Development of a Quasi-static Model of NiMnGa Magnetic Shape Memory Alloy

Abstract

A quasi-static model for NiMnGa magnetic shape memory alloy is formulated along the lines of the Brinson and Tanaka SMA constitutive models. Since the shape memory effect (SME) and pseudoelasticity exist in both NiTi and NiMnGa, constitutive models for SMAs offer a basis for ferromagnetic shape memory alloys (FSMA) modeling. Two types of quasi-static tests involving constant external magnetic field and constant stress are conducted to identify nine model parameters. These model parameters include free strain, Young's moduli, fundamental critical stresses, fundamental critical threshold fields, and stress-influence coefficients. The Young's moduli of the material in its field and stress preferred states are determined to be 450 and 820 MPa respectively, while the free strain is measured to be 6.5%. These test data are used to assemble a critical stress—magnetic field intensity profile that is useful for determining the model parameters and for predicting the various states of the material for a wide range of magnetic or mechanical loading conditions. Although all of the parameters can be obtained from constant magnetic field testing, useful insight into NiMnGa actuator behavior can be gained from constant axial stress tests. Once implemented, the analytical model shows good correlation with the test data, capturing both the magnetic shape memory effect and pseudoelasticity. Because the model is piecewise linear, it does not capture material behavior resulting from nonlinear effects such as magnetic saturation. Despite its inherent limitations, this model shows encouraging results, providing a solid basis for future modeling efforts.