Simulations of Mechanical Response of Superelastic NiTi Helical Spring and its Relation to Fatigue Resistance

  • P. Sedlák
  • M. Frost
  • A. Kruisová
  • K. Hiřmanová
  • L. Heller
  • P. Šittner
Article

Abstract

Behavior of NiTi shape memory alloys under complex loading is still a subject of both experimental and theoretical investigations. One of the simplest geometries, in which the material is loaded in combined mode and which has also several practical applications, is a simple helical spring. In this contribution, mechanical response of NiTi superelastic spring is analyzed in detail by numerical simulation and the results are compared to experiments. The simulations show complex stress state, which develops during spring stretching. Analyzing fatigue tests with respect to simulated behavior allowed us to find relation between fatigue resistance and periodic changes in volume fraction of martensite induced by cyclic mechanical loading. The work also underlines an extension of the range of stroke amplitudes guaranteeing enhanced life performance of the spring when material transforms through the R-phase.

Keywords

helical spring non-proportional loading numerical modeling R-phase shape memory alloys 

Notes

Acknowledgments

We would like to thank to prof. T. Ben Zineb for providing access to CLCM computation cluster (Centre Lorrain de calcul haute performance en mécanique, France). This work has been conducted within the institutional project RVO: 61388998 of IT ASCR, v.v.i., and within the CENTEM project CZ.1.05/2.1.00/03.0088. The research has also been supported by the Grant Agency of the Czech Republic through grant projects Nos. 13-13616S, 14-28306P, and 14-15264S and by Academy of Sciences through internal project No. M100761203.

References

  1. 1.
    D.J. Hartl, D.C. Lagoudas, F.T. Calkins, and J.H. Mabe, Use of a Ni60Ti Shape Memory Alloy for Active Jet Engine Chevron Application: I. Thermomechanical Characterization, Smart Mater. Struct., 2009, 19, p 015020CrossRefGoogle Scholar
  2. 2.
    L.G. Machado and M.A. Savi, Medical Applications of Shape Memory Alloys, Braz. J. Med. Biol. Res., 2003, 36, p 683–691Google Scholar
  3. 3.
    D. Vokoun, D. Majtás, M. Frost, P. Sedlák, and P. Šittner, Shape Memory Hooks Employed in Fasteners, J. Mater. Eng. Perform., 2009, 18, p 706–710CrossRefGoogle Scholar
  4. 4.
    P. Sittner, L. Heller, J. Pilch et al., Roundrobin SMA Modeling, ESOMAT 2009: The 8th European Symposium on Martensitic Transformations, EDP Sciences, P. Sittner, L. Heller, and V. Paidar, Eds., 2009, p 08001Google Scholar
  5. 5.
    J. Arghavani, F. Auricchio, R. Naghdabadi, A. Reali, and S. Sohrabpour, A 3-D Phenomenological Constitutive Model for Shape Memory Alloys Under Multiaxial Loadings, Int. J. Plast., 2010, 26, p 976–991CrossRefGoogle Scholar
  6. 6.
    Y. Chemisky, A. Duval, E. Patoor, and T. Ben Zineb, Constitutive Model for Shape Memory Alloys Including Phase Transformation, Martensitic Reorientation and Twins Accommodation, Mech. Mater., 2011, 43, p 361–376CrossRefGoogle Scholar
  7. 7.
    D.C. Lagoudas, D.J. Hartl, Y. Chemisky, L.G. Machado, and P. Popov, Constitutive Model for the Numerical Analysis of Phase Transformation in Polycrystalline Shape Memory Alloys, Int. J. Plast., 2012, 32–33, p 155–183CrossRefGoogle Scholar
  8. 8.
    M. Panico and L.C. Brinson, A Three-Dimensional Phenomenological Model for Martensite Reorientation in Shape Memory Alloys, J. Mech. Phys. Solids, 2007, 55, p 2491–2511CrossRefGoogle Scholar
  9. 9.
    Z. Moumni, W. Zaki, and Q.S. Nguyen, Theoretical and Numerical Modeling of Solid-Solid Phase Change: Application to the Description of the Thermomechanical Behavior of Shape Memory Alloys, Int. J. Plast., 2008, 24, p 614–645CrossRefGoogle Scholar
  10. 10.
    A.F. Saleeb, S.A. Padula, and A.A. Kumar, A Multi-Axial, Multimechanism Based Constitutive Model for the Comprehensive Representation of the Evolutionary Response of SMAs Under General Thermomechanical Loading Conditions, Int. J. Plast., 2011, 27, p 655–687CrossRefGoogle Scholar
  11. 11.
    L. Saint-Sulpice, S. Arbab Chirani, and S. Calloch, A 3D Super-Elastic Model for Shape Memory Alloys Taking into Account Progressive Strain Under Cyclic Loadings, Mech. Mater., 2009, 41, p 12–26CrossRefGoogle Scholar
  12. 12.
    P. Sedlak, M. Frost, B. Benesova, P. Sittner, and T. Ben Zineb, Thermomechanical Model for NiTi-Based Shape Memory Alloys Including R-phase and Material Anisotropy Under Multi-Axial Loadings, Int. J. Plast., 2012, 39, p 132–151CrossRefGoogle Scholar
  13. 13.
    C. Liang, A Rogers Design of Shape Memory Alloy Actuators, J. Intell. Mater. Syst. Struct., 1997, 8, p 303–313CrossRefGoogle Scholar
  14. 14.
    Y. Toi, J.-B. Lee, and M. Taya, Finite Element Analysis of Superelastic, Large Deformation Behavior of Shape Memory Alloy Helical Springs, Comput. Struct., 2004, 82, p 1685–1693CrossRefGoogle Scholar
  15. 15.
    R. Mirzaeifar, R. DesRoches, and A. Yavari, A Combined Analytical, Numerical, and Experimental Study of Shape-Memory-Alloy Helical Springs, Int. J. Solids Struct., 2011, 48, p 611–624CrossRefGoogle Scholar
  16. 16.
    A.F. Saleeb, B. Dhakal, M.S. Hosseini, and S.A. Padula, Large Scale Simulation of NiTi Helical Spring Actuators Under Repeated Thermomechanical Cycles, Smart Mater. Struct., 2013, 22, p 094006CrossRefGoogle Scholar
  17. 17.
    K. Hirmanova, J. Pilch, J. Racek, L. Heller, P. Sittner, L. Recman, M. Petrenec, and P. Sedlak, Physical Simulation of the Random Failure of Implanted Braided NiTi Stents, J. Mater. Eng. Perform, accepted inGoogle Scholar
  18. 18.
    A. Sadjadpour and K. Bhattacharya, A Micromechanics-Inspired Constitutive Model for Shape-Memory Alloys: the One-Dimensional Case, Smart Mater. Struct., 2007, 16, p S51–S62CrossRefGoogle Scholar
  19. 19.
    C. Grabe and O.T. Bruhns, On the Viscous and Strain Rate Dependent Behavior of Polycrystalline NiTi, Int. J. Solids Struct., 2008, 45, p 1876–1895CrossRefGoogle Scholar
  20. 20.
    Q.S. Nguyen, Stability and Nonlinear Solid Mechanics, John Wiley, New York, 2000, p 17–40Google Scholar
  21. 21.
    K. Hackl and F.D. Fischer, On the Relation Between the Principle of Maximum Dissipation and Inelastic Evolution Given by Dissipation Potentials, Proc. R. Soc. A, 2008, 464, p 117–132CrossRefGoogle Scholar
  22. 22.
    M. Frost, B. Benesova, and P. Sedlak, A Microscopically Motivated Constitutive Model for Shape Memory Alloys: Formulation, Analysis and Computations, Math. Mech. Solids, accepted inGoogle Scholar
  23. 23.
    S. Qiu, B. Clausen, S.A. Padula, R.D. Noebe, and R. Vaidyanathan, On Elastic Moduli and Elastic Anisotropy in Polycrystalline Martensitic NiTi, Acta Mater., 2011, 59, p 5055–5066CrossRefGoogle Scholar
  24. 24.
    P. Sittner, M. Landa, P. Lukas, and V. Novak, R-phase Transformation Phenomena in Thermomechanically Loaded NiTi Polycrystals, Mech. Mater., 2006, 38, p 475–492CrossRefGoogle Scholar
  25. 25.
    K. Gall, H. Sehitoglu, Y.I. Chumlyakov, and I.V. Kireeva, Tension-Compression Asymmetry of the Stress-Strain Response in Aged Single Crystal and Polycrystalline NiTi, Acta Mater., 1999, 43, p 1203–1217CrossRefGoogle Scholar
  26. 26.
    V. Grolleau, H. Louche, V. Delobelle, A. Penin, G. Rio, Y. Liu, and D. Favier, Assessment of Tension-Compression Asymmetry of NiTi Using Circular Bulge Testing of Thin Plates, Scr. Mater., 2011, 65, p 347–350CrossRefGoogle Scholar
  27. 27.
    S.C. Mao, J.F. Luo, Z. Zhang, M.H. Wub, Y. Liu, and X.D. Han, EBSD Studies of the Stress-Induced B2-B19’ Martensitic Transformation in NiTi Tubes Under Uniaxial Tension and Compression, Acta Mater., 2010, 58, p 3357–3366CrossRefGoogle Scholar
  28. 28.
    Y.C. Shu and K. Bhattacharya, The Influence of Texture on the Shape-Memory Effect in Polycrystals, Acta Mater., 1998, 46, p 5457–5473CrossRefGoogle Scholar
  29. 29.
    B. Reedlunn, C.B. Churchill, E.E. Nelson, J.A. Shaw, and S.H. Daly, Tension, Compression, and Bending of Superelastic Shape Memory Alloy Tubes, J. Mech. Phys. Solids, 2014, 63, p 506–537Google Scholar
  30. 30.
    S. Miyazaki and K. Otsuka, Deformation and Transition Behavior Associated with the R-phase in Ti-Ni Alloys, Metall. Trans. A, 1986, 17A, p 53–63CrossRefGoogle Scholar
  31. 31.
    T. Atanacković and M. Achenbach, Moment-Curvature Relations for a Pseudoelastic Beam, Contin. Mech. Thermodyn., 1989, 1(1), p 73–80CrossRefGoogle Scholar
  32. 32.
  33. 33.
    R. Mirzaeifar, R. DesRoches, A. Yavari, and K. Gall, Coupled Thermo-Mechanical Analysis of Shape Memory Alloy Circular Bars in Pure Torsion, Int. J. Non-Linear Mech., 2012, 47, p 118–128CrossRefGoogle Scholar
  34. 34.
    M. Frost, P. Sedlak, A. Kruisova, and M. Landa, Simulations of Self-Expanding Braided Stent Using Macroscopic Model of NiTi Shape Memory Alloys Covering R-Phase, J. Mater. Eng. Perform., submitted toGoogle Scholar

Copyright information

© ASM International 2014

Authors and Affiliations

  • P. Sedlák
    • 1
    • 2
  • M. Frost
    • 1
    • 3
  • A. Kruisová
    • 1
  • K. Hiřmanová
    • 4
  • L. Heller
    • 4
  • P. Šittner
    • 4
  1. 1.Institute of Thermomechanics ASCRPragueCzech Republic
  2. 2.Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePragueCzech Republic
  3. 3.New Technologies - Research CenterUniversity of West BohemiaPlzeňCzech Republic
  4. 4.Department of Functional MaterialsInstitute of Physics ASCRPragueCzech Republic

Personalised recommendations