A quasi-static model for NiMnGa magnetic shape memory alloy

Abstract

A quasi-static model for NiMnGa magnetic shape memory alloy (MSMA) is formulated inparallel to the Brinson and Tanaka thermal SMA constitutive models. Since the shapememory effect (SME) and pseudoelasticity exist in both NiTi and NiMnGa, constitutivemodels for SMAs can serve as a basis for MSMA behavioral modeling. The simplified,linear, quasi-static model for NiMnGa was characterized by nine material parametersidentified by conducting a series of uniaxial compression tests in a constant fieldenvironment. These model parameters include free strain, Young’s modulus, fundamentalcritical stresses, fundamental threshold fields, and stress-influence coefficients. The Young’smoduli of the material in both its field and stress preferred configurations were determinedto be 450 MPa and 820 MPa respectively, while the free strain was measured to be 5.8%.These test data were used to assemble a critical stress profile that is useful for determiningmodel parameters and for understanding the dependence of critical stresses onmagnetic fields. Once implemented, the analytical model shows good correlationwith test data for all modes of NiMnGa quasi-static behavior, capturing both themagnetic shape memory effect and pseudoelasticity. Furthermore, the model isalso capable of predicting partial pseudoelasticity, minor hysteretic loops andstress–strain behaviors. To correct for the effects of magnetic saturation, a series ofstress influence functions were developed from the critical stress profile. Althoughrequiring further refinement, the model’s results are encouraging, indicating thatthe model is a useful analytical tool for predicting NiMnGa actuator behavior.