Development of a numerical model for high-temperature shape memory alloys

A new thermomechanical hysteresis model for a high-temperature shape memory alloy (HTSMA) actuator material is presented. The proposed Brinson-Preisach model is capable of predicting the strain output of a tensile-loaded HTSMA when excited by arbitrary temperature-stress inputs for the purpose of actuator and control design. Quasistatic generalized Preisach hysteresis models available in the literature require large sets of experimental data for model identification at a particular operating point, and substantially more data for multiple operating points. The minor loop algorithm is an alternate approach to common Preisach methods that is better suited for research-stage alloys, such as recently developed HTSMAs, for which a complete identification database is not yet available. A detailed description of the minor loop hysteresis algorithm is presented in this paper and a methodology for determination of model parameters is introduced. The algorithm is assembled together with a modified form of the one-dimensional Brinson constitutive equation to provide a continuous thermomechanical response even within the characteristically wide detwinning region of the HTSMA. The computationally efficient algorithm is shown to demonstrate each of the unique characteristics of Preisach minor loop hysteresis over the usable actuation range in high-stress, high-temperature applications.