). doi:10.1007/s10338-008-0801-x

    Google Scholar 

  14. Peng C., Yan Y., Wang X.Y., Huo Y.Z.: Analysis of microstructure evolution during tensile stress induced martensitic transformations. ASME Conference Proceedings 2008(43314), 217–223 (2008). doi:10.1115/smasis2008-358

    Google Scholar 

  15. Feng P., Sun Q.P.: Experimental investigation on macroscopic domain formation and evolution in polycrystalline NiTi microtubing under mechanical force. J. Mech. Phys. Solids 54(8), 1568–1603 (2006). doi:10.1016/j.jmps.2006.02.005

    Article  ADS  Google Scholar 

  16. Shaw J.A., Churchill C.B., Iadicola M.A.: Tips and tricks for characterizing shape memory alloy wire: part 1—differential scanning calorimetry and basic phenomena. Exp. Tech. 32(5), 55–62 (2008)

    Article  Google Scholar 

  17. Churchill C.B., Shaw J.A., Iadicola M.A.: Tips and tricks for characterizing shape memory alloy wire: part 2-fundamental isothermal responses. Exp. Tech. 33(1), 51–62 (2009). doi:10.1111/j.1747-1567.2008.00460.x

    Article  Google Scholar 

  18. Churchill C.B., Shaw J.A., Iadicola M.A.: Tips and tricks for characterizing shape memory alloy wire: part 3-localization and propagation phenomena. Exp. Tech. 33(5), 70–78 (2009)

    Article  Google Scholar 

  19. Churchill C.B., Shaw J.A., Iadicola M.A.: Tips and tricks for characterizing shape memory alloy wire: part 4-thermo-mechanical coupling. Exp. Tech. 34(2), 63–80 (2010). doi:10.1111/j.1747-1567.2010.00619.x

    Article  Google Scholar 

  20. Van Humbeeck J.: Damping capacity of thermoelastic martensite in shape memory alloys. J. Alloy. Compound. 355(1–2), 58–64 (2003). doi:10.1016/s0925-8388(03)00268-8

    Article  Google Scholar 

  21. Achenbach M., Muller I.: Creep and yield in martensitic transformations. Ing. Arch. 53(2), 73–83 (1983)

    Article  MATH  Google Scholar 

  22. 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(8), 2477–2485 (1993)

    Article  Google Scholar 

  23. Shaw J.A., Kyriakides S.: Thermomechanical aspects of NiTi. J. Mech. Phys. Solids 43(8), 1243–1281 (1995)

    Article  ADS  Google Scholar 

  24. Shaw J.A., Kyriakides S.: On the nucleation and propagation of phase transformation fronts in a NiTi alloy. Acta Mater. 45(2), 683–700 (1997)

    Article  Google Scholar 

  25. Iadicola M.A., Shaw J.A.: Rate and thermal sensitivities of unstable transformation behavior in a shape memory alloy. Int. J. Plast. 20(4–5), 577–605 (2004)

    Article  MATH  Google Scholar 

  26. Schmidt I., Lammering R.: The damping behaviour of superelastic NiTi components. Mater. Sci. Eng. Struct. 378(1–2), 70–75 (2004)

    Article  Google Scholar 

  27. Nemat-Nasser S., Choi J.Y.: Strain rate dependence of deformation mechanisms in a Ni-Ti-Cr shape-memory alloy. Acta Mater. 53(2), 449–454 (2005)

    Article  Google Scholar 

  28. Pieczyska E., Gadaj S., Nowacki W.K., Hoshio K., Makino Y., Tobushi H.: Characteristics of energy storage and dissipation in TiNi shape memory alloy. Sci. Technol. Adv. Mater. 6(8), 889–894 (2005)

    Article  Google Scholar 

  29. Pieczyska E.A., Gadaj S.P., Nowacki W.K., Tobushi H.: Phase-transformation fronts evolution for stress- and strain-controlled tension tests in TiNi shape memory alloy. Exp. Mech. 46(4), 531–542 (2006)

    Article  Google Scholar 

  30. Adharapurapu R.R., Jiang F.C., Vecchio K.S., Gray G.T.: Response of NiTi shape memory alloy at high strain rate: a systematic investigation of temperature effects on tension-compression asymmetry. Acta Mater. 54(17), 4609–4620 (2006)

    Article  Google Scholar 

  31. Grabe C., Bruhns O.T.: On the viscous and strain rate dependent behavior of polycrystalline NiTi. Int. J. Solids Struct. 45(7–8), 1876–1895 (2008)

    Article  MATH  Google Scholar 

  32. He Y.J., Sun Q.P.: Rate-dependent domain spacing in a stretched NiTi strip. Int. J. Solids Struct. 47(20), 2775–2783 (2010)

    Article  MATH  Google Scholar 

  33. He Y.J., Yin H., Zhou R.H., Sun Q.P.: Ambient effect on damping peak of NiTi shape memory alloy. Mater. Lett. 64(13), 1483–1486 (2010)

    Article  Google Scholar 

  34. He Y.J., Sun Q.P.: On non-monotonic rate dependence of stress hysteresis of superelastic shape memory alloy bars. Int. J. Solids Struct. 48(11–12), 1688–1695 (2011)

    Article  MATH  Google Scholar 

  35. Zhang X.H., Feng P., He Y.J., Yu T.X., Sun Q.P.: Experimental study on rate dependence of macroscopic domain and stress hysteresis in NiTi shape memory alloy strips. Int. J. Mech. Sci. 52(12), 1660–1670 (2010). doi:10.1016/j.ijmecsci.2010.08.007

    Article  Google Scholar 

  36. He Y.J., Sun Q.P.: Effects of structural and material length scales on stress-induced martensite macro-domain patterns in tube configurations. Int. J. Solids Struct. 46(16), 3045–3060 (2009)

    Article  MATH  Google Scholar 

  37. Richter F., Kastner O., Eggeler G.: Implementation of the Müller-Achenbach-Seelecke model for shape memory alloys in ABAQUS. J. Mater. Eng. Perform. 18(5), 626–630 (2009). doi:10.1007/s11665-009-9483-x

    Article  Google Scholar 

  38. Young M.L., Wagner M.F.X., Frenzel J., Schmahl W.W., Eggeler G.: Phase volume fractions and strain measurements in an ultrafine-grained NiTi shape-memory alloy during tensile loading. Acta Mater. 58(7), 2344–2354 (2010). doi:10.1016/j.actamat.2009.12.021

    Article  Google Scholar 

  39. Shaw J.A.: Simulations of localized thermo-mechanical behavior in a NiTi shape memory alloy. Int. J. Plast. 16(5), 541–562 (2000). doi:10.1016/s0749-6419(99)00075-3

    Article  MATH  Google Scholar 

  40. Müller I.: Model for a body with shape-memory. Arch. Ration. Mech. Anal. 70(1), 61–77 (1979)

    Article  MATH  Google Scholar 

  41. Achenbach M., Muller I.: A model for shape memory. J. Phys. Paris 43(Nc-4), 163–167 (1982)

    Google Scholar 

  42. Achenbach M., Muller I.: Simulation of material behavior of alloys with shape memory. Arch Mech. 37(6), 573–585 (1985)

    Google Scholar 

  43. Huo Y., Muller I.: Nonequilibrium thermodynamics of pseudoelasticity. Continuum Mech. Thermodyn. 5(3), 163–204 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. Fu S., Huo Y., Muller I.: Thermodynamics of pseudoelasticity—an analytical approach. Acta Mech. 99(1–4), 1–19 (1993)

    Article  Google Scholar 

  45. Huo, Y., Müller, I., Seelecke, S.: Quasiplasticity and pseudoelasticity in shape memory alloys phase transitions and hysteresis. In: Lecture Notes in Mathematics, vol. 1584, pp. 87–146. Springer, Berlin (1994)

  46. Atanackovic T., Muller I.: A new form of the coherency energy in pseudoelasticity. Meccanica 30(5), 467–474 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  47. Müller I.: Thermodynamics of ideal pseudoelasticity. J. Phys. Iv 5(C2), 423–431 (1995)

    Google Scholar 

  48. Müller I., Seelecke S.: Thermodynamic aspects of shape memory alloys. Math. Comput. Model 34(12–13), 1307–1355 (2001)

    Article  MATH  Google Scholar 

  49. Abdullah N., Kastner O., Muller I., Musolff A., Xu H., Zak G.: Observations on CuAlNi single crystals. Int. J. Nonlinear Mech. 37(8), 1263–1274 (2002)

    Article  MATH  Google Scholar 

  50. Huo Y., Muller I.: Interfacial and inhomogeneity penalties in phase transitions. Continuum Mech. Thermodyn. 15(4), 395–407 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. Musolff A., Sahota H.: Phase transitions in the shape memory alloy CuAlNi. Continuum Mech Thermodyn. 16(6), 539–549 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. Seelecke S., Müller I.: Shape memory alloy actuators in smart structures: modelling and simulation. Appl. Mech. Rev. 57(1), 27–46 (2004)

    Article  ADS  Google Scholar 

  53. McCormick J., DesRoches R., Fugazza D., Auricchio F.: Seismic vibration control using superelastic shape memory alloys. J. Eng. Mater. Technol. 128(3), 294–301 (2006). doi:10.1115/1.2203109

    Article  Google Scholar 

  54. Brinson L.C., Schmidt I., Lammering R.: Micro and macromechanical investigations of CuAlNi single crystal and CuAlMnZn polycrystalline shape memory alloys. J. Intell. Mat. Syst. Str. 13(12), 761–772 (2002). doi:10.1177/1045389x02013012002

    Article  Google Scholar 

  55. Gastien R., Corbellani C.E., Sade M., Lovey F.C.: Thermal and pseudoelastic cycling in Cu-14.1Al-4.2Ni(wt%) single crystals. Acta Mater. 53(6), 1685–1691 (2005)

    Article  Google Scholar 

  56. Müller I.: Thermodynamics. Pitman Pub, London (1985)

    MATH  Google Scholar 

  57. Müller I.: Entropy and Energy: A Universal Competition. Springer, Berlin (2005)

    MATH  Google Scholar 

  58. Müller I., Müller W.: Fundamentals of Thermodynamics and Applications. Springer, Berlin (2009)

    MATH  Google Scholar 

  59. Ortin J., Planes A.: Thermodynamics of thermoelastic martensitic transformations. Acta Metall. 37(5), 1433–1441 (1989)

    Article  Google Scholar 

  60. Ortin J., Delaey L.: Hysteresis in shape-memory alloys. Int. J. Nonlinear Mech. 37(8), 1275–1281 (2002)

    Article  ADS  MATH  Google Scholar 

  61. Batra R.C.: Elements of Continuum Mechanics. Wiley, Reston (2006)

    Book  MATH  Google Scholar 

  62. Bruno O.P., Leo P.H., Reitich F.: Free-boundary conditions at austenite martensite interfaces. Phys. Rev. Lett. 74(5), 746–749 (1995)

    Article  ADS  Google Scholar 

  63. Holman J.P.: Heat Transfer. McGraw-Hill, Singapore (2010)

    Google Scholar 

  64. Wagner M.F.X., Schaefer A.: Macroscopic versus local strain rates during tensile testing of pseudoelastic NiTi. Scripta Mater. 63(8), 863–866 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Engineering Science, Fudan University, Shanghai, 200433, China

    Y. Yan & Y. Huo

  2. Department of Mechanics and Engineering, The Hong Kong University of Science and Technology, Hong Kong, China

    H. Yin & Q. P. Sun

Authors
  1. Y. Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Q. P. Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. Huo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. Huo.

Additional information

Communicated by Oliver Kastner.

Dedicated to Professor Ingo Müller on his 75th birthday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yan, Y., Yin, H., Sun, Q.P. et al. Rate dependence of temperature fields and energy dissipations in non-static pseudoelasticity. Continuum Mech. Thermodyn. 24, 675–695 (2012). https://doi.org/10.1007/s00161-012-0254-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-012-0254-9

Keywords

Search

Navigation