Strain Model for Ni-Mn-Ga With Collinear Field and Stress

Abstract

Ferromagnetic shape memory alloys in the Ni-Mn-Ga system exhibit large reversible deformations of up to 9.5% in response to magnetic fields. Prior experimental measurements by the authors demonstrated large reversible strains of −0.41% along the [001] crystal direction of a cylindrical Ni50Mn28.7Ga21.3 rod driven with a magnetic field along the same direction and no external restoring force. This represents an unusual configuration which can lead to solenoid transducers with enhanced energy density and bandwidth relative to standard electromagnet devices. The paper builds on a previous thermodynamic framework which accurately quantifies several reversible and irreversible effects in the polarization of ferroic materials. The switching between two variant orientations in the presence of Zeeman energy and pinning energy is formulated through a Gibbs energy functional for the crystal lattice. The presence of nonhomogeneous local interaction fields, nonhomogeneous pinning distributions, and complex crystallographic features in real Ni-Mn-Ga alloys is addressed through stochastic homogenization techniques. Attributes of the model are illustrated through comparison of model results with experimental data.