Modeling of partial transformation cycles of SMAs with a modified hardening function

A physical constitutive model is combined with a new function expression that describes the hardening behaviour of Shape Memory Alloys to enable the accurate and efficient prediction of partial transformations during cyclic thermo-mechanical loading. The reversal point memory and the associated memory wipe-out are successfully modeled for single partial transformation cycles by introducing a pair of interpolation functions to scale the martensitic volume fraction predicted by the original model. Isobaric, thermally induced, partial transformation cycle experiments are performed on Ni₅₁Ti₄₉ wt% wires. Predicted partial transformation response results using the proposed model modification are presented and compared with two other approaches and correlated with obtained experimental data for four different cases of partial transformation cycles. Very good agreement is obtained with measured partial cycles, without need of additional calibration, especially for partial transformation branches formed near the middle of the major hysteresis loop. The new constitutive equations are suitable for inclusion into finite element frameworks due to their simple implementation and high accuracy. A case study of a morphing strip actuated by a single SMA wire is considered to demonstrate the capabilities of the modified constitutive equations under combined thermal and mechanical loading conditions. (paper)