Nonlinear magnetomechanical modeling and characterization of Galfenol and system-level modeling of Galfenol-based transducers

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. Although its energy density and coupling factor is less than that of other materials like Terfenol-D and piezoelectric materials, this is compensated by its ease of packaging and manufacturability. In terms of reliability, it is far superior and makes possible a new class of devices with innovative geometries capable of combined sensing and actuation in 3-D. Unique among smart materials, Galfenol can serve both as a structural element and as an actuator or sensor. Motivated by the need to utilize the full-scale, i.e., nonlinear, range of Galfenol transduction, this work presents nonlinear characterization and modeling of magnetization and strain from magnetic field and stress, and details the incorporation of the material model into system-level models for Galfenol-based transducers. The system-level modeling is carried out in 3-D and is an enabling tool for creating Galfenol-based systems with innovative 3-D geometries.;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 with special attention to hysteresis properties. An elementary hysteron, derived from the first and second laws, describes the underlying nature of the nonlinearities and hysteresis. Minimization of the energy of a single magnetic domain, the microscopic unit responsible for magnetization and magnetostriction, gives analytic expressions for the states of the hysteron and accurately describes certain features of the constitutive behavior, including the stress dependence in the magnetization regions identified for force sensing and the stress dependence of the location of the burst magnetization region. The switching of the hysteron, or domain orientation change, is characterized by a coercive energy, an energy loss analogous to overcoming dry-friction. The energy loss in major magnetization hysteresis loops of research grade Galfenol is found to be 873 J/m3 and for production grade it is 1149 J/m3. Stochastic homogenization of certain parameters in the hysteron yields a homogenized energy model for the bulk magnetization and strain that agrees with the 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 shown to be 100 times faster than previous models for Galfenol. While the homogenized energy model bridges the gap between the domain scale and the macroscopic scale through stochastic homogenization, the efficient model does this with energy-weighted averaging. The enabling feature for faster computation is careful choice of which domain orientations to include in the averaging scheme. The orientations are the same as those derived from energy principles in the homogenized energy model. Both models utilize a new energy formulation for magnetic anisotropy, the form of which depends explicitly on the energetically preferred magnetization directions. This new formulation can describe any anisotropy symmetry which is important for Galfenol, given that its anisotropy can be manipulated through post-processing techniques such as stress-annealing.;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.