Hyperelastic Models Describing Superelastic Alloys

The deformational nonelastic behavior of superelastic nickel-titanium alloy Ti₄₉Ni₅₁ is examined using models of an incompressible hyperelastic body. The parameters of the models and statistical indices of correspondence are calculated for the experimental and the model data sets. A polynomial model of the second order (SD = 0.016, δ = 0.026, δ_max = 4.133%, R = 0.9949) is found to suit best to describe the mechanical behavior of Ti₄₉Ni₅₁. The Ogden models (SD = 0.161, δ = 0.295, δ_max = 47.217%, R = 0.8164) and the neo-Hookean model (SD = 0.159, δ = 0.156, δ_max = 24.918%, R = 0.82) are the least suitable for this purpose. On the basis of the Hill–Drucker criterion, the mechanical stability is explored in the selected hyperelastic models. It is shown that not all models are mechanically stable (∂σ/∂ε > 0 and ∂σ/∂λ > 0), and some models lose stability in the deformation range corresponding to the martensitic transition. Thus, the range of losing stability is found to coincide with that in the crystalline lattice of the alloy for the hyperelastic models during the martensitic transformation B2→B19'. The martensitic nonelasticity caused by phase transitions correlates with the hyperelasticity of the alloy material. The models considered are used to calculate the values of the initial elastic modulus of TiNi.