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On stability of elastic domain during isothermal solid-solid phase transformation in a tube configuration

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Abstract

Under isothermal quasi-static stretching the phase transition of a superelastic NiTi tube involves the formation (during loading) and vanishing (in unloading) of a high strain (martensite) domain. The two events are accompanied by a rapid stress drop/rise due to the formation/vanishing of domain fronts. From a thermodynamic point of view, both are instability phenomena that occur once the system reaches its critical state. This paper investigates the stability of a shrinking cylindrical domain in a tube configuration during unloading. The energetics and thermodynamic driving force of the cylindrical domain are quantified by using an elastic inclusion model. It is demonstrated that the two domain fronts exhibit strong interaction when they come close to each other, which brings a peak in the total energy and a sign change in the thermodynamic driving force. It is proved that such domain front interaction plays an important role in controlling the stability of the domain and in the occurrence of stress jumps during domain vanishing. It is also shown that the process is governed by two nondimensional length scales (the normalized tube length and normalized wall-thickness) and that the length scale dependence of the critical domain length and stress jump for the domain vanishing can be quantified by the elastic inclusion model.

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References

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

    Google Scholar 

  2. Yoneyama, T., Miyazaki, S.: Shape Memory Alloys for Biomedical Applications. Woodhead Publishing Limited, Cambridge (2009)

    Book  Google Scholar 

  3. Siddons, D.J., Moon, J.R.: Tensile and compression performance of superelastic NiTi tubing. Mater. Sci. Tech. 17, 1073–1078 (2001)

    Google Scholar 

  4. Li, Z. Q., Sun, Q. P.: The initiation and growth of macroscopic martensite band in nano-grained NiTi microtube under tension. Int. J. Plast. 18, 1481–1498 (2002)

    Article  Google Scholar 

  5. Sun, Q. P., Li, Z. Q.: Phase transformation in superelastic NiTi polycrystalline micro-tubes under tension and torsion-from localization to homogeneous deformation. Int. J. Solids Struct. 39, 3797–3809 (2002)

    Article  Google Scholar 

  6. McNaney, J. M., Imbeni, V., Jung, Y., et al.: An experimental study of the superelastic effect in a shape-memory Nitinol alloy under biaxial loading. Mech. Mater. 35, 969–986 (2003)

    Article  Google Scholar 

  7. Matsui, R., Tobushi, H., Furuichi, Y., et al.: Tensile deformation and rotating-bending fatigue properties of a high elastic thin wire, a superelastic thin wire, and a superelastic thin tube of NiTi alloys. J. Engng. Mater. Tech. 126, 384–391 (2004)

    Article  Google Scholar 

  8. Ng, K. L., Sun, Q. P.: Stress-induced phase transformation and detwinning in NiTi polycrystalline shape memory alloy tubes. Mech. Mater. 38, 41–56 (2006)

    Article  Google Scholar 

  9. Feng P., Sun, Q. P.: In situ profilometry for non-uniform strain field measurement of NiTi shape memory alloy microtubing under complex stress states. Smart Mater. Struct. 16, 179–186 (2007)

    Article  Google Scholar 

  10. 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, 1568–1603 (2006)

    Article  Google Scholar 

  11. Favier, D., Louche, H., Schlosser, P., et al.: Homogeneous and heterogeneous deformation mechanisms in an austenitic polycrystalline Ti-50.8 at.% Ni thin tube under tension-investigation via temperature and strain fields measurements. Acta Mater. 55, 5310–5322 (2007)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  13. Grabe, C., Bruhns, O. T.: Tension/torsion tests of pseudoelastic, polycrystalline NiTi shape memory alloys under temperature control. Mater. Sci. Engng.: A 481–482, 109–113 (2008b)

    Article  Google Scholar 

  14. Grabe, C., Bruhns, O. T.: Path dependence and multiaxial behavior of a polycrystalline NiTi alloy within the pseudoelastic and pseudoplastic temperature regimes. Int. J. Plast. 25, 513–545 (2009)

    Article  MATH  Google Scholar 

  15. 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, 3045–3060 (2009)

    Article  MATH  Google Scholar 

  16. He, Y. J., Sun, Q. P.: Scaling relationship on macroscopic helical domains in NiTi tubes. Int. J. Solids Struct. 46, 4242–4251 (2009)

    Article  MATH  Google Scholar 

  17. Zhou, R. H.: Macroscopic domain pattern selectrion in shape memory alloys: effects of length and time scales. [Ph.D. Thesis]. The Hong Kong University of Science and Technology Hongkong China (2011)

  18. 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)

    Article  Google Scholar 

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

    Article  Google Scholar 

  20. Shield, T.W., Leo, P. H., Grebner, W. C. C.: Quasi-static extension of shape memory wires under constant load. Acta Mater. 45, 67–74 (1997)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Tobushi, H., Shimeno, Y., Hachisuka, T., et al.: Influence of strain rate on superelastic properties of TiNi shape memory alloy. Mech. Mater. 30, 141–150 (1998)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  25. Vitiello, A., Giorleo, G., Morace, R. E.: Analysis of thermomechanical behaviour of Nitinol wires with high strain rates. Smart Mater. Struct. 14, 215–221 (2005)

    Article  Google Scholar 

  26. Pieczyska, E. A., Gadaj, S. P., Nowacki, W. K., et al.: Phasetransformation fronts evolution for stress- and strain-controlled tension tests in TiNi shape memory alloy. Exp. Mech. 46, 531–542 (2006)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  28. Zhang, X. H., Feng, P., He, Y. J., et al.: Experimental study on rate dependence of macroscopic domain and stress hysteresis in NiTi shape memory alloy strips. Int. J. Mech. Sci. 52, 1660–1670 (2010)

    Article  Google Scholar 

  29. Sun, Q. P., Zhong, Z.: An inclusion theory for the propagation of martensite band in NiTi shape memory alloy wires under tension. Int. J. Plast. 16, 1169–1187 (2000)

    Article  MATH  Google Scholar 

  30. Zhong, Z., Sun, Q. P., Tong, P.: On the elastic axisymmetric deformation of a rod containing a single cylindrical inclusion. Int. J. Solids Struct. 37, 5934–5955 (2000)

    Article  Google Scholar 

  31. Yu, X. B., Sun, Q. P., Zhong, Z.: Effect of elastic matrix constraint on the tensile deformation of NiTi superelastic fiber. Int. J. Solids Struct. 41, 2659–2683 (2004)

    Article  MATH  Google Scholar 

  32. Mura, T.: Micromechanics of Defects in Solids, (2nd edn). Kluwer Academic Publishers, Dordrecht Netherlands Boston (1987)

    Book  Google Scholar 

  33. Landau, L. D., Lifshitz, E.M.: Theory of Elasticity. Pergamon, Oxford (1986)

    Google Scholar 

  34. Cook, R. D., Young, W. C.: Advanced Mechanics of Materials, (2nd edn). Prentice-Hall, Englewood Cliffs, NJ (1999).

    Google Scholar 

  35. Eshelby, J. D.: The force on an elastic singularity. Phil. Trans. Roy. Soc. London A 224, 87–112 (1951)

    Google Scholar 

  36. Eshelby, J. D.: Energy relations and the energy-momentum tensor in continuum mechanics. In: Kanninen MF, Adler WF, Rosefield AR, Jaffe RI (eds) Inelastic Behavior of Solids. McGraw-Hill. New York, 77–114 (1970)

    Google Scholar 

  37. Eshelby, J. D.: The elastic energy-momentum tensor. J. Elast. 5, 321–335 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  38. Knowles, J. K.: On the dissipation associated with equilibrium shocks in finite elasticity. J. Elast. 9, 131–158 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  39. Abeyaratne, R., Knowles, J. K.: On the driving traction acting on a surface of discontinuity in a continuum. J. Mech. Phys. Solids 40, 345–360 (1990)

    Article  MathSciNet  Google Scholar 

  40. Maugin, G. A.: Material Inhomogeneities in Elasticity, (1st edn). Chapman and Hall, London New York (1993)

    MATH  Google Scholar 

  41. Fried, E., Gurtin, M.E.: Coherent solid-state phase transitions with atomic diffusion: a thermomechanical treatment. J. Stat. Phys. 95, 1361–1427 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  42. Gurtin, M.E.: Configurational Forces as Basic Concept of Continuum Physics. Springer, New York (2000)

    Google Scholar 

  43. Mueller, R., Kolling, S., Gross, D.: On configurational forces in context of the finite element method. Int. J. Numer. Meth. Engng. 53, 1557–1574 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  44. Gross, D., Kolling, S., Mueller, R., et al.: Configurational forces and their application in solid mechanics. Eur. J. Mech. A/Solids 22, 669–692 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  45. Dong, L., Sun, Q. P.: On equilibrium domains in superelastic NiTi tubes — helix versus cylinder. Int. J. Solids Struct. 49, 1063–1076 (2012)

    Article  Google Scholar 

  46. Rice, J. R.: Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433–455 (1971)

    Article  MATH  Google Scholar 

  47. Cahn, J.W., Hilliard, J. E.: Free energy of a nonuniform system I. Interfacial free energy. J. Chem. Phys. 28, 258–267 (1958)

    Article  Google Scholar 

  48. Cahn, J. W.: On spinodal decomposition. Acta Metal. 9, 795–801 (1961)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China

    Liang Dong & Qing-Ping Sun

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  1. Liang Dong
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  2. Qing-Ping Sun
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Correspondence to Qing-Ping Sun.

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The project was supported by the Hong Kong Research Grants Council (GRF619511) and from the National Natural Science Foundation of China (11128204).

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Dong, L., Sun, QP. On stability of elastic domain during isothermal solid-solid phase transformation in a tube configuration. Acta Mech Sin 28, 683–694 (2012). https://doi.org/10.1007/s10409-012-0110-y

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  • DOI: https://doi.org/10.1007/s10409-012-0110-y

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