An inclusion theory for the propagation of martensite band in NiTi shape memory alloy wires under tension

In this paper, we present analytical modelling for the pure mechanical response of uniaxial tensioned NiTi wire that experiences stress-induced martensitic transformation via a propagating martensite band at the superelastic temperature regime. The model aims to predict the overall behavior of the SMA wire as a structural response containing propagating instabilities. Based on the systematic experimental investigation of Shaw and Kyriakides (Shaw, J.A., Kyriakides, S., 1995. Thermomechemical aspects of NiTi. J. Mech. Phys. Solids 43, T243–1281 and Shaw, J.A., Kyriakides, S., 1997. On the nucleation and propogation of phase transformation fronts in a NiTi alloy. Acta Mater. 45(2), 638–700), the wire is modeled as an elastic rod containing a single cylindrical transformation inclusion with a uniform axisymmetric eigenstrain. The analytical expression of the free energy of this special matrix-inclusion system is formulated and the length of the martensite band is identified as the key variable describing the transformation process of the system. Theoretical predictions on the peak stress and the subsequent steady-state propagation stress of the wire during forward and reverse transformations are provided and compared with the available experimental data. Specimen size effect on the nominal stress-strain curves and general deformation features of the wire are discussed.