A two species thermodynamic Preisach model for the torsional response of shape memory alloy wires and springs under superelastic conditions

In this work, a model to simulate the superelastic response for shape memory alloy wires and springs subjected to torsional loading is constructed by combining thermodynamics principles along with preisach models. Following Doraiswamy et al. (2011), a Gibbs potential based formulation is employed to separate the thermoelastic response of the shape memory alloys from its dissipative response. The dissipative part is then modeled with a discrete Preisach approach. Rather than beginning with a full three dimensional model and solving for non-homogeneous shear stresses across the specimen cross-section, a “strength of materials” approach that can directly model the torsional response using experimentally measurable quantities such as torque and angle of twist is developed. The model results are verified with experiments performed on shape memory alloy springs at three different temperatures. The model is also used to predict torsion response of shape memory alloy wires at different twists and temperatures using experimental results for only one twist or temperature case respectively. The torsional response for three different wire diameters were predicted using experimental data for one diameter case.