An Investigation into the Simple Tensile Test of SMA Wires Considering Stress Concentration of Grippers


To simulate the behaviors of shape memory alloy (SMA) wires, several 1-D constitutive models have been proposed most of which assume a homogeneous behavior for the material. However, stress concentration caused by the grippers would lead to inhomogeneous behavior of an SMA during the tensile test. In this paper, effect of stress concentration caused by the grippers is studied on the stress-strain response of an SMA wire during tension. At first, a relation for minimum required gripping force is provided. Then the extent of influence of stress concentration is estimated, and a minimum length is proposed for the test sample of ordinary materials. Using this result and by finite element simulating the effect of stress concentration caused by grippers, a minimum length for an SMA tensile test sample is proposed. By considering this minimum length, it is possible to simulate the material behaviors neglecting the stress concentration caused by grippers and to determine material parameters with a reasonable precision using a constitutive model in which inhomogeneous behaviors are not taken into account. A simple tensile test is performed on an SMA wire whose length is more than the recommended number, and a good agreement is seen between predicted stress-strain curve based on uniform stress distribution throughout the wire and the obtained experimental results.

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\( C_{\text{M}} , C_{\text{A}} \) :

Slopes of the transformation strips in the SMA phase diagram (MPaK−1)

\( d \) :

Diameter of the wire (mm)

\( E \) :

Young’s modulus (GPa)

\( E_{\text{A}} \) :

Austenite Young’s modulus (GPa)

\( E_{\text{M}} \) :

Martensite Young’s modulus (GPa)

\( F \) :

Tensile force (N)

\( G \) :

Gripper length (mm)

\( N \) :

Fastening force of grippers (N)

\( P \) :

Tensile stress (Pa)

\( S \) :

The extent of influence of stress concentration

\( S_{\text{y}} \) :

Yield stress (Pa)

\( \upvarepsilon^{\text{el}} \) :

Elastic strain

\( \upvarepsilon^{\text{tr}} \) :

Transformation-induced strain

\( \upvarepsilon_{\text{l}} \) :

Maximum recoverable strain

\( \upxi \) :

Martensite volume fraction

\( \upxi_{\text{T}} \) :

Twinned martensite volume fraction

\( \upxi_{\text{s}} \) :

Detwinned martensite volume fraction

\( \upsigma_{\text{s}}^{\text{cr}} \), \( \upsigma_{\text{f}}^{\text{cr}} \) :

Critical stresses for the start and end of detwinning, respectively, MPa

\( {{\upmu }} \) :

Coefficient of friction

\( \upnu \) :

Poisson ratio


  1. 1.

    Standard Test Methods for Tension Testing of Metallic Materials, ASTM E8M-04, American Society for Testing and Materials, 2008

  2. 2.

    L.C. Brinson, One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermo Mechanical Derivation with Non-constant Material Functions and Redefined Martensite Internal Variable, J. Intell. Mater. Syst. Struct., 1993, 4(2), p 229–242

    Article  Google Scholar 

  3. 3.

    F. Auricchio and J. Lubliner, A Uniaxial Model for Shape-Memory Alloys, Int. J. Solids Struct., 1997, 34(27), p 3601–3618

    Article  Google Scholar 

  4. 4.

    R. Wang, C. Cho, C. Kim, and Q. Pan, A Proposed Phenomenological Model for Shape Memory Alloys, J. Smart Mater. Struct., 2006, 15(2), p 393–400

    Article  Google Scholar 

  5. 5.

    M. Frost, P. Sedlak, M. Sippola, and P. Sittner, Thermomechanical Model for NiTi Shape Memory Wires, J. Smart Mater. Struct., 2010, 19(9), p 353–368

    Article  Google Scholar 

  6. 6.

    J.A. Shaw, Simulations of Localized Thermo-Mechanical Behavior in a NiTi Shape Memory Alloy, Int. J. Plasticity, 2000, 16, p 541–562

    Article  Google Scholar 

  7. 7.

    J.A. Shaw, C.B. Churchill, and M.A. Iadicola, Tips and Tricks for Characterizing Shape Memory Alloy Wire: Part 3-Localization and Propagation Phenomena, Exp. Tech., 2009, 33(5), p 70–78

    Article  Google Scholar 

  8. 8.

    I. Mulier and X.U. Huibin, On the Pseudoelastic Hysteresis, Acta Metal. Mater., 1991, 39(3), p 263–271

    Article  Google Scholar 

  9. 9.

    F. Falk, Model Free Energy, Mechanics and Thermodynamics of Shape Memory Alloy, Acta Metal., 1980, 28, p 1773–1780

    Article  Google Scholar 

  10. 10.

    M.A. Iadicola and J.A. Shaw, Rate and Thermal Sensitivities of Unstable Transformation Behavior in a Shape Memory Alloy, Int. J. Plasticity, 2004, 20, p 577–605

    Article  Google Scholar 

  11. 11.

    B. Azadi, R.K.N.D. Rajapakse, and D.M. Maijer, One-Dimensional Thermo Mechanical Model for Dynamic Pseudoelastic Response of Shape Memory Alloys, J. Smart Mater. Struct., 2006, 15, p 996–1008

    Article  Google Scholar 

  12. 12.

    A. Duval, M. Haboussi, and T.B. Zineb, Modeling of SMA Superelastic Behavior with Nonlocal Approach, Phys. Procedia, 2010, 10, p 33–38

    Article  Google Scholar 

  13. 13.

    A. Duval, M. Haboussi, and B. Zineb, Modeling of Localization and Propagation of Phase Transformation in Superelastic SMA by a Gradient Nonlocal Approach, Int. J. Solids. Struct., 2011, 48(13), p 1879–1893

    Article  Google Scholar 

  14. 14.

    J.A. Shaw and S. Kyriakides, On the Nucleation and Propagation of Phase Transformation Fronts in NiTi Alloys, Acta Matterial, 1997, 45(2), p 683–700

    Article  Google Scholar 

  15. 15.

    X. Zhang, P. Feng, Y. He, T. Yu, and Q. Sun, Experimental Study on Rate Dependence of Macroscopic Domain and Stress Hysteresis in NiTi Shape Memory Alloy Strips, Int. J. Mech. Sci., 2010, 52(12), p 1660–1670

    Article  Google Scholar 

  16. 16.

    D. Mandru, I. Lungu, S. Noveanu, and O. Tatar, Applications of Shape Memory Alloy Actuators in Biomedical Engineering, Annals of the Oradea University, Fascicle Manage. Technol. Eng., 2008, 7, p 922–927

    Google Scholar 

  17. 17.

    S. Matsubara, S. Okamoto, and J.H. Lee, Prosthetic Hand Using Shape Memory Alloy Type Artificial Muscle, International Multi Conference of Engineers and Computer Scientists, Vol 2, March 14–16, 2012, Hong Kong

  18. 18.

    C. Pfeiffer, K. De Laurentiis, and C. Mavroidis, Shape Memory Alloy Robot Prostheses: Initial Experiments, Proceedings of the 1999 IEEE International Conference on Robotics and Automation, Vol 3, Detroit, 1999, p 2385–2391

  19. 19.

    K.J. De Laurentiis and C. Mavroidis, Development of a Shape Memory Alloy Actuator Robotic Hand, J. Technol. Health Care, 2002, 10(2), p 91–106

    Google Scholar 

  20. 20.

    K.J. De Laurentiis and C. Mavroidis, Mechanical Design of a Shape Memory Alloy Actuated Prosthetic Hand, Technol. Health Care, 2002, 10, p 91–106

    Article  Google Scholar 

  21. 21.

    C. Giuseppe, Grasping in Robotics, Springer, London, 2013

    Google Scholar 

  22. 22.

    R.G. Budynass, and J.K. Nisbett, Shigley’s Mechanical Engineering Design, 8th ed., McGraw-Hill, New York, 2008, p 1003

  23. 23.

    W.C. Crone, P.H. Leo, and T.W. Shield, Comparisons Between Load Controlled and Displacement Controlled Extension of NiTi Wires, Scr. Mater., 1998, 38(12), p 1825–1828

    Article  Google Scholar 

  24. 24.

    M. Kamrani, Investigation on the Effects of Stress Concentration on the Mechanical Responses of SMA Wires, MSc. Thesis, Isfahan University of Technology, Isfahan, Iran, 2012 [In Persian]

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Correspondence to Mahmoud Kadkhodaei.

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Kamarni, M., Kadkhodaei, M. An Investigation into the Simple Tensile Test of SMA Wires Considering Stress Concentration of Grippers. J. of Materi Eng and Perform 23, 1114–1123 (2014).

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  • gripper
  • inhomogeneous behavior
  • minimum length
  • shape memory alloy
  • stress concentration
  • tensile test