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

Abstract

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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Abbreviations

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

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

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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). https://doi.org/10.1007/s11665-013-0847-x

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Keywords

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