Magnetostrictive materials have the ability to transfer energy between the magnetic and mechanical domains. They deform in response to magnetic fields and magnetize in response to stresses. Further, their stiffness and permeability depend on both magnetic field and stress. Galfenol, an alloy of iron and gallium, is an emerging magnetostrictive material which is unique for its combination of high magnetomechanical coupling and steel-like structural properties. Unique among smart materials, Galfenol can serve both as a structural element and as an actuator or sensor. This work presents nonlinear characterization and modeling of magnetization and strain of Galfenol, and a 3-D system-level model for Galfenol-based transducers.
Magnetomechanical measurements are presented which reveal that Galfenol constitutive behavior is kinematically reversible and thermodynamically irreversible. Magnetic hysteresis resulting from thermodynamic irreversibilities is shown to arise from a common mechanism for both magnetic field and stress application. Linear regions in constant-stress magnetization curves are identified as promising for force sensing applications. It is shown that the slope of these linear regions, or the magnetic susceptibility, is highly sensitive to stress. This observation can be used for force sensing; the 19-22 at. % Ga range is identified as a favorable Galfenol composition for sensing, due to its low anisotropy with moderate magnetostriction and saturation magnetization.
A thermodynamic framework is constructed to describe the magnetization and strain. An elementary hysteron, derived from the first and second laws, describes the underlying nonlinearities and hysteresis. Minimization of the energy of a single magnetic domain gives expressions for the hysteron states and accurately describes features of the constitutive behavior, including the stress dependence in the magnetization regions and the stress dependence of the location of the burst magnetization region. Stochastic homogenization of parameters in the hysteron yields a model for bulk magnetization and strain that agrees with measurements, including the hysteresis properties.
An alternate model is developed with special attention given to achieving high accuracy at minimal computational expense. The model is 100 times faster than previous models. This is accomplished with energy-weighted averaging. The enabling feature for faster computation is careful choice of which domain orientations to include in the averaging scheme. The model utilizes a new energy formulation for magnetic anisotropy, the form of which depends explicitly on the energetically preferred magnetization directions.
The efficient model is adopted in a transducer-level model implemented with the finite element method. The transducer-level model consists of Maxwell's equations describing eddy currents and flux leakage and the force balance equations from the conservation of linear momentum. These equations are solved over a geometry that includes a current carrying coil, an air volume, a magnetic circuit of steel, Galfenol and additional structural materials. The efficient constitutive model based on energy-weighted averaging is used for Galfenol. A broad range of effects are described such as energy losses affecting device efficiency, dynamic magnetostructural effects, delay and remanence from hysteresis, and eddy currents. This framework enables design optimization of efficient and innovative Galfenol-based devices which take advantage of the full transduction range of Galfenol.