Reversible-strain criteria of ferromagnetic shape memory alloys under cyclic 3D magneto-mechanical loadings

Recent researches revealed that ferromagnetic shape memory alloys (FSMA) in 2D/3D configurations (with multi-axial stresses) had much more advantages (e.g., higher working stress and more application flexibility) than that in 1D configuration (with uniaxial stress). In literature, however, there is no simple criterion to judge whether a cyclic 3D magneto-mechanical loading can induce a large reversible strain (via martensite reorientation in FSMA). In this paper, a 3D magneto-mechanical energy analysis is proposed and incorporated into a phase diagram in terms of deviatoric stresses (including mechanical and magneto-stresses) to study the path-dependent (hysteretic) martensite reorientation in FSMA under 3D cyclic loadings. Based on the phase diagram (a plane graph), general criteria for obtaining reversible strain under cyclic magneto-mechanical loadings are derived, which provide basic guidelines for FSMA's applications under multi-axial loadings. Particularly for FSMA actuators driven by cyclic magnetic fields, the criteria of setting the 3D mechanical stresses to allow field-induced reversible strain are formulated. The 3D criteria can be reduced to 1D and 2D criteria which agree with the existing 1D/2D theoretical and experimental studies.