Two-dimensional analysis to improve the output stress in ferromagnetic shape memory alloys

Most existing experiments investigating the martensite-variants reorientation (switching) of ferromagnetic shape memory alloys (FSMA) are in a simple 1D condition: An axial compressive stress and a transverse magnetic field. To obtain field-induced variant switching, however, the compressive stress (output stress) is limited by a small blocking stress (<10 MPa, mainly governed by the materials' magnetic anisotropic energy). In this paper, to overcome the stress limit, we suggest using the materials in two-dimensional (2D) configurations: Two (axial and transverse) compressive stresses and a magnetic field. Based on a 2D magneto-mechanical energy analysis, it is found that only the difference between the two stresses is limited; each of the two stresses can be larger than the blocking stress. The energy analysis is also incorporated into the field-stress phase diagrams (including hysteretic effect) to study the variant switching in different loading paths: rotating/non-rotating field-induced strain and field-assisted superelasticity. Properly setting the two stresses can control the switching parameters (field magnitude and rotation angle) and the variants' time fractions in cyclic loadings, which provide much flexibility of FSMA applications. Our 2D energy analysis can be easily reduced to 1D case, where the theoretical predictions of the switching stresses/fields/angles agree with the existing experiments.