Numerical simulation of the phase transition control in torsion of a hollow cylinder made of Heusler alloy

The paper discusses ferromagnetic alloys with shape memory (Heusler alloys) undergoing a phase transformation 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 due to the application of mechanical stresses. Since the critical temperatures of the process depend on the magnetic field and stress fields, in such alloys it is possible to control the austenite - martensite phase transformation process by applying a magnetic field. In this work, within the framework of finite deformations a model has been presented to describe the process of controlling the forward (austenite - martensite) and reverse (martensite - austenite) phase transformation by applying a magnetic field in ferromagnetic polycrystalline materials with shape memory under the action of external force, thermal and magnetic fields. Since the magnetic field affects the strain of the material, which in turn changes the magnetic field, a connected boundary value problem has been constructed. The problem of azimuthal torsion of a long hollow cylinder (plane deformation) from a Heusler alloy has been solved numerically by the finite element method using the step-by-step loading procedure. The accumulation of phase strains occurred during the forward phase transformation in a cylinder, the outer surface of which was previously twisted in the azimuthal direction with respect to a fixed inner. In this case, the value of the accumulated phase strains depended on the boundary conditions (force or kinematic), that produced twisting the outer surface of the cylinder. The complete removal of the accumulated strains and the unwinding of the outer surface of the cylinder occurred both when the sample was heated in the temperature range of the reverse phase transformation in the absence of a magnetic field, and at a constant temperature exceeding this interval, when the magnetic field applied previously in the martensitic state was removed.