A Multi-Scale Study of Shape Memory Alloys


Co-Project Leaders: Arash Yavari and Ken Gall
Student: Reza Mirzaeifar

Shape memory alloys (SMAs) are widely used in a broad variety of applications in multiscale devices ranging from nano-actuators used in nano-electrical-mechanical systems (NEMS) to large energy absorbing elements in civil engineering applications. This research introduces a multiscale analysis for SMAs, particularly Nickel-Titanium alloys (NiTi). SMAs are studied in a variety of length scales ranging from macroscale to nanoscale. In macroscale, a phenomenological constitutive framework is adopted and developed by adding the effect of phase transformation latent heat. Analytical closed-form solutions are obtained for modeling the coupled thermomechanical behavior of various large polycrystalline SMA devices subjected to different loadings, including uniaxial loads, torsion, and bending.


Thermomechanical responses of several SMA devices are analyzed using the introduced solutions and the results are validated by performing various experiments on some large SMA elements. In order to study some important properties of polycrystalline SMAs that the macroscopic phenomenological frameworks cannot capture, including the texture and in tergranular effects in polycrystalline SMAs, a micromechanical framework with a realistic modeling of the grains based on Voronoi tessellations is used. The local form of the first law of thermodynamics is used and the energy balance relations for the polycrystalline SMAs are obtained.

Generalized coupled thermomechanical governing equations considering the phase transformation latent heat are derived for polycrystalline SMAs. A three-dimensional finite element framework is used and different polycrystalline samples are modeled. By considering appropriate distributions of crystallographic orientations in the grains obtained from experimental texture measurements of NiTi samples the effects of texture and the tension-compression asymmetry on the thermomechanical response of polycrystalline SMAs are studied. The interaction between the stress state (tensile or compressive), number of grains, and the texture on the thermomechanical response of polycrystalline SMAs is also studied. For studying some aspects of the thermomechanical properties of SMAs that cannot be studied neither by the phenomenological constitutive models nor by the micromechanical models, molecular dynamics simulations are used to explore the martensitic phase transformation in NiTi alloys at the atomistic level.

The martensite reorientation, austenite to martensite phase transformation, and twinning mechanisms in NiTi nanostructures are analyzed and the effect of various parameters including the temperature and size on the phase transformation at the atomistic level is studied. Results of this research provide insight into studying pseudoelasticity and shape memory response of NiTi alloys at different length scales and are useful for better understanding the solid-to-solid phase transformation at the atomistic level, and the effects of this transformation on the microstructure of polycrystal.

Selected Publications

  1. Mirzaeifar, R., DesRoches, R., Yavari, A., Gall, K. (2013). “A Micromechanical Analysis of the Coupled Thermomechanical Superelastic Response of Textured and Untextured Polycrystalline NiTi Shape Memory Alloys,” Acta Materialia61(12): 4542-4558.
  2. Mirzaeifar, R., DesRoches, R., Yavari, A., Gall, K. (2013). “On Superelastic Bending of Shape Memory Alloy Beams,” International Journal of Solids and Structures 48(10): 1664-1680.
  3. Mirzaeifar, R., DesRoches, R., Yavari, A., and Gall, K. (2012). “Coupled Thermo-Mechanical Analysis of Shape Memory Alloy Circular Bars in Pure Torsion,” International Journal of Non-Linear MechanicsVol 47, No. 3, pp. 118-128, April, 2012.
  4. Mirzaeifar, R., DesRoches, R., and Yavari, A. (2011). “Analysis of the Rate-Dependent Coupled Thermo-Mechanical Response of Shape Memory Alloy Bars and Wires in Tension Continuum Mechanics and Thermodynamics,” Continuum Mechanics and Thermodynamics23: 363-385, May, 2011. DOI 10.1007/s00161-011-0187-8.
  5. Mirzaefar, R., Shakeri, M., DesRoches, R., and Yavari, A. (2011). “A Semi-Analytic Analysis of Shape Memory Alloy Thick Walled Cylinders Under Pressure,” Archive of Applied Mechanics81:1093-1116 June, 2011.  DOI 10.1007/s00419-010-0468-x.
  6. Mirzaeifar, R., DesRoches, R., and Yavari, A. (2011). “A Combined Analytical, Numerical, and Experimental Study of Shape-Memory-Alloy Helical Springs,” International Journal of Solids and StructuresVol. 48, No. 3-4, pp. 611-624, February, 2011.
  7. Gao, N., Jeon, J.-S., Hodgson, D.E., and DesRoches, R. (2016). “An innovative seismic bracing system based on a shape memory alloy ring,” Smart Materials and StructuresVol. 25, No. 5, pp. 1-16
  8. Mirzaeifar, R., Gall, K., Zhu, T., Yavari, A., DesRoches, R. (2014). “Structural Transformations and Reorientations in NiTi Shape Memory Alloy Nanowires”. Journal of Applied Physics115 (19), 194307.