Journal of Materials Engineering and Performance

, Volume 24, Issue 10, pp 4096–4105 | Cite as

A Unit Cell Model for Simulating The Stress-Strain Response of Porous Shape Memory Alloys

Article

Abstract

Porous shape memory alloys are a new class of advanced materials with combined advantages of both shape memory alloys and porous materials. In order to manufacture a porous shape memory alloy with the desired mechanical properties, it is important to predict its mechanical properties before fabrication. In this paper, a new unit cell model is proposed to simulate the mechanical stress-strain response of porous shape memory alloys. Microplane theory is used to attribute mechanical constitutive relations of shape memory alloys to the bulk material, and the finite element method is employed for numerical simulations. The results show a good agreement with the experimental stress-strain behavior reported in the literature. The effect of pore volume fraction on the stress-strain response is also studied using the proposed approach. Random microstructures are generated in the FE model, and the effects of randomness on the mechanical behavior of porous shape memory alloys are also investigated for different values of pore volume fraction.

Keywords

constitutive modeling finite element modeling porous shape memory alloys stress-strain response superelasticity unit cell model 

Supplementary material

11665_2015_1653_MOESM1_ESM.mp4 (4.8 mb)
Supplementary material 1 (MP4 4881 kb)
11665_2015_1653_MOESM2_ESM.mp4 (14.6 mb)
Supplementary material 2 (MP4 14962 kb)
11665_2015_1653_MOESM3_ESM.mp4 (2.8 mb)
Supplementary material 3 (MP4 2880 kb)

References

  1. 1.
    P. Bassani et al., Porous NiTi Shape Memory Alloys Produced by SHS: Microstructure and Biocompatibility in Comparison with Ti2Ni and TiNi3, J. Mater. Sci. Mater. Med., 2014, 25(10), p 2277–2285CrossRefGoogle Scholar
  2. 2.
    M. Köhl et al., Characterization of Porous, Net-Shaped NiTi Alloy Regarding Its Damping and Energy-Absorbing Capacity, Mater. Sci. Eng. A, 2011, 528(6), p 2454–2462CrossRefGoogle Scholar
  3. 3.
    M. Elahinia, M.T. Andani, and C. Haberland, Shape Memory and Superelastic Alloys, High Temperature Materials and Mechanisms, ed. by Y. Bar-Cohen (Taylor & Francis, 2014)Google Scholar
  4. 4.
    C. Liang and C. Rogers, One-dimensional Thermomechanical Constitutive Relations for Shape Memory Materials, J. Intell. Mater. Syst. Struct., 1990, 1(2), p 207–234CrossRefGoogle Scholar
  5. 5.
    L. Brinson, One-dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-constant Material Functions and Redefined Martensite Internal Variable, J. Intell. Mater. Syst. Struct., 1993, 4(2), p 229–242CrossRefGoogle Scholar
  6. 6.
    K. Tanaka, F. Nishimura, and H. Tobushi, Phenomenological Analysis on Subloops in Shape Memory Alloys Due to Incomplete Transformations, J. Intell. Mater. Syst. Struct., 1994, 5(4), p 487–493CrossRefGoogle Scholar
  7. 7.
    J.G. Boyd and D.C. Lagoudas, A Thermodynamical Constitutive Model for Shape Memory Materials. Part I. The Monolithic Shape Memory Alloy, Int. J. Plast., 1996, 12(6), p 805–842CrossRefGoogle Scholar
  8. 8.
    C. Liang and C. Rogers, A Multi-dimensional Constitutive Model for Shape Memory Alloys, J. Eng. Math., 1992, 26(3), p 429–443CrossRefGoogle Scholar
  9. 9.
    E. Graesser and F. Cozzarelli, A Proposed Three-Dimensional Constitutive Model for Shape Memory Alloys, J. Intell. Mater. Syst. Struct., 1994, 5(1), p 78–89CrossRefGoogle Scholar
  10. 10.
    D.C. Lagoudas and P.B. Entchev, Modeling of Transformation-Induced Plasticity and Its Effect on the Behavior of Porous Shape Memory Alloys. Part I: Constitutive Model for Fully Dense SMAs, Mech. Mater., 2004, 36(9), p 865–892CrossRefGoogle Scholar
  11. 11.
    M. Panico and L. Brinson, A Three-Dimensional Phenomenological Model for Martensite Reorientation in Shape Memory Alloys, J. Mech. Phys. Solids, 2007, 55(11), p 2491–2511CrossRefGoogle Scholar
  12. 12.
    P. Popov and D.C. Lagoudas, A 3-D Constitutive Model for Shape Memory Alloys Incorporating Pseudoelasticity and Detwinning of Self-Accommodated Martensite, Int. J. Plast., 2007, 23(10), p 1679–1720CrossRefGoogle Scholar
  13. 13.
    J. Arghavani et al., A 3-D Phenomenological Constitutive Model for Shape Memory Alloys Under Multiaxial Loadings, Int. J. Plast., 2010, 26(7), p 976–991CrossRefGoogle Scholar
  14. 14.
    M. Brocca, L. Brinson, and Z. Bažant, Three-Dimensional Constitutive Model for Shape Memory Alloys Based on Microplane Model, J. Mech. Phys. Solids, 2002, 50(5), p 1051–1077CrossRefGoogle Scholar
  15. 15.
    M. Kadkhodaei et al., Microplane Modelling of Shape Memory Alloys, Phys. Scr., 2007, 2007(T129), p 329CrossRefGoogle Scholar
  16. 16.
    M. Kadkhodaei et al., Modeling of Shape Memory Alloys Based on Microplane Theory, J. Intell. Mater. Syst. Struct., 2008, 19(5), p 541–550CrossRefGoogle Scholar
  17. 17.
    R. Mehrabi and M. Kadkhodaei, 3D Phenomenological Constitutive Modeling of Shape Memory Alloys Based on Microplane Theory, Smart Mater. Struct., 2013, 22(2), p 025017CrossRefGoogle Scholar
  18. 18.
    R. Mehrabi, M. Kadkhodaei, and M. Elahinia, A Thermodynamically-Consistent Microplane Model for Shape Memory Alloys, Int. J. Solids Struct., 2014, 51(14), p 2666–2675CrossRefGoogle Scholar
  19. 19.
    R. Mehrabi et al., Microplane Modeling of Shape Memory Alloy Tubes Under Tension, Torsion, and Proportional Tension–Torsion Loading. J. Intell. Mater. Syst. Struct., 2014. doi:10.1177/1045389X14522532
  20. 20.
    R. Mehrabi et al., Anisotropic Behavior of Superelastic NiTi Shape Memory Alloys; An Experimental Investigation and Constitutive Modeling, Mech. Mater., 2014, 77, p 110–124CrossRefGoogle Scholar
  21. 21.
    R. Mehrabi, M. Kadkhodaei, and M. Elahinia, Constitutive Modeling of Tension-Torsion Coupling and Tension-Compression Asymmetry in NiTi Shape Memory Alloys, Smart Mater. Struct., 2014, 23(7), p 75021–75035CrossRefGoogle Scholar
  22. 22.
    M. Karamooz Ravari, M. Kadkhodaei, and A. Ghaei, A Microplane Constitutive Model for Shape Memory Alloys Considering Tension–Compression Asymmetry, Smart Mater. Struct., 2015, 24(7), p 075016CrossRefGoogle Scholar
  23. 23.
    N. Goncharuk et al., Characteristics of Superelasticity and Shape Memory Sintered Porous Titanium Nickelide. Poroshk. Metall. (USSR), 1992, (4): p. 56–60.Google Scholar
  24. 24.
    V. Itin et al., Mechanical Properties and Shape Memory of Porous Nitinol, Mater. Charact., 1994, 32(3), p 179–187CrossRefGoogle Scholar
  25. 25.
    I. Martynova et al., Shape Memory and Superelasticity Behaviour of Porous Ti-Ni Material, Le Journal de Physique IV, 1991, 1(C4), p C4-421–C4-426Google Scholar
  26. 26.
    O. Shevchenko et al., Obtaining Fe—Ni—Co—Ti Alloys Having a Thermoelastic Martensite Transformation, Powder Metall. Met. Ceram., 1997, 36(1–2), p 71–76CrossRefGoogle Scholar
  27. 27.
    B. Li, L. Rong, and Y. Li, Microstructure and Superelasticity of Porous NiTi Alloy, Sci. China Ser. E, 1999, 42(1), p 94–99CrossRefGoogle Scholar
  28. 28.
    B.-Y. Li et al., Transformation Behavior of Sintered Porous NiTi Alloys, Metall. Mater. Trans. A, 1999, 30(11), p 2753–2756CrossRefGoogle Scholar
  29. 29.
    P.B. Entchev and D.C. Lagoudas, Modeling Porous Shape Memory Alloys Using Micromechanical Averaging Techniques, Mech. Mater., 2002, 34(1), p 1–24CrossRefGoogle Scholar
  30. 30.
    Y. Zhao et al., Compression Behavior of Porous NiTi Shape Memory Alloy, Acta Mater., 2005, 53(2), p 337–343CrossRefGoogle Scholar
  31. 31.
    P.B. Entchev and D.C. Lagoudas, Modeling of Transformation-Induced Plasticity and Its Effect on the Behavior of Porous Shape Memory Alloys. Part II: Porous SMA Response, Mech. Mater., 2004, 36(9), p 893–913CrossRefGoogle Scholar
  32. 32.
    S. Nemat-Nasser et al., Experimental Characterization and Micromechanical Modeling of Superelastic Response of a Porous NiTi Shape-Memory Alloy, J. Mech. Phys. Solids, 2005, 53(10), p 2320–2346CrossRefGoogle Scholar
  33. 33.
    Y. Zhao and M. Taya, Analytical Modeling for Stress-Strain Curve of a Porous NiTi, J. Appl. Mech., 2007, 74(2), p 291CrossRefGoogle Scholar
  34. 34.
    Y. Toi and D. Choi, Constitutive Modeling of Porous Shape Memory Alloys Considering Strain Rate Effect, J. Comput. Sci. Technol., 2008, 2(4), p 511–522CrossRefGoogle Scholar
  35. 35.
    B. Liu et al., Comparison of Constitutive Models Using Different Yield Functions for Porous Shape Memory Alloy with Experimental Date, Struct. Longev., 2010, 4(3), p 113–120Google Scholar
  36. 36.
    Y. Zhu and G. Dui, A model considering hydrostatic stress of porous NiTi shape memory alloy, Acta Mech. Solida Sin., 2011, 24(4), p 289–298CrossRefGoogle Scholar
  37. 37.
    J.S. Olsen and Z.L. Zhang, Effect of Spherical Micro-voids in Shape Memory Alloys Subjected to Uniaxial Loading, Int. J. Solids Struct., 2012, 49(14), p 1947–1960CrossRefGoogle Scholar
  38. 38.
    B. Liu et al., A Constitutive Model of Porous SMAs Considering Tensile–Compressive Asymmetry Behaviors, J. Mech. Behav. Biomed. Mater., 2014, 32, p 185–191CrossRefGoogle Scholar
  39. 39.
    M.A. Qidwai et al., Modeling of the Thermomechanical Behavior of Porous Shape Memory Alloys, Int. J. Solids Struct., 2001, 38(48), p 8653–8671CrossRefGoogle Scholar
  40. 40.
    V.G. DeGiorgi and M.A. Qidwai, A Computational Mesoscale Evaluation of Material Characteristics of Porous Shape Memory Alloys, Smart Mater. Struct., 2002, 11(3), p 435CrossRefGoogle Scholar
  41. 41.
    M. Panico and L.C. Brinson, Computational Modeling of Porous Shape Memory Alloys, Int. J. Solids Struct., 2008, 45(21), p 5613–5626CrossRefGoogle Scholar
  42. 42.
    V. Sepe, S. Marfia, and F. Auricchio, Response of Porous SMA: A Micromechanical Study, Fract. Struct. Integr., 2014, 29, p 85–96Google Scholar
  43. 43.
    T.E. Sayed, E. Gürses, and A. Siddiq, A Phenomenological Two-Phase Constitutive Model for Porous Shape Memory Alloys, Comput. Mater. Sci., 2012, 60, p 44–52CrossRefGoogle Scholar
  44. 44.
    G. Maîtrejean, P. Terriault, and V. Brailovski, Density Dependence of the Superelastic Behavior of Porous Shape Memory Alloys: Representative Volume Element and Scaling Relation Approaches, Comput. Mater. Sci., 2013, 77, p 93–101CrossRefGoogle Scholar
  45. 45.
    G. Maîtrejean, P. Terriault, and V. Brailovski, Density Dependence of the Macroscale Superelastic Behavior of Porous Shape Memory Alloys: A Two-Dimensional Approach, Smart Mater. Res., 2013, 2013, p 1–13CrossRefGoogle Scholar
  46. 46.
    L.J. Gibson and M.F. Ashby, Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, 1999Google Scholar
  47. 47.
    B. Liu, G. Dui, and Y. Zhu, On Phase Transformation Behavior of Porous Shape Memory Alloys, J. Mech. Behav. Biomed. Mater., 2012, 5(1), p 9–15CrossRefGoogle Scholar
  48. 48.
    M. Ashrafi, et al., A Three-Dimensional Phenomenological Constitutive Model for Porous Shape Memory Alloys Including Plasticity Effects. J. Intell. Mater. Syst. Struct., 2015. doi:10.1177/1045389X15575085
  49. 49.
    M. Ashrafi et al., A 3-D Constitutive Model for Pressure-Dependent Phase Transformation of Porous Shape Memory Alloys, J. Mech. Behav. Biomed. Mater., 2015, 42, p 292–310CrossRefGoogle Scholar
  50. 50.
    I. Carol and Z.P. Bazant, Damage and Plasticity in Microplane Theory, Int. J. Solids Struct., 1997, 34(29), p 3807–3835CrossRefGoogle Scholar
  51. 51.
    L. Brinson and M. Huang, Simplifications and Comparisons of Shape Memory Alloy Constitutive Models, J. Intell. Mater. Syst. Struct., 1996, 7, p 108–114CrossRefGoogle Scholar
  52. 52.
    M.R. Karamooz Ravari and M. Kadkhodaei, A Computationally Efficient Modeling Approach for Predicting Mechanical Behavior of Cellular Lattice Structures, J. Mater. Eng. Perform., 2015, 24, p 245–252CrossRefGoogle Scholar
  53. 53.
    M.R. Karamooz Ravari et al., Numerical Investigation on Mechanical Properties of Cellular Lattice Structures Fabricated by Fused Deposition Modeling, Int. J. Mech. Sci., 2014, 88, p 154–161CrossRefGoogle Scholar
  54. 54.
    S. Li, Boundary Conditions for Unit Cells from Periodic Microstructures and Their Implications, Compos. Sci. Technol., 2008, 68(9), p 1962–1974CrossRefGoogle Scholar

Copyright information

© ASM International 2015

Authors and Affiliations

  • M. R. Karamooz Ravari
    • 1
  • M. Kadkhodaei
    • 1
  • A. Ghaei
    • 1
  1. 1.Department of Mechanical EngineeringIsfahan University of TechnologyIsfahanIran

Personalised recommendations