Numerical Simulation of the Phase Transition Control in a Cylindrical Sample Made of Ferromagnetic Shape Memory Alloy

Abstract

The paper considers ferromagnetic alloys, which exhibit the shape memory effect during phase transition from the high-temperature cubic phase (austenite) to the low-temperature tetragonal phase (martensite) in the ferromagnetic state. In these alloys, significant macroscopic strains are generated during the direct temperature phase transition from the austenitic to the martensitic state, provided that the process proceeds under the action of the applied mechanical stresses. The critical phase transition temperatures in such alloys depend not only on the stress fields, but also on the magnetic field. By changing the magnetic field, it is possible to control the process of phase transition. In this work, within the framework of the finite deformation theory, we develop a model that allows us to describe the process of the control of the direct (austenite-martensite) and reverse (martensite-austenite) phase transitions in ferromagnetic shape memory polycrystalline materials under the action of external force, thermal, and magnetic fields with the aid of the magnetic field. In view of the fact that the magnetic field affects the material deformation, which, in turn, changes the magnetic field, we formulated and solved a coupled boundary value problem. As an example, we considered the problem of a shift of the outer surface of a long hollow cylinder made of ferromagnetic alloy. The numerical implementation of the problem was based on the finite element method using the step-by-step loading procedure. Complete recovery of the strains accumulated during the direct phase transition and reverting of the axially-displaced outer surface of the cylinder to its original position occurred both on heating of the sample to the temperatures of the reverse phase transition and at a constant temperature, when the magnetic field previously applied in the martensitic state was removed.