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Micromechanics of precipitated near-equiatomic Ni-rich NiTi shape memory alloys

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Abstract

The specific thermo-mechanical behavior of precipitated, near-equiatomic Ni-rich NiTi shape memory alloys, i.e., thermal actuation under stress and pseudoelasticity, are investigated via the finite element method. The deformation response of the material-at-large is simulated using a representative volume element, taking into account the structural effect of the precipitates, as well as the effect of the Ni-concentration gradient in the matrix. An existing rate-independent constitutive model, similar to the one employed to describe the matrix behavior, is calibrated based on the deformation response of the representative volume elements. The actuation and pseudoelastic response of the homogenized material are found to be very close to those of the representative volume elements. The obtained results reproduce and provide important insight into several of the experimentally observed precipitation-induced changes on the transformation characteristics of these materials.

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References

  1. Abaqus: Analysis User’s Manual. Dassault Systèmes of America Corp., Woodlands Hills, CA (2009)

  2. Azadi B., Rajapakse R.K.N.D., Maijer D.M.: One-dimensional thermomechanical model for dynamic pseudoelastic response of shape memory alloys. Smart Mater. Struct. 15, 429–442 (2003)

    Google Scholar 

  3. Benveniste Y.: A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech. Mater. 6, 147–157 (1987)

    Article  Google Scholar 

  4. Birman V.: Properties and response of composite material with spheroidal super elastic shape memory alloy inclusions subject to three dimensional stress state. J. Phys. D Appl. Phys. 43, 225402 (2010)

    Article  Google Scholar 

  5. Bo Z., Lagoudas D.C.: Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part I: theoretical derivations. Int. J. Eng. Sci. 37, 1089–1140 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bo Z., Lagoudas D.C., Miller D.: Material characterization of SMA actuators under nonproportional thermomechanical loading. J. Eng. Mater. Technol. Trans. ASME 121, 75–85 (1999)

    Article  Google Scholar 

  7. Boyd J.G., Lagoudas D.C.: Thermomechanical response of shape memory composites. J. Intell. Math. Syst. Struct. 5, 333–346 (1994)

    Article  Google Scholar 

  8. Boyd J.G., Lagoudas D.C.: A thermodynamical constitutive model for shape memory materials. Part II. The SMA composite material. Int. J. Plast. 12, 843–873 (1996)

    Article  MATH  Google Scholar 

  9. Collard C., Ben Zineb T.: Simulation of the effect of elastic precipitates in SMA materials based on a micromechanical model. Compos. Part B Eng. 43, 2560–2576 (2012)

    Article  Google Scholar 

  10. Collard C., Ben Zineb T., Patoor E., Ben Salah M.O.: Micromechanical analysis of precipitate effects on shape memory alloys behavior. Mater. Sci. Eng. A 481–482, 366–370 (2008)

    Article  Google Scholar 

  11. Eggeler G., Hornbogen E., Yawny A., Heckmann A., Wagner M.: Structural and functional fatigue of NiTi shape memory alloys. Mater. Sci. Eng. 378, 24–33 (2004)

    Article  Google Scholar 

  12. Eshelby J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. Ser. A 241, 376–396 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  13. Filip P., Mazanec K.: On precipitation kinetics in TiNi shape memory alloys. Scr. Mater. 45, 701–707 (2001)

    Article  Google Scholar 

  14. Frenzel J., George E.P., Dlouhy A., Somsen C., Wagner M.F.-X., Eggeler G.: Influence of Ni on martensitic phase transformations in NiTi shape memory alloys. Acta Mater. 58, 3444–3458 (2010)

    Article  Google Scholar 

  15. Gall K., Sehitoglu H., Chumlyakov Y., Kireeva I., Maier H.: The influence of aging on critical transformation stress levels and martensite start temperatures in NiTi. J. Eng. Mater. Technol. 121, 19–37 (1999)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  17. Hartl, D.J., Lagoudas D.C.: Aerospace applications of shape memory alloys. In: Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. SAGE, pp. 535–552 (2007)

  18. Hartl D.J., Lagoudas D.C., Calkins F.T., Mabe J.H.: Use of a Ni60Ti shape memory alloy for active jet engine chevron application: I. Thermomechanical characterization. Smart Mater. Struct. 19, 015020 (2010)

    Article  Google Scholar 

  19. Hartl D.J., Mooney J.T., Lagoudas D.C., Calkins F.T., Mabe J.H.: Use of a Ni60Ti shape memory alloy for active jet engine chevron application: II. Experimentally validated numerical analysis. Smart Mater. Struct. 19, 015021 (2010)

    Article  Google Scholar 

  20. Luo H.A., Weng G.J.: On Eshelby’s inclusion problem in a three-phase spherically concentric solid, and a modification of Mori–Tanaka’s method. Mech. Mater. 6, 347–361 (1987)

    Article  Google Scholar 

  21. Kanit T., Forest S., Galliet I., Mounoury V., Jeulin D.: Determination of the size of the representative volume element for random composites: Statistical and numerical approach. Int. J. Solids Struct. 40, 3647–3679 (2003)

    Article  MATH  Google Scholar 

  22. Khalil-Allafi, J., Dlouhy, A., Eggeler, G.: Ni4Ti3-precipitation during aging of NiTi shape memory alloys and its influence on martensitic phase transformations. Acta Mater. 50, 4255–4274 (2002)

    Google Scholar 

  23. Kröger A., Dziaszyk S., Frenzel J., Somsen C., Dlouhy A., Eggeler G.: Direct transmission electron microscopy observations of martensitic transformations in Ni-rich NiTi single crystals during in situ cooling and straining. Mater. Sci. Eng. A 481–482, 452–456 (2008)

    Article  Google Scholar 

  24. Lagoudas D., Bo Z., Qidwai M.A.: A unified thermodynamic constitutive model for sma and finite element analysis of active metal matrix composites. Mech. Comput. Mater. Struct. 4, 153–179 (1996)

    Article  Google Scholar 

  25. Lagoudas, D.C. (eds): Shape Memory Alloys: Modelling and Engineering Applications. Springer, New-York (2008)

    Google Scholar 

  26. Lagoudas D.C., Hartl D., Chemisky Y., Machado L., Popov P.: Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys. Int. J. Plast. 32–33, 155–183 (2012)

    Article  Google Scholar 

  27. Lejeunes, S., Bourgeois, S.: Abaqus plugins for generating boundary conditions for homogenization problems (2010)

  28. Lester B.T., Chemisky Y., Lagoudas D.C.: Transformation characteristics of shape memory alloy composites. Smart Mater. Struct. 20, 094002 (2011)

    Article  Google Scholar 

  29. Li S., Wongsto A.: Unit cells for micromechanical analyses of particle-reinforced composites. Mech. Mater. 36, 543–572 (2004)

    Article  Google Scholar 

  30. Lu Z., Weng G.: Martensitic transformation and stress–strain relations of shape-memory alloys. J. Mech. Phys. Solids 45, 1905–1928 (1997)

    Article  Google Scholar 

  31. Lu Z., Weng G.: A self-consistent model for the stress–strain behavior of shape-memory alloy polycrystals. Acta Mater. 46, 5423–5433 (1998)

    Article  Google Scholar 

  32. Michutta J., Somsen C., Yawny A., Dlouhy A., Eggeler G.: Elementary martensitic transformation processes in Ni-rich NiTi single crystals with Ni4Ti3 precipitates. Acta Mater. 54, 3525–3542 (2006)

    Article  Google Scholar 

  33. 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)

    Article  MATH  Google Scholar 

  34. Otsuka K., Ren X.: Physical metallurgy of Ti-Ni-based shape memory alloys. Prog. Mater. Sci. 50, 511–678 (2005)

    Article  Google Scholar 

  35. Petrini L., Migliavacca F.: Biomedical applications of shape memory alloys. J. Metall. 2011, 501483 (2011)

    Article  Google Scholar 

  36. Prahlad H., Chopra I.: Development of a strain-rate dependent model for uniaxial loading of SMA wires. J. Intel. Mater. Syst. Struct. 14, 429–442 (2003)

    Article  Google Scholar 

  37. Rahim M., Frenzel J., Frotscher M., Pfetzing-Micklich J., Steegmüller R., Wohlschlgel M., Mughrabi H., Eggeler G.: Impurity levels and fatigue lives of pseudoelastic NiTi shape memory alloys. Acta Mater. 61, 3667–3686 (2013)

    Article  Google Scholar 

  38. Schryvers D., Tirry W., Yang Z.: Measuring strain fields and concentration gradients around Ni4Ti3 precipitates. Mater. Sci. Eng. A 438, 485–488 (2006)

    Article  Google Scholar 

  39. Shaw J.A., Kyriakides S.: A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loadings. J. Mech. Phys. Solids 43, 1243–1281 (1995)

    Article  Google Scholar 

  40. Song G., Ma N., Li H.-N.: Application of shape memory alloys in civil structures. Eng. Struct. 28, 1266–1274 (2006)

    Article  Google Scholar 

  41. Tanaka K., Mori T.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. Mater. 21, 571–574 (1970)

    Google Scholar 

  42. Tang W., Sundman B., Sandström R., Qiu C.: New modelling of the B2 phase and its associated martensitic transformation in the Ti-Ni system. Acta Mater. 47, 3457–3468 (1999)

    Article  Google Scholar 

  43. Wagner M., Windl W.: Elastic anisotropy of Ni4Ti3 from first principles. Scr. Mater. 60, 207–210 (2009)

    Article  Google Scholar 

  44. Weng G.J.: Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int. J. Eng. Sci. 22, 845–856 (1984)

    Article  MATH  Google Scholar 

  45. Zhou N., Shen C., Wagner M.-X., Eggeler G., Mills M., Wang Y.: Effect of Ni4Ti3 precipitation on martensitic transformation in Ti-Ni. Acta Mater. 58, 6685–6694 (2010)

    Article  Google Scholar 

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Baxevanis, T., Cox, A. & Lagoudas, D.C. Micromechanics of precipitated near-equiatomic Ni-rich NiTi shape memory alloys. Acta Mech 225, 1167–1185 (2014). https://doi.org/10.1007/s00707-013-1071-3

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  • DOI: https://doi.org/10.1007/s00707-013-1071-3

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